true if they are equal, false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian3.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left.x === right.x &&
left.y === right.y &&
left.z === right.z)
);
};
/**
* @private
*/
Cartesian3.equalsArray = function (cartesian, array, offset) {
return (
cartesian.x === array[offset] &&
cartesian.y === array[offset + 1] &&
cartesian.z === array[offset + 2]
);
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian3.equalsEpsilon = function (
left,
right,
relativeEpsilon,
absoluteEpsilon
) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.z,
right.z,
relativeEpsilon,
absoluteEpsilon
))
);
};
/**
* Computes the cross (outer) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The cross product.
*/
Cartesian3.cross = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const leftX = left.x;
const leftY = left.y;
const leftZ = left.z;
const rightX = right.x;
const rightY = right.y;
const rightZ = right.z;
const x = leftY * rightZ - leftZ * rightY;
const y = leftZ * rightX - leftX * rightZ;
const z = leftX * rightY - leftY * rightX;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the midpoint between the right and left Cartesian.
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The midpoint.
*/
Cartesian3.midpoint = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = (left.x + right.x) * 0.5;
result.y = (left.y + right.y) * 0.5;
result.z = (left.z + right.z) * 0.5;
return result;
};
/**
* Returns a Cartesian3 position from longitude and latitude values given in degrees.
*
* @param {Number} longitude The longitude, in degrees
* @param {Number} latitude The latitude, in degrees
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* const position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
*/
Cartesian3.fromDegrees = function (
longitude,
latitude,
height,
ellipsoid,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("longitude", longitude);
RuntimeError.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
longitude = ComponentDatatype.CesiumMath.toRadians(longitude);
latitude = ComponentDatatype.CesiumMath.toRadians(latitude);
return Cartesian3.fromRadians(longitude, latitude, height, ellipsoid, result);
};
let scratchN = new Cartesian3();
let scratchK = new Cartesian3();
const wgs84RadiiSquared = new Cartesian3(
6378137.0 * 6378137.0,
6378137.0 * 6378137.0,
6356752.3142451793 * 6356752.3142451793
);
/**
* Returns a Cartesian3 position from longitude and latitude values given in radians.
*
* @param {Number} longitude The longitude, in radians
* @param {Number} latitude The latitude, in radians
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* const position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
*/
Cartesian3.fromRadians = function (
longitude,
latitude,
height,
ellipsoid,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("longitude", longitude);
RuntimeError.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
height = defaultValue.defaultValue(height, 0.0);
const radiiSquared = defaultValue.defined(ellipsoid)
? ellipsoid.radiiSquared
: wgs84RadiiSquared;
const cosLatitude = Math.cos(latitude);
scratchN.x = cosLatitude * Math.cos(longitude);
scratchN.y = cosLatitude * Math.sin(longitude);
scratchN.z = Math.sin(latitude);
scratchN = Cartesian3.normalize(scratchN, scratchN);
Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
const gamma = Math.sqrt(Cartesian3.dot(scratchN, scratchK));
scratchK = Cartesian3.divideByScalar(scratchK, gamma, scratchK);
scratchN = Cartesian3.multiplyByScalar(scratchN, height, scratchN);
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(scratchK, scratchN, result);
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
*/
Cartesian3.fromDegreesArray = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new RuntimeError.DeveloperError(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
//>>includeEnd('debug');
const length = coordinates.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (let i = 0; i < length; i += 2) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const index = i / 2;
result[index] = Cartesian3.fromDegrees(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
*
* @param {Number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
*/
Cartesian3.fromRadiansArray = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new RuntimeError.DeveloperError(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
//>>includeEnd('debug');
const length = coordinates.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (let i = 0; i < length; i += 2) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const index = i / 2;
result[index] = Cartesian3.fromRadians(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
*/
Cartesian3.fromDegreesArrayHeights = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new RuntimeError.DeveloperError(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
//>>includeEnd('debug');
const length = coordinates.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (let i = 0; i < length; i += 3) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const height = coordinates[i + 2];
const index = i / 3;
result[index] = Cartesian3.fromDegrees(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
};
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
*
* @param {Number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
*/
Cartesian3.fromRadiansArrayHeights = function (coordinates, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new RuntimeError.DeveloperError(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
//>>includeEnd('debug');
const length = coordinates.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (let i = 0; i < length; i += 3) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const height = coordinates[i + 2];
const index = i / 3;
result[index] = Cartesian3.fromRadians(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
};
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.ZERO = Object.freeze(new Cartesian3(0.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (1.0, 1.0, 1.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.ONE = Object.freeze(new Cartesian3(1.0, 1.0, 1.0));
/**
* An immutable Cartesian3 instance initialized to (1.0, 0.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_X = Object.freeze(new Cartesian3(1.0, 0.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 1.0, 0.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Y = Object.freeze(new Cartesian3(0.0, 1.0, 0.0));
/**
* An immutable Cartesian3 instance initialized to (0.0, 0.0, 1.0).
*
* @type {Cartesian3}
* @constant
*/
Cartesian3.UNIT_Z = Object.freeze(new Cartesian3(0.0, 0.0, 1.0));
/**
* Duplicates this Cartesian3 instance.
*
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
Cartesian3.prototype.clone = function (result) {
return Cartesian3.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian3.prototype.equals = function (right) {
return Cartesian3.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian3.prototype.equalsEpsilon = function (
right,
relativeEpsilon,
absoluteEpsilon
) {
return Cartesian3.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
};
/**
* Creates a string representing this Cartesian in the format '(x, y, z)'.
*
* @returns {String} A string representing this Cartesian in the format '(x, y, z)'.
*/
Cartesian3.prototype.toString = function () {
return `(${this.x}, ${this.y}, ${this.z})`;
};
const scaleToGeodeticSurfaceIntersection = new Cartesian3();
const scaleToGeodeticSurfaceGradient = new Cartesian3();
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} oneOverRadii One over radii of the ellipsoid.
* @param {Cartesian3} oneOverRadiiSquared One over radii squared of the ellipsoid.
* @param {Number} centerToleranceSquared Tolerance for closeness to the center.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*
* @function scaleToGeodeticSurface
*
* @private
*/
function scaleToGeodeticSurface(
cartesian,
oneOverRadii,
oneOverRadiiSquared,
centerToleranceSquared,
result
) {
//>>includeStart('debug', pragmas.debug);
if (!defaultValue.defined(cartesian)) {
throw new RuntimeError.DeveloperError("cartesian is required.");
}
if (!defaultValue.defined(oneOverRadii)) {
throw new RuntimeError.DeveloperError("oneOverRadii is required.");
}
if (!defaultValue.defined(oneOverRadiiSquared)) {
throw new RuntimeError.DeveloperError("oneOverRadiiSquared is required.");
}
if (!defaultValue.defined(centerToleranceSquared)) {
throw new RuntimeError.DeveloperError("centerToleranceSquared is required.");
}
//>>includeEnd('debug');
const positionX = cartesian.x;
const positionY = cartesian.y;
const positionZ = cartesian.z;
const oneOverRadiiX = oneOverRadii.x;
const oneOverRadiiY = oneOverRadii.y;
const oneOverRadiiZ = oneOverRadii.z;
const x2 = positionX * positionX * oneOverRadiiX * oneOverRadiiX;
const y2 = positionY * positionY * oneOverRadiiY * oneOverRadiiY;
const z2 = positionZ * positionZ * oneOverRadiiZ * oneOverRadiiZ;
// Compute the squared ellipsoid norm.
const squaredNorm = x2 + y2 + z2;
const ratio = Math.sqrt(1.0 / squaredNorm);
// As an initial approximation, assume that the radial intersection is the projection point.
const intersection = Cartesian3.multiplyByScalar(
cartesian,
ratio,
scaleToGeodeticSurfaceIntersection
);
// If the position is near the center, the iteration will not converge.
if (squaredNorm < centerToleranceSquared) {
return !isFinite(ratio)
? undefined
: Cartesian3.clone(intersection, result);
}
const oneOverRadiiSquaredX = oneOverRadiiSquared.x;
const oneOverRadiiSquaredY = oneOverRadiiSquared.y;
const oneOverRadiiSquaredZ = oneOverRadiiSquared.z;
// Use the gradient at the intersection point in place of the true unit normal.
// The difference in magnitude will be absorbed in the multiplier.
const gradient = scaleToGeodeticSurfaceGradient;
gradient.x = intersection.x * oneOverRadiiSquaredX * 2.0;
gradient.y = intersection.y * oneOverRadiiSquaredY * 2.0;
gradient.z = intersection.z * oneOverRadiiSquaredZ * 2.0;
// Compute the initial guess at the normal vector multiplier, lambda.
let lambda =
((1.0 - ratio) * Cartesian3.magnitude(cartesian)) /
(0.5 * Cartesian3.magnitude(gradient));
let correction = 0.0;
let func;
let denominator;
let xMultiplier;
let yMultiplier;
let zMultiplier;
let xMultiplier2;
let yMultiplier2;
let zMultiplier2;
let xMultiplier3;
let yMultiplier3;
let zMultiplier3;
do {
lambda -= correction;
xMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredX);
yMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredY);
zMultiplier = 1.0 / (1.0 + lambda * oneOverRadiiSquaredZ);
xMultiplier2 = xMultiplier * xMultiplier;
yMultiplier2 = yMultiplier * yMultiplier;
zMultiplier2 = zMultiplier * zMultiplier;
xMultiplier3 = xMultiplier2 * xMultiplier;
yMultiplier3 = yMultiplier2 * yMultiplier;
zMultiplier3 = zMultiplier2 * zMultiplier;
func = x2 * xMultiplier2 + y2 * yMultiplier2 + z2 * zMultiplier2 - 1.0;
// "denominator" here refers to the use of this expression in the velocity and acceleration
// computations in the sections to follow.
denominator =
x2 * xMultiplier3 * oneOverRadiiSquaredX +
y2 * yMultiplier3 * oneOverRadiiSquaredY +
z2 * zMultiplier3 * oneOverRadiiSquaredZ;
const derivative = -2.0 * denominator;
correction = func / derivative;
} while (Math.abs(func) > ComponentDatatype.CesiumMath.EPSILON12);
if (!defaultValue.defined(result)) {
return new Cartesian3(
positionX * xMultiplier,
positionY * yMultiplier,
positionZ * zMultiplier
);
}
result.x = positionX * xMultiplier;
result.y = positionY * yMultiplier;
result.z = positionZ * zMultiplier;
return result;
}
/**
* A position defined by longitude, latitude, and height.
* @alias Cartographic
* @constructor
*
* @param {Number} [longitude=0.0] The longitude, in radians.
* @param {Number} [latitude=0.0] The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
*
* @see Ellipsoid
*/
function Cartographic(longitude, latitude, height) {
/**
* The longitude, in radians.
* @type {Number}
* @default 0.0
*/
this.longitude = defaultValue.defaultValue(longitude, 0.0);
/**
* The latitude, in radians.
* @type {Number}
* @default 0.0
*/
this.latitude = defaultValue.defaultValue(latitude, 0.0);
/**
* The height, in meters, above the ellipsoid.
* @type {Number}
* @default 0.0
*/
this.height = defaultValue.defaultValue(height, 0.0);
}
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in radians.
*
* @param {Number} longitude The longitude, in radians.
* @param {Number} latitude The latitude, in radians.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromRadians = function (longitude, latitude, height, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("longitude", longitude);
RuntimeError.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
height = defaultValue.defaultValue(height, 0.0);
if (!defaultValue.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Creates a new Cartographic instance from longitude and latitude
* specified in degrees. The values in the resulting object will
* be in radians.
*
* @param {Number} longitude The longitude, in degrees.
* @param {Number} latitude The latitude, in degrees.
* @param {Number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.fromDegrees = function (longitude, latitude, height, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("longitude", longitude);
RuntimeError.Check.typeOf.number("latitude", latitude);
//>>includeEnd('debug');
longitude = ComponentDatatype.CesiumMath.toRadians(longitude);
latitude = ComponentDatatype.CesiumMath.toRadians(latitude);
return Cartographic.fromRadians(longitude, latitude, height, result);
};
const cartesianToCartographicN$1 = new Cartesian3();
const cartesianToCartographicP$1 = new Cartesian3();
const cartesianToCartographicH$1 = new Cartesian3();
const wgs84OneOverRadii = new Cartesian3(
1.0 / 6378137.0,
1.0 / 6378137.0,
1.0 / 6356752.3142451793
);
const wgs84OneOverRadiiSquared = new Cartesian3(
1.0 / (6378137.0 * 6378137.0),
1.0 / (6378137.0 * 6378137.0),
1.0 / (6356752.3142451793 * 6356752.3142451793)
);
const wgs84CenterToleranceSquared = ComponentDatatype.CesiumMath.EPSILON1;
/**
* Creates a new Cartographic instance from a Cartesian position. The values in the
* resulting object will be in radians.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*/
Cartographic.fromCartesian = function (cartesian, ellipsoid, result) {
const oneOverRadii = defaultValue.defined(ellipsoid)
? ellipsoid.oneOverRadii
: wgs84OneOverRadii;
const oneOverRadiiSquared = defaultValue.defined(ellipsoid)
? ellipsoid.oneOverRadiiSquared
: wgs84OneOverRadiiSquared;
const centerToleranceSquared = defaultValue.defined(ellipsoid)
? ellipsoid._centerToleranceSquared
: wgs84CenterToleranceSquared;
//`cartesian is required.` is thrown from scaleToGeodeticSurface
const p = scaleToGeodeticSurface(
cartesian,
oneOverRadii,
oneOverRadiiSquared,
centerToleranceSquared,
cartesianToCartographicP$1
);
if (!defaultValue.defined(p)) {
return undefined;
}
let n = Cartesian3.multiplyComponents(
p,
oneOverRadiiSquared,
cartesianToCartographicN$1
);
n = Cartesian3.normalize(n, n);
const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH$1);
const longitude = Math.atan2(n.y, n.x);
const latitude = Math.asin(n.z);
const height =
ComponentDatatype.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!defaultValue.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Creates a new Cartesian3 instance from a Cartographic input. The values in the inputted
* object should be in radians.
*
* @param {Cartographic} cartographic Input to be converted into a Cartesian3 output.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*/
Cartographic.toCartesian = function (cartographic, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("cartographic", cartographic);
//>>includeEnd('debug');
return Cartesian3.fromRadians(
cartographic.longitude,
cartographic.latitude,
cartographic.height,
ellipsoid,
result
);
};
/**
* Duplicates a Cartographic instance.
*
* @param {Cartographic} cartographic The cartographic to duplicate.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided. (Returns undefined if cartographic is undefined)
*/
Cartographic.clone = function (cartographic, result) {
if (!defaultValue.defined(cartographic)) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Cartographic(
cartographic.longitude,
cartographic.latitude,
cartographic.height
);
}
result.longitude = cartographic.longitude;
result.latitude = cartographic.latitude;
result.height = cartographic.height;
return result;
};
/**
* Compares the provided cartographics componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartographic.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left.longitude === right.longitude &&
left.latitude === right.latitude &&
left.height === right.height)
);
};
/**
* Compares the provided cartographics componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Cartographic} [left] The first cartographic.
* @param {Cartographic} [right] The second cartographic.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartographic.equalsEpsilon = function (left, right, epsilon) {
epsilon = defaultValue.defaultValue(epsilon, 0);
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
Math.abs(left.longitude - right.longitude) <= epsilon &&
Math.abs(left.latitude - right.latitude) <= epsilon &&
Math.abs(left.height - right.height) <= epsilon)
);
};
/**
* An immutable Cartographic instance initialized to (0.0, 0.0, 0.0).
*
* @type {Cartographic}
* @constant
*/
Cartographic.ZERO = Object.freeze(new Cartographic(0.0, 0.0, 0.0));
/**
* Duplicates this instance.
*
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if one was not provided.
*/
Cartographic.prototype.clone = function (result) {
return Cartographic.clone(this, result);
};
/**
* Compares the provided against this cartographic componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartographic.prototype.equals = function (right) {
return Cartographic.equals(this, right);
};
/**
* Compares the provided against this cartographic componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Cartographic} [right] The second cartographic.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartographic.prototype.equalsEpsilon = function (right, epsilon) {
return Cartographic.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this cartographic in the format '(longitude, latitude, height)'.
*
* @returns {String} A string representing the provided cartographic in the format '(longitude, latitude, height)'.
*/
Cartographic.prototype.toString = function () {
return `(${this.longitude}, ${this.latitude}, ${this.height})`;
};
function initialize(ellipsoid, x, y, z) {
x = defaultValue.defaultValue(x, 0.0);
y = defaultValue.defaultValue(y, 0.0);
z = defaultValue.defaultValue(z, 0.0);
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("x", x, 0.0);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("y", y, 0.0);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("z", z, 0.0);
//>>includeEnd('debug');
ellipsoid._radii = new Cartesian3(x, y, z);
ellipsoid._radiiSquared = new Cartesian3(x * x, y * y, z * z);
ellipsoid._radiiToTheFourth = new Cartesian3(
x * x * x * x,
y * y * y * y,
z * z * z * z
);
ellipsoid._oneOverRadii = new Cartesian3(
x === 0.0 ? 0.0 : 1.0 / x,
y === 0.0 ? 0.0 : 1.0 / y,
z === 0.0 ? 0.0 : 1.0 / z
);
ellipsoid._oneOverRadiiSquared = new Cartesian3(
x === 0.0 ? 0.0 : 1.0 / (x * x),
y === 0.0 ? 0.0 : 1.0 / (y * y),
z === 0.0 ? 0.0 : 1.0 / (z * z)
);
ellipsoid._minimumRadius = Math.min(x, y, z);
ellipsoid._maximumRadius = Math.max(x, y, z);
ellipsoid._centerToleranceSquared = ComponentDatatype.CesiumMath.EPSILON1;
if (ellipsoid._radiiSquared.z !== 0) {
ellipsoid._squaredXOverSquaredZ =
ellipsoid._radiiSquared.x / ellipsoid._radiiSquared.z;
}
}
/**
* A quadratic surface defined in Cartesian coordinates by the equation
* (x / a)^2 + (y / b)^2 + (z / c)^2 = 1. Primarily used
* by Cesium to represent the shape of planetary bodies.
*
* Rather than constructing this object directly, one of the provided
* constants is normally used.
* @alias Ellipsoid
* @constructor
*
* @param {Number} [x=0] The radius in the x direction.
* @param {Number} [y=0] The radius in the y direction.
* @param {Number} [z=0] The radius in the z direction.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.fromCartesian3
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
function Ellipsoid(x, y, z) {
this._radii = undefined;
this._radiiSquared = undefined;
this._radiiToTheFourth = undefined;
this._oneOverRadii = undefined;
this._oneOverRadiiSquared = undefined;
this._minimumRadius = undefined;
this._maximumRadius = undefined;
this._centerToleranceSquared = undefined;
this._squaredXOverSquaredZ = undefined;
initialize(this, x, y, z);
}
Object.defineProperties(Ellipsoid.prototype, {
/**
* Gets the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radii: {
get: function () {
return this._radii;
},
},
/**
* Gets the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiSquared: {
get: function () {
return this._radiiSquared;
},
},
/**
* Gets the radii of the ellipsoid raise to the fourth power.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
radiiToTheFourth: {
get: function () {
return this._radiiToTheFourth;
},
},
/**
* Gets one over the radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadii: {
get: function () {
return this._oneOverRadii;
},
},
/**
* Gets one over the squared radii of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Cartesian3}
* @readonly
*/
oneOverRadiiSquared: {
get: function () {
return this._oneOverRadiiSquared;
},
},
/**
* Gets the minimum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
minimumRadius: {
get: function () {
return this._minimumRadius;
},
},
/**
* Gets the maximum radius of the ellipsoid.
* @memberof Ellipsoid.prototype
* @type {Number}
* @readonly
*/
maximumRadius: {
get: function () {
return this._maximumRadius;
},
},
});
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} ellipsoid The ellipsoid to duplicate.
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid. (Returns undefined if ellipsoid is undefined)
*/
Ellipsoid.clone = function (ellipsoid, result) {
if (!defaultValue.defined(ellipsoid)) {
return undefined;
}
const radii = ellipsoid._radii;
if (!defaultValue.defined(result)) {
return new Ellipsoid(radii.x, radii.y, radii.z);
}
Cartesian3.clone(radii, result._radii);
Cartesian3.clone(ellipsoid._radiiSquared, result._radiiSquared);
Cartesian3.clone(ellipsoid._radiiToTheFourth, result._radiiToTheFourth);
Cartesian3.clone(ellipsoid._oneOverRadii, result._oneOverRadii);
Cartesian3.clone(ellipsoid._oneOverRadiiSquared, result._oneOverRadiiSquared);
result._minimumRadius = ellipsoid._minimumRadius;
result._maximumRadius = ellipsoid._maximumRadius;
result._centerToleranceSquared = ellipsoid._centerToleranceSquared;
return result;
};
/**
* Computes an Ellipsoid from a Cartesian specifying the radii in x, y, and z directions.
*
* @param {Cartesian3} [cartesian=Cartesian3.ZERO] The ellipsoid's radius in the x, y, and z directions.
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} A new Ellipsoid instance.
*
* @exception {DeveloperError} All radii components must be greater than or equal to zero.
*
* @see Ellipsoid.WGS84
* @see Ellipsoid.UNIT_SPHERE
*/
Ellipsoid.fromCartesian3 = function (cartesian, result) {
if (!defaultValue.defined(result)) {
result = new Ellipsoid();
}
if (!defaultValue.defined(cartesian)) {
return result;
}
initialize(result, cartesian.x, cartesian.y, cartesian.z);
return result;
};
/**
* An Ellipsoid instance initialized to the WGS84 standard.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.WGS84 = Object.freeze(
new Ellipsoid(6378137.0, 6378137.0, 6356752.3142451793)
);
/**
* An Ellipsoid instance initialized to radii of (1.0, 1.0, 1.0).
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.UNIT_SPHERE = Object.freeze(new Ellipsoid(1.0, 1.0, 1.0));
/**
* An Ellipsoid instance initialized to a sphere with the lunar radius.
*
* @type {Ellipsoid}
* @constant
*/
Ellipsoid.MOON = Object.freeze(
new Ellipsoid(
ComponentDatatype.CesiumMath.LUNAR_RADIUS,
ComponentDatatype.CesiumMath.LUNAR_RADIUS,
ComponentDatatype.CesiumMath.LUNAR_RADIUS
)
);
/**
* Duplicates an Ellipsoid instance.
*
* @param {Ellipsoid} [result] The object onto which to store the result, or undefined if a new
* instance should be created.
* @returns {Ellipsoid} The cloned Ellipsoid.
*/
Ellipsoid.prototype.clone = function (result) {
return Ellipsoid.clone(this, result);
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Ellipsoid.packedLength = Cartesian3.packedLength;
/**
* Stores the provided instance into the provided array.
*
* @param {Ellipsoid} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Ellipsoid.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
Cartesian3.pack(value._radii, array, startingIndex);
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Ellipsoid} [result] The object into which to store the result.
* @returns {Ellipsoid} The modified result parameter or a new Ellipsoid instance if one was not provided.
*/
Ellipsoid.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
const radii = Cartesian3.unpack(array, startingIndex);
return Ellipsoid.fromCartesian3(radii, result);
};
/**
* Computes the unit vector directed from the center of this ellipsoid toward the provided Cartesian position.
* @function
*
* @param {Cartesian3} cartesian The Cartesian for which to to determine the geocentric normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geocentricSurfaceNormal = Cartesian3.normalize;
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartographic} cartographic The cartographic position for which to to determine the geodetic normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.geodeticSurfaceNormalCartographic = function (
cartographic,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
const longitude = cartographic.longitude;
const latitude = cartographic.latitude;
const cosLatitude = Math.cos(latitude);
const x = cosLatitude * Math.cos(longitude);
const y = cosLatitude * Math.sin(longitude);
const z = Math.sin(latitude);
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
result.x = x;
result.y = y;
result.z = z;
return Cartesian3.normalize(result, result);
};
/**
* Computes the normal of the plane tangent to the surface of the ellipsoid at the provided position.
*
* @param {Cartesian3} cartesian The Cartesian position for which to to determine the surface normal.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided, or undefined if a normal cannot be found.
*/
Ellipsoid.prototype.geodeticSurfaceNormal = function (cartesian, result) {
if (
Cartesian3.equalsEpsilon(cartesian, Cartesian3.ZERO, ComponentDatatype.CesiumMath.EPSILON14)
) {
return undefined;
}
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
result = Cartesian3.multiplyComponents(
cartesian,
this._oneOverRadiiSquared,
result
);
return Cartesian3.normalize(result, result);
};
const cartographicToCartesianNormal = new Cartesian3();
const cartographicToCartesianK = new Cartesian3();
/**
* Converts the provided cartographic to Cartesian representation.
*
* @param {Cartographic} cartographic The cartographic position.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*
* @example
* //Create a Cartographic and determine it's Cartesian representation on a WGS84 ellipsoid.
* const position = new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 5000);
* const cartesianPosition = Cesium.Ellipsoid.WGS84.cartographicToCartesian(position);
*/
Ellipsoid.prototype.cartographicToCartesian = function (cartographic, result) {
//`cartographic is required` is thrown from geodeticSurfaceNormalCartographic.
const n = cartographicToCartesianNormal;
const k = cartographicToCartesianK;
this.geodeticSurfaceNormalCartographic(cartographic, n);
Cartesian3.multiplyComponents(this._radiiSquared, n, k);
const gamma = Math.sqrt(Cartesian3.dot(n, k));
Cartesian3.divideByScalar(k, gamma, k);
Cartesian3.multiplyByScalar(n, cartographic.height, n);
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.add(k, n, result);
};
/**
* Converts the provided array of cartographics to an array of Cartesians.
*
* @param {Cartographic[]} cartographics An array of cartographic positions.
* @param {Cartesian3[]} [result] The object onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Convert an array of Cartographics and determine their Cartesian representation on a WGS84 ellipsoid.
* const positions = [new Cesium.Cartographic(Cesium.Math.toRadians(21), Cesium.Math.toRadians(78), 0),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.321), Cesium.Math.toRadians(78.123), 100),
* new Cesium.Cartographic(Cesium.Math.toRadians(21.645), Cesium.Math.toRadians(78.456), 250)];
* const cartesianPositions = Cesium.Ellipsoid.WGS84.cartographicArrayToCartesianArray(positions);
*/
Ellipsoid.prototype.cartographicArrayToCartesianArray = function (
cartographics,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("cartographics", cartographics);
//>>includeEnd('debug')
const length = cartographics.length;
if (!defaultValue.defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for (let i = 0; i < length; i++) {
result[i] = this.cartographicToCartesian(cartographics[i], result[i]);
}
return result;
};
const cartesianToCartographicN = new Cartesian3();
const cartesianToCartographicP = new Cartesian3();
const cartesianToCartographicH = new Cartesian3();
/**
* Converts the provided cartesian to cartographic representation.
* The cartesian is undefined at the center of the ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to convert to cartographic representation.
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter, new Cartographic instance if none was provided, or undefined if the cartesian is at the center of the ellipsoid.
*
* @example
* //Create a Cartesian and determine it's Cartographic representation on a WGS84 ellipsoid.
* const position = new Cesium.Cartesian3(17832.12, 83234.52, 952313.73);
* const cartographicPosition = Cesium.Ellipsoid.WGS84.cartesianToCartographic(position);
*/
Ellipsoid.prototype.cartesianToCartographic = function (cartesian, result) {
//`cartesian is required.` is thrown from scaleToGeodeticSurface
const p = this.scaleToGeodeticSurface(cartesian, cartesianToCartographicP);
if (!defaultValue.defined(p)) {
return undefined;
}
const n = this.geodeticSurfaceNormal(p, cartesianToCartographicN);
const h = Cartesian3.subtract(cartesian, p, cartesianToCartographicH);
const longitude = Math.atan2(n.y, n.x);
const latitude = Math.asin(n.z);
const height =
ComponentDatatype.CesiumMath.sign(Cartesian3.dot(h, cartesian)) * Cartesian3.magnitude(h);
if (!defaultValue.defined(result)) {
return new Cartographic(longitude, latitude, height);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = height;
return result;
};
/**
* Converts the provided array of cartesians to an array of cartographics.
*
* @param {Cartesian3[]} cartesians An array of Cartesian positions.
* @param {Cartographic[]} [result] The object onto which to store the result.
* @returns {Cartographic[]} The modified result parameter or a new Array instance if none was provided.
*
* @example
* //Create an array of Cartesians and determine their Cartographic representation on a WGS84 ellipsoid.
* const positions = [new Cesium.Cartesian3(17832.12, 83234.52, 952313.73),
* new Cesium.Cartesian3(17832.13, 83234.53, 952313.73),
* new Cesium.Cartesian3(17832.14, 83234.54, 952313.73)]
* const cartographicPositions = Cesium.Ellipsoid.WGS84.cartesianArrayToCartographicArray(positions);
*/
Ellipsoid.prototype.cartesianArrayToCartographicArray = function (
cartesians,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("cartesians", cartesians);
//>>includeEnd('debug');
const length = cartesians.length;
if (!defaultValue.defined(result)) {
result = new Array(length);
} else {
result.length = length;
}
for (let i = 0; i < length; ++i) {
result[i] = this.cartesianToCartographic(cartesians[i], result[i]);
}
return result;
};
/**
* Scales the provided Cartesian position along the geodetic surface normal
* so that it is on the surface of this ellipsoid. If the position is
* at the center of the ellipsoid, this function returns undefined.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter, a new Cartesian3 instance if none was provided, or undefined if the position is at the center.
*/
Ellipsoid.prototype.scaleToGeodeticSurface = function (cartesian, result) {
return scaleToGeodeticSurface(
cartesian,
this._oneOverRadii,
this._oneOverRadiiSquared,
this._centerToleranceSquared,
result
);
};
/**
* Scales the provided Cartesian position along the geocentric surface normal
* so that it is on the surface of this ellipsoid.
*
* @param {Cartesian3} cartesian The Cartesian position to scale.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if none was provided.
*/
Ellipsoid.prototype.scaleToGeocentricSurface = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
const positionX = cartesian.x;
const positionY = cartesian.y;
const positionZ = cartesian.z;
const oneOverRadiiSquared = this._oneOverRadiiSquared;
const beta =
1.0 /
Math.sqrt(
positionX * positionX * oneOverRadiiSquared.x +
positionY * positionY * oneOverRadiiSquared.y +
positionZ * positionZ * oneOverRadiiSquared.z
);
return Cartesian3.multiplyByScalar(cartesian, beta, result);
};
/**
* Transforms a Cartesian X, Y, Z position to the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#oneOverRadii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the scaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionToScaledSpace = function (
position,
result
) {
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._oneOverRadii, result);
};
/**
* Transforms a Cartesian X, Y, Z position from the ellipsoid-scaled space by multiplying
* its components by the result of {@link Ellipsoid#radii}.
*
* @param {Cartesian3} position The position to transform.
* @param {Cartesian3} [result] The position to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3} The position expressed in the unscaled space. The returned instance is the
* one passed as the result parameter if it is not undefined, or a new instance of it is.
*/
Ellipsoid.prototype.transformPositionFromScaledSpace = function (
position,
result
) {
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
return Cartesian3.multiplyComponents(position, this._radii, result);
};
/**
* Compares this Ellipsoid against the provided Ellipsoid componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Ellipsoid} [right] The other Ellipsoid.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Ellipsoid.prototype.equals = function (right) {
return (
this === right ||
(defaultValue.defined(right) && Cartesian3.equals(this._radii, right._radii))
);
};
/**
* Creates a string representing this Ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*
* @returns {String} A string representing this ellipsoid in the format '(radii.x, radii.y, radii.z)'.
*/
Ellipsoid.prototype.toString = function () {
return this._radii.toString();
};
/**
* Computes a point which is the intersection of the surface normal with the z-axis.
*
* @param {Cartesian3} position the position. must be on the surface of the ellipsoid.
* @param {Number} [buffer = 0.0] A buffer to subtract from the ellipsoid size when checking if the point is inside the ellipsoid.
* In earth case, with common earth datums, there is no need for this buffer since the intersection point is always (relatively) very close to the center.
* In WGS84 datum, intersection point is at max z = +-42841.31151331382 (0.673% of z-axis).
* Intersection point could be outside the ellipsoid if the ratio of MajorAxis / AxisOfRotation is bigger than the square root of 2
* @param {Cartesian3} [result] The cartesian to which to copy the result, or undefined to create and
* return a new instance.
* @returns {Cartesian3 | undefined} the intersection point if it's inside the ellipsoid, undefined otherwise
*
* @exception {DeveloperError} position is required.
* @exception {DeveloperError} Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y).
* @exception {DeveloperError} Ellipsoid.radii.z must be greater than 0.
*/
Ellipsoid.prototype.getSurfaceNormalIntersectionWithZAxis = function (
position,
buffer,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("position", position);
if (
!ComponentDatatype.CesiumMath.equalsEpsilon(
this._radii.x,
this._radii.y,
ComponentDatatype.CesiumMath.EPSILON15
)
) {
throw new RuntimeError.DeveloperError(
"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)"
);
}
RuntimeError.Check.typeOf.number.greaterThan("Ellipsoid.radii.z", this._radii.z, 0);
//>>includeEnd('debug');
buffer = defaultValue.defaultValue(buffer, 0.0);
const squaredXOverSquaredZ = this._squaredXOverSquaredZ;
if (!defaultValue.defined(result)) {
result = new Cartesian3();
}
result.x = 0.0;
result.y = 0.0;
result.z = position.z * (1 - squaredXOverSquaredZ);
if (Math.abs(result.z) >= this._radii.z - buffer) {
return undefined;
}
return result;
};
const abscissas = [
0.14887433898163,
0.43339539412925,
0.67940956829902,
0.86506336668898,
0.97390652851717,
0.0,
];
const weights = [
0.29552422471475,
0.26926671930999,
0.21908636251598,
0.14945134915058,
0.066671344308684,
0.0,
];
/**
* Compute the 10th order Gauss-Legendre Quadrature of the given definite integral.
*
* @param {Number} a The lower bound for the integration.
* @param {Number} b The upper bound for the integration.
* @param {Ellipsoid~RealValuedScalarFunction} func The function to integrate.
* @returns {Number} The value of the integral of the given function over the given domain.
*
* @private
*/
function gaussLegendreQuadrature(a, b, func) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("a", a);
RuntimeError.Check.typeOf.number("b", b);
RuntimeError.Check.typeOf.func("func", func);
//>>includeEnd('debug');
// The range is half of the normal range since the five weights add to one (ten weights add to two).
// The values of the abscissas are multiplied by two to account for this.
const xMean = 0.5 * (b + a);
const xRange = 0.5 * (b - a);
let sum = 0.0;
for (let i = 0; i < 5; i++) {
const dx = xRange * abscissas[i];
sum += weights[i] * (func(xMean + dx) + func(xMean - dx));
}
// Scale the sum to the range of x.
sum *= xRange;
return sum;
}
/**
* A real valued scalar function.
* @callback Ellipsoid~RealValuedScalarFunction
*
* @param {Number} x The value used to evaluate the function.
* @returns {Number} The value of the function at x.
*
* @private
*/
/**
* Computes an approximation of the surface area of a rectangle on the surface of an ellipsoid using
* Gauss-Legendre 10th order quadrature.
*
* @param {Rectangle} rectangle The rectangle used for computing the surface area.
* @returns {Number} The approximate area of the rectangle on the surface of this ellipsoid.
*/
Ellipsoid.prototype.surfaceArea = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
const minLongitude = rectangle.west;
let maxLongitude = rectangle.east;
const minLatitude = rectangle.south;
const maxLatitude = rectangle.north;
while (maxLongitude < minLongitude) {
maxLongitude += ComponentDatatype.CesiumMath.TWO_PI;
}
const radiiSquared = this._radiiSquared;
const a2 = radiiSquared.x;
const b2 = radiiSquared.y;
const c2 = radiiSquared.z;
const a2b2 = a2 * b2;
return gaussLegendreQuadrature(minLatitude, maxLatitude, function (lat) {
// phi represents the angle measured from the north pole
// sin(phi) = sin(pi / 2 - lat) = cos(lat), cos(phi) is similar
const sinPhi = Math.cos(lat);
const cosPhi = Math.sin(lat);
return (
Math.cos(lat) *
gaussLegendreQuadrature(minLongitude, maxLongitude, function (lon) {
const cosTheta = Math.cos(lon);
const sinTheta = Math.sin(lon);
return Math.sqrt(
a2b2 * cosPhi * cosPhi +
c2 *
(b2 * cosTheta * cosTheta + a2 * sinTheta * sinTheta) *
sinPhi *
sinPhi
);
})
);
});
};
/**
* A 3x3 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix3
* @constructor
* @implements {ArrayLike
* Returns a diagonal matrix and unitary matrix such that:
* matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)
*
* The values along the diagonal of the diagonal matrix are the eigenvalues. The columns * of the unitary matrix are the corresponding eigenvectors. *
* * @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric. * @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result. * @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively. * * @example * const a = //... symetric matrix * const result = { * unitary : new Cesium.Matrix3(), * diagonal : new Cesium.Matrix3() * }; * Cesium.Matrix3.computeEigenDecomposition(a, result); * * const unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3()); * const b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3()); * Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a * * const lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue * const v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector * const c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v) */ Matrix3.computeEigenDecomposition = function (matrix, result) { //>>includeStart('debug', pragmas.debug); RuntimeError.Check.typeOf.object("matrix", matrix); //>>includeEnd('debug'); // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan, // section 8.4.3 The Classical Jacobi Algorithm const tolerance = ComponentDatatype.CesiumMath.EPSILON20; const maxSweeps = 10; let count = 0; let sweep = 0; if (!defaultValue.defined(result)) { result = {}; } const unitaryMatrix = (result.unitary = Matrix3.clone( Matrix3.IDENTITY, result.unitary )); const diagMatrix = (result.diagonal = Matrix3.clone(matrix, result.diagonal)); const epsilon = tolerance * computeFrobeniusNorm(diagMatrix); while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) { shurDecomposition(diagMatrix, jMatrix); Matrix3.transpose(jMatrix, jMatrixTranspose); Matrix3.multiply(diagMatrix, jMatrix, diagMatrix); Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix); Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix); if (++count > 2) { ++sweep; count = 0; } } return result; }; /** * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements. * * @param {Matrix3} matrix The matrix with signed elements. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. */ Matrix3.abs = function (matrix, result) { //>>includeStart('debug', pragmas.debug); RuntimeError.Check.typeOf.object("matrix", matrix); RuntimeError.Check.typeOf.object("result", result); //>>includeEnd('debug'); result[0] = Math.abs(matrix[0]); result[1] = Math.abs(matrix[1]); result[2] = Math.abs(matrix[2]); result[3] = Math.abs(matrix[3]); result[4] = Math.abs(matrix[4]); result[5] = Math.abs(matrix[5]); result[6] = Math.abs(matrix[6]); result[7] = Math.abs(matrix[7]); result[8] = Math.abs(matrix[8]); return result; }; /** * Computes the determinant of the provided matrix. * * @param {Matrix3} matrix The matrix to use. * @returns {Number} The value of the determinant of the matrix. */ Matrix3.determinant = function (matrix) { //>>includeStart('debug', pragmas.debug); RuntimeError.Check.typeOf.object("matrix", matrix); //>>includeEnd('debug'); const m11 = matrix[0]; const m21 = matrix[3]; const m31 = matrix[6]; const m12 = matrix[1]; const m22 = matrix[4]; const m32 = matrix[7]; const m13 = matrix[2]; const m23 = matrix[5]; const m33 = matrix[8]; return ( m11 * (m22 * m33 - m23 * m32) + m12 * (m23 * m31 - m21 * m33) + m13 * (m21 * m32 - m22 * m31) ); }; /** * Computes the inverse of the provided matrix. * * @param {Matrix3} matrix The matrix to invert. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. * * @exception {DeveloperError} matrix is not invertible. */ Matrix3.inverse = function (matrix, result) { //>>includeStart('debug', pragmas.debug); RuntimeError.Check.typeOf.object("matrix", matrix); RuntimeError.Check.typeOf.object("result", result); //>>includeEnd('debug'); const m11 = matrix[0]; const m21 = matrix[1]; const m31 = matrix[2]; const m12 = matrix[3]; const m22 = matrix[4]; const m32 = matrix[5]; const m13 = matrix[6]; const m23 = matrix[7]; const m33 = matrix[8]; const determinant = Matrix3.determinant(matrix); //>>includeStart('debug', pragmas.debug); if (Math.abs(determinant) <= ComponentDatatype.CesiumMath.EPSILON15) { throw new RuntimeError.DeveloperError("matrix is not invertible"); } //>>includeEnd('debug'); result[0] = m22 * m33 - m23 * m32; result[1] = m23 * m31 - m21 * m33; result[2] = m21 * m32 - m22 * m31; result[3] = m13 * m32 - m12 * m33; result[4] = m11 * m33 - m13 * m31; result[5] = m12 * m31 - m11 * m32; result[6] = m12 * m23 - m13 * m22; result[7] = m13 * m21 - m11 * m23; result[8] = m11 * m22 - m12 * m21; const scale = 1.0 / determinant; return Matrix3.multiplyByScalar(result, scale, result); }; const scratchTransposeMatrix$1 = new Matrix3(); /** * Computes the inverse transpose of a matrix. * * @param {Matrix3} matrix The matrix to transpose and invert. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. */ Matrix3.inverseTranspose = function (matrix, result) { //>>includeStart('debug', pragmas.debug); RuntimeError.Check.typeOf.object("matrix", matrix); RuntimeError.Check.typeOf.object("result", result); //>>includeEnd('debug'); return Matrix3.inverse( Matrix3.transpose(matrix, scratchTransposeMatrix$1), result ); }; /** * Compares the provided matrices componentwise and returns *true if they are equal, false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Matrix3.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[3] === right[3] &&
left[4] === right[4] &&
left[5] === right[5] &&
left[6] === right[6] &&
left[7] === right[7] &&
left[8] === right[8])
);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Matrix3.equalsEpsilon = function (left, right, epsilon) {
epsilon = defaultValue.defaultValue(epsilon, 0);
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon &&
Math.abs(left[4] - right[4]) <= epsilon &&
Math.abs(left[5] - right[5]) <= epsilon &&
Math.abs(left[6] - right[6]) <= epsilon &&
Math.abs(left[7] - right[7]) <= epsilon &&
Math.abs(left[8] - right[8]) <= epsilon)
);
};
/**
* An immutable Matrix3 instance initialized to the identity matrix.
*
* @type {Matrix3}
* @constant
*/
Matrix3.IDENTITY = Object.freeze(
new Matrix3(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)
);
/**
* An immutable Matrix3 instance initialized to the zero matrix.
*
* @type {Matrix3}
* @constant
*/
Matrix3.ZERO = Object.freeze(
new Matrix3(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
);
/**
* The index into Matrix3 for column 0, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW0 = 0;
/**
* The index into Matrix3 for column 0, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW1 = 1;
/**
* The index into Matrix3 for column 0, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN0ROW2 = 2;
/**
* The index into Matrix3 for column 1, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW0 = 3;
/**
* The index into Matrix3 for column 1, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW1 = 4;
/**
* The index into Matrix3 for column 1, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN1ROW2 = 5;
/**
* The index into Matrix3 for column 2, row 0.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW0 = 6;
/**
* The index into Matrix3 for column 2, row 1.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW1 = 7;
/**
* The index into Matrix3 for column 2, row 2.
*
* @type {Number}
* @constant
*/
Matrix3.COLUMN2ROW2 = 8;
Object.defineProperties(Matrix3.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix3.prototype
*
* @type {Number}
*/
length: {
get: function () {
return Matrix3.packedLength;
},
},
});
/**
* Duplicates the provided Matrix3 instance.
*
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
Matrix3.prototype.clone = function (result) {
return Matrix3.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix3.prototype.equals = function (right) {
return Matrix3.equals(this, right);
};
/**
* @private
*/
Matrix3.equalsArray = function (matrix, array, offset) {
return (
matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3] &&
matrix[4] === array[offset + 4] &&
matrix[5] === array[offset + 5] &&
matrix[6] === array[offset + 6] &&
matrix[7] === array[offset + 7] &&
matrix[8] === array[offset + 8]
);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix3.prototype.equalsEpsilon = function (right, epsilon) {
return Matrix3.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1, column2)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
*/
Matrix3.prototype.toString = function () {
return (
`(${this[0]}, ${this[3]}, ${this[6]})\n` +
`(${this[1]}, ${this[4]}, ${this[7]})\n` +
`(${this[2]}, ${this[5]}, ${this[8]})`
);
};
/**
* A 4D Cartesian point.
* @alias Cartesian4
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
* @param {Number} [w=0.0] The W component.
*
* @see Cartesian2
* @see Cartesian3
* @see Packable
*/
function Cartesian4(x, y, z, w) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue.defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue.defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = defaultValue.defaultValue(z, 0.0);
/**
* The W component.
* @type {Number}
* @default 0.0
*/
this.w = defaultValue.defaultValue(w, 0.0);
}
/**
* Creates a Cartesian4 instance from x, y, z and w coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Number} z The z coordinate.
* @param {Number} w The w coordinate.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.fromElements = function (x, y, z, w, result) {
if (!defaultValue.defined(result)) {
return new Cartesian4(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Creates a Cartesian4 instance from a {@link Color}. red, green, blue,
* and alpha map to x, y, z, and w, respectively.
*
* @param {Color} color The source color.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.fromColor = function (color, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("color", color);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
return new Cartesian4(color.red, color.green, color.blue, color.alpha);
}
result.x = color.red;
result.y = color.green;
result.z = color.blue;
result.w = color.alpha;
return result;
};
/**
* Duplicates a Cartesian4 instance.
*
* @param {Cartesian4} cartesian The Cartesian to duplicate.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian4.clone = function (cartesian, result) {
if (!defaultValue.defined(cartesian)) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Cartesian4(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
}
result.x = cartesian.x;
result.y = cartesian.y;
result.z = cartesian.z;
result.w = cartesian.w;
return result;
};
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian4.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian4} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian4.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex++] = value.z;
array[startingIndex] = value.w;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian4} [result] The object into which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
if (!defaultValue.defined(result)) {
result = new Cartesian4();
}
result.x = array[startingIndex++];
result.y = array[startingIndex++];
result.z = array[startingIndex++];
result.w = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian4s into an array of components.
*
* @param {Cartesian4[]} array The array of cartesians to pack.
* @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 4 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 4) elements.
* @returns {Number[]} The packed array.
*/
Cartesian4.packArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
const length = array.length;
const resultLength = length * 4;
if (!defaultValue.defined(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
//>>includeStart('debug', pragmas.debug);
throw new RuntimeError.DeveloperError(
"If result is a typed array, it must have exactly array.length * 4 elements"
);
//>>includeEnd('debug');
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (let i = 0; i < length; ++i) {
Cartesian4.pack(array[i], result, i * 4);
}
return result;
};
/**
* Unpacks an array of cartesian components into an array of Cartesian4s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian4[]} [result] The array onto which to store the result.
* @returns {Cartesian4[]} The unpacked array.
*/
Cartesian4.unpackArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 4);
if (array.length % 4 !== 0) {
throw new RuntimeError.DeveloperError("array length must be a multiple of 4.");
}
//>>includeEnd('debug');
const length = array.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 4);
} else {
result.length = length / 4;
}
for (let i = 0; i < length; i += 4) {
const index = i / 4;
result[index] = Cartesian4.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian4 from four consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose four consecutive elements correspond to the x, y, z, and w components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*
* @example
* // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0)
* const v = [1.0, 2.0, 3.0, 4.0];
* const p = Cesium.Cartesian4.fromArray(v);
*
* // Create a Cartesian4 with (1.0, 2.0, 3.0, 4.0) using an offset into an array
* const v2 = [0.0, 0.0, 1.0, 2.0, 3.0, 4.0];
* const p2 = Cesium.Cartesian4.fromArray(v2, 2);
*/
Cartesian4.fromArray = Cartesian4.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian4} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian4.maximumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.max(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian4} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian4.minimumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.min(cartesian.x, cartesian.y, cartesian.z, cartesian.w);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian4} first A cartesian to compare.
* @param {Cartesian4} second A cartesian to compare.
* @param {Cartesian4} result The object into which to store the result.
* @returns {Cartesian4} A cartesian with the minimum components.
*/
Cartesian4.minimumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("first", first);
RuntimeError.Check.typeOf.object("second", second);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
result.z = Math.min(first.z, second.z);
result.w = Math.min(first.w, second.w);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian4} first A cartesian to compare.
* @param {Cartesian4} second A cartesian to compare.
* @param {Cartesian4} result The object into which to store the result.
* @returns {Cartesian4} A cartesian with the maximum components.
*/
Cartesian4.maximumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("first", first);
RuntimeError.Check.typeOf.object("second", second);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
result.z = Math.max(first.z, second.z);
result.w = Math.max(first.w, second.w);
return result;
};
/**
* Constrain a value to lie between two values.
*
* @param {Cartesian4} value The value to clamp.
* @param {Cartesian4} min The minimum bound.
* @param {Cartesian4} max The maximum bound.
* @param {Cartesian4} result The object into which to store the result.
* @returns {Cartesian4} The clamped value such that min <= result <= max.
*/
Cartesian4.clamp = function (value, min, max, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.typeOf.object("min", min);
RuntimeError.Check.typeOf.object("max", max);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const x = ComponentDatatype.CesiumMath.clamp(value.x, min.x, max.x);
const y = ComponentDatatype.CesiumMath.clamp(value.y, min.y, max.y);
const z = ComponentDatatype.CesiumMath.clamp(value.z, min.z, max.z);
const w = ComponentDatatype.CesiumMath.clamp(value.w, min.w, max.w);
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian4} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian4.magnitudeSquared = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return (
cartesian.x * cartesian.x +
cartesian.y * cartesian.y +
cartesian.z * cartesian.z +
cartesian.w * cartesian.w
);
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian4} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian4.magnitude = function (cartesian) {
return Math.sqrt(Cartesian4.magnitudeSquared(cartesian));
};
const distanceScratch$1 = new Cartesian4();
/**
* Computes the 4-space distance between two points.
*
* @param {Cartesian4} left The first point to compute the distance from.
* @param {Cartesian4} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* const d = Cesium.Cartesian4.distance(
* new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
* new Cesium.Cartesian4(2.0, 0.0, 0.0, 0.0));
*/
Cartesian4.distance = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian4.subtract(left, right, distanceScratch$1);
return Cartesian4.magnitude(distanceScratch$1);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian4#distance}.
*
* @param {Cartesian4} left The first point to compute the distance from.
* @param {Cartesian4} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* const d = Cesium.Cartesian4.distance(
* new Cesium.Cartesian4(1.0, 0.0, 0.0, 0.0),
* new Cesium.Cartesian4(3.0, 0.0, 0.0, 0.0));
*/
Cartesian4.distanceSquared = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian4.subtract(left, right, distanceScratch$1);
return Cartesian4.magnitudeSquared(distanceScratch$1);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian to be normalized.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.normalize = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const magnitude = Cartesian4.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
result.z = cartesian.z / magnitude;
result.w = cartesian.w / magnitude;
//>>includeStart('debug', pragmas.debug);
if (
isNaN(result.x) ||
isNaN(result.y) ||
isNaN(result.z) ||
isNaN(result.w)
) {
throw new RuntimeError.DeveloperError("normalized result is not a number");
}
//>>includeEnd('debug');
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian4.dot = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return (
left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w
);
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.multiplyComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x * right.x;
result.y = left.y * right.y;
result.z = left.z * right.z;
result.w = left.w * right.w;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.divideComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x / right.x;
result.y = left.y / right.y;
result.z = left.z / right.z;
result.w = left.w / right.w;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.add = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
result.w = left.w + right.w;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian4} left The first Cartesian.
* @param {Cartesian4} right The second Cartesian.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.subtract = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
result.w = left.w - right.w;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian4} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.multiplyByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.number("scalar", scalar);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
result.z = cartesian.z * scalar;
result.w = cartesian.w * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian4} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.divideByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.number("scalar", scalar);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
result.z = cartesian.z / scalar;
result.w = cartesian.w / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian to be negated.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.negate = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -cartesian.x;
result.y = -cartesian.y;
result.z = -cartesian.z;
result.w = -cartesian.w;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.abs = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
result.z = Math.abs(cartesian.z);
result.w = Math.abs(cartesian.w);
return result;
};
const lerpScratch$1 = new Cartesian4();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian4} start The value corresponding to t at 0.0.
* @param {Cartesian4}end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Cartesian4.lerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("start", start);
RuntimeError.Check.typeOf.object("end", end);
RuntimeError.Check.typeOf.number("t", t);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
Cartesian4.multiplyByScalar(end, t, lerpScratch$1);
result = Cartesian4.multiplyByScalar(start, 1.0 - t, result);
return Cartesian4.add(lerpScratch$1, result, result);
};
const mostOrthogonalAxisScratch$1 = new Cartesian4();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian4} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The most orthogonal axis.
*/
Cartesian4.mostOrthogonalAxis = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const f = Cartesian4.normalize(cartesian, mostOrthogonalAxisScratch$1);
Cartesian4.abs(f, f);
if (f.x <= f.y) {
if (f.x <= f.z) {
if (f.x <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_X, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.z <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.y <= f.z) {
if (f.y <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Y, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
} else if (f.z <= f.w) {
result = Cartesian4.clone(Cartesian4.UNIT_Z, result);
} else {
result = Cartesian4.clone(Cartesian4.UNIT_W, result);
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian4} [left] The first Cartesian.
* @param {Cartesian4} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian4.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left.x === right.x &&
left.y === right.y &&
left.z === right.z &&
left.w === right.w)
);
};
/**
* @private
*/
Cartesian4.equalsArray = function (cartesian, array, offset) {
return (
cartesian.x === array[offset] &&
cartesian.y === array[offset + 1] &&
cartesian.z === array[offset + 2] &&
cartesian.w === array[offset + 3]
);
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian4} [left] The first Cartesian.
* @param {Cartesian4} [right] The second Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian4.equalsEpsilon = function (
left,
right,
relativeEpsilon,
absoluteEpsilon
) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.z,
right.z,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.w,
right.w,
relativeEpsilon,
absoluteEpsilon
))
);
};
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.ZERO = Object.freeze(new Cartesian4(0.0, 0.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (1.0, 1.0, 1.0, 1.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.ONE = Object.freeze(new Cartesian4(1.0, 1.0, 1.0, 1.0));
/**
* An immutable Cartesian4 instance initialized to (1.0, 0.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_X = Object.freeze(new Cartesian4(1.0, 0.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 1.0, 0.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_Y = Object.freeze(new Cartesian4(0.0, 1.0, 0.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 1.0, 0.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_Z = Object.freeze(new Cartesian4(0.0, 0.0, 1.0, 0.0));
/**
* An immutable Cartesian4 instance initialized to (0.0, 0.0, 0.0, 1.0).
*
* @type {Cartesian4}
* @constant
*/
Cartesian4.UNIT_W = Object.freeze(new Cartesian4(0.0, 0.0, 0.0, 1.0));
/**
* Duplicates this Cartesian4 instance.
*
* @param {Cartesian4} [result] The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter or a new Cartesian4 instance if one was not provided.
*/
Cartesian4.prototype.clone = function (result) {
return Cartesian4.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian4} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian4.prototype.equals = function (right) {
return Cartesian4.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian4} [right] The right hand side Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian4.prototype.equalsEpsilon = function (
right,
relativeEpsilon,
absoluteEpsilon
) {
return Cartesian4.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
};
/**
* Creates a string representing this Cartesian in the format '(x, y, z, w)'.
*
* @returns {String} A string representing the provided Cartesian in the format '(x, y, z, w)'.
*/
Cartesian4.prototype.toString = function () {
return `(${this.x}, ${this.y}, ${this.z}, ${this.w})`;
};
// scratchU8Array and scratchF32Array are views into the same buffer
const scratchF32Array = new Float32Array(1);
const scratchU8Array = new Uint8Array(scratchF32Array.buffer);
const testU32 = new Uint32Array([0x11223344]);
const testU8 = new Uint8Array(testU32.buffer);
const littleEndian = testU8[0] === 0x44;
/**
* Packs an arbitrary floating point value to 4 values representable using uint8.
*
* @param {Number} value A floating point number.
* @param {Cartesian4} [result] The Cartesian4 that will contain the packed float.
* @returns {Cartesian4} A Cartesian4 representing the float packed to values in x, y, z, and w.
*/
Cartesian4.packFloat = function (value, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.number("value", value);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
result = new Cartesian4();
}
// scratchU8Array and scratchF32Array are views into the same buffer
scratchF32Array[0] = value;
if (littleEndian) {
result.x = scratchU8Array[0];
result.y = scratchU8Array[1];
result.z = scratchU8Array[2];
result.w = scratchU8Array[3];
} else {
// convert from big-endian to little-endian
result.x = scratchU8Array[3];
result.y = scratchU8Array[2];
result.z = scratchU8Array[1];
result.w = scratchU8Array[0];
}
return result;
};
/**
* Unpacks a float packed using Cartesian4.packFloat.
*
* @param {Cartesian4} packedFloat A Cartesian4 containing a float packed to 4 values representable using uint8.
* @returns {Number} The unpacked float.
* @private
*/
Cartesian4.unpackFloat = function (packedFloat) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("packedFloat", packedFloat);
//>>includeEnd('debug');
// scratchU8Array and scratchF32Array are views into the same buffer
if (littleEndian) {
scratchU8Array[0] = packedFloat.x;
scratchU8Array[1] = packedFloat.y;
scratchU8Array[2] = packedFloat.z;
scratchU8Array[3] = packedFloat.w;
} else {
// convert from little-endian to big-endian
scratchU8Array[0] = packedFloat.w;
scratchU8Array[1] = packedFloat.z;
scratchU8Array[2] = packedFloat.y;
scratchU8Array[3] = packedFloat.x;
}
return scratchF32Array[0];
};
/**
* A 4x4 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix4
* @constructor
* @implements {ArrayLike[0.0, 0.0, 0.0, 1.0])
* by a 3x3 rotation matrix. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m); with less allocations and arithmetic operations.
*
* @param {Matrix4} matrix The matrix on the left-hand side.
* @param {Matrix3} rotation The 3x3 rotation matrix on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);
* Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);
*/
Matrix4.multiplyByMatrix3 = function (matrix, rotation, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("rotation", rotation);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const left0 = matrix[0];
const left1 = matrix[1];
const left2 = matrix[2];
const left4 = matrix[4];
const left5 = matrix[5];
const left6 = matrix[6];
const left8 = matrix[8];
const left9 = matrix[9];
const left10 = matrix[10];
const right0 = rotation[0];
const right1 = rotation[1];
const right2 = rotation[2];
const right4 = rotation[3];
const right5 = rotation[4];
const right6 = rotation[5];
const right8 = rotation[6];
const right9 = rotation[7];
const right10 = rotation[8];
const column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
const column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
const column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
const column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
const column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
const column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
const column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
const column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
const column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = 0.0;
result[4] = column1Row0;
result[5] = column1Row1;
result[6] = column1Row2;
result[7] = 0.0;
result[8] = column2Row0;
result[9] = column2Row1;
result[10] = column2Row2;
result[11] = 0.0;
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Multiplies a transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by an implicit translation matrix defined by a {@link Cartesian3}. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromTranslation(position), m); with less allocations and arithmetic operations.
*
* @param {Matrix4} matrix The matrix on the left-hand side.
* @param {Cartesian3} translation The translation on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);
* Cesium.Matrix4.multiplyByTranslation(m, position, m);
*/
Matrix4.multiplyByTranslation = function (matrix, translation, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("translation", translation);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const x = translation.x;
const y = translation.y;
const z = translation.z;
const tx = x * matrix[0] + y * matrix[4] + z * matrix[8] + matrix[12];
const ty = x * matrix[1] + y * matrix[5] + z * matrix[9] + matrix[13];
const tz = x * matrix[2] + y * matrix[6] + z * matrix[10] + matrix[14];
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
result[9] = matrix[9];
result[10] = matrix[10];
result[11] = matrix[11];
result[12] = tx;
result[13] = ty;
result[14] = tz;
result[15] = matrix[15];
return result;
};
/**
* Multiplies an affine transformation matrix (with a bottom row of [0.0, 0.0, 0.0, 1.0])
* by an implicit non-uniform scale matrix. This is an optimization
* for Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);, where
* m must be an affine matrix.
* This function performs fewer allocations and arithmetic operations.
*
* @param {Matrix4} matrix The affine matrix on the left-hand side.
* @param {Cartesian3} scale The non-uniform scale on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);
* Cesium.Matrix4.multiplyByScale(m, scale, m);
*
* @see Matrix4.multiplyByUniformScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.setScale
* @see Matrix4.setUniformScale
* @see Matrix4.getScale
*/
Matrix4.multiplyByScale = function (matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("scale", scale);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const scaleX = scale.x;
const scaleY = scale.y;
const scaleZ = scale.z;
// Faster than Cartesian3.equals
if (scaleX === 1.0 && scaleY === 1.0 && scaleZ === 1.0) {
return Matrix4.clone(matrix, result);
}
result[0] = scaleX * matrix[0];
result[1] = scaleX * matrix[1];
result[2] = scaleX * matrix[2];
result[3] = matrix[3];
result[4] = scaleY * matrix[4];
result[5] = scaleY * matrix[5];
result[6] = scaleY * matrix[6];
result[7] = matrix[7];
result[8] = scaleZ * matrix[8];
result[9] = scaleZ * matrix[9];
result[10] = scaleZ * matrix[10];
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.
*
* @param {Matrix4} matrix The matrix on the left-hand side.
* @param {Number} scale The uniform scale on the right-hand side.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);
* Cesium.Matrix4.multiplyByUniformScale(m, scale, m);
*
* @see Matrix4.multiplyByScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.setScale
* @see Matrix4.setUniformScale
* @see Matrix4.getScale
*/
Matrix4.multiplyByUniformScale = function (matrix, scale, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.number("scale", scale);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0] * scale;
result[1] = matrix[1] * scale;
result[2] = matrix[2] * scale;
result[3] = matrix[3];
result[4] = matrix[4] * scale;
result[5] = matrix[5] * scale;
result[6] = matrix[6] * scale;
result[7] = matrix[7];
result[8] = matrix[8] * scale;
result[9] = matrix[9] * scale;
result[10] = matrix[10] * scale;
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian4} cartesian The vector.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*/
Matrix4.multiplyByVector = function (matrix, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const vW = cartesian.w;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;
const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;
const w = matrix[3] * vX + matrix[7] * vY + matrix[11] * vZ + matrix[15] * vW;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
* with a {@link Cartesian4} with a w component of zero.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian3} cartesian The point.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @example
* const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* const result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());
* // A shortcut for
* // Cartesian3 p = ...
* // Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);
*/
Matrix4.multiplyByPointAsVector = function (matrix, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;
const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ;
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
* with a {@link Cartesian4} with a w component of 1, but returns a {@link Cartesian3} instead of a {@link Cartesian4}.
*
* @param {Matrix4} matrix The matrix.
* @param {Cartesian3} cartesian The point.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @example
* const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* const result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());
*/
Matrix4.multiplyByPoint = function (matrix, cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];
const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14];
result.x = x;
result.y = y;
result.z = z;
return result;
};
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix4} matrix The matrix.
* @param {Number} scalar The number to multiply by.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //create a Matrix4 instance which is a scaled version of the supplied Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* const a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());
*
* // m remains the same
* // a = [-20.0, -22.0, -24.0, -26.0]
* // [-28.0, -30.0, -32.0, -34.0]
* // [-36.0, -38.0, -40.0, -42.0]
* // [-44.0, -46.0, -48.0, -50.0]
*/
Matrix4.multiplyByScalar = function (matrix, scalar, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.number("scalar", scalar);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
result[4] = matrix[4] * scalar;
result[5] = matrix[5] * scalar;
result[6] = matrix[6] * scalar;
result[7] = matrix[7] * scalar;
result[8] = matrix[8] * scalar;
result[9] = matrix[9] * scalar;
result[10] = matrix[10] * scalar;
result[11] = matrix[11] * scalar;
result[12] = matrix[12] * scalar;
result[13] = matrix[13] * scalar;
result[14] = matrix[14] * scalar;
result[15] = matrix[15] * scalar;
return result;
};
/**
* Computes a negated copy of the provided matrix.
*
* @param {Matrix4} matrix The matrix to negate.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //create a new Matrix4 instance which is a negation of a Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* const a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());
*
* // m remains the same
* // a = [-10.0, -11.0, -12.0, -13.0]
* // [-14.0, -15.0, -16.0, -17.0]
* // [-18.0, -19.0, -20.0, -21.0]
* // [-22.0, -23.0, -24.0, -25.0]
*/
Matrix4.negate = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
result[4] = -matrix[4];
result[5] = -matrix[5];
result[6] = -matrix[6];
result[7] = -matrix[7];
result[8] = -matrix[8];
result[9] = -matrix[9];
result[10] = -matrix[10];
result[11] = -matrix[11];
result[12] = -matrix[12];
result[13] = -matrix[13];
result[14] = -matrix[14];
result[15] = -matrix[15];
return result;
};
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix4} matrix The matrix to transpose.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @example
* //returns transpose of a Matrix4
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* const a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());
*
* // m remains the same
* // a = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*/
Matrix4.transpose = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const matrix1 = matrix[1];
const matrix2 = matrix[2];
const matrix3 = matrix[3];
const matrix6 = matrix[6];
const matrix7 = matrix[7];
const matrix11 = matrix[11];
result[0] = matrix[0];
result[1] = matrix[4];
result[2] = matrix[8];
result[3] = matrix[12];
result[4] = matrix1;
result[5] = matrix[5];
result[6] = matrix[9];
result[7] = matrix[13];
result[8] = matrix2;
result[9] = matrix6;
result[10] = matrix[10];
result[11] = matrix[14];
result[12] = matrix3;
result[13] = matrix7;
result[14] = matrix11;
result[15] = matrix[15];
return result;
};
/**
* Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
*
* @param {Matrix4} matrix The matrix with signed elements.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.abs = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = Math.abs(matrix[0]);
result[1] = Math.abs(matrix[1]);
result[2] = Math.abs(matrix[2]);
result[3] = Math.abs(matrix[3]);
result[4] = Math.abs(matrix[4]);
result[5] = Math.abs(matrix[5]);
result[6] = Math.abs(matrix[6]);
result[7] = Math.abs(matrix[7]);
result[8] = Math.abs(matrix[8]);
result[9] = Math.abs(matrix[9]);
result[10] = Math.abs(matrix[10]);
result[11] = Math.abs(matrix[11]);
result[12] = Math.abs(matrix[12]);
result[13] = Math.abs(matrix[13]);
result[14] = Math.abs(matrix[14]);
result[15] = Math.abs(matrix[15]);
return result;
};
/**
* Compares the provided matrices componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix4} [left] The first matrix.
* @param {Matrix4} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*
* @example
* //compares two Matrix4 instances
*
* // a = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* // b = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* if(Cesium.Matrix4.equals(a,b)) {
* console.log("Both matrices are equal");
* } else {
* console.log("They are not equal");
* }
*
* //Prints "Both matrices are equal" on the console
*/
Matrix4.equals = function (left, right) {
// Given that most matrices will be transformation matrices, the elements
// are tested in order such that the test is likely to fail as early
// as possible. I _think_ this is just as friendly to the L1 cache
// as testing in index order. It is certainty faster in practice.
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
// Translation
left[12] === right[12] &&
left[13] === right[13] &&
left[14] === right[14] &&
// Rotation/scale
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[4] === right[4] &&
left[5] === right[5] &&
left[6] === right[6] &&
left[8] === right[8] &&
left[9] === right[9] &&
left[10] === right[10] &&
// Bottom row
left[3] === right[3] &&
left[7] === right[7] &&
left[11] === right[11] &&
left[15] === right[15])
);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix4} [left] The first matrix.
* @param {Matrix4} [right] The second matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*
* @example
* //compares two Matrix4 instances
*
* // a = [10.5, 14.5, 18.5, 22.5]
* // [11.5, 15.5, 19.5, 23.5]
* // [12.5, 16.5, 20.5, 24.5]
* // [13.5, 17.5, 21.5, 25.5]
*
* // b = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){
* console.log("Difference between both the matrices is less than 0.1");
* } else {
* console.log("Difference between both the matrices is not less than 0.1");
* }
*
* //Prints "Difference between both the matrices is not less than 0.1" on the console
*/
Matrix4.equalsEpsilon = function (left, right, epsilon) {
epsilon = defaultValue.defaultValue(epsilon, 0);
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon &&
Math.abs(left[4] - right[4]) <= epsilon &&
Math.abs(left[5] - right[5]) <= epsilon &&
Math.abs(left[6] - right[6]) <= epsilon &&
Math.abs(left[7] - right[7]) <= epsilon &&
Math.abs(left[8] - right[8]) <= epsilon &&
Math.abs(left[9] - right[9]) <= epsilon &&
Math.abs(left[10] - right[10]) <= epsilon &&
Math.abs(left[11] - right[11]) <= epsilon &&
Math.abs(left[12] - right[12]) <= epsilon &&
Math.abs(left[13] - right[13]) <= epsilon &&
Math.abs(left[14] - right[14]) <= epsilon &&
Math.abs(left[15] - right[15]) <= epsilon)
);
};
/**
* Gets the translation portion of the provided matrix, assuming the matrix is an affine transformation matrix.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Matrix4.getTranslation = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = matrix[12];
result.y = matrix[13];
result.z = matrix[14];
return result;
};
/**
* Gets the upper left 3x3 matrix of the provided matrix.
*
* @param {Matrix4} matrix The matrix to use.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @example
* // returns a Matrix3 instance from a Matrix4 instance
*
* // m = [10.0, 14.0, 18.0, 22.0]
* // [11.0, 15.0, 19.0, 23.0]
* // [12.0, 16.0, 20.0, 24.0]
* // [13.0, 17.0, 21.0, 25.0]
*
* const b = new Cesium.Matrix3();
* Cesium.Matrix4.getMatrix3(m,b);
*
* // b = [10.0, 14.0, 18.0]
* // [11.0, 15.0, 19.0]
* // [12.0, 16.0, 20.0]
*/
Matrix4.getMatrix3 = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[4];
result[4] = matrix[5];
result[5] = matrix[6];
result[6] = matrix[8];
result[7] = matrix[9];
result[8] = matrix[10];
return result;
};
const scratchInverseRotation = new Matrix3();
const scratchMatrix3Zero = new Matrix3();
const scratchBottomRow = new Cartesian4();
const scratchExpectedBottomRow = new Cartesian4(0.0, 0.0, 0.0, 1.0);
/**
* Computes the inverse of the provided matrix using Cramers Rule.
* If the determinant is zero, the matrix can not be inverted, and an exception is thrown.
* If the matrix is a proper rigid transformation, it is more efficient
* to invert it with {@link Matrix4.inverseTransformation}.
*
* @param {Matrix4} matrix The matrix to invert.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @exception {RuntimeError} matrix is not invertible because its determinate is zero.
*/
Matrix4.inverse = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
//
// Ported from:
// ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf
//
const src0 = matrix[0];
const src1 = matrix[4];
const src2 = matrix[8];
const src3 = matrix[12];
const src4 = matrix[1];
const src5 = matrix[5];
const src6 = matrix[9];
const src7 = matrix[13];
const src8 = matrix[2];
const src9 = matrix[6];
const src10 = matrix[10];
const src11 = matrix[14];
const src12 = matrix[3];
const src13 = matrix[7];
const src14 = matrix[11];
const src15 = matrix[15];
// calculate pairs for first 8 elements (cofactors)
let tmp0 = src10 * src15;
let tmp1 = src11 * src14;
let tmp2 = src9 * src15;
let tmp3 = src11 * src13;
let tmp4 = src9 * src14;
let tmp5 = src10 * src13;
let tmp6 = src8 * src15;
let tmp7 = src11 * src12;
let tmp8 = src8 * src14;
let tmp9 = src10 * src12;
let tmp10 = src8 * src13;
let tmp11 = src9 * src12;
// calculate first 8 elements (cofactors)
const dst0 =
tmp0 * src5 +
tmp3 * src6 +
tmp4 * src7 -
(tmp1 * src5 + tmp2 * src6 + tmp5 * src7);
const dst1 =
tmp1 * src4 +
tmp6 * src6 +
tmp9 * src7 -
(tmp0 * src4 + tmp7 * src6 + tmp8 * src7);
const dst2 =
tmp2 * src4 +
tmp7 * src5 +
tmp10 * src7 -
(tmp3 * src4 + tmp6 * src5 + tmp11 * src7);
const dst3 =
tmp5 * src4 +
tmp8 * src5 +
tmp11 * src6 -
(tmp4 * src4 + tmp9 * src5 + tmp10 * src6);
const dst4 =
tmp1 * src1 +
tmp2 * src2 +
tmp5 * src3 -
(tmp0 * src1 + tmp3 * src2 + tmp4 * src3);
const dst5 =
tmp0 * src0 +
tmp7 * src2 +
tmp8 * src3 -
(tmp1 * src0 + tmp6 * src2 + tmp9 * src3);
const dst6 =
tmp3 * src0 +
tmp6 * src1 +
tmp11 * src3 -
(tmp2 * src0 + tmp7 * src1 + tmp10 * src3);
const dst7 =
tmp4 * src0 +
tmp9 * src1 +
tmp10 * src2 -
(tmp5 * src0 + tmp8 * src1 + tmp11 * src2);
// calculate pairs for second 8 elements (cofactors)
tmp0 = src2 * src7;
tmp1 = src3 * src6;
tmp2 = src1 * src7;
tmp3 = src3 * src5;
tmp4 = src1 * src6;
tmp5 = src2 * src5;
tmp6 = src0 * src7;
tmp7 = src3 * src4;
tmp8 = src0 * src6;
tmp9 = src2 * src4;
tmp10 = src0 * src5;
tmp11 = src1 * src4;
// calculate second 8 elements (cofactors)
const dst8 =
tmp0 * src13 +
tmp3 * src14 +
tmp4 * src15 -
(tmp1 * src13 + tmp2 * src14 + tmp5 * src15);
const dst9 =
tmp1 * src12 +
tmp6 * src14 +
tmp9 * src15 -
(tmp0 * src12 + tmp7 * src14 + tmp8 * src15);
const dst10 =
tmp2 * src12 +
tmp7 * src13 +
tmp10 * src15 -
(tmp3 * src12 + tmp6 * src13 + tmp11 * src15);
const dst11 =
tmp5 * src12 +
tmp8 * src13 +
tmp11 * src14 -
(tmp4 * src12 + tmp9 * src13 + tmp10 * src14);
const dst12 =
tmp2 * src10 +
tmp5 * src11 +
tmp1 * src9 -
(tmp4 * src11 + tmp0 * src9 + tmp3 * src10);
const dst13 =
tmp8 * src11 +
tmp0 * src8 +
tmp7 * src10 -
(tmp6 * src10 + tmp9 * src11 + tmp1 * src8);
const dst14 =
tmp6 * src9 +
tmp11 * src11 +
tmp3 * src8 -
(tmp10 * src11 + tmp2 * src8 + tmp7 * src9);
const dst15 =
tmp10 * src10 +
tmp4 * src8 +
tmp9 * src9 -
(tmp8 * src9 + tmp11 * src10 + tmp5 * src8);
// calculate determinant
let det = src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
if (Math.abs(det) < ComponentDatatype.CesiumMath.EPSILON21) {
// Special case for a zero scale matrix that can occur, for example,
// when a model's node has a [0, 0, 0] scale.
if (
Matrix3.equalsEpsilon(
Matrix4.getMatrix3(matrix, scratchInverseRotation),
scratchMatrix3Zero,
ComponentDatatype.CesiumMath.EPSILON7
) &&
Cartesian4.equals(
Matrix4.getRow(matrix, 3, scratchBottomRow),
scratchExpectedBottomRow
)
) {
result[0] = 0.0;
result[1] = 0.0;
result[2] = 0.0;
result[3] = 0.0;
result[4] = 0.0;
result[5] = 0.0;
result[6] = 0.0;
result[7] = 0.0;
result[8] = 0.0;
result[9] = 0.0;
result[10] = 0.0;
result[11] = 0.0;
result[12] = -matrix[12];
result[13] = -matrix[13];
result[14] = -matrix[14];
result[15] = 1.0;
return result;
}
throw new RuntimeError.RuntimeError(
"matrix is not invertible because its determinate is zero."
);
}
// calculate matrix inverse
det = 1.0 / det;
result[0] = dst0 * det;
result[1] = dst1 * det;
result[2] = dst2 * det;
result[3] = dst3 * det;
result[4] = dst4 * det;
result[5] = dst5 * det;
result[6] = dst6 * det;
result[7] = dst7 * det;
result[8] = dst8 * det;
result[9] = dst9 * det;
result[10] = dst10 * det;
result[11] = dst11 * det;
result[12] = dst12 * det;
result[13] = dst13 * det;
result[14] = dst14 * det;
result[15] = dst15 * det;
return result;
};
/**
* Computes the inverse of the provided matrix assuming it is a proper rigid matrix,
* where the upper left 3x3 elements are a rotation matrix,
* and the upper three elements in the fourth column are the translation.
* The bottom row is assumed to be [0, 0, 0, 1].
* The matrix is not verified to be in the proper form.
* This method is faster than computing the inverse for a general 4x4
* matrix using {@link Matrix4.inverse}.
*
* @param {Matrix4} matrix The matrix to invert.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.inverseTransformation = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
//This function is an optimized version of the below 4 lines.
//const rT = Matrix3.transpose(Matrix4.getMatrix3(matrix));
//const rTN = Matrix3.negate(rT);
//const rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));
//return Matrix4.fromRotationTranslation(rT, rTT, result);
const matrix0 = matrix[0];
const matrix1 = matrix[1];
const matrix2 = matrix[2];
const matrix4 = matrix[4];
const matrix5 = matrix[5];
const matrix6 = matrix[6];
const matrix8 = matrix[8];
const matrix9 = matrix[9];
const matrix10 = matrix[10];
const vX = matrix[12];
const vY = matrix[13];
const vZ = matrix[14];
const x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;
const y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;
const z = -matrix8 * vX - matrix9 * vY - matrix10 * vZ;
result[0] = matrix0;
result[1] = matrix4;
result[2] = matrix8;
result[3] = 0.0;
result[4] = matrix1;
result[5] = matrix5;
result[6] = matrix9;
result[7] = 0.0;
result[8] = matrix2;
result[9] = matrix6;
result[10] = matrix10;
result[11] = 0.0;
result[12] = x;
result[13] = y;
result[14] = z;
result[15] = 1.0;
return result;
};
const scratchTransposeMatrix = new Matrix4();
/**
* Computes the inverse transpose of a matrix.
*
* @param {Matrix4} matrix The matrix to transpose and invert.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*/
Matrix4.inverseTranspose = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("matrix", matrix);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
return Matrix4.inverse(
Matrix4.transpose(matrix, scratchTransposeMatrix),
result
);
};
/**
* An immutable Matrix4 instance initialized to the identity matrix.
*
* @type {Matrix4}
* @constant
*/
Matrix4.IDENTITY = Object.freeze(
new Matrix4(
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0,
0.0,
0.0,
0.0,
0.0,
1.0
)
);
/**
* An immutable Matrix4 instance initialized to the zero matrix.
*
* @type {Matrix4}
* @constant
*/
Matrix4.ZERO = Object.freeze(
new Matrix4(
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0
)
);
/**
* The index into Matrix4 for column 0, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW0 = 0;
/**
* The index into Matrix4 for column 0, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW1 = 1;
/**
* The index into Matrix4 for column 0, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW2 = 2;
/**
* The index into Matrix4 for column 0, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN0ROW3 = 3;
/**
* The index into Matrix4 for column 1, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW0 = 4;
/**
* The index into Matrix4 for column 1, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW1 = 5;
/**
* The index into Matrix4 for column 1, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW2 = 6;
/**
* The index into Matrix4 for column 1, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN1ROW3 = 7;
/**
* The index into Matrix4 for column 2, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW0 = 8;
/**
* The index into Matrix4 for column 2, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW1 = 9;
/**
* The index into Matrix4 for column 2, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW2 = 10;
/**
* The index into Matrix4 for column 2, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN2ROW3 = 11;
/**
* The index into Matrix4 for column 3, row 0.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW0 = 12;
/**
* The index into Matrix4 for column 3, row 1.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW1 = 13;
/**
* The index into Matrix4 for column 3, row 2.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW2 = 14;
/**
* The index into Matrix4 for column 3, row 3.
*
* @type {Number}
* @constant
*/
Matrix4.COLUMN3ROW3 = 15;
Object.defineProperties(Matrix4.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix4.prototype
*
* @type {Number}
*/
length: {
get: function () {
return Matrix4.packedLength;
},
},
});
/**
* Duplicates the provided Matrix4 instance.
*
* @param {Matrix4} [result] The object onto which to store the result.
* @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
*/
Matrix4.prototype.clone = function (result) {
return Matrix4.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix4} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix4.prototype.equals = function (right) {
return Matrix4.equals(this, right);
};
/**
* @private
*/
Matrix4.equalsArray = function (matrix, array, offset) {
return (
matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3] &&
matrix[4] === array[offset + 4] &&
matrix[5] === array[offset + 5] &&
matrix[6] === array[offset + 6] &&
matrix[7] === array[offset + 7] &&
matrix[8] === array[offset + 8] &&
matrix[9] === array[offset + 9] &&
matrix[10] === array[offset + 10] &&
matrix[11] === array[offset + 11] &&
matrix[12] === array[offset + 12] &&
matrix[13] === array[offset + 13] &&
matrix[14] === array[offset + 14] &&
matrix[15] === array[offset + 15]
);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix4} [right] The right hand side matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix4.prototype.equalsEpsilon = function (right, epsilon) {
return Matrix4.equalsEpsilon(this, right, epsilon);
};
/**
* Computes a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1, column2, column3)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.
*/
Matrix4.prototype.toString = function () {
return (
`(${this[0]}, ${this[4]}, ${this[8]}, ${this[12]})\n` +
`(${this[1]}, ${this[5]}, ${this[9]}, ${this[13]})\n` +
`(${this[2]}, ${this[6]}, ${this[10]}, ${this[14]})\n` +
`(${this[3]}, ${this[7]}, ${this[11]}, ${this[15]})`
);
};
/**
* A two dimensional region specified as longitude and latitude coordinates.
*
* @alias Rectangle
* @constructor
*
* @param {Number} [west=0.0] The westernmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [south=0.0] The southernmost latitude, in radians, in the range [-Pi/2, Pi/2].
* @param {Number} [east=0.0] The easternmost longitude, in radians, in the range [-Pi, Pi].
* @param {Number} [north=0.0] The northernmost latitude, in radians, in the range [-Pi/2, Pi/2].
*
* @see Packable
*/
function Rectangle(west, south, east, north) {
/**
* The westernmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.west = defaultValue.defaultValue(west, 0.0);
/**
* The southernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.south = defaultValue.defaultValue(south, 0.0);
/**
* The easternmost longitude in radians in the range [-Pi, Pi].
*
* @type {Number}
* @default 0.0
*/
this.east = defaultValue.defaultValue(east, 0.0);
/**
* The northernmost latitude in radians in the range [-Pi/2, Pi/2].
*
* @type {Number}
* @default 0.0
*/
this.north = defaultValue.defaultValue(north, 0.0);
}
Object.defineProperties(Rectangle.prototype, {
/**
* Gets the width of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
* @readonly
*/
width: {
get: function () {
return Rectangle.computeWidth(this);
},
},
/**
* Gets the height of the rectangle in radians.
* @memberof Rectangle.prototype
* @type {Number}
* @readonly
*/
height: {
get: function () {
return Rectangle.computeHeight(this);
},
},
});
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Rectangle.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Rectangle} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Rectangle.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
array[startingIndex++] = value.west;
array[startingIndex++] = value.south;
array[startingIndex++] = value.east;
array[startingIndex] = value.north;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Rectangle} [result] The object into which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
if (!defaultValue.defined(result)) {
result = new Rectangle();
}
result.west = array[startingIndex++];
result.south = array[startingIndex++];
result.east = array[startingIndex++];
result.north = array[startingIndex];
return result;
};
/**
* Computes the width of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the width of.
* @returns {Number} The width.
*/
Rectangle.computeWidth = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
let east = rectangle.east;
const west = rectangle.west;
if (east < west) {
east += ComponentDatatype.CesiumMath.TWO_PI;
}
return east - west;
};
/**
* Computes the height of a rectangle in radians.
* @param {Rectangle} rectangle The rectangle to compute the height of.
* @returns {Number} The height.
*/
Rectangle.computeHeight = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
return rectangle.north - rectangle.south;
};
/**
* Creates a rectangle given the boundary longitude and latitude in degrees.
*
* @param {Number} [west=0.0] The westernmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [south=0.0] The southernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Number} [east=0.0] The easternmost longitude in degrees in the range [-180.0, 180.0].
* @param {Number} [north=0.0] The northernmost latitude in degrees in the range [-90.0, 90.0].
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*
* @example
* const rectangle = Cesium.Rectangle.fromDegrees(0.0, 20.0, 10.0, 30.0);
*/
Rectangle.fromDegrees = function (west, south, east, north, result) {
west = ComponentDatatype.CesiumMath.toRadians(defaultValue.defaultValue(west, 0.0));
south = ComponentDatatype.CesiumMath.toRadians(defaultValue.defaultValue(south, 0.0));
east = ComponentDatatype.CesiumMath.toRadians(defaultValue.defaultValue(east, 0.0));
north = ComponentDatatype.CesiumMath.toRadians(defaultValue.defaultValue(north, 0.0));
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates a rectangle given the boundary longitude and latitude in radians.
*
* @param {Number} [west=0.0] The westernmost longitude in radians in the range [-Math.PI, Math.PI].
* @param {Number} [south=0.0] The southernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
* @param {Number} [east=0.0] The easternmost longitude in radians in the range [-Math.PI, Math.PI].
* @param {Number} [north=0.0] The northernmost latitude in radians in the range [-Math.PI/2, Math.PI/2].
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*
* @example
* const rectangle = Cesium.Rectangle.fromRadians(0.0, Math.PI/4, Math.PI/8, 3*Math.PI/4);
*/
Rectangle.fromRadians = function (west, south, east, north, result) {
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = defaultValue.defaultValue(west, 0.0);
result.south = defaultValue.defaultValue(south, 0.0);
result.east = defaultValue.defaultValue(east, 0.0);
result.north = defaultValue.defaultValue(north, 0.0);
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartographic[]} cartographics The list of Cartographic instances.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartographicArray = function (cartographics, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("cartographics", cartographics);
//>>includeEnd('debug');
let west = Number.MAX_VALUE;
let east = -Number.MAX_VALUE;
let westOverIDL = Number.MAX_VALUE;
let eastOverIDL = -Number.MAX_VALUE;
let south = Number.MAX_VALUE;
let north = -Number.MAX_VALUE;
for (let i = 0, len = cartographics.length; i < len; i++) {
const position = cartographics[i];
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
const lonAdjusted =
position.longitude >= 0
? position.longitude
: position.longitude + ComponentDatatype.CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if (east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > ComponentDatatype.CesiumMath.PI) {
east = east - ComponentDatatype.CesiumMath.TWO_PI;
}
if (west > ComponentDatatype.CesiumMath.PI) {
west = west - ComponentDatatype.CesiumMath.TWO_PI;
}
}
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Creates the smallest possible Rectangle that encloses all positions in the provided array.
*
* @param {Cartesian3[]} cartesians The list of Cartesian instances.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid the cartesians are on.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.fromCartesianArray = function (cartesians, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("cartesians", cartesians);
//>>includeEnd('debug');
ellipsoid = defaultValue.defaultValue(ellipsoid, Ellipsoid.WGS84);
let west = Number.MAX_VALUE;
let east = -Number.MAX_VALUE;
let westOverIDL = Number.MAX_VALUE;
let eastOverIDL = -Number.MAX_VALUE;
let south = Number.MAX_VALUE;
let north = -Number.MAX_VALUE;
for (let i = 0, len = cartesians.length; i < len; i++) {
const position = ellipsoid.cartesianToCartographic(cartesians[i]);
west = Math.min(west, position.longitude);
east = Math.max(east, position.longitude);
south = Math.min(south, position.latitude);
north = Math.max(north, position.latitude);
const lonAdjusted =
position.longitude >= 0
? position.longitude
: position.longitude + ComponentDatatype.CesiumMath.TWO_PI;
westOverIDL = Math.min(westOverIDL, lonAdjusted);
eastOverIDL = Math.max(eastOverIDL, lonAdjusted);
}
if (east - west > eastOverIDL - westOverIDL) {
west = westOverIDL;
east = eastOverIDL;
if (east > ComponentDatatype.CesiumMath.PI) {
east = east - ComponentDatatype.CesiumMath.TWO_PI;
}
if (west > ComponentDatatype.CesiumMath.PI) {
west = west - ComponentDatatype.CesiumMath.TWO_PI;
}
}
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Duplicates a Rectangle.
*
* @param {Rectangle} rectangle The rectangle to clone.
* @param {Rectangle} [result] The object onto which to store the result, or undefined if a new instance should be created.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided. (Returns undefined if rectangle is undefined)
*/
Rectangle.clone = function (rectangle, result) {
if (!defaultValue.defined(rectangle)) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Rectangle(
rectangle.west,
rectangle.south,
rectangle.east,
rectangle.north
);
}
result.west = rectangle.west;
result.south = rectangle.south;
result.east = rectangle.east;
result.north = rectangle.north;
return result;
};
/**
* Compares the provided Rectangles componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Rectangle} [left] The first Rectangle.
* @param {Rectangle} [right] The second Rectangle.
* @param {Number} [absoluteEpsilon=0] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Rectangle.equalsEpsilon = function (left, right, absoluteEpsilon) {
absoluteEpsilon = defaultValue.defaultValue(absoluteEpsilon, 0);
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
Math.abs(left.west - right.west) <= absoluteEpsilon &&
Math.abs(left.south - right.south) <= absoluteEpsilon &&
Math.abs(left.east - right.east) <= absoluteEpsilon &&
Math.abs(left.north - right.north) <= absoluteEpsilon)
);
};
/**
* Duplicates this Rectangle.
*
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.prototype.clone = function (result) {
return Rectangle.clone(this, result);
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @returns {Boolean} true if the Rectangles are equal, false otherwise.
*/
Rectangle.prototype.equals = function (other) {
return Rectangle.equals(this, other);
};
/**
* Compares the provided rectangles and returns true if they are equal,
* false otherwise.
*
* @param {Rectangle} [left] The first Rectangle.
* @param {Rectangle} [right] The second Rectangle.
* @returns {Boolean} true if left and right are equal; otherwise false.
*/
Rectangle.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left.west === right.west &&
left.south === right.south &&
left.east === right.east &&
left.north === right.north)
);
};
/**
* Compares the provided Rectangle with this Rectangle componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Rectangle} [other] The Rectangle to compare.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if the Rectangles are within the provided epsilon, false otherwise.
*/
Rectangle.prototype.equalsEpsilon = function (other, epsilon) {
return Rectangle.equalsEpsilon(this, other, epsilon);
};
/**
* Checks a Rectangle's properties and throws if they are not in valid ranges.
*
* @param {Rectangle} rectangle The rectangle to validate
*
* @exception {DeveloperError} north must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} south must be in the interval [-Pi/2, Pi/2].
* @exception {DeveloperError} east must be in the interval [-Pi, Pi].
* @exception {DeveloperError} west must be in the interval [-Pi, Pi].
*/
Rectangle.validate = function (rectangle) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
const north = rectangle.north;
RuntimeError.Check.typeOf.number.greaterThanOrEquals(
"north",
north,
-ComponentDatatype.CesiumMath.PI_OVER_TWO
);
RuntimeError.Check.typeOf.number.lessThanOrEquals("north", north, ComponentDatatype.CesiumMath.PI_OVER_TWO);
const south = rectangle.south;
RuntimeError.Check.typeOf.number.greaterThanOrEquals(
"south",
south,
-ComponentDatatype.CesiumMath.PI_OVER_TWO
);
RuntimeError.Check.typeOf.number.lessThanOrEquals("south", south, ComponentDatatype.CesiumMath.PI_OVER_TWO);
const west = rectangle.west;
RuntimeError.Check.typeOf.number.greaterThanOrEquals("west", west, -Math.PI);
RuntimeError.Check.typeOf.number.lessThanOrEquals("west", west, Math.PI);
const east = rectangle.east;
RuntimeError.Check.typeOf.number.greaterThanOrEquals("east", east, -Math.PI);
RuntimeError.Check.typeOf.number.lessThanOrEquals("east", east, Math.PI);
//>>includeEnd('debug');
};
/**
* Computes the southwest corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southwest = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
return new Cartographic(rectangle.west, rectangle.south);
}
result.longitude = rectangle.west;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the northwest corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northwest = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
return new Cartographic(rectangle.west, rectangle.north);
}
result.longitude = rectangle.west;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the northeast corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.northeast = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
return new Cartographic(rectangle.east, rectangle.north);
}
result.longitude = rectangle.east;
result.latitude = rectangle.north;
result.height = 0.0;
return result;
};
/**
* Computes the southeast corner of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the corner
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.southeast = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
return new Cartographic(rectangle.east, rectangle.south);
}
result.longitude = rectangle.east;
result.latitude = rectangle.south;
result.height = 0.0;
return result;
};
/**
* Computes the center of a rectangle.
*
* @param {Rectangle} rectangle The rectangle for which to find the center
* @param {Cartographic} [result] The object onto which to store the result.
* @returns {Cartographic} The modified result parameter or a new Cartographic instance if none was provided.
*/
Rectangle.center = function (rectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
let east = rectangle.east;
const west = rectangle.west;
if (east < west) {
east += ComponentDatatype.CesiumMath.TWO_PI;
}
const longitude = ComponentDatatype.CesiumMath.negativePiToPi((west + east) * 0.5);
const latitude = (rectangle.south + rectangle.north) * 0.5;
if (!defaultValue.defined(result)) {
return new Cartographic(longitude, latitude);
}
result.longitude = longitude;
result.latitude = latitude;
result.height = 0.0;
return result;
};
/**
* Computes the intersection of two rectangles. This function assumes that the rectangle's coordinates are
* latitude and longitude in radians and produces a correct intersection, taking into account the fact that
* the same angle can be represented with multiple values as well as the wrapping of longitude at the
* anti-meridian. For a simple intersection that ignores these factors and can be used with projected
* coordinates, see {@link Rectangle.simpleIntersection}.
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.intersection = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
let rectangleEast = rectangle.east;
let rectangleWest = rectangle.west;
let otherRectangleEast = otherRectangle.east;
let otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += ComponentDatatype.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += ComponentDatatype.CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += ComponentDatatype.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += ComponentDatatype.CesiumMath.TWO_PI;
}
const west = ComponentDatatype.CesiumMath.negativePiToPi(
Math.max(rectangleWest, otherRectangleWest)
);
const east = ComponentDatatype.CesiumMath.negativePiToPi(
Math.min(rectangleEast, otherRectangleEast)
);
if (
(rectangle.west < rectangle.east ||
otherRectangle.west < otherRectangle.east) &&
east <= west
) {
return undefined;
}
const south = Math.max(rectangle.south, otherRectangle.south);
const north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a simple intersection of two rectangles. Unlike {@link Rectangle.intersection}, this function
* does not attempt to put the angular coordinates into a consistent range or to account for crossing the
* anti-meridian. As such, it can be used for rectangles where the coordinates are not simply latitude
* and longitude (i.e. projected coordinates).
*
* @param {Rectangle} rectangle On rectangle to find an intersection
* @param {Rectangle} otherRectangle Another rectangle to find an intersection
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle|undefined} The modified result parameter, a new Rectangle instance if none was provided or undefined if there is no intersection.
*/
Rectangle.simpleIntersection = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
const west = Math.max(rectangle.west, otherRectangle.west);
const south = Math.max(rectangle.south, otherRectangle.south);
const east = Math.min(rectangle.east, otherRectangle.east);
const north = Math.min(rectangle.north, otherRectangle.north);
if (south >= north || west >= east) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Rectangle(west, south, east, north);
}
result.west = west;
result.south = south;
result.east = east;
result.north = north;
return result;
};
/**
* Computes a rectangle that is the union of two rectangles.
*
* @param {Rectangle} rectangle A rectangle to enclose in rectangle.
* @param {Rectangle} otherRectangle A rectangle to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.union = function (rectangle, otherRectangle, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.object("otherRectangle", otherRectangle);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
result = new Rectangle();
}
let rectangleEast = rectangle.east;
let rectangleWest = rectangle.west;
let otherRectangleEast = otherRectangle.east;
let otherRectangleWest = otherRectangle.west;
if (rectangleEast < rectangleWest && otherRectangleEast > 0.0) {
rectangleEast += ComponentDatatype.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleEast > 0.0) {
otherRectangleEast += ComponentDatatype.CesiumMath.TWO_PI;
}
if (rectangleEast < rectangleWest && otherRectangleWest < 0.0) {
otherRectangleWest += ComponentDatatype.CesiumMath.TWO_PI;
} else if (otherRectangleEast < otherRectangleWest && rectangleWest < 0.0) {
rectangleWest += ComponentDatatype.CesiumMath.TWO_PI;
}
const west = ComponentDatatype.CesiumMath.negativePiToPi(
Math.min(rectangleWest, otherRectangleWest)
);
const east = ComponentDatatype.CesiumMath.negativePiToPi(
Math.max(rectangleEast, otherRectangleEast)
);
result.west = west;
result.south = Math.min(rectangle.south, otherRectangle.south);
result.east = east;
result.north = Math.max(rectangle.north, otherRectangle.north);
return result;
};
/**
* Computes a rectangle by enlarging the provided rectangle until it contains the provided cartographic.
*
* @param {Rectangle} rectangle A rectangle to expand.
* @param {Cartographic} cartographic A cartographic to enclose in a rectangle.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if one was not provided.
*/
Rectangle.expand = function (rectangle, cartographic, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
result = new Rectangle();
}
result.west = Math.min(rectangle.west, cartographic.longitude);
result.south = Math.min(rectangle.south, cartographic.latitude);
result.east = Math.max(rectangle.east, cartographic.longitude);
result.north = Math.max(rectangle.north, cartographic.latitude);
return result;
};
/**
* Returns true if the cartographic is on or inside the rectangle, false otherwise.
*
* @param {Rectangle} rectangle The rectangle
* @param {Cartographic} cartographic The cartographic to test.
* @returns {Boolean} true if the provided cartographic is inside the rectangle, false otherwise.
*/
Rectangle.contains = function (rectangle, cartographic) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.object("cartographic", cartographic);
//>>includeEnd('debug');
let longitude = cartographic.longitude;
const latitude = cartographic.latitude;
const west = rectangle.west;
let east = rectangle.east;
if (east < west) {
east += ComponentDatatype.CesiumMath.TWO_PI;
if (longitude < 0.0) {
longitude += ComponentDatatype.CesiumMath.TWO_PI;
}
}
return (
(longitude > west ||
ComponentDatatype.CesiumMath.equalsEpsilon(longitude, west, ComponentDatatype.CesiumMath.EPSILON14)) &&
(longitude < east ||
ComponentDatatype.CesiumMath.equalsEpsilon(longitude, east, ComponentDatatype.CesiumMath.EPSILON14)) &&
latitude >= rectangle.south &&
latitude <= rectangle.north
);
};
const subsampleLlaScratch = new Cartographic();
/**
* Samples a rectangle so that it includes a list of Cartesian points suitable for passing to
* {@link BoundingSphere#fromPoints}. Sampling is necessary to account
* for rectangles that cover the poles or cross the equator.
*
* @param {Rectangle} rectangle The rectangle to subsample.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid to use.
* @param {Number} [surfaceHeight=0.0] The height of the rectangle above the ellipsoid.
* @param {Cartesian3[]} [result] The array of Cartesians onto which to store the result.
* @returns {Cartesian3[]} The modified result parameter or a new Array of Cartesians instances if none was provided.
*/
Rectangle.subsample = function (rectangle, ellipsoid, surfaceHeight, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
ellipsoid = defaultValue.defaultValue(ellipsoid, Ellipsoid.WGS84);
surfaceHeight = defaultValue.defaultValue(surfaceHeight, 0.0);
if (!defaultValue.defined(result)) {
result = [];
}
let length = 0;
const north = rectangle.north;
const south = rectangle.south;
const east = rectangle.east;
const west = rectangle.west;
const lla = subsampleLlaScratch;
lla.height = surfaceHeight;
lla.longitude = west;
lla.latitude = north;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.latitude = south;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
if (north < 0.0) {
lla.latitude = north;
} else if (south > 0.0) {
lla.latitude = south;
} else {
lla.latitude = 0.0;
}
for (let i = 1; i < 8; ++i) {
lla.longitude = -Math.PI + i * ComponentDatatype.CesiumMath.PI_OVER_TWO;
if (Rectangle.contains(rectangle, lla)) {
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
}
if (lla.latitude === 0.0) {
lla.longitude = west;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
lla.longitude = east;
result[length] = ellipsoid.cartographicToCartesian(lla, result[length]);
length++;
}
result.length = length;
return result;
};
/**
* Computes a subsection of a rectangle from normalized coordinates in the range [0.0, 1.0].
*
* @param {Rectangle} rectangle The rectangle to subsection.
* @param {Number} westLerp The west interpolation factor in the range [0.0, 1.0]. Must be less than or equal to eastLerp.
* @param {Number} southLerp The south interpolation factor in the range [0.0, 1.0]. Must be less than or equal to northLerp.
* @param {Number} eastLerp The east interpolation factor in the range [0.0, 1.0]. Must be greater than or equal to westLerp.
* @param {Number} northLerp The north interpolation factor in the range [0.0, 1.0]. Must be greater than or equal to southLerp.
* @param {Rectangle} [result] The object onto which to store the result.
* @returns {Rectangle} The modified result parameter or a new Rectangle instance if none was provided.
*/
Rectangle.subsection = function (
rectangle,
westLerp,
southLerp,
eastLerp,
northLerp,
result
) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("rectangle", rectangle);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("westLerp", westLerp, 0.0);
RuntimeError.Check.typeOf.number.lessThanOrEquals("westLerp", westLerp, 1.0);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("southLerp", southLerp, 0.0);
RuntimeError.Check.typeOf.number.lessThanOrEquals("southLerp", southLerp, 1.0);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("eastLerp", eastLerp, 0.0);
RuntimeError.Check.typeOf.number.lessThanOrEquals("eastLerp", eastLerp, 1.0);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("northLerp", northLerp, 0.0);
RuntimeError.Check.typeOf.number.lessThanOrEquals("northLerp", northLerp, 1.0);
RuntimeError.Check.typeOf.number.lessThanOrEquals("westLerp", westLerp, eastLerp);
RuntimeError.Check.typeOf.number.lessThanOrEquals("southLerp", southLerp, northLerp);
//>>includeEnd('debug');
if (!defaultValue.defined(result)) {
result = new Rectangle();
}
// This function doesn't use CesiumMath.lerp because it has floating point precision problems
// when the start and end values are the same but the t changes.
if (rectangle.west <= rectangle.east) {
const width = rectangle.east - rectangle.west;
result.west = rectangle.west + westLerp * width;
result.east = rectangle.west + eastLerp * width;
} else {
const width = ComponentDatatype.CesiumMath.TWO_PI + rectangle.east - rectangle.west;
result.west = ComponentDatatype.CesiumMath.negativePiToPi(rectangle.west + westLerp * width);
result.east = ComponentDatatype.CesiumMath.negativePiToPi(rectangle.west + eastLerp * width);
}
const height = rectangle.north - rectangle.south;
result.south = rectangle.south + southLerp * height;
result.north = rectangle.south + northLerp * height;
// Fix floating point precision problems when t = 1
if (westLerp === 1.0) {
result.west = rectangle.east;
}
if (eastLerp === 1.0) {
result.east = rectangle.east;
}
if (southLerp === 1.0) {
result.south = rectangle.north;
}
if (northLerp === 1.0) {
result.north = rectangle.north;
}
return result;
};
/**
* The largest possible rectangle.
*
* @type {Rectangle}
* @constant
*/
Rectangle.MAX_VALUE = Object.freeze(
new Rectangle(
-Math.PI,
-ComponentDatatype.CesiumMath.PI_OVER_TWO,
Math.PI,
ComponentDatatype.CesiumMath.PI_OVER_TWO
)
);
/**
* A 2D Cartesian point.
* @alias Cartesian2
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
*
* @see Cartesian3
* @see Cartesian4
* @see Packable
*/
function Cartesian2(x, y) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue.defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue.defaultValue(y, 0.0);
}
/**
* Creates a Cartesian2 instance from x and y coordinates.
*
* @param {Number} x The x coordinate.
* @param {Number} y The y coordinate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromElements = function (x, y, result) {
if (!defaultValue.defined(result)) {
return new Cartesian2(x, y);
}
result.x = x;
result.y = y;
return result;
};
/**
* Duplicates a Cartesian2 instance.
*
* @param {Cartesian2} cartesian The Cartesian to duplicate.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided. (Returns undefined if cartesian is undefined)
*/
Cartesian2.clone = function (cartesian, result) {
if (!defaultValue.defined(cartesian)) {
return undefined;
}
if (!defaultValue.defined(result)) {
return new Cartesian2(cartesian.x, cartesian.y);
}
result.x = cartesian.x;
result.y = cartesian.y;
return result;
};
/**
* Creates a Cartesian2 instance from an existing Cartesian3. This simply takes the
* x and y properties of the Cartesian3 and drops z.
* @function
*
* @param {Cartesian3} cartesian The Cartesian3 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian3 = Cartesian2.clone;
/**
* Creates a Cartesian2 instance from an existing Cartesian4. This simply takes the
* x and y properties of the Cartesian4 and drops z and w.
* @function
*
* @param {Cartesian4} cartesian The Cartesian4 instance to create a Cartesian2 instance from.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.fromCartesian4 = Cartesian2.clone;
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Cartesian2.packedLength = 2;
/**
* Stores the provided instance into the provided array.
*
* @param {Cartesian2} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Cartesian2.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex] = value.y;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Cartesian2} [result] The object into which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue.defaultValue(startingIndex, 0);
if (!defaultValue.defined(result)) {
result = new Cartesian2();
}
result.x = array[startingIndex++];
result.y = array[startingIndex];
return result;
};
/**
* Flattens an array of Cartesian2s into an array of components.
*
* @param {Cartesian2[]} array The array of cartesians to pack.
* @param {Number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 2 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 2) elements.
* @returns {Number[]} The packed array.
*/
Cartesian2.packArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
//>>includeEnd('debug');
const length = array.length;
const resultLength = length * 2;
if (!defaultValue.defined(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
//>>includeStart('debug', pragmas.debug);
throw new RuntimeError.DeveloperError(
"If result is a typed array, it must have exactly array.length * 2 elements"
);
//>>includeEnd('debug');
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (let i = 0; i < length; ++i) {
Cartesian2.pack(array[i], result, i * 2);
}
return result;
};
/**
* Unpacks an array of cartesian components into an array of Cartesian2s.
*
* @param {Number[]} array The array of components to unpack.
* @param {Cartesian2[]} [result] The array onto which to store the result.
* @returns {Cartesian2[]} The unpacked array.
*/
Cartesian2.unpackArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.defined("array", array);
RuntimeError.Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 2);
if (array.length % 2 !== 0) {
throw new RuntimeError.DeveloperError("array length must be a multiple of 2.");
}
//>>includeEnd('debug');
const length = array.length;
if (!defaultValue.defined(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (let i = 0; i < length; i += 2) {
const index = i / 2;
result[index] = Cartesian2.unpack(array, i, result[index]);
}
return result;
};
/**
* Creates a Cartesian2 from two consecutive elements in an array.
* @function
*
* @param {Number[]} array The array whose two consecutive elements correspond to the x and y components, respectively.
* @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to the x component.
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*
* @example
* // Create a Cartesian2 with (1.0, 2.0)
* const v = [1.0, 2.0];
* const p = Cesium.Cartesian2.fromArray(v);
*
* // Create a Cartesian2 with (1.0, 2.0) using an offset into an array
* const v2 = [0.0, 0.0, 1.0, 2.0];
* const p2 = Cesium.Cartesian2.fromArray(v2, 2);
*/
Cartesian2.fromArray = Cartesian2.unpack;
/**
* Computes the value of the maximum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the maximum component.
*/
Cartesian2.maximumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.max(cartesian.x, cartesian.y);
};
/**
* Computes the value of the minimum component for the supplied Cartesian.
*
* @param {Cartesian2} cartesian The cartesian to use.
* @returns {Number} The value of the minimum component.
*/
Cartesian2.minimumComponent = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return Math.min(cartesian.x, cartesian.y);
};
/**
* Compares two Cartesians and computes a Cartesian which contains the minimum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the minimum components.
*/
Cartesian2.minimumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("first", first);
RuntimeError.Check.typeOf.object("second", second);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.min(first.x, second.x);
result.y = Math.min(first.y, second.y);
return result;
};
/**
* Compares two Cartesians and computes a Cartesian which contains the maximum components of the supplied Cartesians.
*
* @param {Cartesian2} first A cartesian to compare.
* @param {Cartesian2} second A cartesian to compare.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} A cartesian with the maximum components.
*/
Cartesian2.maximumByComponent = function (first, second, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("first", first);
RuntimeError.Check.typeOf.object("second", second);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.max(first.x, second.x);
result.y = Math.max(first.y, second.y);
return result;
};
/**
* Constrain a value to lie between two values.
*
* @param {Cartesian2} value The value to clamp.
* @param {Cartesian2} min The minimum bound.
* @param {Cartesian2} max The maximum bound.
* @param {Cartesian2} result The object into which to store the result.
* @returns {Cartesian2} The clamped value such that min <= result <= max.
*/
Cartesian2.clamp = function (value, min, max, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("value", value);
RuntimeError.Check.typeOf.object("min", min);
RuntimeError.Check.typeOf.object("max", max);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const x = ComponentDatatype.CesiumMath.clamp(value.x, min.x, max.x);
const y = ComponentDatatype.CesiumMath.clamp(value.y, min.y, max.y);
result.x = x;
result.y = y;
return result;
};
/**
* Computes the provided Cartesian's squared magnitude.
*
* @param {Cartesian2} cartesian The Cartesian instance whose squared magnitude is to be computed.
* @returns {Number} The squared magnitude.
*/
Cartesian2.magnitudeSquared = function (cartesian) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
//>>includeEnd('debug');
return cartesian.x * cartesian.x + cartesian.y * cartesian.y;
};
/**
* Computes the Cartesian's magnitude (length).
*
* @param {Cartesian2} cartesian The Cartesian instance whose magnitude is to be computed.
* @returns {Number} The magnitude.
*/
Cartesian2.magnitude = function (cartesian) {
return Math.sqrt(Cartesian2.magnitudeSquared(cartesian));
};
const distanceScratch = new Cartesian2();
/**
* Computes the distance between two points.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 1.0
* const d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(2.0, 0.0));
*/
Cartesian2.distance = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitude(distanceScratch);
};
/**
* Computes the squared distance between two points. Comparing squared distances
* using this function is more efficient than comparing distances using {@link Cartesian2#distance}.
*
* @param {Cartesian2} left The first point to compute the distance from.
* @param {Cartesian2} right The second point to compute the distance to.
* @returns {Number} The distance between two points.
*
* @example
* // Returns 4.0, not 2.0
* const d = Cesium.Cartesian2.distance(new Cesium.Cartesian2(1.0, 0.0), new Cesium.Cartesian2(3.0, 0.0));
*/
Cartesian2.distanceSquared = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.subtract(left, right, distanceScratch);
return Cartesian2.magnitudeSquared(distanceScratch);
};
/**
* Computes the normalized form of the supplied Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be normalized.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.normalize = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const magnitude = Cartesian2.magnitude(cartesian);
result.x = cartesian.x / magnitude;
result.y = cartesian.y / magnitude;
//>>includeStart('debug', pragmas.debug);
if (isNaN(result.x) || isNaN(result.y)) {
throw new RuntimeError.DeveloperError("normalized result is not a number");
}
//>>includeEnd('debug');
return result;
};
/**
* Computes the dot (scalar) product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The dot product.
*/
Cartesian2.dot = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return left.x * right.x + left.y * right.y;
};
/**
* Computes the magnitude of the cross product that would result from implicitly setting the Z coordinate of the input vectors to 0
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The cross product.
*/
Cartesian2.cross = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
return left.x * right.y - left.y * right.x;
};
/**
* Computes the componentwise product of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x * right.x;
result.y = left.y * right.y;
return result;
};
/**
* Computes the componentwise quotient of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideComponents = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x / right.x;
result.y = left.y / right.y;
return result;
};
/**
* Computes the componentwise sum of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.add = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x + right.x;
result.y = left.y + right.y;
return result;
};
/**
* Computes the componentwise difference of two Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.subtract = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x - right.x;
result.y = left.y - right.y;
return result;
};
/**
* Multiplies the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.multiplyByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.number("scalar", scalar);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x * scalar;
result.y = cartesian.y * scalar;
return result;
};
/**
* Divides the provided Cartesian componentwise by the provided scalar.
*
* @param {Cartesian2} cartesian The Cartesian to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.divideByScalar = function (cartesian, scalar, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.number("scalar", scalar);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = cartesian.x / scalar;
result.y = cartesian.y / scalar;
return result;
};
/**
* Negates the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian to be negated.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.negate = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -cartesian.x;
result.y = -cartesian.y;
return result;
};
/**
* Computes the absolute value of the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian whose absolute value is to be computed.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.abs = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = Math.abs(cartesian.x);
result.y = Math.abs(cartesian.y);
return result;
};
const lerpScratch = new Cartesian2();
/**
* Computes the linear interpolation or extrapolation at t using the provided cartesians.
*
* @param {Cartesian2} start The value corresponding to t at 0.0.
* @param {Cartesian2} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter.
*/
Cartesian2.lerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("start", start);
RuntimeError.Check.typeOf.object("end", end);
RuntimeError.Check.typeOf.number("t", t);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
Cartesian2.multiplyByScalar(end, t, lerpScratch);
result = Cartesian2.multiplyByScalar(start, 1.0 - t, result);
return Cartesian2.add(lerpScratch, result, result);
};
const angleBetweenScratch = new Cartesian2();
const angleBetweenScratch2 = new Cartesian2();
/**
* Returns the angle, in radians, between the provided Cartesians.
*
* @param {Cartesian2} left The first Cartesian.
* @param {Cartesian2} right The second Cartesian.
* @returns {Number} The angle between the Cartesians.
*/
Cartesian2.angleBetween = function (left, right) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("left", left);
RuntimeError.Check.typeOf.object("right", right);
//>>includeEnd('debug');
Cartesian2.normalize(left, angleBetweenScratch);
Cartesian2.normalize(right, angleBetweenScratch2);
return ComponentDatatype.CesiumMath.acosClamped(
Cartesian2.dot(angleBetweenScratch, angleBetweenScratch2)
);
};
const mostOrthogonalAxisScratch = new Cartesian2();
/**
* Returns the axis that is most orthogonal to the provided Cartesian.
*
* @param {Cartesian2} cartesian The Cartesian on which to find the most orthogonal axis.
* @param {Cartesian2} result The object onto which to store the result.
* @returns {Cartesian2} The most orthogonal axis.
*/
Cartesian2.mostOrthogonalAxis = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
RuntimeError.Check.typeOf.object("cartesian", cartesian);
RuntimeError.Check.typeOf.object("result", result);
//>>includeEnd('debug');
const f = Cartesian2.normalize(cartesian, mostOrthogonalAxisScratch);
Cartesian2.abs(f, f);
if (f.x <= f.y) {
result = Cartesian2.clone(Cartesian2.UNIT_X, result);
} else {
result = Cartesian2.clone(Cartesian2.UNIT_Y, result);
}
return result;
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Cartesian2.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left.x === right.x &&
left.y === right.y)
);
};
/**
* @private
*/
Cartesian2.equalsArray = function (cartesian, array, offset) {
return cartesian.x === array[offset] && cartesian.y === array[offset + 1];
};
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian2} [left] The first Cartesian.
* @param {Cartesian2} [right] The second Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Cartesian2.equalsEpsilon = function (
left,
right,
relativeEpsilon,
absoluteEpsilon
) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) &&
ComponentDatatype.CesiumMath.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
))
);
};
/**
* An immutable Cartesian2 instance initialized to (0.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.ZERO = Object.freeze(new Cartesian2(0.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (1.0, 1.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.ONE = Object.freeze(new Cartesian2(1.0, 1.0));
/**
* An immutable Cartesian2 instance initialized to (1.0, 0.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_X = Object.freeze(new Cartesian2(1.0, 0.0));
/**
* An immutable Cartesian2 instance initialized to (0.0, 1.0).
*
* @type {Cartesian2}
* @constant
*/
Cartesian2.UNIT_Y = Object.freeze(new Cartesian2(0.0, 1.0));
/**
* Duplicates this Cartesian2 instance.
*
* @param {Cartesian2} [result] The object onto which to store the result.
* @returns {Cartesian2} The modified result parameter or a new Cartesian2 instance if one was not provided.
*/
Cartesian2.prototype.clone = function (result) {
return Cartesian2.clone(this, result);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Cartesian2.prototype.equals = function (right) {
return Cartesian2.equals(this, right);
};
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian2} [right] The right hand side Cartesian.
* @param {Number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {Number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Cartesian2.prototype.equalsEpsilon = function (
right,
relativeEpsilon,
absoluteEpsilon
) {
return Cartesian2.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
};
/**
* Creates a string representing this Cartesian in the format '(x, y)'.
*
* @returns {String} A string representing the provided Cartesian in the format '(x, y)'.
*/
Cartesian2.prototype.toString = function () {
return `(${this.x}, ${this.y})`;
};
/**
* A 2x2 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
* @alias Matrix2
* @constructor
* @implements {ArrayLiketrue if they are equal, false otherwise.
*
* @param {Matrix2} [left] The first matrix.
* @param {Matrix2} [right] The second matrix.
* @returns {Boolean} true if left and right are equal, false otherwise.
*/
Matrix2.equals = function (left, right) {
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
left[0] === right[0] &&
left[1] === right[1] &&
left[2] === right[2] &&
left[3] === right[3])
);
};
/**
* @private
*/
Matrix2.equalsArray = function (matrix, array, offset) {
return (
matrix[0] === array[offset] &&
matrix[1] === array[offset + 1] &&
matrix[2] === array[offset + 2] &&
matrix[3] === array[offset + 3]
);
};
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix2} [left] The first matrix.
* @param {Matrix2} [right] The second matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if left and right are within the provided epsilon, false otherwise.
*/
Matrix2.equalsEpsilon = function (left, right, epsilon) {
epsilon = defaultValue.defaultValue(epsilon, 0);
return (
left === right ||
(defaultValue.defined(left) &&
defaultValue.defined(right) &&
Math.abs(left[0] - right[0]) <= epsilon &&
Math.abs(left[1] - right[1]) <= epsilon &&
Math.abs(left[2] - right[2]) <= epsilon &&
Math.abs(left[3] - right[3]) <= epsilon)
);
};
/**
* An immutable Matrix2 instance initialized to the identity matrix.
*
* @type {Matrix2}
* @constant
*/
Matrix2.IDENTITY = Object.freeze(new Matrix2(1.0, 0.0, 0.0, 1.0));
/**
* An immutable Matrix2 instance initialized to the zero matrix.
*
* @type {Matrix2}
* @constant
*/
Matrix2.ZERO = Object.freeze(new Matrix2(0.0, 0.0, 0.0, 0.0));
/**
* The index into Matrix2 for column 0, row 0.
*
* @type {Number}
* @constant
*
* @example
* const matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN0ROW0] = 5.0; // set column 0, row 0 to 5.0
*/
Matrix2.COLUMN0ROW0 = 0;
/**
* The index into Matrix2 for column 0, row 1.
*
* @type {Number}
* @constant
*
* @example
* const matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN0ROW1] = 5.0; // set column 0, row 1 to 5.0
*/
Matrix2.COLUMN0ROW1 = 1;
/**
* The index into Matrix2 for column 1, row 0.
*
* @type {Number}
* @constant
*
* @example
* const matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN1ROW0] = 5.0; // set column 1, row 0 to 5.0
*/
Matrix2.COLUMN1ROW0 = 2;
/**
* The index into Matrix2 for column 1, row 1.
*
* @type {Number}
* @constant
*
* @example
* const matrix = new Cesium.Matrix2();
* matrix[Cesium.Matrix2.COLUMN1ROW1] = 5.0; // set column 1, row 1 to 5.0
*/
Matrix2.COLUMN1ROW1 = 3;
Object.defineProperties(Matrix2.prototype, {
/**
* Gets the number of items in the collection.
* @memberof Matrix2.prototype
*
* @type {Number}
*/
length: {
get: function () {
return Matrix2.packedLength;
},
},
});
/**
* Duplicates the provided Matrix2 instance.
*
* @param {Matrix2} [result] The object onto which to store the result.
* @returns {Matrix2} The modified result parameter or a new Matrix2 instance if one was not provided.
*/
Matrix2.prototype.clone = function (result) {
return Matrix2.clone(this, result);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix2} [right] The right hand side matrix.
* @returns {Boolean} true if they are equal, false otherwise.
*/
Matrix2.prototype.equals = function (right) {
return Matrix2.equals(this, right);
};
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix2} [right] The right hand side matrix.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} true if they are within the provided epsilon, false otherwise.
*/
Matrix2.prototype.equalsEpsilon = function (right, epsilon) {
return Matrix2.equalsEpsilon(this, right, epsilon);
};
/**
* Creates a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1)'.
*
* @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1)'.
*/
Matrix2.prototype.toString = function () {
return `(${this[0]}, ${this[2]})\n` + `(${this[1]}, ${this[3]})`;
};
exports.Cartesian2 = Cartesian2;
exports.Cartesian3 = Cartesian3;
exports.Cartesian4 = Cartesian4;
exports.Cartographic = Cartographic;
exports.Ellipsoid = Ellipsoid;
exports.Matrix2 = Matrix2;
exports.Matrix3 = Matrix3;
exports.Matrix4 = Matrix4;
exports.Rectangle = Rectangle;
}));
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