import MersenneTwister from "mersenne-twister"; import Check from "./Check.js"; import defaultValue from "./defaultValue.js"; import defined from "./defined.js"; import DeveloperError from "./DeveloperError.js"; /** * Math functions. * * @exports CesiumMath * @alias Math */ const CesiumMath = {}; /** * 0.1 * @type {number} * @constant */ CesiumMath.EPSILON1 = 0.1; /** * 0.01 * @type {number} * @constant */ CesiumMath.EPSILON2 = 0.01; /** * 0.001 * @type {number} * @constant */ CesiumMath.EPSILON3 = 0.001; /** * 0.0001 * @type {number} * @constant */ CesiumMath.EPSILON4 = 0.0001; /** * 0.00001 * @type {number} * @constant */ CesiumMath.EPSILON5 = 0.00001; /** * 0.000001 * @type {number} * @constant */ CesiumMath.EPSILON6 = 0.000001; /** * 0.0000001 * @type {number} * @constant */ CesiumMath.EPSILON7 = 0.0000001; /** * 0.00000001 * @type {number} * @constant */ CesiumMath.EPSILON8 = 0.00000001; /** * 0.000000001 * @type {number} * @constant */ CesiumMath.EPSILON9 = 0.000000001; /** * 0.0000000001 * @type {number} * @constant */ CesiumMath.EPSILON10 = 0.0000000001; /** * 0.00000000001 * @type {number} * @constant */ CesiumMath.EPSILON11 = 0.00000000001; /** * 0.000000000001 * @type {number} * @constant */ CesiumMath.EPSILON12 = 0.000000000001; /** * 0.0000000000001 * @type {number} * @constant */ CesiumMath.EPSILON13 = 0.0000000000001; /** * 0.00000000000001 * @type {number} * @constant */ CesiumMath.EPSILON14 = 0.00000000000001; /** * 0.000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON15 = 0.000000000000001; /** * 0.0000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON16 = 0.0000000000000001; /** * 0.00000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON17 = 0.00000000000000001; /** * 0.000000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON18 = 0.000000000000000001; /** * 0.0000000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON19 = 0.0000000000000000001; /** * 0.00000000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON20 = 0.00000000000000000001; /** * 0.000000000000000000001 * @type {number} * @constant */ CesiumMath.EPSILON21 = 0.000000000000000000001; /** * The gravitational parameter of the Earth in meters cubed * per second squared as defined by the WGS84 model: 3.986004418e14 * @type {number} * @constant */ CesiumMath.GRAVITATIONALPARAMETER = 3.986004418e14; /** * Radius of the sun in meters: 6.955e8 * @type {number} * @constant */ CesiumMath.SOLAR_RADIUS = 6.955e8; /** * The mean radius of the moon, according to the "Report of the IAU/IAG Working Group on * Cartographic Coordinates and Rotational Elements of the Planets and satellites: 2000", * Celestial Mechanics 82: 83-110, 2002. * @type {number} * @constant */ CesiumMath.LUNAR_RADIUS = 1737400.0; /** * 64 * 1024 * @type {number} * @constant */ CesiumMath.SIXTY_FOUR_KILOBYTES = 64 * 1024; /** * 4 * 1024 * 1024 * 1024 * @type {number} * @constant */ CesiumMath.FOUR_GIGABYTES = 4 * 1024 * 1024 * 1024; /** * Returns the sign of the value; 1 if the value is positive, -1 if the value is * negative, or 0 if the value is 0. * * @function * @param {number} value The value to return the sign of. * @returns {number} The sign of value. */ // eslint-disable-next-line es/no-math-sign CesiumMath.sign = defaultValue(Math.sign, function sign(value) { value = +value; // coerce to number if (value === 0 || value !== value) { // zero or NaN return value; } return value > 0 ? 1 : -1; }); /** * Returns 1.0 if the given value is positive or zero, and -1.0 if it is negative. * This is similar to {@link CesiumMath#sign} except that returns 1.0 instead of * 0.0 when the input value is 0.0. * @param {number} value The value to return the sign of. * @returns {number} The sign of value. */ CesiumMath.signNotZero = function (value) { return value < 0.0 ? -1.0 : 1.0; }; /** * Converts a scalar value in the range [-1.0, 1.0] to a SNORM in the range [0, rangeMaximum] * @param {number} value The scalar value in the range [-1.0, 1.0] * @param {number} [rangeMaximum=255] The maximum value in the mapped range, 255 by default. * @returns {number} A SNORM value, where 0 maps to -1.0 and rangeMaximum maps to 1.0. * * @see CesiumMath.fromSNorm */ CesiumMath.toSNorm = function (value, rangeMaximum) { rangeMaximum = defaultValue(rangeMaximum, 255); return Math.round( (CesiumMath.clamp(value, -1.0, 1.0) * 0.5 + 0.5) * rangeMaximum ); }; /** * Converts a SNORM value in the range [0, rangeMaximum] to a scalar in the range [-1.0, 1.0]. * @param {number} value SNORM value in the range [0, rangeMaximum] * @param {number} [rangeMaximum=255] The maximum value in the SNORM range, 255 by default. * @returns {number} Scalar in the range [-1.0, 1.0]. * * @see CesiumMath.toSNorm */ CesiumMath.fromSNorm = function (value, rangeMaximum) { rangeMaximum = defaultValue(rangeMaximum, 255); return ( (CesiumMath.clamp(value, 0.0, rangeMaximum) / rangeMaximum) * 2.0 - 1.0 ); }; /** * Converts a scalar value in the range [rangeMinimum, rangeMaximum] to a scalar in the range [0.0, 1.0] * @param {number} value The scalar value in the range [rangeMinimum, rangeMaximum] * @param {number} rangeMinimum The minimum value in the mapped range. * @param {number} rangeMaximum The maximum value in the mapped range. * @returns {number} A scalar value, where rangeMinimum maps to 0.0 and rangeMaximum maps to 1.0. */ CesiumMath.normalize = function (value, rangeMinimum, rangeMaximum) { rangeMaximum = Math.max(rangeMaximum - rangeMinimum, 0.0); return rangeMaximum === 0.0 ? 0.0 : CesiumMath.clamp((value - rangeMinimum) / rangeMaximum, 0.0, 1.0); }; /** * Returns the hyperbolic sine of a number. * The hyperbolic sine of value is defined to be * (ex - e-x)/2.0 * where e is Euler's number, approximately 2.71828183. * *

Special cases: *

*

* * @function * @param {number} value The number whose hyperbolic sine is to be returned. * @returns {number} The hyperbolic sine of value. */ // eslint-disable-next-line es/no-math-sinh CesiumMath.sinh = defaultValue(Math.sinh, function sinh(value) { return (Math.exp(value) - Math.exp(-value)) / 2.0; }); /** * Returns the hyperbolic cosine of a number. * The hyperbolic cosine of value is defined to be * (ex + e-x)/2.0 * where e is Euler's number, approximately 2.71828183. * *

Special cases: *

*

* * @function * @param {number} value The number whose hyperbolic cosine is to be returned. * @returns {number} The hyperbolic cosine of value. */ // eslint-disable-next-line es/no-math-cosh CesiumMath.cosh = defaultValue(Math.cosh, function cosh(value) { return (Math.exp(value) + Math.exp(-value)) / 2.0; }); /** * Computes the linear interpolation of two values. * * @param {number} p The start value to interpolate. * @param {number} q The end value to interpolate. * @param {number} time The time of interpolation generally in the range [0.0, 1.0]. * @returns {number} The linearly interpolated value. * * @example * const n = Cesium.Math.lerp(0.0, 2.0, 0.5); // returns 1.0 */ CesiumMath.lerp = function (p, q, time) { return (1.0 - time) * p + time * q; }; /** * pi * * @type {number} * @constant */ CesiumMath.PI = Math.PI; /** * 1/pi * * @type {number} * @constant */ CesiumMath.ONE_OVER_PI = 1.0 / Math.PI; /** * pi/2 * * @type {number} * @constant */ CesiumMath.PI_OVER_TWO = Math.PI / 2.0; /** * pi/3 * * @type {number} * @constant */ CesiumMath.PI_OVER_THREE = Math.PI / 3.0; /** * pi/4 * * @type {number} * @constant */ CesiumMath.PI_OVER_FOUR = Math.PI / 4.0; /** * pi/6 * * @type {number} * @constant */ CesiumMath.PI_OVER_SIX = Math.PI / 6.0; /** * 3pi/2 * * @type {number} * @constant */ CesiumMath.THREE_PI_OVER_TWO = (3.0 * Math.PI) / 2.0; /** * 2pi * * @type {number} * @constant */ CesiumMath.TWO_PI = 2.0 * Math.PI; /** * 1/2pi * * @type {number} * @constant */ CesiumMath.ONE_OVER_TWO_PI = 1.0 / (2.0 * Math.PI); /** * The number of radians in a degree. * * @type {number} * @constant */ CesiumMath.RADIANS_PER_DEGREE = Math.PI / 180.0; /** * The number of degrees in a radian. * * @type {number} * @constant */ CesiumMath.DEGREES_PER_RADIAN = 180.0 / Math.PI; /** * The number of radians in an arc second. * * @type {number} * @constant */ CesiumMath.RADIANS_PER_ARCSECOND = CesiumMath.RADIANS_PER_DEGREE / 3600.0; /** * Converts degrees to radians. * @param {number} degrees The angle to convert in degrees. * @returns {number} The corresponding angle in radians. */ CesiumMath.toRadians = function (degrees) { //>>includeStart('debug', pragmas.debug); if (!defined(degrees)) { throw new DeveloperError("degrees is required."); } //>>includeEnd('debug'); return degrees * CesiumMath.RADIANS_PER_DEGREE; }; /** * Converts radians to degrees. * @param {number} radians The angle to convert in radians. * @returns {number} The corresponding angle in degrees. */ CesiumMath.toDegrees = function (radians) { //>>includeStart('debug', pragmas.debug); if (!defined(radians)) { throw new DeveloperError("radians is required."); } //>>includeEnd('debug'); return radians * CesiumMath.DEGREES_PER_RADIAN; }; /** * Converts a longitude value, in radians, to the range [-Math.PI, Math.PI). * * @param {number} angle The longitude value, in radians, to convert to the range [-Math.PI, Math.PI). * @returns {number} The equivalent longitude value in the range [-Math.PI, Math.PI). * * @example * // Convert 270 degrees to -90 degrees longitude * const longitude = Cesium.Math.convertLongitudeRange(Cesium.Math.toRadians(270.0)); */ CesiumMath.convertLongitudeRange = function (angle) { //>>includeStart('debug', pragmas.debug); if (!defined(angle)) { throw new DeveloperError("angle is required."); } //>>includeEnd('debug'); const twoPi = CesiumMath.TWO_PI; const simplified = angle - Math.floor(angle / twoPi) * twoPi; if (simplified < -Math.PI) { return simplified + twoPi; } if (simplified >= Math.PI) { return simplified - twoPi; } return simplified; }; /** * Convenience function that clamps a latitude value, in radians, to the range [-Math.PI/2, Math.PI/2). * Useful for sanitizing data before use in objects requiring correct range. * * @param {number} angle The latitude value, in radians, to clamp to the range [-Math.PI/2, Math.PI/2). * @returns {number} The latitude value clamped to the range [-Math.PI/2, Math.PI/2). * * @example * // Clamp 108 degrees latitude to 90 degrees latitude * const latitude = Cesium.Math.clampToLatitudeRange(Cesium.Math.toRadians(108.0)); */ CesiumMath.clampToLatitudeRange = function (angle) { //>>includeStart('debug', pragmas.debug); if (!defined(angle)) { throw new DeveloperError("angle is required."); } //>>includeEnd('debug'); return CesiumMath.clamp( angle, -1 * CesiumMath.PI_OVER_TWO, CesiumMath.PI_OVER_TWO ); }; /** * Produces an angle in the range -Pi <= angle <= Pi which is equivalent to the provided angle. * * @param {number} angle in radians * @returns {number} The angle in the range [-CesiumMath.PI, CesiumMath.PI]. */ CesiumMath.negativePiToPi = function (angle) { //>>includeStart('debug', pragmas.debug); if (!defined(angle)) { throw new DeveloperError("angle is required."); } //>>includeEnd('debug'); if (angle >= -CesiumMath.PI && angle <= CesiumMath.PI) { // Early exit if the input is already inside the range. This avoids // unnecessary math which could introduce floating point error. return angle; } return CesiumMath.zeroToTwoPi(angle + CesiumMath.PI) - CesiumMath.PI; }; /** * Produces an angle in the range 0 <= angle <= 2Pi which is equivalent to the provided angle. * * @param {number} angle in radians * @returns {number} The angle in the range [0, CesiumMath.TWO_PI]. */ CesiumMath.zeroToTwoPi = function (angle) { //>>includeStart('debug', pragmas.debug); if (!defined(angle)) { throw new DeveloperError("angle is required."); } //>>includeEnd('debug'); if (angle >= 0 && angle <= CesiumMath.TWO_PI) { // Early exit if the input is already inside the range. This avoids // unnecessary math which could introduce floating point error. return angle; } const mod = CesiumMath.mod(angle, CesiumMath.TWO_PI); if ( Math.abs(mod) < CesiumMath.EPSILON14 && Math.abs(angle) > CesiumMath.EPSILON14 ) { return CesiumMath.TWO_PI; } return mod; }; /** * The modulo operation that also works for negative dividends. * * @param {number} m The dividend. * @param {number} n The divisor. * @returns {number} The remainder. */ CesiumMath.mod = function (m, n) { //>>includeStart('debug', pragmas.debug); if (!defined(m)) { throw new DeveloperError("m is required."); } if (!defined(n)) { throw new DeveloperError("n is required."); } if (n === 0.0) { throw new DeveloperError("divisor cannot be 0."); } //>>includeEnd('debug'); if (CesiumMath.sign(m) === CesiumMath.sign(n) && Math.abs(m) < Math.abs(n)) { // Early exit if the input does not need to be modded. This avoids // unnecessary math which could introduce floating point error. return m; } return ((m % n) + n) % n; }; /** * Determines if two values are equal using an absolute or relative tolerance test. This is useful * to avoid problems due to roundoff error when comparing floating-point values directly. The values are * first compared using an absolute tolerance test. If that fails, a relative tolerance test is performed. * Use this test if you are unsure of the magnitudes of left and right. * * @param {number} left The first value to compare. * @param {number} right The other value to compare. * @param {number} [relativeEpsilon=0] The maximum inclusive delta between left and right for the relative tolerance test. * @param {number} [absoluteEpsilon=relativeEpsilon] The maximum inclusive delta between left and right for the absolute tolerance test. * @returns {boolean} true if the values are equal within the epsilon; otherwise, false. * * @example * const a = Cesium.Math.equalsEpsilon(0.0, 0.01, Cesium.Math.EPSILON2); // true * const b = Cesium.Math.equalsEpsilon(0.0, 0.1, Cesium.Math.EPSILON2); // false * const c = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON7); // true * const d = Cesium.Math.equalsEpsilon(3699175.1634344, 3699175.2, Cesium.Math.EPSILON9); // false */ CesiumMath.equalsEpsilon = function ( left, right, relativeEpsilon, absoluteEpsilon ) { //>>includeStart('debug', pragmas.debug); if (!defined(left)) { throw new DeveloperError("left is required."); } if (!defined(right)) { throw new DeveloperError("right is required."); } //>>includeEnd('debug'); relativeEpsilon = defaultValue(relativeEpsilon, 0.0); absoluteEpsilon = defaultValue(absoluteEpsilon, relativeEpsilon); const absDiff = Math.abs(left - right); return ( absDiff <= absoluteEpsilon || absDiff <= relativeEpsilon * Math.max(Math.abs(left), Math.abs(right)) ); }; /** * Determines if the left value is less than the right value. If the two values are within * absoluteEpsilon of each other, they are considered equal and this function returns false. * * @param {number} left The first number to compare. * @param {number} right The second number to compare. * @param {number} absoluteEpsilon The absolute epsilon to use in comparison. * @returns {boolean} true if left is less than right by more than * absoluteEpsilon. false if left is greater or if the two * values are nearly equal. */ CesiumMath.lessThan = function (left, right, absoluteEpsilon) { //>>includeStart('debug', pragmas.debug); if (!defined(left)) { throw new DeveloperError("first is required."); } if (!defined(right)) { throw new DeveloperError("second is required."); } if (!defined(absoluteEpsilon)) { throw new DeveloperError("absoluteEpsilon is required."); } //>>includeEnd('debug'); return left - right < -absoluteEpsilon; }; /** * Determines if the left value is less than or equal to the right value. If the two values are within * absoluteEpsilon of each other, they are considered equal and this function returns true. * * @param {number} left The first number to compare. * @param {number} right The second number to compare. * @param {number} absoluteEpsilon The absolute epsilon to use in comparison. * @returns {boolean} true if left is less than right or if the * the values are nearly equal. */ CesiumMath.lessThanOrEquals = function (left, right, absoluteEpsilon) { //>>includeStart('debug', pragmas.debug); if (!defined(left)) { throw new DeveloperError("first is required."); } if (!defined(right)) { throw new DeveloperError("second is required."); } if (!defined(absoluteEpsilon)) { throw new DeveloperError("absoluteEpsilon is required."); } //>>includeEnd('debug'); return left - right < absoluteEpsilon; }; /** * Determines if the left value is greater the right value. If the two values are within * absoluteEpsilon of each other, they are considered equal and this function returns false. * * @param {number} left The first number to compare. * @param {number} right The second number to compare. * @param {number} absoluteEpsilon The absolute epsilon to use in comparison. * @returns {boolean} true if left is greater than right by more than * absoluteEpsilon. false if left is less or if the two * values are nearly equal. */ CesiumMath.greaterThan = function (left, right, absoluteEpsilon) { //>>includeStart('debug', pragmas.debug); if (!defined(left)) { throw new DeveloperError("first is required."); } if (!defined(right)) { throw new DeveloperError("second is required."); } if (!defined(absoluteEpsilon)) { throw new DeveloperError("absoluteEpsilon is required."); } //>>includeEnd('debug'); return left - right > absoluteEpsilon; }; /** * Determines if the left value is greater than or equal to the right value. If the two values are within * absoluteEpsilon of each other, they are considered equal and this function returns true. * * @param {number} left The first number to compare. * @param {number} right The second number to compare. * @param {number} absoluteEpsilon The absolute epsilon to use in comparison. * @returns {boolean} true if left is greater than right or if the * the values are nearly equal. */ CesiumMath.greaterThanOrEquals = function (left, right, absoluteEpsilon) { //>>includeStart('debug', pragmas.debug); if (!defined(left)) { throw new DeveloperError("first is required."); } if (!defined(right)) { throw new DeveloperError("second is required."); } if (!defined(absoluteEpsilon)) { throw new DeveloperError("absoluteEpsilon is required."); } //>>includeEnd('debug'); return left - right > -absoluteEpsilon; }; const factorials = [1]; /** * Computes the factorial of the provided number. * * @param {number} n The number whose factorial is to be computed. * @returns {number} The factorial of the provided number or undefined if the number is less than 0. * * @exception {DeveloperError} A number greater than or equal to 0 is required. * * * @example * //Compute 7!, which is equal to 5040 * const computedFactorial = Cesium.Math.factorial(7); * * @see {@link http://en.wikipedia.org/wiki/Factorial|Factorial on Wikipedia} */ CesiumMath.factorial = function (n) { //>>includeStart('debug', pragmas.debug); if (typeof n !== "number" || n < 0) { throw new DeveloperError( "A number greater than or equal to 0 is required." ); } //>>includeEnd('debug'); const length = factorials.length; if (n >= length) { let sum = factorials[length - 1]; for (let i = length; i <= n; i++) { const next = sum * i; factorials.push(next); sum = next; } } return factorials[n]; }; /** * Increments a number with a wrapping to a minimum value if the number exceeds the maximum value. * * @param {number} [n] The number to be incremented. * @param {number} [maximumValue] The maximum incremented value before rolling over to the minimum value. * @param {number} [minimumValue=0.0] The number reset to after the maximum value has been exceeded. * @returns {number} The incremented number. * * @exception {DeveloperError} Maximum value must be greater than minimum value. * * @example * const n = Cesium.Math.incrementWrap(5, 10, 0); // returns 6 * const m = Cesium.Math.incrementWrap(10, 10, 0); // returns 0 */ CesiumMath.incrementWrap = function (n, maximumValue, minimumValue) { minimumValue = defaultValue(minimumValue, 0.0); //>>includeStart('debug', pragmas.debug); if (!defined(n)) { throw new DeveloperError("n is required."); } if (maximumValue <= minimumValue) { throw new DeveloperError("maximumValue must be greater than minimumValue."); } //>>includeEnd('debug'); ++n; if (n > maximumValue) { n = minimumValue; } return n; }; /** * Determines if a non-negative integer is a power of two. * The maximum allowed input is (2^32)-1 due to 32-bit bitwise operator limitation in Javascript. * * @param {number} n The integer to test in the range [0, (2^32)-1]. * @returns {boolean} true if the number if a power of two; otherwise, false. * * @exception {DeveloperError} A number between 0 and (2^32)-1 is required. * * @example * const t = Cesium.Math.isPowerOfTwo(16); // true * const f = Cesium.Math.isPowerOfTwo(20); // false */ CesiumMath.isPowerOfTwo = function (n) { //>>includeStart('debug', pragmas.debug); if (typeof n !== "number" || n < 0 || n > 4294967295) { throw new DeveloperError("A number between 0 and (2^32)-1 is required."); } //>>includeEnd('debug'); return n !== 0 && (n & (n - 1)) === 0; }; /** * Computes the next power-of-two integer greater than or equal to the provided non-negative integer. * The maximum allowed input is 2^31 due to 32-bit bitwise operator limitation in Javascript. * * @param {number} n The integer to test in the range [0, 2^31]. * @returns {number} The next power-of-two integer. * * @exception {DeveloperError} A number between 0 and 2^31 is required. * * @example * const n = Cesium.Math.nextPowerOfTwo(29); // 32 * const m = Cesium.Math.nextPowerOfTwo(32); // 32 */ CesiumMath.nextPowerOfTwo = function (n) { //>>includeStart('debug', pragmas.debug); if (typeof n !== "number" || n < 0 || n > 2147483648) { throw new DeveloperError("A number between 0 and 2^31 is required."); } //>>includeEnd('debug'); // From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 --n; n |= n >> 1; n |= n >> 2; n |= n >> 4; n |= n >> 8; n |= n >> 16; ++n; return n; }; /** * Computes the previous power-of-two integer less than or equal to the provided non-negative integer. * The maximum allowed input is (2^32)-1 due to 32-bit bitwise operator limitation in Javascript. * * @param {number} n The integer to test in the range [0, (2^32)-1]. * @returns {number} The previous power-of-two integer. * * @exception {DeveloperError} A number between 0 and (2^32)-1 is required. * * @example * const n = Cesium.Math.previousPowerOfTwo(29); // 16 * const m = Cesium.Math.previousPowerOfTwo(32); // 32 */ CesiumMath.previousPowerOfTwo = function (n) { //>>includeStart('debug', pragmas.debug); if (typeof n !== "number" || n < 0 || n > 4294967295) { throw new DeveloperError("A number between 0 and (2^32)-1 is required."); } //>>includeEnd('debug'); n |= n >> 1; n |= n >> 2; n |= n >> 4; n |= n >> 8; n |= n >> 16; n |= n >> 32; // The previous bitwise operations implicitly convert to signed 32-bit. Use `>>>` to convert to unsigned n = (n >>> 0) - (n >>> 1); return n; }; /** * Constraint a value to lie between two values. * * @param {number} value The value to clamp. * @param {number} min The minimum value. * @param {number} max The maximum value. * @returns {number} The clamped value such that min <= result <= max. */ CesiumMath.clamp = function (value, min, max) { //>>includeStart('debug', pragmas.debug); Check.typeOf.number("value", value); Check.typeOf.number("min", min); Check.typeOf.number("max", max); //>>includeEnd('debug'); return value < min ? min : value > max ? max : value; }; let randomNumberGenerator = new MersenneTwister(); /** * Sets the seed used by the random number generator * in {@link CesiumMath#nextRandomNumber}. * * @param {number} seed An integer used as the seed. */ CesiumMath.setRandomNumberSeed = function (seed) { //>>includeStart('debug', pragmas.debug); if (!defined(seed)) { throw new DeveloperError("seed is required."); } //>>includeEnd('debug'); randomNumberGenerator = new MersenneTwister(seed); }; /** * Generates a random floating point number in the range of [0.0, 1.0) * using a Mersenne twister. * * @returns {number} A random number in the range of [0.0, 1.0). * * @see CesiumMath.setRandomNumberSeed * @see {@link http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne twister on Wikipedia} */ CesiumMath.nextRandomNumber = function () { return randomNumberGenerator.random(); }; /** * Generates a random number between two numbers. * * @param {number} min The minimum value. * @param {number} max The maximum value. * @returns {number} A random number between the min and max. */ CesiumMath.randomBetween = function (min, max) { return CesiumMath.nextRandomNumber() * (max - min) + min; }; /** * Computes Math.acos(value), but first clamps value to the range [-1.0, 1.0] * so that the function will never return NaN. * * @param {number} value The value for which to compute acos. * @returns {number} The acos of the value if the value is in the range [-1.0, 1.0], or the acos of -1.0 or 1.0, * whichever is closer, if the value is outside the range. */ CesiumMath.acosClamped = function (value) { //>>includeStart('debug', pragmas.debug); if (!defined(value)) { throw new DeveloperError("value is required."); } //>>includeEnd('debug'); return Math.acos(CesiumMath.clamp(value, -1.0, 1.0)); }; /** * Computes Math.asin(value), but first clamps value to the range [-1.0, 1.0] * so that the function will never return NaN. * * @param {number} value The value for which to compute asin. * @returns {number} The asin of the value if the value is in the range [-1.0, 1.0], or the asin of -1.0 or 1.0, * whichever is closer, if the value is outside the range. */ CesiumMath.asinClamped = function (value) { //>>includeStart('debug', pragmas.debug); if (!defined(value)) { throw new DeveloperError("value is required."); } //>>includeEnd('debug'); return Math.asin(CesiumMath.clamp(value, -1.0, 1.0)); }; /** * Finds the chord length between two points given the circle's radius and the angle between the points. * * @param {number} angle The angle between the two points. * @param {number} radius The radius of the circle. * @returns {number} The chord length. */ CesiumMath.chordLength = function (angle, radius) { //>>includeStart('debug', pragmas.debug); if (!defined(angle)) { throw new DeveloperError("angle is required."); } if (!defined(radius)) { throw new DeveloperError("radius is required."); } //>>includeEnd('debug'); return 2.0 * radius * Math.sin(angle * 0.5); }; /** * Finds the logarithm of a number to a base. * * @param {number} number The number. * @param {number} base The base. * @returns {number} The result. */ CesiumMath.logBase = function (number, base) { //>>includeStart('debug', pragmas.debug); if (!defined(number)) { throw new DeveloperError("number is required."); } if (!defined(base)) { throw new DeveloperError("base is required."); } //>>includeEnd('debug'); return Math.log(number) / Math.log(base); }; /** * Finds the cube root of a number. * Returns NaN if number is not provided. * * @function * @param {number} [number] The number. * @returns {number} The result. */ // eslint-disable-next-line es/no-math-cbrt CesiumMath.cbrt = defaultValue(Math.cbrt, function cbrt(number) { const result = Math.pow(Math.abs(number), 1.0 / 3.0); return number < 0.0 ? -result : result; }); /** * Finds the base 2 logarithm of a number. * * @function * @param {number} number The number. * @returns {number} The result. */ // eslint-disable-next-line es/no-math-log2 CesiumMath.log2 = defaultValue(Math.log2, function log2(number) { return Math.log(number) * Math.LOG2E; }); /** * @private */ CesiumMath.fog = function (distanceToCamera, density) { const scalar = distanceToCamera * density; return 1.0 - Math.exp(-(scalar * scalar)); }; /** * Computes a fast approximation of Atan for input in the range [-1, 1]. * * Based on Michal Drobot's approximation from ShaderFastLibs, * which in turn is based on "Efficient approximations for the arctangent function," * Rajan, S. Sichun Wang Inkol, R. Joyal, A., May 2006. * Adapted from ShaderFastLibs under MIT License. * * @param {number} x An input number in the range [-1, 1] * @returns {number} An approximation of atan(x) */ CesiumMath.fastApproximateAtan = function (x) { //>>includeStart('debug', pragmas.debug); Check.typeOf.number("x", x); //>>includeEnd('debug'); return x * (-0.1784 * Math.abs(x) - 0.0663 * x * x + 1.0301); }; /** * Computes a fast approximation of Atan2(x, y) for arbitrary input scalars. * * Range reduction math based on nvidia's cg reference implementation: http://developer.download.nvidia.com/cg/atan2.html * * @param {number} x An input number that isn't zero if y is zero. * @param {number} y An input number that isn't zero if x is zero. * @returns {number} An approximation of atan2(x, y) */ CesiumMath.fastApproximateAtan2 = function (x, y) { //>>includeStart('debug', pragmas.debug); Check.typeOf.number("x", x); Check.typeOf.number("y", y); //>>includeEnd('debug'); // atan approximations are usually only reliable over [-1, 1] // So reduce the range by flipping whether x or y is on top based on which is bigger. let opposite; let t = Math.abs(x); // t used as swap and atan result. opposite = Math.abs(y); const adjacent = Math.max(t, opposite); opposite = Math.min(t, opposite); const oppositeOverAdjacent = opposite / adjacent; //>>includeStart('debug', pragmas.debug); if (isNaN(oppositeOverAdjacent)) { throw new DeveloperError("either x or y must be nonzero"); } //>>includeEnd('debug'); t = CesiumMath.fastApproximateAtan(oppositeOverAdjacent); // Undo range reduction t = Math.abs(y) > Math.abs(x) ? CesiumMath.PI_OVER_TWO - t : t; t = x < 0.0 ? CesiumMath.PI - t : t; t = y < 0.0 ? -t : t; return t; }; export default CesiumMath;