vec3 lambertianDiffuse(vec3 diffuseColor)
{
    return diffuseColor / czm_pi;
}

vec3 fresnelSchlick2(vec3 f0, vec3 f90, float VdotH)
{
    return f0 + (f90 - f0) * pow(clamp(1.0 - VdotH, 0.0, 1.0), 5.0);
}

float smithVisibilityG1(float NdotV, float roughness)
{
    // this is the k value for direct lighting.
    // for image based lighting it will be roughness^2 / 2
    float k = (roughness + 1.0) * (roughness + 1.0) / 8.0;
    return NdotV / (NdotV * (1.0 - k) + k);
}

float smithVisibilityGGX(float roughness, float NdotL, float NdotV)
{
    return (
        smithVisibilityG1(NdotL, roughness) *
        smithVisibilityG1(NdotV, roughness)
    );
}

float GGX(float roughness, float NdotH)
{
    float roughnessSquared = roughness * roughness;
    float f = (NdotH * roughnessSquared - NdotH) * NdotH + 1.0;
    return roughnessSquared / (czm_pi * f * f);
}

/**
 * Compute the diffuse and specular contributions using physically based
 * rendering. This function only handles direct lighting.
 * <p>
 * This function only handles the lighting calculations. Metallic/roughness
 * and specular/glossy must be handled separately. See {@czm_pbrMetallicRoughnessMaterial}, {@czm_pbrSpecularGlossinessMaterial} and {@czm_defaultPbrMaterial}
 * </p>
 *
 * @name czm_pbrlighting
 * @glslFunction
 *
 * @param {vec3} positionEC The position of the fragment in eye coordinates
 * @param {vec3} normalEC The surface normal in eye coordinates
 * @param {vec3} lightDirectionEC Unit vector pointing to the light source in eye coordinates.
 * @param {vec3} lightColorHdr radiance of the light source. This is a HDR value.
 * @param {czm_pbrParameters} The computed PBR parameters.
 * @return {vec3} The computed HDR color
 *
 * @example
 * czm_pbrParameters pbrParameters = czm_pbrMetallicRoughnessMaterial(
 *  baseColor,
 *  metallic,
 *  roughness
 * );
 * vec3 color = czm_pbrlighting(
 *  positionEC,
 *  normalEC,
 *  lightDirectionEC,
 *  lightColorHdr,
 *  pbrParameters);
 */
vec3 czm_pbrLighting(
    vec3 positionEC,
    vec3 normalEC,
    vec3 lightDirectionEC,
    vec3 lightColorHdr,
    czm_pbrParameters pbrParameters
)
{
    vec3 v = -normalize(positionEC);
    vec3 l = normalize(lightDirectionEC);
    vec3 h = normalize(v + l);
    vec3 n = normalEC;
    float NdotL = clamp(dot(n, l), 0.001, 1.0);
    float NdotV = abs(dot(n, v)) + 0.001;
    float NdotH = clamp(dot(n, h), 0.0, 1.0);
    float LdotH = clamp(dot(l, h), 0.0, 1.0);
    float VdotH = clamp(dot(v, h), 0.0, 1.0);

    vec3 f0 = pbrParameters.f0;
    float reflectance = max(max(f0.r, f0.g), f0.b);
    vec3 f90 = vec3(clamp(reflectance * 25.0, 0.0, 1.0));
    vec3 F = fresnelSchlick2(f0, f90, VdotH);

    float alpha = pbrParameters.roughness;
    float G = smithVisibilityGGX(alpha, NdotL, NdotV);
    float D = GGX(alpha, NdotH);
    vec3 specularContribution = F * G * D / (4.0 * NdotL * NdotV);

    vec3 diffuseColor = pbrParameters.diffuseColor;
    // F here represents the specular contribution
    vec3 diffuseContribution = (1.0 - F) * lambertianDiffuse(diffuseColor);

    // Lo = (diffuse + specular) * Li * NdotL
    return (diffuseContribution + specularContribution) * NdotL * lightColorHdr;
}