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#ifndef __MATH_INC
#define __MATH_INC
#define PI 3.14159265358979f
#define RCP_PI (1.0f / PI)
// Wrap a dot product. Assume it's already clamped.
// At k=0, you get standard lambertian shading.
// At k=0.5, you get half-lambertian shading.
// At k=1.0, you get flat shading.
// k must be on [0, 1].
// Energy preserving, within some small bound.
float wrapDotProduct(float XoY, float k) {
float lambertian = XoY;
float half_lambertian = pow(max(1e-4, (XoY + 0.5f) / (1.0f + 0.5f)), 2);
float flat = RCP_PI;
if (k < 0.5) {
return lerp(lambertian, half_lambertian, k * 2.0f);
} else {
return lerp(half_lambertian, flat, k * 2.0f - 1.0f);
}
}
#endif // __MATH_INC
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