#ifndef __MATH_INC
#define __MATH_INC

#define PI 3.14159265358979f
#define RCP_PI (1.0f / PI)
#define TAU (2.0f * PI)
#define SQRT_3 1.73205081f

float sin_noise_3d(float3 uvw) {
  return sin(uvw[0]) * sin(uvw[1]) * sin(uvw[2]);
}

float sin_noise_3d_fbm(float3 uvw, uint octaves, float k, float strength) {
  float result = 0;
  float factor = 1.0f;
  for (uint i = 0; i < octaves; i++) {
    result += sin_noise_3d(uvw) * factor * strength;
    uvw *= k;
    factor /= k;
  }
  return result;
}

// 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