inline float3 uv_to_sphere(const float2 uv, const float2 image_size)
{
  float2 st = (uv+float2(0.5f)) / image_size;
  float latitude = (st.y - 0.5f) * PI;
  float longitude = (st.x - 0.5f) * 2 * PI;
  float radiusAtLat = cos(latitude);
  float3 normal;
  normal.x = radiusAtLat * cos(longitude);
  normal.y = sin(latitude);
  normal.z = radiusAtLat * sin(longitude);
  return normal;
}

inline float2 sphere_to_uv(const float3 normal, const float2 image_size)
{
  float latitude = asin(normal.y);
  float radiusAtLat = cos(latitude);
  float longitude = atan2(normal.z, normal.x);
  float2 st = float2(longitude/ (2 * PI) + 0.5f, latitude / PI + 0.5f);
  return st*image_size-float2(0.5f);
}


kernel Irradiance : ImageComputationKernel<ePixelWise>
{
  Image<eRead, eAccessRandom, eEdgeConstant> src;
  Image<eWrite, eAccessPoint> dst;

  param:
    float sampleDelta;
    float2 size;

  void define() {
    defineParam(sampleDelta, "SampleDelta", 0.25f);
    defineParam(size, "Image Size", float2(1280.0f, 720.0f));
  }

  void process(int2 pos)
  {
    SampleType(src) irradiance(0);
    float2 fpos = float2(pos.x,pos.y);
    float3 normal = normalize(uv_to_sphere(fpos, size));


    float3 up    = float3(0.0f, 1.0f, 0.0f);
    float3 right = cross(up, normal);
    up           = cross(normal, right);

    int nrSamples = 0.0;
    for(float phi = 0.0; phi < 2.0 * PI; phi += sampleDelta)
    {
        for(float theta = 0.0; theta < 0.5 * PI; theta += sampleDelta)
        {
            // spherical to cartesian (in tangent space)
            float3 tangentSample = float3(sin(theta) * cos(phi),  sin(theta) * sin(phi), cos(theta));
            // tangent space to world
            float3 sampleVec = tangentSample.x * right + tangentSample.y * up + tangentSample.z * normal;

            float2 coordinates = sphere_to_uv(sampleVec, size);

            irradiance += bilinear(src, coordinates.x, coordinates.y) * cos(theta) * sin(theta);
            nrSamples++;
        }
    }
    irradiance = PI * irradiance * (1.0 / float(nrSamples));

    //Use a bilinear filter to get the value at that src position.
    dst() = irradiance;
  }

};