static float2 poissonDisk[16] = 
{
   float2( -0.94201624, -0.39906216 ), 
   float2( 0.94558609, -0.76890725 ), 
   float2( -0.094184101, -0.92938870 ), 
   float2( 0.34495938, 0.29387760 ), 
   float2( -0.91588581, 0.45771432 ), 
   float2( -0.81544232, -0.87912464 ), 
   float2( -0.38277543, 0.27676845 ), 
   float2( 0.97484398, 0.75648379 ), 
   float2( 0.44323325, -0.97511554 ), 
   float2( 0.53742981, -0.47373420 ), 
   float2( -0.26496911, -0.41893023 ), 
   float2( 0.79197514, 0.19090188 ), 
   float2( -0.24188840, 0.99706507 ), 
   float2( -0.81409955, 0.91437590 ), 
   float2( 0.19984126, 0.78641367 ), 
   float2( 0.14383161, -0.14100790 ) 
};

// TODO: this should probably sample a noise texture instead
// Returns a random number based on a vec3 and an int.
float random(float3 seed, int i){
	float4 seed4 = float4(seed, i);
	float dot_product = dot(seed4, float4(12.9898,78.233,45.164,94.673));
	return frac(sin(dot_product) * 43758.5453);
}

float PoissonCoord(sampler shadowMap, float3 worldPosition, float2 texCoord, float fragmentDepth, float bias)
{
    float visibility = 1.0;

    for (int i = 0; i < 16; i++)
    {
        int index = int(16.0 * random(floor(worldPosition * 1000.0), i)) % 16;

        if (tex2D(shadowMap, texCoord + poissonDisk[index] / 1024.0).r < fragmentDepth - bias)
        {
            visibility -= 0.05;
        }
    }

    return visibility;
}

float PoissonShadow(
    float3 positionWorldSpace, 
    float3 N, 
    float3 L,
    float4x4 lightSpaceMatrix,
    sampler shadowMap,
    int shadowMapSize
) {
    float bias = 0.005 * tan(acos(dot(N, L)));
    bias = clamp(bias, 0, 0.01);

    float4 positionLightSpace = mul(float4(positionWorldSpace, 1.0), lightSpaceMatrix);

    // maps to [-1, 1]
    float3 projectionCoords = positionLightSpace.xyz / positionLightSpace.w;

    // maps to [0, 1]
    // NOTE: In XNA, clip space z is [0, 1] range
    projectionCoords.x = (projectionCoords.x * 0.5) + 0.5;
    projectionCoords.y = (projectionCoords.y * 0.5) + 0.5;
    projectionCoords.y *= -1;

    if (projectionCoords.z > 1.0)
    {
        return 1.0;
    }

    float inc = 1.0 / shadowMapSize;

    // Poisson soft shadows
    float visibility = 0.0;

    visibility = PoissonCoord(
        shadowMap, 
        positionWorldSpace,
        projectionCoords.xy,
        projectionCoords.z,
        bias
    );

    return visibility;
}