BansheeEngine/Data/Raw/Engine/Shaders/ReflectionCubeImportanceSample.bsl

#include "$ENGINE$\PPBase.bslinc"
#include "$ENGINE$\ReflectionCubemapCommon.bslinc"

Parameters =
{
	int			gCubeFace;
	SamplerCUBE	gInputSamp : alias("gInputTex");
	TextureCUBE gInputTex;
};

Blocks =
{
	Block Input;
};

Technique
 : inherits("PPBase")
 : inherits("ReflectionCubemapCommon") =
{
	Pass =
	{
		Fragment =
		{
			#define PI 3.1415926
		
			// From Hacker's Delight
			float reverseBits(uint bits)  
			{
				bits = (bits << 16u) | (bits >> 16u);
				bits = ((bits & 0x55555555u) << 1u) | ((bits & 0xAAAAAAAAu) >> 1u);
				bits = ((bits & 0x33333333u) << 2u) | ((bits & 0xCCCCCCCCu) >> 2u);
				bits = ((bits & 0x0F0F0F0Fu) << 4u) | ((bits & 0xF0F0F0F0u) >> 4u);
				bits = ((bits & 0x00FF00FFu) << 8u) | ((bits & 0xFF00FF00u) >> 8u);
				
				return float(bits) * 2.3283064365386963e-10; // 0x100000000
			}
			
			float2 hammersleySequence(uint i, uint count)
			{
				float2 output;
				output.x = i / (float)count;
				output.y = reverseBits(i);
				
				return output;
			}
			
			// Returns cos(theta) in x and phi in y
			float2 importanceSampleGGX(float2 e, float roughness4)
			{
				// See GGXImportanceSample.nb for derivation (essentially, take base GGX, normalize it,
				// generate PDF, split PDF into marginal probability for theta and conditional probability
				// for phi. Plug those into the CDF, invert it.)				
				float cosTheta = sqrt((1.0f - e.x) / (1.0f + (roughness4 - 1.0f) * e.x));
				float phi = 2.0f * PI * e.y;
				
				return float2(cosTheta, phi);
			}
			
			float3 sphericalToCartesian(float cosTheta, float sinTheta, float phi)
			{
				float3 output;
				output.x = sinTheta * cos(phi);
				output.y = sinTheta * sin(phi);
				output.z = cosTheta;
				
				return output;
			}
			
			float pdfGGX(float cosTheta, float sinTheta, float roughness4)
			{
				float d = (cosTheta*roughness4 - cosTheta) * cosTheta + 1;
				return roughness4 * cosTheta * sinTheta / (d*d*PI);
			}
			
			cbuffer Input
			{
				int gCubeFace;
				int gMipLevel;
				int gNumMips;
				float gPrecomputedMipFactor;
			}	
		
			SamplerState gInputSamp;
			TextureCube gInputTex;

			float4 main(VStoFS input) : SV_Target0
			{
				float2 scaledUV = input.uv0 * 2.0f - 1.0f;
										
				float3 N = getDirFromCubeFace(gCubeFace, scaledUV);
				N = normalize(N);
				
				// Determine which mip level to sample from depending on PDF and cube -> sphere mapping distortion
				float distortion = rcp(pow(N.x * N.x + N.y * N.y + N.z * N.z, 3.0f/2.0f));
				
				float roughness = mapMipLevelToRoughness(gMipLevel, gNumMips);
				float roughness2 = roughness * roughness;
				float roughness4 = roughness2 * roughness2;
				
				float4 sum = 0;
				for(uint i = 0; i < NUM_SAMPLES; i++)
				{
					float2 random = hammersleySequence(i, NUM_SAMPLES);
					float2 sphericalH = importanceSampleGGX(random, roughness4);
					
					float cosTheta = sphericalH.x;
					float phi = sphericalH.y;
					
					float sinTheta = sqrt(1.0f - cosTheta * cosTheta);
					
					float3 H = sphericalToCartesian(cosTheta, sinTheta, phi);
					float PDF = pdfGGX(cosTheta, sinTheta, roughness4);
					
					// Transform H to world space
					float3 up = abs(H.z) < 0.999 ? float3(0, 0, 1) : float3(1, 0, 0);
					float3 tangentX = normalize(cross(up, N));
					float3 tangentY = cross(N, tangentX);
					
					H = tangentX * H.x + tangentY * H.y + N * H.z; 
					
					// Calculating mip level from distortion and pdf and described by http://http.developer.nvidia.com/GPUGems3/gpugems3_ch20.html
					int mipLevel = max(gPrecomputedMipFactor - 0.5f * log2(PDF * distortion), 0);
					
					// Note: Adding +1 bias as it looks better
					mipLevel++;
					
					// We need a light direction to properly evaluate the NoL term of the evaluation integral
					//  Li(u) * brdf(u, v) * (u.n) / pdf(u, v)
					// which we don't have, so we assume a viewing direction is equal to normal and calculate lighting dir from it and half-vector
					float3 L = 2 * dot(N, H) * H - N;
					float NoL = saturate(dot(N, L));
					
					// sum += radiance * GGX(h, roughness) * NoL / PDF. In GGX/PDF most factors cancel out and we're left with 1/cos (sine factor of the PDF only needed for the integral (I think), so we don't include it)
					if(NoL > 0)
						sum += gInputTex.SampleLevel(gInputSamp, H, mipLevel) * NoL / cosTheta;
				}
				
				return sum / NUM_SAMPLES;
			}	
		};
	};
};