From b13243634484f9fa0fba4985c452475760ba5662 Mon Sep 17 00:00:00 2001 From: SebH Date: Sat, 27 Oct 2018 17:10:40 +0200 Subject: [PATCH] Added first version of all the files. --- README.md | 18 +- SphericalHarmonics.hlsl | 196 +++++++++++ sh2.nb | 706 ++++++++++++++++++++++++++++++++++++++++ sh2.pdf | Bin 0 -> 1227237 bytes 4 files changed, 919 insertions(+), 1 deletion(-) create mode 100644 SphericalHarmonics.hlsl create mode 100644 sh2.nb create mode 100644 sh2.pdf diff --git a/README.md b/README.md index d8dd5e1..69f1713 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,18 @@ # HLSL-Spherical-Harmonics -A collection of HLSL functions one can include to use spherical harmonics in shaders. This repository can be simply be used as a submodule. + +## Description + +A collection of HLSL functions one can include to use spherical harmonics in shaders. +This is very practical when generating and consuming SH on the GPU. +This repository can be simply be used as a submodule. + +As of today, only 2nd order spherical harmonics functions are provided. + +Do not hesitate to send suggestions or improvements. + +## Exemples + +Precomputed occlusion as SH for cloud ambient lighting. Result as video and as image (left directional occlusion as SH, right final cloud render): + +cloud +cloud diff --git a/SphericalHarmonics.hlsl b/SphericalHarmonics.hlsl new file mode 100644 index 0000000..6cbaf2b --- /dev/null +++ b/SphericalHarmonics.hlsl @@ -0,0 +1,196 @@ + +// SphericalHarmonics.hlsl from https://github.com/sebh/HLSL-Spherical-Harmonics + +// Great documents about spherical harmonics: +// [1] http://silviojemma.com/public/papers/lighting/spherical-harmonic-lighting.pdf +// [2] https://www.ppsloan.org/publications/StupidSH36.pdf +// [3] https://cseweb.ucsd.edu/~ravir/papers/envmap/envmap.pdf +// [4] https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2011/06/10-14.pdf +// [5] https://github.com/kayru/Probulator +// [6] https://www.ppsloan.org/publications/SHJCGT.pdf +// [7] http://www.patapom.com/blog/SHPortal/ +// [8] https://grahamhazel.com/blog/2017/12/22/converting-sh-radiance-to-irradiance/ +// [9] http://www.ppsloan.org/publications/shdering.pdf +// [10] http://limbicsoft.com/volker/prosem_paper.pdf +// [11] https://bartwronski.files.wordpress.com/2014/08/bwronski_volumetric_fog_siggraph2014.pdf +// + +// +//**** HOW TO PROJECT RADIANCE FROM A SPHERE INTO SH? +// +// // Initialise sh to 0 +// sh2 shR = shZero(); +// sh2 shG = shZero(); +// sh2 shB = shZero(); +// +// // Accumulate coefficients according to surounding direction/color tuples. +// for (float az = 0.5f; az < axisSampleCount; az += 1.0f) +// for (float ze = 0.5f; ze < axisSampleCount; ze += 1.0f) +// { +// float3 rayDir = shGetUniformSphereSample(az / axisSampleCount, ze / axisSampleCount); +// float3 color = [...]; +// +// sh2 sh = shEvaluate(rayDir); +// shR = shAdd(shR, shScale(sh, color.r)); +// shG = shAdd(shG, shScale(sh, color.g)); +// shB = shAdd(shB, shScale(sh, color.b)); +// } +// +// // integrating over a sphere so each sample has a weight of 4*PI/samplecount (uniform solid angle, for each sample) +// float shFactor = 4.0 * shPI / (axisSampleCount * axisSampleCount); +// shR = shScale(shR, shFactor ); +// shG = shScale(shG, shFactor ); +// shB = shScale(shB, shFactor ); +// +// +//**** HOW TO VIZUALISE A SPHERICAL FUNCTION REPRESENTED AS SH? +// +// sh2 shR = fromSomewhere.Load(...); +// sh2 shG = fromSomewhere.Load(...); +// sh2 shB = fromSomewhere.Load(...); +// float3 rayDir = compute(...); // the direction for which you want to know the color +// float3 rgbColor = max(0.0f, shUnproject(shR, shG, shB, rayDir)); // A "max" is usually recomended to avoid negative values (can happen with SH) +// + + + +#define shPI 3.1415926536f + + + +// Generate uniform distribution of direction over a sphere. (from [1]) +// azimuthX and zenithY are both in [0, 1]. You can use random value, stratified, etc. +// Top and bottom sphere pole (+-zenith) are along the Y axis. +float3 shGetUniformSphereSample(float azimuthX, float zenithY) +{ + float phi = 2.0f * shPI * azimuthX; + float theta = 2.0f * acos(sqrt(1.0f - zenithY)); + float3 dir = float3(sin(theta)*cos(phi), cos(theta), sin(theta)*sin(phi)); + return dir; +} + + + +#define sh2 float4 +// TODO sh3 + +sh2 shZero() +{ + return float4(0.0f, 0.0f, 0.0f, 0.0f); +} + +// Evaluate spherical harmonics from direction. (from [2] Appendix A2) +// (evaluating the associated legendre polynomial using the polynomial form) +sh2 shEvaluate(float3 dir) +{ + sh2 result; + result.x = 0.28209479177387814347403972578039f; // L=0 , M= 0 + result.y =-0.48860251190291992158638462283836f * dir.y; // L=1 , M=-1 + result.z = 0.48860251190291992158638462283836f * dir.z; // L=1 , M= 0 + result.w =-0.48860251190291992158638462283836f * dir.x; // L=1 , M= 1 + return result; +} + +// Recover the value of a function represented as SH in the direction dir. +float shUnproject(sh2 functionSh, float3 dir) +{ + sh2 sh = shEvaluate(dir); + return dot(functionSh, sh); +} +float3 shUnproject(sh2 functionShX, sh2 functionShY, sh2 functionShZ, float3 dir) +{ + sh2 sh = shEvaluate(dir); + return float3(dot(functionShX, sh), dot(functionShY, sh), dot(functionShZ, sh)); +} + +// Project a cosine lobe function, with peak value in direction dir, into SH (from [4]) +// Integral over unit sphere is PI. +sh2 shEvaluateCosineLobe(float3 dir) +{ + sh2 result; + result.x = 0.8862269254527580137f; // L=0 , M= 0 + result.y =-1.0233267079464884885f * dir.y; // L=1 , M=-1 + result.z = 1.0233267079464884885f * dir.z; // L=1 , M= 0 + result.w =-1.0233267079464884885f * dir.x; // L=1 , M= 1 + return result; +} + +// Project a Henyey-Greenstein phase function, with peak value in direction dir, into SH. (from [11]) +// Integral over unit sphere is 1. +sh2 evaluatePhaseHG(float3 dir, float g) +{ + sh2 result; + const float factor = 0.48860251190291992158638462283836 * g; + result.x = 0.28209479177387814347403972578039; // L=0 , M= 0 + result.y =-factor * dir.y; // L=1 , M=-1 + result.z = factor * dir.z; // L=1 , M= 0 + result.w =-factor * dir.x; // L=1 , M= 1 + return result; +} + +// Adds two functions represented by SH coefficients +sh2 shAdd(sh2 shL, sh2 shR) +{ + return shL + shR; +} + +// Scale a function uniformly +sh2 shScale(sh2 sh, float v) +{ + return sh * v; +} + +// Operate a rotation of the function represented by SH. +sh2 shRotate(sh2 sh, float3x3 rotation) +{ + // TODO verify and optimize + sh2 result; + result.x = sh.x; + float3 tmp = float3(sh.w, sh.y, sh.z); // undo direction component shuffle to match function space + result.yzw = mul(tmp, rotation).yzx; // apply rotation and re-shuffle + return result; +} + +// Integrate the product of two functions a and b represented by SH coefficients +float shFuncProductIntegral(sh2 shL, sh2 shR) +{ + return dot(shL, shR); +} + +// Compute the SH coefficients of the projection of two functions that have been multiplied (from [4]) +sh2 shProduct(sh2 shL, sh2 shR) +{ + const float factor = 1.0f / (2.0f * sqrt(shPI)); + return factor * sh2( + shL.x*shR.w + shL.w+shR.x, + shL.y*shR.w + shL.w*shR.y, + shL.z*shR.w + shL.w*shR.z, + dot(shL,shR) + ); +} + +// Convolve the function using a Hanning filtering. This helps reducing ringing and negative values. (from [2], Windowing p.16) +// A lower value of w will reduce ringing (like the width of a filter) +sh2 shHanningConvolution( sh2 sh, float w ) +{ + sh2 result = sh; + float invW = 1.0 / w; + float factorBand1 =(1.0 + cos( shPI * invW )) / 2.0f; + result.y *= factorBand1; + result.z *= factorBand1; + result.w *= factorBand1; + return result; +} + +// Convolve the sh using a cosine lob. This is interesting to transform radiance to irradiance. 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