Torque3D/Engine/source/T3D/lighting/IBLUtilities.cpp
2021-10-07 00:27:39 -04:00

645 lines
22 KiB
C++

//-----------------------------------------------------------------------------
// Copyright (c) 2012 GarageGames, LLC
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
//-----------------------------------------------------------------------------
#include "T3D/lighting/IBLUtilities.h"
#include "console/engineAPI.h"
#include "materials/shaderData.h"
#include "gfx/gfxTextureManager.h"
#include "gfx/gfxTransformSaver.h"
#include "gfx/bitmap/cubemapSaver.h"
#include "core/stream/fileStream.h"
#include "gfx/bitmap/imageUtils.h"
namespace IBLUtilities
{
void GenerateIrradianceMap(GFXTextureTargetRef renderTarget, GFXCubemapHandle cubemap, GFXCubemapHandle &cubemapOut)
{
GFXTransformSaver saver;
GFXStateBlockRef irrStateBlock;
ShaderData *irrShaderData;
GFXShaderRef irrShader = Sim::findObject("IrradianceShader", irrShaderData) ? irrShaderData->getShader() : NULL;
if (!irrShader)
{
Con::errorf("IBLUtilities::GenerateIrradianceMap() - could not find IrradianceShader");
return;
}
GFXShaderConstBufferRef irrConsts = irrShader->allocConstBuffer();
GFXShaderConstHandle* irrFaceSC = irrShader->getShaderConstHandle("$face");
GFXStateBlockDesc desc;
desc.zEnable = false;
desc.samplersDefined = true;
desc.samplers[0].addressModeU = GFXAddressClamp;
desc.samplers[0].addressModeV = GFXAddressClamp;
desc.samplers[0].addressModeW = GFXAddressClamp;
desc.samplers[0].magFilter = GFXTextureFilterLinear;
desc.samplers[0].minFilter = GFXTextureFilterLinear;
desc.samplers[0].mipFilter = GFXTextureFilterLinear;
irrStateBlock = GFX->createStateBlock(desc);
GFX->pushActiveRenderTarget();
GFX->setShader(irrShader);
GFX->setShaderConstBuffer(irrConsts);
GFX->setStateBlock(irrStateBlock);
GFX->setVertexBuffer(NULL);
GFX->setCubeTexture(0, cubemap);
for (U32 i = 0; i < 6; i++)
{
renderTarget->attachTexture(GFXTextureTarget::Color0, cubemapOut, i);
irrConsts->setSafe(irrFaceSC, (S32)i);
GFX->setActiveRenderTarget(renderTarget);
GFX->clear(GFXClearTarget, LinearColorF::BLACK, 1.0f, 0);
GFX->drawPrimitive(GFXTriangleList, 0, 1);
renderTarget->resolve();
}
GFX->popActiveRenderTarget();
}
void GenerateAndSaveIrradianceMap(String outputPath, S32 resolution, GFXCubemapHandle cubemap, GFXCubemapHandle &cubemapOut)
{
if (outputPath.isEmpty())
{
Con::errorf("IBLUtilities::GenerateAndSaveIrradianceMap - Cannot save to an empty path!");
return;
}
GFXTextureTargetRef renderTarget = GFX->allocRenderToTextureTarget(false);
IBLUtilities::GenerateIrradianceMap(renderTarget, cubemap, cubemapOut);
//Write it out
CubemapSaver::save(cubemapOut, outputPath);
if (!Platform::isFile(outputPath))
{
Con::errorf("IBLUtilities::GenerateAndSaveIrradianceMap - Failed to properly save out the baked irradiance!");
}
}
void SaveCubeMap(String outputPath, GFXCubemapHandle &cubemap)
{
if (outputPath.isEmpty())
{
Con::errorf("IBLUtilities::SaveCubeMap - Cannot save to an empty path!");
return;
}
//Write it out
CubemapSaver::save(cubemap, outputPath);
if (!Platform::isFile(outputPath))
{
Con::errorf("IBLUtilities::SaveCubeMap - Failed to properly save out the baked irradiance!");
}
}
void GeneratePrefilterMap(GFXTextureTargetRef renderTarget, GFXCubemapHandle cubemap, U32 mipLevels, GFXCubemapHandle &cubemapOut)
{
GFXTransformSaver saver;
ShaderData *prefilterShaderData;
GFXShaderRef prefilterShader = Sim::findObject("PrefiterCubemapShader", prefilterShaderData) ? prefilterShaderData->getShader() : NULL;
if (!prefilterShader)
{
Con::errorf("IBLUtilities::GeneratePrefilterMap() - could not find PrefiterCubemapShader");
return;
}
GFXShaderConstBufferRef prefilterConsts = prefilterShader->allocConstBuffer();
GFXShaderConstHandle* prefilterFaceSC = prefilterShader->getShaderConstHandle("$face");
GFXShaderConstHandle* prefilterRoughnessSC = prefilterShader->getShaderConstHandle("$roughness");
GFXShaderConstHandle* prefilterMipSizeSC = prefilterShader->getShaderConstHandle("$mipSize");
GFXShaderConstHandle* prefilterResolutionSC = prefilterShader->getShaderConstHandle("$resolution");
GFXStateBlockDesc desc;
desc.zEnable = false;
desc.samplersDefined = true;
desc.samplers[0].addressModeU = GFXAddressClamp;
desc.samplers[0].addressModeV = GFXAddressClamp;
desc.samplers[0].addressModeW = GFXAddressClamp;
desc.samplers[0].magFilter = GFXTextureFilterLinear;
desc.samplers[0].minFilter = GFXTextureFilterLinear;
desc.samplers[0].mipFilter = GFXTextureFilterLinear;
GFXStateBlockRef preStateBlock;
preStateBlock = GFX->createStateBlock(desc);
GFX->setStateBlock(preStateBlock);
GFX->pushActiveRenderTarget();
GFX->setShader(prefilterShader);
GFX->setShaderConstBuffer(prefilterConsts);
GFX->setCubeTexture(0, cubemap);
U32 prefilterSize = cubemapOut->getSize();
U32 resolutionSize = prefilterSize;
for (U32 face = 0; face < 6; face++)
{
prefilterConsts->setSafe(prefilterFaceSC, (S32)face);
prefilterConsts->setSafe(prefilterResolutionSC, (S32)resolutionSize);
for (U32 mip = 0; mip < mipLevels; mip++)
{
S32 mipSize = prefilterSize >> mip;
F32 roughness = (float)mip / (float)(mipLevels - 1);
prefilterConsts->setSafe(prefilterRoughnessSC, roughness);
prefilterConsts->setSafe(prefilterMipSizeSC, mipSize);
U32 size = prefilterSize * mPow(0.5f, mip);
renderTarget->attachTexture(GFXTextureTarget::Color0, cubemapOut, face, mip);
GFX->setActiveRenderTarget(renderTarget, false);//we set the viewport ourselves
GFX->setViewport(RectI(0, 0, size, size));
GFX->clear(GFXClearTarget, LinearColorF::BLACK, 1.0f, 0);
GFX->drawPrimitive(GFXTriangleList, 0, 1);
renderTarget->resolve();
}
}
GFX->popActiveRenderTarget();
}
void GenerateAndSavePrefilterMap(String outputPath, S32 resolution, GFXCubemapHandle cubemap, U32 mipLevels, GFXCubemapHandle &cubemapOut)
{
if (outputPath.isEmpty())
{
Con::errorf("IBLUtilities::GenerateAndSavePrefilterMap - Cannot save to an empty path!");
return;
}
GFXTextureTargetRef renderTarget = GFX->allocRenderToTextureTarget(false);
IBLUtilities::GeneratePrefilterMap(renderTarget, cubemap, mipLevels, cubemapOut);
//Write it out
CubemapSaver::save(cubemapOut, outputPath);
if (!Platform::isFile(outputPath))
{
Con::errorf("IBLUtilities::GenerateAndSavePrefilterMap - Failed to properly save out the baked irradiance!");
}
}
void bakeReflection(String outputPath, S32 resolution)
{
//GFXDEBUGEVENT_SCOPE(ReflectionProbe_Bake, ColorI::WHITE);
/*PostEffect *preCapture = dynamic_cast<PostEffect*>(Sim::findObject("AL_PreCapture"));
PostEffect *deferredShading = dynamic_cast<PostEffect*>(Sim::findObject("AL_DeferredShading"));
if (preCapture)
preCapture->enable();
if (deferredShading)
deferredShading->disable();
//if (mReflectionModeType == StaticCubemap || mReflectionModeType == BakedCubemap || mReflectionModeType == SkyLight)
{
if (!mCubemap)
{
mCubemap = new CubemapData();
mCubemap->registerObject();
}
}
if (mReflectionModeType == DynamicCubemap && mDynamicCubemap.isNull())
{
//mCubemap->createMap();
mDynamicCubemap = GFX->createCubemap();
mDynamicCubemap->initDynamic(resolution, GFXFormatR8G8B8);
}
else if (mReflectionModeType != DynamicCubemap)
{
if (mReflectionPath.isEmpty() || !mPersistentId)
{
if (!mPersistentId)
mPersistentId = getOrCreatePersistentId();
mReflectionPath = outputPath.c_str();
mProbeUniqueID = std::to_string(mPersistentId->getUUID().getHash()).c_str();
}
}
bool validCubemap = true;
// Save the current transforms so we can restore
// it for child control rendering below.
GFXTransformSaver saver;
//bool saveEditingMission = gEditingMission;
//gEditingMission = false;
//Set this to true to use the prior method where it goes through the SPT_Reflect path for the bake
bool probeRenderState = ReflectionProbe::smRenderReflectionProbes;
ReflectionProbe::smRenderReflectionProbes = false;
for (U32 i = 0; i < 6; ++i)
{
GFXTexHandle blendTex;
blendTex.set(resolution, resolution, GFXFormatR8G8B8A8, &GFXRenderTargetProfile, "");
GFXTextureTargetRef mBaseTarget = GFX->allocRenderToTextureTarget();
GFX->clearTextureStateImmediate(0);
if (mReflectionModeType == DynamicCubemap)
mBaseTarget->attachTexture(GFXTextureTarget::Color0, mDynamicCubemap, i);
else
mBaseTarget->attachTexture(GFXTextureTarget::Color0, blendTex);
// Standard view that will be overridden below.
VectorF vLookatPt(0.0f, 0.0f, 0.0f), vUpVec(0.0f, 0.0f, 0.0f), vRight(0.0f, 0.0f, 0.0f);
switch (i)
{
case 0: // D3DCUBEMAP_FACE_POSITIVE_X:
vLookatPt = VectorF(1.0f, 0.0f, 0.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 1: // D3DCUBEMAP_FACE_NEGATIVE_X:
vLookatPt = VectorF(-1.0f, 0.0f, 0.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 2: // D3DCUBEMAP_FACE_POSITIVE_Y:
vLookatPt = VectorF(0.0f, 1.0f, 0.0f);
vUpVec = VectorF(0.0f, 0.0f, -1.0f);
break;
case 3: // D3DCUBEMAP_FACE_NEGATIVE_Y:
vLookatPt = VectorF(0.0f, -1.0f, 0.0f);
vUpVec = VectorF(0.0f, 0.0f, 1.0f);
break;
case 4: // D3DCUBEMAP_FACE_POSITIVE_Z:
vLookatPt = VectorF(0.0f, 0.0f, 1.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 5: // D3DCUBEMAP_FACE_NEGATIVE_Z:
vLookatPt = VectorF(0.0f, 0.0f, -1.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
}
// create camera matrix
VectorF cross = mCross(vUpVec, vLookatPt);
cross.normalizeSafe();
MatrixF matView(true);
matView.setColumn(0, cross);
matView.setColumn(1, vLookatPt);
matView.setColumn(2, vUpVec);
matView.setPosition(getPosition());
matView.inverse();
// set projection to 90 degrees vertical and horizontal
F32 left, right, top, bottom;
F32 nearPlane = 0.01f;
F32 farDist = 1000.f;
MathUtils::makeFrustum(&left, &right, &top, &bottom, M_HALFPI_F, 1.0f, nearPlane);
Frustum frustum(false, left, right, top, bottom, nearPlane, farDist);
renderFrame(&mBaseTarget, matView, frustum, StaticObjectType | StaticShapeObjectType & EDITOR_RENDER_TYPEMASK, gCanvasClearColor);
mBaseTarget->resolve();
mCubemap->setCubeFaceTexture(i, blendTex);
}
if (mReflectionModeType != DynamicCubemap && validCubemap)
{
if (mCubemap->mCubemap)
mCubemap->updateFaces();
else
mCubemap->createMap();
char fileName[256];
dSprintf(fileName, 256, "%s%s.DDS", mReflectionPath.c_str(), mProbeUniqueID.c_str());
CubemapSaver::save(mCubemap->mCubemap, fileName);
if (!Platform::isFile(fileName))
{
validCubemap = false; //if we didn't save right, just
Con::errorf("Failed to properly save out the skylight baked cubemap!");
}
mDirty = false;
}
//calculateSHTerms();
ReflectionProbe::smRenderReflectionProbes = probeRenderState;
setMaskBits(-1);
if (preCapture)
preCapture->disable();
if (deferredShading)
deferredShading->enable();*/
}
LinearColorF decodeSH(Point3F normal, const LinearColorF SHTerms[9], const F32 SHConstants[5])
{
float x = normal.x;
float y = normal.y;
float z = normal.z;
LinearColorF l00 = SHTerms[0];
LinearColorF l10 = SHTerms[1];
LinearColorF l11 = SHTerms[2];
LinearColorF l12 = SHTerms[3];
LinearColorF l20 = SHTerms[4];
LinearColorF l21 = SHTerms[5];
LinearColorF l22 = SHTerms[6];
LinearColorF l23 = SHTerms[7];
LinearColorF l24 = SHTerms[8];
LinearColorF result = (
l00 * SHConstants[0] +
l12 * SHConstants[1] * x +
l10 * SHConstants[1] * y +
l11 * SHConstants[1] * z +
l20 * SHConstants[2] * x*y +
l21 * SHConstants[2] * y*z +
l22 * SHConstants[3] * (3.0*z*z - 1.0) +
l23 * SHConstants[2] * x*z +
l24 * SHConstants[4] * (x*x - y * y)
);
return LinearColorF(mMax(result.red, 0), mMax(result.green, 0), mMax(result.blue, 0));
}
MatrixF getSideMatrix(U32 side)
{
// Standard view that will be overridden below.
VectorF vLookatPt(0.0f, 0.0f, 0.0f), vUpVec(0.0f, 0.0f, 0.0f), vRight(0.0f, 0.0f, 0.0f);
switch (side)
{
case 0: // D3DCUBEMAP_FACE_POSITIVE_X:
vLookatPt = VectorF(1.0f, 0.0f, 0.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 1: // D3DCUBEMAP_FACE_NEGATIVE_X:
vLookatPt = VectorF(-1.0f, 0.0f, 0.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 2: // D3DCUBEMAP_FACE_POSITIVE_Y:
vLookatPt = VectorF(0.0f, 1.0f, 0.0f);
vUpVec = VectorF(0.0f, 0.0f, -1.0f);
break;
case 3: // D3DCUBEMAP_FACE_NEGATIVE_Y:
vLookatPt = VectorF(0.0f, -1.0f, 0.0f);
vUpVec = VectorF(0.0f, 0.0f, 1.0f);
break;
case 4: // D3DCUBEMAP_FACE_POSITIVE_Z:
vLookatPt = VectorF(0.0f, 0.0f, 1.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
case 5: // D3DCUBEMAP_FACE_NEGATIVE_Z:
vLookatPt = VectorF(0.0f, 0.0f, -1.0f);
vUpVec = VectorF(0.0f, 1.0f, 0.0f);
break;
}
// create camera matrix
VectorF cross = mCross(vUpVec, vLookatPt);
cross.normalizeSafe();
MatrixF rotMat(true);
rotMat.setColumn(0, cross);
rotMat.setColumn(1, vLookatPt);
rotMat.setColumn(2, vUpVec);
//rotMat.inverse();
return rotMat;
}
F32 harmonics(U32 termId, Point3F normal)
{
F32 x = normal.x;
F32 y = normal.y;
F32 z = normal.z;
switch (termId)
{
case 0:
return 1.0;
case 1:
return y;
case 2:
return z;
case 3:
return x;
case 4:
return x * y;
case 5:
return y * z;
case 6:
return 3.0*z*z - 1.0;
case 7:
return x * z;
default:
return x * x - y * y;
}
}
LinearColorF sampleSide(GBitmap* cubeFaceBitmaps[6], const U32& cubemapResolution, const U32& termindex, const U32& sideIndex)
{
MatrixF sideRot = getSideMatrix(sideIndex);
LinearColorF result = LinearColorF::ZERO;
F32 divider = 0;
for (int y = 0; y<cubemapResolution; y++)
{
for (int x = 0; x<cubemapResolution; x++)
{
Point2F sidecoord = ((Point2F(x, y) + Point2F(0.5, 0.5)) / Point2F(cubemapResolution, cubemapResolution))*2.0 - Point2F(1.0, 1.0);
Point3F normal = Point3F(sidecoord.x, sidecoord.y, -1.0);
normal.normalize();
F32 minBrightness = Con::getFloatVariable("$pref::GI::Cubemap_Sample_MinBrightness", 0.001f);
LinearColorF texel = cubeFaceBitmaps[sideIndex]->sampleTexel(y, x);
texel = LinearColorF(mMax(texel.red, minBrightness), mMax(texel.green, minBrightness), mMax(texel.blue, minBrightness)) * Con::getFloatVariable("$pref::GI::Cubemap_Gain", 1.5);
Point3F dir;
sideRot.mulP(normal, &dir);
result += texel * harmonics(termindex, dir) * -normal.z;
divider += -normal.z;
}
}
result /= divider;
return result;
}
//
//SH Calculations
// From http://sunandblackcat.com/tipFullView.php?l=eng&topicid=32&topic=Spherical-Harmonics-From-Cube-Texture
// With shader decode logic from https://github.com/nicknikolov/cubemap-sh
void calculateSHTerms(GFXCubemapHandle cubemap, LinearColorF SHTerms[9], F32 SHConstants[5])
{
if (!cubemap)
return;
const VectorF cubemapFaceNormals[6] =
{
// D3DCUBEMAP_FACE_POSITIVE_X:
VectorF(1.0f, 0.0f, 0.0f),
// D3DCUBEMAP_FACE_NEGATIVE_X:
VectorF(-1.0f, 0.0f, 0.0f),
// D3DCUBEMAP_FACE_POSITIVE_Y:
VectorF(0.0f, 1.0f, 0.0f),
// D3DCUBEMAP_FACE_NEGATIVE_Y:
VectorF(0.0f, -1.0f, 0.0f),
// D3DCUBEMAP_FACE_POSITIVE_Z:
VectorF(0.0f, 0.0f, 1.0f),
// D3DCUBEMAP_FACE_NEGATIVE_Z:
VectorF(0.0f, 0.0f, -1.0f),
};
U32 cubemapResolution = cubemap->getSize();
GBitmap* cubeFaceBitmaps[6];
for (U32 i = 0; i < 6; i++)
{
cubeFaceBitmaps[i] = new GBitmap(cubemapResolution, cubemapResolution, false, GFXFormatR16G16B16A16F);
}
//If we fail to parse the cubemap for whatever reason, we really can't continue
if (!CubemapSaver::getBitmaps(cubemap, GFXFormatR8G8B8A8, cubeFaceBitmaps))
return;
//Set up our constants
F32 L0 = Con::getFloatVariable("$pref::GI::SH_Term_L0", 1.0f);
F32 L1 = Con::getFloatVariable("$pref::GI::SH_Term_L1", 1.8f);
F32 L2 = Con::getFloatVariable("$pref::GI::SH_Term_L2", 0.83f);
F32 L2m2_L2m1_L21 = Con::getFloatVariable("$pref::GI::SH_Term_L2m2", 2.9f);
F32 L20 = Con::getFloatVariable("$pref::GI::SH_Term_L20", 0.58f);
F32 L22 = Con::getFloatVariable("$pref::GI::SH_Term_L22", 1.1f);
SHConstants[0] = L0;
SHConstants[1] = L1;
SHConstants[2] = L2 * L2m2_L2m1_L21;
SHConstants[3] = L2 * L20;
SHConstants[4] = L2 * L22;
for (U32 i = 0; i < 9; i++)
{
//Clear it, just to be sure
SHTerms[i] = LinearColorF(0.f, 0.f, 0.f);
//Now, encode for each side
SHTerms[i] = sampleSide(cubeFaceBitmaps, cubemapResolution, i, 0); //POS_X
SHTerms[i] += sampleSide(cubeFaceBitmaps, cubemapResolution, i, 1); //NEG_X
SHTerms[i] += sampleSide(cubeFaceBitmaps, cubemapResolution, i, 2); //POS_Y
SHTerms[i] += sampleSide(cubeFaceBitmaps, cubemapResolution, i, 3); //NEG_Y
SHTerms[i] += sampleSide(cubeFaceBitmaps, cubemapResolution, i, 4); //POS_Z
SHTerms[i] += sampleSide(cubeFaceBitmaps, cubemapResolution, i, 5); //NEG_Z
//Average
SHTerms[i] /= 6;
}
for (U32 i = 0; i < 6; i++)
SAFE_DELETE(cubeFaceBitmaps[i]);
/*bool mExportSHTerms = false;
if (mExportSHTerms)
{
for (U32 f = 0; f < 6; f++)
{
char fileName[256];
dSprintf(fileName, 256, "%s%s_DecodedFaces_%d.png", mReflectionPath.c_str(),
mProbeUniqueID.c_str(), f);
LinearColorF color = decodeSH(cubemapFaceNormals[f]);
FileStream stream;
if (stream.open(fileName, Torque::FS::File::Write))
{
GBitmap bitmap(mCubemapResolution, mCubemapResolution, false, GFXFormatR8G8B8);
bitmap.fill(color.toColorI());
bitmap.writeBitmap("png", stream);
}
}
for (U32 f = 0; f < 9; f++)
{
char fileName[256];
dSprintf(fileName, 256, "%s%s_SHTerms_%d.png", mReflectionPath.c_str(),
mProbeUniqueID.c_str(), f);
LinearColorF color = mProbeInfo->SHTerms[f];
FileStream stream;
if (stream.open(fileName, Torque::FS::File::Write))
{
GBitmap bitmap(mCubemapResolution, mCubemapResolution, false, GFXFormatR8G8B8);
bitmap.fill(color.toColorI());
bitmap.writeBitmap("png", stream);
}
}
}*/
}
F32 areaElement(F32 x, F32 y)
{
return mAtan2(x * y, (F32)mSqrt(x * x + y * y + 1.0));
}
F32 texelSolidAngle(F32 aU, F32 aV, U32 width, U32 height)
{
// transform from [0..res - 1] to [- (1 - 1 / res) .. (1 - 1 / res)]
// ( 0.5 is for texel center addressing)
const F32 U = (2.0 * (aU + 0.5) / width) - 1.0;
const F32 V = (2.0 * (aV + 0.5) / height) - 1.0;
// shift from a demi texel, mean 1.0 / size with U and V in [-1..1]
const F32 invResolutionW = 1.0 / width;
const F32 invResolutionH = 1.0 / height;
// U and V are the -1..1 texture coordinate on the current face.
// get projected area for this texel
const F32 x0 = U - invResolutionW;
const F32 y0 = V - invResolutionH;
const F32 x1 = U + invResolutionW;
const F32 y1 = V + invResolutionH;
const F32 angle = areaElement(x0, y0) - areaElement(x0, y1) - areaElement(x1, y0) + areaElement(x1, y1);
return angle;
}
};