解讀unity內置的軟陰影處理方式

解讀unity內置的軟陰影處理方式：
參考網址：
https://blog.csdn.net/cgy56191948/article/details/105726682
https://blog.csdn.net/weixin_45776473/article/details/119582218
https://tajourney.games/5482/
上面的博客已經論述了，為何出現鋸齒，并從連續性角度，論述了pcf解決方案，使得陰影能夠軟。
本文主要是針對算法的實現上，剖析其實現的細節。

* PCF tent shadowmap filtering based on a 3x3 kernel (optimized with 4 taps)
*/
half UnitySampleShadowmap_PCF3x3Tent(float4 coord, float3 receiverPlaneDepthBias)
{half shadow = 1;#ifdef SHADOWMAPSAMPLER_AND_TEXELSIZE_DEFINED#ifndef SHADOWS_NATIVE// when we don't have hardware PCF sampling, fallback to a simple 3x3 sampling with averaged results.return UnitySampleShadowmap_PCF3x3NoHardwareSupport(coord, receiverPlaneDepthBias);#endif// tent base is 3x3 base thus covering from 9 to 12 texels, thus we need 4 bilinear PCF fetchesfloat2 tentCenterInTexelSpace = coord.xy * _ShadowMapTexture_TexelSize.zw;float2 centerOfFetchesInTexelSpace = floor(tentCenterInTexelSpace + 0.5);float2 offsetFromTentCenterToCenterOfFetches = tentCenterInTexelSpace - centerOfFetchesInTexelSpace;// find the weight of each texel basedfloat4 texelsWeightsU, texelsWeightsV;_UnityInternalGetWeightPerTexel_3TexelsWideTriangleFilter(offsetFromTentCenterToCenterOfFetches.x, texelsWeightsU);_UnityInternalGetWeightPerTexel_3TexelsWideTriangleFilter(offsetFromTentCenterToCenterOfFetches.y, texelsWeightsV);// each fetch will cover a group of 2x2 texels, the weight of each group is the sum of the weights of the texelsfloat2 fetchesWeightsU = texelsWeightsU.xz + texelsWeightsU.yw;float2 fetchesWeightsV = texelsWeightsV.xz + texelsWeightsV.yw;// move the PCF bilinear fetches to respect texels weightsfloat2 fetchesOffsetsU = texelsWeightsU.yw / fetchesWeightsU.xy + float2(-1.5,0.5);float2 fetchesOffsetsV = texelsWeightsV.yw / fetchesWeightsV.xy + float2(-1.5,0.5);fetchesOffsetsU *= _ShadowMapTexture_TexelSize.xx;fetchesOffsetsV *= _ShadowMapTexture_TexelSize.yy;// fetch !float2 bilinearFetchOrigin = centerOfFetchesInTexelSpace * _ShadowMapTexture_TexelSize.xy;shadow =  fetchesWeightsU.x * fetchesWeightsV.x * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.x, fetchesOffsetsV.x), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.y * fetchesWeightsV.x * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.y, fetchesOffsetsV.x), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.x * fetchesWeightsV.y * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.x, fetchesOffsetsV.y), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.y * fetchesWeightsV.y * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.y, fetchesOffsetsV.y), coord.z, receiverPlaneDepthBias));
#endifreturn shadow;
}

傳入的參數：float4 coord是(0,1)陰影貼圖的紋理坐標值。
接下來說明三角形面積的計算方式：
在這里插入圖片描述
如上圖所示，紅色的p點為陰影處的點。我們要對它進行軟陰影處理。
情況1）三角形偏移為0時，三角形面積被分為4個部分的面積情況。
三角形的底為3，高為1.5，之所以使用這樣的三角形，因為計算簡單。
紅色面積：1/8
橙色面積：1
綠色面積：1
藍色面積：1/8
情況2）三角形偏移為-0.5時，三角形面積被分為4個部分的面積情況。
在這里插入圖片描述
紅色面積：0.5
橙色面積：1.25
綠色面積：0.5
藍色面積：0
情況3）三角形偏移為0.5時，三角形面積被分為4個部分的面積情況

紅色面積：0
橙色面積：0.5
綠色面積：1.25
藍色面積：0.5
然后推廣到更一般的情況，給定偏移offset，計算三角形被分割的四個部分的面積是多少，公式為：
在這里插入圖片描述
對應的這段代碼是：

// ------------------------------------------------------------------
//  PCF Filtering helpers
// ------------------------------------------------------------------/**
* Assuming a isoceles rectangle triangle of height "triangleHeight" (as drawn below).
* This function return the area of the triangle above the first texel.
*
* |\      <-- 45 degree slop isosceles rectangle triangle
* | \
* ----    <-- length of this side is "triangleHeight"
* _ _ _ _ <-- texels
*/
float _UnityInternalGetAreaAboveFirstTexelUnderAIsocelesRectangleTriangle(float triangleHeight)
{return triangleHeight - 0.5;
}/**
* Assuming a isoceles triangle of 1.5 texels height and 3 texels wide lying on 4 texels.
* This function return the area of the triangle above each of those texels.
*    |    <-- offset from -0.5 to 0.5, 0 meaning triangle is exactly in the center
*   / \   <-- 45 degree slop isosceles triangle (ie tent projected in 2D)
*  /   \
* _ _ _ _ <-- texels
* X Y Z W <-- result indices (in computedArea.xyzw and computedAreaUncut.xyzw)
*/
void _UnityInternalGetAreaPerTexel_3TexelsWideTriangleFilter(float offset, out float4 computedArea, out float4 computedAreaUncut)
{//Compute the exterior areasfloat offset01SquaredHalved = (offset + 0.5) * (offset + 0.5) * 0.5;computedAreaUncut.x = computedArea.x = offset01SquaredHalved - offset;computedAreaUncut.w = computedArea.w = offset01SquaredHalved;//Compute the middle areas//For Y : We find the area in Y of as if the left section of the isoceles triangle would//intersect the axis between Y and Z (ie where offset = 0).computedAreaUncut.y = _UnityInternalGetAreaAboveFirstTexelUnderAIsocelesRectangleTriangle(1.5 - offset);//This area is superior to the one we are looking for if (offset < 0) thus we need to//subtract the area of the triangle defined by (0,1.5-offset), (0,1.5+offset), (-offset,1.5).float clampedOffsetLeft = min(offset,0);float areaOfSmallLeftTriangle = clampedOffsetLeft * clampedOffsetLeft;computedArea.y = computedAreaUncut.y - areaOfSmallLeftTriangle;//We do the same for the Z but with the right part of the isoceles trianglecomputedAreaUncut.z = _UnityInternalGetAreaAboveFirstTexelUnderAIsocelesRectangleTriangle(1.5 + offset);float clampedOffsetRight = max(offset,0);float areaOfSmallRightTriangle = clampedOffsetRight * clampedOffsetRight;computedArea.z = computedAreaUncut.z - areaOfSmallRightTriangle;
}

這個公式后面會給出詳細的證明。
然后計算四個劃分的面積占總面積的多少，由于等腰直角三角形的底是3，高為1.5，所以面積是9/4，求權重比，對應的代碼是：

/*** Assuming a isoceles triangle of 1.5 texels height and 3 texels wide lying on 4 texels.* This function return the weight of each texels area relative to the full triangle area.*/
void _UnityInternalGetWeightPerTexel_3TexelsWideTriangleFilter(float offset, out float4 computedWeight)
{float4 dummy;_UnityInternalGetAreaPerTexel_3TexelsWideTriangleFilter(offset, computedWeight, dummy);computedWeight *= 0.44444;//0.44 == 1/(the triangle area)
}

此時得到了水平方向的四個權重，然后我們同樣的方法得到垂直方向的四個權重，然后咋辦？
在這里插入圖片描述
我們可以把x和y兩個看成連續的塊，然后把z和w看成連續的塊，然后對應代碼：

    // each fetch will cover a group of 2x2 texels, the weight of each group is the sum of the weights of the texelsfloat2 fetchesWeightsU = texelsWeightsU.xz + texelsWeightsU.yw;

于是fetchesWeightU.x = texelsWeightsU.x + texelsWeightsU.y
fetchesWeightU.y = texelsWeightsU.z + texelsWeightsU.w
然后，就是計算y占(x+y)的百分比，w占(z+w)的百分比

    // move the PCF bilinear fetches to respect texels weightsfloat2 fetchesOffsetsU = texelsWeightsU.yw / fetchesWeightsU.xy + float2(-1.5,0.5);

fetchesOffsetsU.x = texelsWeightsU.y / (texelsWeightsU.x + texelsWeightsU.y)
fetchesOffsetsU.y = texelsWeightsU.w / (texelsWeightsU.z + texelsWeightsU.w)
這樣就得到的fetchesOffsetsU，是大于等于0的偏移，所以為了得到相對的偏移得歸一化到起點。
在這里插入圖片描述
如上圖粉色框框起來的x和y點，其水平起點為三角形的底/2，取負，所以是-1.5

而又因為是相鄰每兩個像素的歸一化，所以綠色框住的起點是-1.5+2=0.5，于是得到上面的偏移：+float2(-1.5,0.5);
同樣的垂直方向上也是類似的計算方式，最終我們得到了：

// move the PCF bilinear fetches to respect texels weightsfloat2 fetchesOffsetsU = texelsWeightsU.yw / fetchesWeightsU.xy + float2(-1.5,0.5);float2 fetchesOffsetsV = texelsWeightsV.yw / fetchesWeightsV.xy + float2(-1.5,0.5);

然后我們將轉換到(0,1)的范圍，直接乘以：

    fetchesOffsetsU *= _ShadowMapTexture_TexelSize.xx;fetchesOffsetsV *= _ShadowMapTexture_TexelSize.yy;

這里的_ShadowMapTexture_TexelSize的x、y、z、w分量分別是陰影貼圖的水平像素個數倒數，垂直像素個數倒數，水平像素個數，垂直像素個數。
然后就是去采樣了：

    // fetch !float2 bilinearFetchOrigin = centerOfFetchesInTexelSpace * _ShadowMapTexture_TexelSize.xy;shadow =  fetchesWeightsU.x * fetchesWeightsV.x * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.x, fetchesOffsetsV.x), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.y * fetchesWeightsV.x * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.y, fetchesOffsetsV.x), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.x * fetchesWeightsV.y * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.x, fetchesOffsetsV.y), coord.z, receiverPlaneDepthBias));shadow += fetchesWeightsU.y * fetchesWeightsV.y * UNITY_SAMPLE_SHADOW(_ShadowMapTexture, UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.y, fetchesOffsetsV.y), coord.z, receiverPlaneDepthBias));
#endif

float2 bilinearFetchOrigin = centerOfFetchesInTexelSpace * _ShadowMapTexture_TexelSize.xy;
是p點，就是要處理的點。
然后就是：
UnityCombineShadowcoordComponents(bilinearFetchOrigin, float2(fetchesOffsetsU.x, fetchesOffsetsV.x), coord.z, receiverPlaneDepthBias)
這個函數

/**
* Combines the different components of a shadow coordinate and returns the final coordinate.
* See UnityGetReceiverPlaneDepthBias
*/
float3 UnityCombineShadowcoordComponents(float2 baseUV, float2 deltaUV, float depth, float3 receiverPlaneDepthBias)
{float3 uv = float3(baseUV + deltaUV, depth + receiverPlaneDepthBias.z);uv.z += dot(deltaUV, receiverPlaneDepthBias.xy);return uv;
}

baseUV + deltaUV，就是進行uv的偏移。然后z值，可以uv和陰影bias點乘，加到z上，最終得到一個三維的采樣坐標。
最終：fetchesWeightsU.x * fetchesWeightsV.x * UNITY_SAMPLE_SHADOW
得到一個點的權重，然后分別做四次即可，得到四個方向上的陰影貢獻值，即可得到最后軟陰影效果了。