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4.2 Multisampling Extension for Gradient Shadow Maps

ohyecloudyhttp://ohyecloudy.com

shader study http://cafe.naver.com/shader.cafe

2010.5.24

Overview of Gradient Shadow Maps

Multisampling and PCF

Merging the Algorithms

Optimizing Texture Look-ups

Conclusion

• Slope-scale depth bias

– gradient를 depth bias에 사용

• Fuzzy depth comparison

– 1 or 0이 아니라 0~1 값을 쓴다.

• Linearly filtered depth values

– point 샘플링이 아니라 보간 해서 사용.

• 예) bilinear filter

float lightVisibility_GSM(float3 lightCoord)

{

// get the magnitude of the gradient, by either method

float gradient = length(getGradientVector(lightCoord));

// get the difference between stored and interpolated depth

// (depthMap should have LINEAR filtering enabled)

float diff = tex2D(depthMap, lightCoord.xy).x – lightCoord.z;

// replace the less-than operator with a smooth function

// for diff >= 0 the result is 1

return saturate(diff/gradient + 1);

}

Overview of Gradient Shadow Maps

Multisampling and PCF Merging the Algorithms

Optimizing Texture Look-ups

Conclusion

float lightVisibility_PCF(float3 ligthCoord)

{

float result = 0;

for (int i = 0; i < n; ++i)

{

float3 offCoord = lightCoord + offset[i];

result +=

lightCoord.z <

tex2D(depthMap, offCoord.xy).x;

}

return result / n;

}

Overview of Gradient Shadow Maps

Multisampling and PCF

Merging the Algorithms Optimizing Texture Look-ups

Conclusion

float lightVisibility_PCF_with_GSM(float3 lightCoord)

{

float result = 0;

for (int i = 0; i < n; ++i)

{

result +=

lightVisibility_GSM(lightCoord + offset[i]);

}

return result / n;

}

incident light

surface

shadow volume

PCF area

incident light

surface

shadow volume

PCF area

float lightVisibility_GSM_modified(float3 lightCoord, float2 offset) { // get the gradient, by either method float2 gradientVector = getGradientVector(lightCoord); float gradient = length(gradientVector); // calculate an offset coordinate // the z coord is moved along with the local gradient // (this is equivalent to having a local plane equation) float3 offCoord = float3( lightCoord.xy + offset, lightCoord.z + dot(offset, gradientVector)); // the rest is straightforward float diff = offCoord.z – tex2D(depthMap, offCoord.xy).x; return saturate(diff/gradient + 1); }

Overview of Gradient Shadow Maps

Multisampling and PCF

Merging the Algorithms

Optimizing Texture Look-ups Conclusion

• depth map에 scalar depth 저장했을 때

– gradient vector : texture loockup 3번

• 추가로 depth sampling 한번, PCF에서 4번

• 전체 PCF 영역에서 평균 gradient를 근사

–최소 제곱 근사값least squares approximation을 찾기 위한 선형회귀linear regression

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공(共)분산 행렬 covariance matrix

yx 제거

float lightVisibility_unrolled_circluar8(float3 lightCoord)

{

const float displace = .5 / depthMapResolution;

const float displaceLong = 1.41421 * displace;

float depths[8] = {

tex2D(depthMap, lightCoord.xy + float2(-displaceLong,0)).x,

tex2D(depthMap, lightCoord.xy + float2(displaceLong,0)).x,

tex2D(depthMap, lightCoord.xy + float2(0,-displaceLong)).x,

tex2D(depthMap, lightCoord.xy + float2(0,displaceLong)).x,

tex2D(depthMap, lightCoord.xy + float2(-displaceLong,-displaceLong)).x,

tex2D(depthMap, lightCoord.xy + float2(displaceLong,-displaceLong)).x,

tex2D(depthMap, lightCoord.xy + float2(-displaceLong, displaceLong)).x,

tex2D(depthMap, lightCoord.xy + float2(displaceLong, displaceLong)).x };

const float inverseCovariance = 1. / (1 + 1+ 2);

float2 gradientVector = float2(

depths[1] * 1.41421 + depths[5] + depths[7]

-depths[0] * 1.41421 – depths[4] – depths[6],

depths[3] * 1.41421 + depths[6] + depths[7]

-depths[2] * 1.41421 – depths[4] – depths[5] ) *

inverseCovariance;

// continue with summation over PCF samples

// using the average gradient

}

8 PCF samples

Overview of Gradient Shadow Maps

Multisampling and PCF

Merging the Algorithms

Optimizing Texture Look-ups

Conclusion

• ShaderX4에서 봤던 Acne 제거 기술 복습

– Slope-scale depth bias,

– Fuzzy depth comparison,

– Linearly filtered depth values

• 추가로 부드러운 그림자 가장자리(edge)를 만들기 위한 기술

– PCF

–샘플링 회수를 줄이기 위한 근사