IndireIndirecct Diffuse and Glossy t Diffuse and Glossy Illumination on the GPUIllumination on the GPU

István Lazányi László Szirmay-Kalos

TU Budapest

Environment mappingfor ideal reflections

[Blinn & Newel, 1976]

Environment map = Fast approximation of environmental effects

If the environment is very (or infinitely) far…

skybox

Environment mappingfor ideal reflections

(enlarged)

(original)

re-render environment map from the new reference

point

If the environment is "close"…

performance ?!

Environment mappingfor ideal reflections

Note: (classic) environment mapping cannot deal with "large" objects

[Approximate Ray-Tracing…, Eurographics 2005]

ray-traced

Environment mappingfor ideal reflections

storing depth information

in the environment map

Ideal reflection vs. indirect illumination:

Adding cosine-weighted contributions:

Environment mappingfor diffuse & glossy reflections - classical

many sampling rays

are necessary!

= convolution

Offline convolution:

preconvolved diffuse/specular map

1. Take an environment map (with depth info. in the alpha channel)

where Δωi (i=1..N) corresponds to the texels of the environment map

ωi = ? from a point x

Environment mappingfor diffuse & glossy reflections – our proposal

2. Evaluate the convolution integral on the fly

Environment mappingfor diffuse & glossy reflections – our proposal

solid angles Δωi can easily be calculated

(no information is necessary about the environment! )

For the reference point:

cosine value is approx. the same

as in the reference point

Environment mappingfor diffuse & glossy reflections – our proposal

distance r’ is known

but cosθ’ is unknown

For an arbitrary point x:

to calculate solid angle Δωi

Instead of storing orientation information about the environment,

assume that the movement is small

Thus, localization means multiplying solid angle with a factor for each texel

precalculation of the convolution integral is not possible

Environment mappingfor diffuse & glossy reflections – our proposal

How about the bunny …?

?

To allow real-time calculation the environment map is downsampled by averaging neighboring texels.

(e.g. 128 x 128 4 x 4)

≈ clustering the texels of the environment into larger area lights

Environment mappingfor diffuse & glossy reflections – our proposal

Results(Diffuse bunny)

classical our proposal (75FPS @ 2x2, 20FPS @ 4x4)

Results(Glossy bunny, s=10)

classical our proposal

Implementation

float4 Lin = texCUBE(LREnvMap, I) ;

float r = texCUBE(LREnvMap, I).a ;

float3 L = r * I – pos ;

float r’ = length(L);

float dw = dw_texel * r2 / r’2

//Illumination formula for N,V,L

L = L / |L|;

float a = kd * max(dot(N, L), 0)

(or texture lookup)

return Lin * a * dw;

Question time!