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UCSD CSE 168 - Lecture

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CSE168Computer Graphics II, RenderingSpring 2006Matthias ZwickerFinal projectRender an awe-inspiring image• Soft shadows• Path tracing• Photon mapping• Illumination from an environment map• Subsurface scattering• Motion blur, depth of field• Procedural modeling, smoke, waterFinal projectPrevious years• See web pageshttp://graphics.ucsd.edu/courses/rendering/2003/, /2004, /2005Final projectOrganization• Work out project description, due next Wednesday May 24• Groups up to 3 students possible, but need to define individual contributions explicitly for individual grading• Project presentation Monday June 12, 7pmFinal projectPrizes• First prize: $1000 contribution to a trip to SIGGRAPH• Grand prize: $100 gift certificate for books• Honorable mention: $50 gift certificate for booksLast time• Explanation of cosine terms in photon transport• Photon mapping rendering algorithmsCosine termsPath tracing Photon tracingPhoton mapping algorithmRecap• Emit and transport photons• Build data structure for fast access• Use stored photons to estimate reflected radianceGlobal illumination[Wann Jensen]100000 photons, 50 photons in radiance estimateVisualization of the photons[Wann Jensen]Global illumination[Wann Jensen]500000 photons, 500 photons in radiance estimatePhotons for indirect illumination[Wann Jensen]10000 photons, 500 photons in radiance estimateSplitting up the reflection equation• Reflection equation•Split up BRDF• Split up incoming radiancePhoton maps• Three photon maps, one for each illumination term–Direct– Indirect diffuse– Caustic (indirect specular)• Finite state machine to keep track of photon typeDirect illumination[Wann Jensen]•Sample light sourcesSpecular reflection[Wann Jensen]• Path tracingCaustics[Wann Jensen]• Radiance estimation using caustic photon mapReflections inside a ring50000 photons, 50 photons for radiance estimationDiffuse indirect illumination[Wann Jensen]Final gathering• Path tracing, final gathering using all three photon maps, radiance estimation using indirect photonsToday• Irradiance caching• RadiosityDiffuse indirect illumination• Path tracing: slow• Final gathering using all three photon maps: slow• Radiance estimation using indirect photons: inaccurate for reasonable number of photons• Other ideas?Global illumination[Wann Jensen]Indirect irradiance[Wann Jensen]Indirect irradiance[Humphreys, Pharr]Indirect irradiance• Changes very smoothly on diffuse surfaces, except for causticsIrradiance caching• “A ray tracing solution for diffuse interreflection”, Ward, Rubinstein, Clear, SIGGRAPH 88• Assume diffuse surfaces• Cache irradiance samples instead of incident radiance as in photon mapping• Interpolate cached samples• Compute new samples only if interpolation failsIrradiance caching algorithmThree components• Irradiance sampling• Irradiance caching• Irradiance interpolation• Similar to photon mapping, but all steps are performed in main rendering passIrradiance samplingIrradiance sampling• Stratified sampling of the hemisphere• Subdivision T,P, uniform random variablesIrradiance samplingIrradiance sampling• Compute using path tracing or photon gathering at the first hit point• For good quality expect tracing 200-5000 paths • Costly, but we will do this only at few locations in the imageIrradiance sampling• Assign a range for each sample, within which it can be used for interpolation• Where irradiance changes quickly, range should be small• Where irradiance changes slowly, range should be large• Rate of change of irradiance depends on distance to visible surfacesIrradiance sampling[Wojciech Jarosz]Irradiance samplingHarmonic mean heuristics• The range is given by a radiuswhere is the number of paths, is the distance to the first intersection along the path• Average would weight infinite distances too heavilyIrradiance cachingstruct irradiance_sample {vector3 E // irradiancevector3 n // normalvector3 p // positionfloat r // range}Irradiance sampleIrradiance caching•Store samples in octree• Add sample to each cell that it overlaps• Adaptively subdivide octree such that each cell has limited number of samplesIrradiance cachingOctree example• Adaptive subdivision such that each cell contains <3 samplesIrradiance sampleSample rangeIrradiance interpolation• Need to determine which samples should be used for interpolationError estimate• Given a point on the surface with normal , estimate the difference to the irradiance cached atIrradiance interpolationError estimate• Ad-hoc estimate for error of sample differencein positiondifference inorientationIrradiance interpolation• Interpolation weights• Interpolated irradianceIrradiance caching algorithmW = 0for( all irradiance samples j in octree cell overlapping with x ) {compute weight w_jif( <sample is valid> ) {W += w_j; wE += w_j*E[j]}}if( W > 0 ) {return wE/W} else {return( compute new irradiance sample )}Irradiance caching algorithm<sample is valid> =dist( x – x[j] ) < r[j] // within range && w_j > 1/a // sufficient weight && dot( x[j] - x, n(x) ) < 0 // x[j] is behind xSample at is invalidNon-diffuse surfacesApproximationNon-diffuse surfacesApproximationHemispherical directional reflectancePhoton mapping and irradiance caching• Caustics break assumptions of irradiance caching• Exclude caustic paths from irradiance samplingAdvanced technique• Use photon map for importance sampling during path tracingIrradiance caching examples[Wann Jensen]1000 sample rays, w>10Irradiance caching examples[Wann Jensen]1000 sample rays, w>10Irradiance caching examples[Wann Jensen]1000 sample rays, w>20Irradiance caching examples[Wann Jensen]1000 sample rays, w>20Irradiance caching examples[Wann Jensen]5000 sample rays, w>10Irradiance caching examples[Wann Jensen]5000 sample rays, w>10Irradiance caching[Humphreys, Pharr]Irradiance caching example[Humphreys, Pharr]Path tracing[Humphreys, Pharr]Approx. same amount of computationNext


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