Global Illumination. Global Illuminaton. Ray Tracing. Ray Tracing. Rendering Equation. Rendering Equation

Transcription

1 Glbal Illuminatn Glbal Illuminatin Adam Finkelstein & Tim Weyrich Princetn University COS 426, Spring Ray Tracing Trace secndary rays frm hit surfaces in directins f specular reflectin and refractin Ray Tracing Assume nly significant indirect illuminatin is frm specular reflectin and refractin Light Camera 3 4 Rendering Equatin Cmpute radiance in utging directin by integrating reflectins ver all incming directins Light Camera Rendering Equatin Cmpute radiance in utging directin by integrating reflectins ver all incming directins Light Camera 5 6

2 Rendering Equatin Rendering Equatin (2) Kajiya 1986 Kajiya Challenge Rendering integrals are difficult t evaluate Multiple dimensins Discntinuities! Partial ccluders! Highlights! Caustics Challenge Rendering integrals are difficult t evaluate Multiple dimensins Discntinuities! Partial ccluders! Highlights! Caustics Drettakis Jensen 9 10 Overview Glbal illuminatin Rendering equatin Slutin methds Sampling! Distributin ray tracing! Mnte Carl path tracing! Bidirectinal path tracing Discretizatin! Radisity Overview Glbal illuminatin Rendering equatin Slutin methds " Sampling! Distributin ray tracing! Mnte Carl path tracing! Bidirectinal path tracing Discretizatin! Radisity 11 12

3 Distributin Ray Tracing Ray Tracing vs. Distributin Ray Tracing Estimate integral fr each reflectin by sampling incming directins Ray tracing Distributin ray tracing Mnte Carl Path Tracing Ray Tracing vs. Path Tracing Estimate integral fr each pixel by sampling paths frm camera Camera where Ray tracing Path tracing Kajiya Bidirectinal Path Tracing Tracing Frm Eye Rle f surce and receiver can be switched 17 18

4 Tracing frm Lights Bidirectinal Path Tracing Bidirectinal Path Tracing Overview Glbal illuminatin Rendering equatin (RenderPark 98) Slutin methds Sampling! Distributin ray tracing! Mnte Carl path tracing! Bidirectinal path tracing Discretizatin! Radisity Radisity Rendering Equatin (2) Indirect diffuse illuminatin LD*E Kajiya

5 Radisity Equatin Radisity Apprximatin Assume everything is Lambertian Discretize the surfaces int elements Cnvert t Radisities where Radisity Apprximatin System f Equatins This is an energy balance equatin Radisity Issues Cmputing frm factrs Selecting basis functins fr radisities Slving linear system f equatins Meshing surfaces int elements Rendering images Radisity Issues Cmputing frm factrs Selecting basis functins fr radisities Slving linear system f equatins Meshing surfaces int elements Rendering images 29 30

6 Frm Factr Fractin f energy leaving element i that arrives at element j Beynd Diffuse Reflectin? Radisity Issues Cmputing frm factrs Selecting basis functins fr radisities Slving linear system f equatins Meshing surfaces int elements Rendering images Slving the System f Equatins Challenges: Size f matrix Cst f cmputing frm factrs Cmputatinal cmplexity A x = b Slving the System f Equatins Slutin methds: Invert the matrix O(n 3 ) Iterative methds O(n 2 ) Hierarchical methds O(n) Gauss-Seidel Iteratin A x = b 35 36

7 Gauss-Seidel Iteratin Tw interpretatins: Iteratively relax rws f linear system Iteratively gather radisity t elements Gauss-Seidel Iteratin Tw interpretatins: Iteratively relax rws f linear system Iteratively gather radisity t elements Prgressive Radisity Interpretatin: Iteratively sht unsht radisity frm elements Select shters in rder f unsht radisity Prgressive Radisity Adaptive refinement Yeap Prgressive Radisity Prgressive Radisity 41 42

8 Hierarchical Radisity Hierarchical Radisity Estimate errrs, refine elements if t large Chen & Wallace 43 Radisity Meshing Issues 44 Stre radisity acrss surface Few elements Represents functin well Few visible artifacts Cmputing frm factrs Selecting basis functins fr radisities Slving linear system f equatins Meshing surfaces int elements Rendering images Chen & Wallace 45 Artifacts f Bad Meshing 46 Adaptive Meshing Refine mesh in areas f high residual Yeap Chen & Wallace 47 48

9 Adaptive Meshing Unifrm mesh Adaptive Meshing Adaptive mesh (table tp frm different angle) Chen & Wallace 49 Discntinuity Meshing 50 Discntinuity Meshing Capture discntinuities in radisity acrss a surface with explicit mesh bundaries Capture discntinuities in radisity acrss a surface with explicit mesh bundaries Discntinuity Mesh Lischinski et al. 51 Summary Glbal illuminatin Rendering equatin Slutin methds Sampling! Distributin ray tracing! Mnte Carl path tracing! Bidirectinal path tracing Discretizatin! Radisity Phtrealistic rendering with glbal illuminatin is an integratin prblem 53 Lischinski et al. 52