adaptive mesh subdivision for precomputed radiance transfer jaroslav křivánek univ. of central...
TRANSCRIPT
![Page 1: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/1.jpg)
Adaptive Mesh Subdivision for Precomputed Radiance Transfer
Jaroslav KřivánekUniv. of Central Florida
CTU Prague
IRISA – INRIA Rennes
Sumanta Pattanaik
Univ. of Central Florida
Jiří ŽáraCTU Prague
ComputerGraphicsGroup
![Page 2: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/2.jpg)
Goal Decrease the interpolation Error
uniform adaptive
![Page 3: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/3.jpg)
Overview Precomputed Radiance Transfer Transfer Operator Sampling Density Subdivision algorithm Triangle error estimate Conclusion
![Page 4: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/4.jpg)
Precomputed Radiance Transfer (PRT)
Restrictions Low-frequency directional lighting
Soft shadows only Per-vertex precomputation
Rigid objects only
Precompute global illumination (per-vertex)
Display GI in real-time under arbitrary lighting
![Page 5: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/5.jpg)
PRT Terminology
![Page 6: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/6.jpg)
PRT Terminology
![Page 7: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/7.jpg)
PRT Terminology
![Page 8: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/8.jpg)
PRT for Diffuse Surfaces
lt ppL )(
Lp … exit radiance at point p (displayed intensity) l … light vector (in SH basis) tp … source-to-exit transfer vector at p
Computed in preprocess Stored per-vertex or per-texel
Non-adaptively
![Page 9: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/9.jpg)
no abrupt change of tp
Transfer Vector
Abrupt changes of tp
Possible abrupt changes of Lp
l1
l2
abrupt change of tp
![Page 10: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/10.jpg)
Our Goal Refined
Adaptive Sampling of tp, subject to
visual error under any lighting is minimized,
# of samples of tp (i.e. # verts) is nimimized
Per-vertex tp adaptive mesh subdivision Subdivision in pre-process
Along with the pre-computation of tp Actual lighting Lp is not known
Subdivision based only on tp, not on Lp
![Page 11: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/11.jpg)
Adaptive Sampling Example
200 verts246 tris
1565 verts2548 tris
1188 verts2828 tris
![Page 12: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/12.jpg)
Adaptive Sampling Example
200 verts246 tris
1565 verts2548 tris
1188 verts2828 tris
![Page 13: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/13.jpg)
Subdivision Algorithm Initial mesh Compute tp for vertices of the initial mesh Compute error estimate for the triangles of the
initial mesh Subdivide according to the error estimate Proceed recursively (priority queue), until
triangle budget is met
![Page 14: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/14.jpg)
Ideal Error Estimate Ideal error estimate for triangle
Error = maximum relative deviation of the interpolated exit radiance from the correct exit radiance over all unit power lighting l and all triangle points x.
Or rather: one of possible ‘ideal error estimates’ other possibilities
avg instead of max ? smoothness of the Gouraud interpolation instead of deviation
from the correct value ?
),(|),(),(| int
,1||||max lxL
lxLlxLxl
![Page 15: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/15.jpg)
Practical Error Estimate (1) Subdivision in preprocess
Error estimate based uniquely on tp Triangle error = Sum edge errors First edge error estimate (triangle edge v1-v2)
Development of (1) from the ‘ideal e. e.’ given in the paper
||||||||2
2),(
1
121
vv
vvvv
tttt
(1)
![Page 16: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/16.jpg)
Results with Error Estimate (1)
Too much subdivision in shadowed areas.
is low is high.|||| 21 vv tt ||||||||2
2
1
1
vv
vv
tttt
![Page 17: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/17.jpg)
Error Estimate (2) Division by promotes subdivision in
shadowed areas. Solution: remove the division by .
New error estimate:
|||| 21 vv tt
|||| 21 vv tt
|||| 2),( 121 vvvv tt (2)
![Page 18: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/18.jpg)
Results with Error Estimate (2)
||||||||2
2),(
1
121
vv
vvvv
tttt
worse
|||| 2),( 121 vvvv tt
Better subdivision around the box / box faces.
better
![Page 19: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/19.jpg)
Problems with Error Estimate (2) Works fine for flat surfaces Exaggerated on curved surfaces
![Page 20: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/20.jpg)
Rectified Error Estimate for Curved Surfaces
Divide by the angle between the normals at v1 and v2.
)arccos(1||||
21),(
2121
nntt
vv
vv (3)
![Page 21: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/21.jpg)
Conclusion Adaptive subdivision
Decreased interpolation error Superior quality compared to uniform
subdivision Subdivision performed in preprocess
no dynamic subdivision in real-time Based on a worst error estimate
![Page 22: Adaptive Mesh Subdivision for Precomputed Radiance Transfer Jaroslav Křivánek Univ. of Central Florida CTU Prague IRISA – INRIA Rennes Sumanta Pattanaik](https://reader035.vdocuments.us/reader035/viewer/2022062312/551b5729550346ae7a8b55cb/html5/thumbnails/22.jpg)
Discussion + Future Work Drawbacks
Final error estimate is a pure heuristic Requires a lot of tweaking to get good results The absolute value of the error estimate is
meaningless Only the ordering is ok
Future Work Extend to arbitrary BRDFs Use textures instead of vertices Perceptually based