Appearance-Preserving Simplification

Transcription

1 Appearance-Preserving Simplification

2 7809 tris 975 tris 488 tris 1951 tris 3905 tris model courtesy of Stanford and Caltech

3 Simplification Create representation for faster rendering Measure representation quality Allow speed-fidelity tradeoff

4 Appearance Preservation Preserve three appearance attributes: Surface Position Surface Curvature Material Color Each may require different sampling

5 Example - normals undersampled 13,433 triangles 1,749 triangles 10 pixels of surface deviation

6 Example - normals properly sampled 13,433 triangles 1,749 triangles, 10 pixels of deviation

7 Talk Organization Overview Creating Maps Texture Error Metric Implementation and Results Conclusions

8 Traditional Polygonal Representation v 2, c 2, n 2 v 3, c 3, n 3 v 1, c 1, n 1 v = vertex coordinate = (x,y,z) c = color = (r,g,b) n = normal = (n x,n y,n z )

9 Traditional Simplification Filters surface position, colors, and normals Must filter all three equally

10 Decoupled Representation v 2, t 2 texture map c 3 c 2 c 1 v 1, t 1 v 3, t 3 v = vertex coordinate = (x,y,z) t = texture coordinate = (u,v) c = color = (r,g,b) n = normal vector = (n x,n y,n z ) normal map n 2 n 3 n 1

11 Decoupled Approach Simplification filters surface position and texture coordinates Color and normal attributes filtered per-pixel (mip-mapping, etc.)

12 Simplification System Architecture Polygonal Surface Representation Conversion Surface Parameterization Map Creation Simplification Surface Approximation Texture Deviation Metric Levels of Detail Texture and Normal Maps

13 Talk Organization Overview Creating Maps Texture Error Metric Implementation and Results Conclusions

14 Creating Maps Resampling Process Scan-convert polygons into map Store color or normal attribute at pixels

15 Sample Normal Map polygonal surface patch normal map

16 Talk Organization Overview Creating Maps Texture Error Metric Implementation and Results Conclusions

17 Error Sources Effects on Image Simplification of vertex coordinates Silhouette deviation Simplification of texture coordinates Texture deviation (distortion) Attribute mip-mapping Overblurring of attributes

18 Texture Deviation Metric Distance between corresponding 3D points Same 2D texture coordinates Projects at run time to 2D pixel deviation Intuitive error tolerance specification Pixels of deviation for both surface position and texture error!

19 Point Correspondence mesh M i (i+1) st edge collapse mesh M i+1 X i X i+1 x P 2D texture domain e i,i+1 (x) = X i+1 - X i E i,i+1 = max e i,i+1 (x) x P

20 Measuring Texture Deviation Texture deviation is piecewise-linear distance function Extrema occur at vertices and edge intersections in 2D texture domain Check only these extrema to find maximum

21 Mapping in Texture Domain = extrema of texture deviation function

22 Video Example Constraining Texture Distortion

23 Lion s Tail 1,743 tris 108 tris 434 tris original mesh only surface deviation measured surface and texture deviation measured 3 pixels of screen-space deviation

24 Talk Organization Overview Creating Maps Texture Error Metric Implementation and Results Conclusions

25 Simplification Preprocess Parameterize and create maps Priority queue of edge collapses 3D surface deviation used to compute new vertex 3D texture deviation determines edge priority Generate LODs with 3D texture error metric

26 Simple Viewer Application User specifies 2D error tolerance in pixels For each object Determine viewing distance Compute bound on 3D tolerance Choose LOD: 3D error < 3D tolerance Use custom normal map shader on PixelFlow

27 Results - Preprocess Torus 79,202 triangles 4.4 mins Lion 86,844 triangles 7.4 mins Armadillo 2,040,000 triangles 190 mins Timings run on MIPS R10000 processor

28 Results - Viewer Trivial overhead for run-time LOD selection

29 Video Demonstration Appearance-Preserving Simplification: The Armadillo Model

30 Armadillo Model model courtesy of Stanford / Cal Tech 1 M triangles 7,800 triangles 7,800 triangles 16 pixels of deviation

31 Talk Organization Overview Creating Maps Measuring Error Implementation and Results Conclusions

32 Hardware Requirements Texture and normal (or bump) map capability Bandwidth for attribute map lookups Per-pixel lighting computation Currently implemented on PixelFlow Coming soon to more commercial hardware

33 Normal Map vs. Bump Map Normal map Absolute normals in object space Constant as object is simplified Same normal map okay for all LODs Bump map Perturbations of triangle normal Changes as object is simplified Need different bump map for each LOD

34 Is This Really Simplification? YES!! Rasterization cost greatly reduced Shading cost depends only on screen resolution (and depth complexity)

35 Contributions Use of decoupled representation for simplification New texture deviation metric Intuitive error tolerance specification Simplification that preserves shaded appearance

36 Future Work Application to view-dependent simplification Parameterizations for better attribute filtering Handling of more degenerate models

37 Related Work - Representation Parameterization Lee et al. 98 Krishnamurthy/Levoy 96 Eck et al. 95 Maillot et al. 93 Kent et al. 92 Graph Drawing Battista et al. 94 Fraysseix 90 Chiba et al. 85 Attribute Maps Peercy et al. 97 Becker and Max 93 Fournier 92 Cabral et al. 87 Kajiya 85 Cook 84 Williams 83 Blinn 78 Catmull 74

38 Related Work - Simplification Surface Deviation Garland/Heckbert 97 Bajaj/Schikore 96 Cohen/Varshney et al. 96 Klein et al. 96 Ronfard/Rossignac 96 Guéziec 95 Kalvin/Taylor 94 Hoppe 93 Rossignac/Borrel 93 Attributes Erikson/Manocha 98 Bastos et al. 97 Xia et al. 97 Klein 97 Certain et al. 96 Hoppe 96 Hughes et al. 96

39 Acknowledgments Stefan Gottschalk Lifeng Wang and Xing Xing Computer Peter Schröder Stanford Computer Graphics Laboratory UNC Walkthrough Project UNC PixelFlow Project Hewlett Packard Visualize PxFl Team

40 Acknowledgments Army Research Office Defense Advanced Research Project Agency Intel National Science Foundation National Institutes of Health Office of Naval Research Alfred P. Sloan Foundation