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Advanced Techniques in Geometry Image Processing for 3D Rendering

This work presents innovative methods for processing irregular meshes and enhancing 3D graphics rendering. By employing semi-regular representations and a detailed cutting algorithm, we achieve efficient parametrization and optimized geometry sampling. The proposed approach minimizes texture coordinates and vertex indices, facilitating compact rendering and reducing computational artifacts. Through the integration of mip-mapping, hierarchical culling, and wavelet-based compression, we demonstrate significant improvements in rendering speed and quality. Future research directions include refining cutting algorithms and exploring feature-sensitive techniques.

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Advanced Techniques in Geometry Image Processing for 3D Rendering

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  1. Geometry Images Xianfeng Gu Harvard University Steven Gortler Harvard University Hugues Hoppe Microsoft Research

  2. Irregular meshes Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 …

  3. Texture mapping Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 … s1 t1 s2 t2 t normal map s

  4. Complicated rendering process Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 2 1 3 Face 4 2 3 … s1 t1 s2 t2 random access! random access! ~40M Δ/sec

  5. Semi-regular representations [Eck et al 1995] [Lee et al 1998] [Khodakovsky 2000] [Guskov et al 2000] … only semi-regular irregular vertex indices

  6. Geometry Image completely regular sampling 3D geometry geometry image257 x 257; 12 bits/channel

  7. Basic idea cut parametrize demo

  8. Basic idea cut sample

  9. Basic idea cut store render [r,g,b] = [x,y,z]

  10. How to cut ? 2D surface disk sphere in 3D

  11. How to cut ? • Genus-0 surface  any tree of edges 2D surface disk sphere in 3D

  12. How to cut ? • Genus-g surface  2g generator loops minimum torus (genus 1)

  13. Surface cutting algorithm (1) Find topologically-sufficient cut: 2g loops[Dey and Schipper 1995] [Erickson and Har-Peled 2002] (2) Allow better parametrization: additional cut paths[Sheffer 2002]

  14. Step 1: Find topologically-sufficient cut (a) retract 2-simplices (b) retract 1-simplices

  15. Results of Step 1 genus 6 genus 3 genus 0

  16. Step 2: Augment cut • Make the cut pass through “extrema” (note: not local phenomena). • Approach: parametrize and look for “bad” areas.

  17. Step 2: Augment cut …iterate while parametrization improves

  18. Results of Steps 1 & 2 genus 1 genus 0

  19. Parametrize boundary Constraints: • cut-path mates identical length • endpoints at grid points a a’ a’ a  no cracks

  20. Parametrize interior • optimizes point-sampled approx. [Sander et al 2002] • Geometric-stretch metric • minimizes undersampling [Sander et al 2001]

  21. Stretch parametrization Previous metrics (Floater, harmonic, uniform, …)

  22. Sample geometry image

  23. Rendering (65x65 geometry image)

  24. Rendering with attributes geometry image 2572 x 12b/ch normal-map image 5122 x 8b/ch rendering

  25. Advantages for hardware rendering • Regular sampling  no vertex indices. • Unified parametrization  no texture coordinates. Raster-scan traversal of source data: geometry & attribute samples in lockstep. Summary: compact, regular, no indirection

  26. Normal-Mapped Demo geometry image129x129; 12b/ch normal map512x512; 8b/ch demo

  27. Pre-shaded Demo geometry image129x129; 12b/ch color map512x512; 8b/ch demo

  28. Results 257x257 normal-map 512x512

  29. Results 257x257 color image 512x512

  30. boundary constraintsset for size 65x65 Mip-mapping 257x257 129x129 65x65

  31. Hierarchical culling view-frustum culling geometry image backface culling normal-map image

  32. Compression Image wavelet-coder 295 KB  1.5 KB fused cut + topological sideband (12 B)

  33. Compression results 295 KB  1.5 KB 3 KB 12 KB 49 KB

  34. Rate distortion

  35. Some artifacts aliasing anisotropic sampling

  36. Summary • Simple rendering: compact, no indirection, raster-scan stream. • Mipmapped geometry • Hierarchical culling • Compressible

  37. Future work • Better cutting algorithms • Feature-sensitive remeshing • Tangent-frame compression • Bilinear and bicubic rendering • Build hardware

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