Mesh colors

1. Mesh Colors Author: Cem Yuksel , John Keyser & Donald House Texas A&M University SIGGRAPH 2010 Speaker: Chung-Yuan Lee Yuan- Ze University

2. O utline Introduction Previous method Proposed method Mesh color Filtering Two-dimensional filtering Mip -map filtering Anisotropic filtering Analysis Summary Reference

3. I ntroduction Previous method – texture mapping

4. Intrinsic problems Mapping discontinuities L imitations to model editing after coloring Incorrect filtering … etc

5. Proposed method – Mesh color There are no mapping discontinuities N o mapping function is necessary MIP-mapping for level-of-detail filtering is supported Models can be edited, after coloring, without resampling The procedure is compatible with the current real-time graphics pipeline

6. M esh color structure Mesh color on triangle faces R means different resolution

7. Mesh color structure [1,0,0] [0,1,0] [0,0,1]

8. M esh color structure Non-uniform Face Resolutions It is straightforward to up-sample or down-sample along an edge, if two faces sharing a common edge have different resolutions

9. M esh color structure Editing Mesh Colored Geometry

10. M esh color structure Non-triangular Meshes Quadrilaterals Triangle pair Quadrilateral positioning NURBS Subdivision surfaces Dividing faces only

11. F iltering For evaluating the color value at any point on the surface or an area, we need a reconstruction filter Two-dimensional filtering Nearest Linear MIP-map filtering Anisotropic filtering

12. Two-dimensional filtering To compute the color value at target point, w e need to find out the weights of nearest 3 point to target point

13. Two-dimensional filtering [1,0,0] [0,1,0] [0,0,1] If w = 0, we are at the sample point B weight

14. Two-dimensional filtering The weights for those color values are w

15. Two-dimensional filtering T he weights are w’ = [1, 1, 1] − w

16. Two-dimensional filtering Nearest U se the color of the sample with the highest weight Linear By blending the colors using the weights

17. MIP-map filtering This face will have n+1 MIP-map levels

18. MIP-map filtering

19. MIP-map filtering Face & Edge Vertex W here Cei is the nearest edge color at the higher level for adjacent edge i

20. Anisotropic filtering Original MIP-map filtering Trilinear filtering Circularity Distortion Mapping Chasm Too fuzzy

21. Anisotropic filtering original 2x Anisotropic filtering 16x MIP-map filtering

22. Filtering

23. Analysis Unified content creation ‧Modeling & Painting together

24. Analysis Memory efficient Reduce 20% memory requirement !

25. Fast Analysis hardware H ardware Texture mapping on hardware is ~20x faster

26. Analysis Correct filtering

27. S ummary No mapping No Discontinuities Guaranteed 1-1 Correspondence Correct MIP-map Filtering Local Resolution Adjustment Modeling with Painting Compatible with Current Pipeline

28. Summary Easy to use (for end user) Easy to implement High quality High performance Mesh Colors will do better than texture mapping , if it has support from Hardware !

29. R eference Pictures for Mesh color Cem Yuksel , John Keyser & Donald H. House Texas A&M University “Mesh Colors,“ ACM Transactions on Graphics (TOG), 29(2) 2010 Pictures for Anisotropic filtering http://www.csie.ntu.edu.tw/~ r89004/hive/mipmap/page_4.html Copyright© 2000, 2001, 2002 Ping- Che Chen