1. PMR: Point to Mesh Rendering, A Feature-Based Approach Tamal K. Dey and James Hudson {tamaldey,jhudson}@cis.ohio-state.edu http://www.cis.ohio-state.edu/~tamaldey October 30, 2002 Department of Computer and Information Science The Ohio State University

2. Department of Computer and Information Science Overview Introduction Algorithm: Two Stages Preprocessing Viewing Results Conclusion

3. Department of Computer and Information Science Hierarchy Construction Points and triangles displayed Feature-dependent, not screen-space Advantageous for large, flat areas Goals: Quality at all viewing distances Adaptive display Adjustable speed vs. quality setting No input mesh needed

4. Department of Computer and Information Science Motivation Triangles good for quality; points for speed Difference is subtle when far away Point-based splatting PMR Zoom in on the nose...

5. Department of Computer and Information Science Splatting vs. PMR Point Splatting PMR When zoomed-in, differences are more noticeable, especially at upper left edge of nose.

6. Department of Computer and Information Science Our Approach Utilizes hierarchy Contains Points and Triangles Hierarchy: scale independent Depends on model's features No surface mesh required More flexibility Simpler data structure

7. Department of Computer and Information Science Preprocessing Decimate input where "redundant" points exist Use features to determine this Threshold guides levels of hierarchy No new points added; only removal  = 0.2  = 0.3  = 0.4

8. Department of Computer and Information Science Feature Detection We use Voronoi diagram to detect features Can be costly: time + memory Solution: Use octree decomposition of space Maximum of 12000 points per node useful

9. Department of Computer and Information Science Feature Detection Dense point set: long, skinny Voronoi cells Capture this via height and radius values Pole vector = estimated normal (AB98) Height estimates distance to medial axis Radius estimates distance between neighbors

10. Department of Computer and Information Science Feature Detection Decimation is based on ratio Remove all points with ratio <  (threshold) Point with small ratio must have close neighbors Repeat for several values of  to give hierarchy We use values from  0.1 to  1.0 Each leaf node N is processed individually radius height

11. Department of Computer and Information Science Point Hierarchy The final point hierarchy contains progressively fewer points  = 0.2  = 0.3  = 0.4

12. Department of Computer and Information Science Triangle Hierarchy For point p: We define umbrella of p Umbrella = set of triangles incident on p and are dual to Voronoi edges intersecting tangent polygon

13. Department of Computer and Information Science Triangle Hierarchy Result: progressively sparser triangle sets  = 0.2  = 0.3  = 0.4

14. Department of Computer and Information Science Disk File For each leaf, store to disk: Points, estimated normals, hierarchy levels  Umbrella triangles per vertex  Umbrella radii per vertex  Average umbrella radius for all points Map file to memory when viewing

15. Department of Computer and Information Science Viewing Must determine pixel size ● Done once per leaf node only ● Closest corner point = the one to use ● Project two world space points to screen ● Gives ratio of world space to screen space ● Conservative estimate

16. Department of Computer and Information Science Choice of Hierarchy Choice of hierarchy level made once per leaf Metric: Use average umbrella size Try to match umbrella size to pixel size  If too dense: more points to process  If too sparse: detail lost User can trade speed for quality via scale factor Just rightToo sparse Too dense

17. Department of Computer and Information Science Pixel vs. Umbrella For each point: choose: Pixel vs. Umbrella Compare umbrella radius to (pixel size)  (scale factor)  scale factor allows trade-off of quality vs. speed Choose umbrella only if size too big; else choose pixel Conservative estimation performed Can draw as pixel Must draw as triangles

18. Department of Computer and Information Science Scale Factor Scale factor allows modification of calculation If scale factor larger, calculations treat pixels as larger Selects sparser hierarchy level Can modify scale factor to selectively slow transition between levels, especially at high levels of decimation

19. Department of Computer and Information Science Scale Factor Transition Need to slow transition between sparser levels Differences invisible when far away  =0.1  =0.3  =0.8  =1.0

20. Department of Computer and Information Science Results System used: Pentium 4, 1.7 Ghz, 2 GB RAM Matrox Millenium G450 graphics card Software-only OpenGL rendering

21. Department of Computer and Information Science Results We varied  from 0.1 to 1.0, steps of 0.1 If  is large (  1.0), features are lost Varying the scale factor  If pixel size is 2 world space units, begin altering  Reduce factor linearly until pixel is 4 world space units  If pixel is 4 or more units: factor is equal to 1  Net effect: as decimation becomes sparser, slow the transition between levels.

22. Department of Computer and Information Science Results 0.11 FPS, 4.5M tris, 0 points (Full detail) 0.77 FPS, 670K tris,48K points (PMR) 0.65 FPS, 650K tris, 377K points (PMR) 1.65 FPS, 215K tris, 204K points (PMR) Varying distances; Blue=triangles, Red=points

23. Department of Computer and Information Science Results Dense level Sparse level

24. Department of Computer and Information Science Results Comparison of full-detail (  =0) vs PMR Full detail, 0.54 FPSPMR, 3.85 FPS

25. Department of Computer and Information Science Results Comparison of full-detail vs PMR Full detail, 0.25 FPSPMR, 0.71 FPS

26. Department of Computer and Information Science Results Comparison of full-detail vs PMR Full detail, 0.11 FPSPMR, 0.61 FPS

27. Department of Computer and Information Science Results Dense level Sparse level Factor=1 0.16 FPS Factor=3 0.74 FPS Factor=5 0.96 FPS

28. Department of Computer and Information Science Results Dragon Happy Blade DavidHead StMatthew 437645 542557 882954 2000646 3382855 0.54 0.43 0.25 0.11 0.072 3.85 3.44 0.71 0.78 0.67 Object VerticesFullPMR Frames per second. Full denotes the full (  =0) mesh; PMR denotes the adaptive hierarchy scheme with a factor of 5.

29. Department of Computer and Information Science Preprocessing Times Dragon Happy Blade DavidHead StMatthew 437645 542557 882954 2000646 3382855 03:53 04:36 09:02 06:36 26:38 97 150 238 512 479 Object VerticesTimeSize (MB) Note: Times are in Hours:Minutes.

30. Department of Computer and Information Science Conclusions A hybrid rendering scheme Points and triangles employed User-adjustable error tolerance No input surface required Future work Applications to volume rendering