1. Progressive Meshes A Talk by Wallner and Wurzer for the overfull MathMeth auditorium

2. Wallner and WurzerVienna University of Technology 2 / 27 What it‘s all about...

3. Wallner and WurzerVienna University of Technology 3 / 27 Overview Advantages PM‘s Advantages PM‘s Definition and Basics Definition and Basics GeoMorphs GeoMorphs Mesh Compression Mesh Compression Selective Refinement Selective Refinement Construction Construction

4. Wallner and WurzerVienna University of Technology 4 / 27 Let‘s start off...

5. Wallner and WurzerVienna University of Technology 5 / 27 Advantages of PM‘s Mesh Simplification Mesh Simplification LOD Approximation LOD Approximation Progressive Transmission Progressive Transmission Mesh Compression Mesh Compression Selective Refinement Selective Refinement

6. Wallner and WurzerVienna University of Technology 6 / 27 Definition and Basics (1) A corner is a (vertex,face) tuple A corner is a (vertex,face) tuple We are speaking of a sharp edge if We are speaking of a sharp edge if  it is a boundary adge  the adjacent faces have different discrete values or  adjacent corners have different scalar values

7. Wallner and WurzerVienna University of Technology 7 / 27 Definition and Basics (2) Traditional Mesh Traditional Mesh Progressive Mesh Progressive Mesh (M 0,{Vsplit 0 … Vsplit n-1 }) (M 0,{Vsplit 0 … Vsplit n-1 }) KV M0M0M0M0

8. Wallner and WurzerVienna University of Technology 8 / 27 Definition and Basics (3)  lossless ! vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr ’ vsplit ecol

9. Wallner and WurzerVienna University of Technology 9 / 27 Definitions and Basics (4) M... Full-Detailed Mesh (all vertices) ^ M 0... Minimal Detailed Version 13,546500152150 M0M0M0M0 M1M1M1M1 M 175 ecol 0 ecol i ecol n-1 M=M n ^

10. Wallner and WurzerVienna University of Technology 10 / 27 Geomorph Smooth visual transition between two meshes M f, M c Smooth visual transition between two meshes M f, M c v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 MfMfMfMf v1v1v1v1 v2v2v2v2 v3v3v3v3 McMcMcMc VF MfcMfcMfcMfc V PM with geomorph

11. Wallner and WurzerVienna University of Technology 11 / 27 Geomorph (2)

12. Wallner and WurzerVienna University of Technology 12 / 27 Mesh Compression vsvsvsvs vlvlvlvl vrvrvrvr vlvlvlvl vrvrvrvr vtvtvtvt ’ vsvsvsvs ’ Record deltas: l v t - v s l v s - v s l … ’ ’ vspl(v s,v l,v r, v s,v t,…) ’ ’

13. Wallner and WurzerVienna University of Technology 13 / 27 Selective Refinement M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1

14. Wallner and WurzerVienna University of Technology 14 / 27 Selective Refinement (2) Rules for the vertex splits: Rules for the vertex splits:  All involved vertices are present  doRefine(v) == TRUE  neighbours should be further refined  vertex is absent  a previous vertex split was not executed, based on the two upper rules

15. Wallner and WurzerVienna University of Technology 15 / 27 Selective Refinement (3) View Frustum...which makes this vertex „not present“ Split not performed......because this split was not performed...

16. Wallner and WurzerVienna University of Technology 16 / 27 Selective Refinement (4) View Frustum if this would be present

17. Wallner and WurzerVienna University of Technology 17 / 27 Construction Task: Construct M n-1, M n-2,... M 0 Naive Algorithm: { select random edge to collapse until resolution M 0 faces select random edge to collapse until resolution M 0 faces}

18. Wallner and WurzerVienna University of Technology 18 / 27 Construction (2) Problems of naive algorithm: Problems of naive algorithm: 1.Geometry is not preserved 2.Color, Normals etc. are not preserved 3.Discontinuities are not preserved

19. Wallner and WurzerVienna University of Technology 19 / 27 Construction (3) Better algorithm: Better algorithm: (Re-)Sample object (Re-)Sample object Simplify Object Simplify Object Use energy function to measure accuracy Use energy function to measure accuracy Extend to preserve... Extend to preserve... surface geometry surface geometry color and normals color and normals discontinuities discontinuities

20. Wallner and WurzerVienna University of Technology 20 / 27 Energy Function E(V)= E dist (V) + E spring (V) + E scalar (V)+E disc (V) E(V)= E dist (V) + E spring (V) + E scalar (V)+E disc (V)  E negative  perform split (= less energy used for simplified mesh) further explanations

21. Wallner and WurzerVienna University of Technology 21 / 27 With better algorithm...

22. Wallner and WurzerVienna University of Technology 22 / 27 Summary PM have many advantages: PM have many advantages:  lossless  captures discrete attributes  captures discontinuities n continuous-resolution n smooth LOD n space-efficient n progressive

23. Wallner and WurzerVienna University of Technology 23 / 27 Links (1) Progressive Meshes Progressive Meshes [ Hoppe ] [ Hoppe ] http://research.microsoft.com/~hoppe/ (all images in this talk except those explicitly labeled courtesy of H. Hoppe)

24. Wallner and WurzerVienna University of Technology 24 / 27 Links (2) quadric error metric scheme quadric error metric scheme [ Garland and Heckbert ] http://graphics.cs.uiuc.edu/~garland/papers.html memoryless scheme memoryless scheme [ Lindstrom and Turk ] http://www.cs.gatech.edu/gvu/people/Phd/Peter.Lindstrom.html

25. Thank you for your attention ! Progressive Meshes Wallner and Wurzer

26. Vienna University of Technology 26 / 27 Discussion Note Problem of this approach: Problem of this approach: pictures courtesy of Markus Gross

27. Wallner and WurzerVienna University of Technology 27 / 27 Discussion Note Better Approach: Better Approach: picture courtesy of Markus Gross