1. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20031 Progressive Meshes (SIGGRAPH ’96) By Hugues Hoppe Presented by Yong Kil and Christopher Co

2. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20032 Previous Work [Schroeder-etal92] (decimation) [Turk92] (re-tiling) [Hoppe-etal93] (mesh optimization) [Rossignac-Borrel93] (vertex clustering) [Cohen-etal96] (simplification envelopes)... MRA (later) 13,000 1,000200 ?

3. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20033 Introduction What is Progressive Mesh? Arbitrary mesh M stored as coarser mesh M 0 together with a sequence of n detail records that indicate how to incrementally refine M 0 exactly back into the original mesh M = M n.150 M0M0M0M0 M1M1M1M1 vspl 0 152 M 175 500 … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 MnMnMnMn

4. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20034 Edge Collapse and Vertex Split ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vt vt vt vt vs vs vs vs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’ vspl(s,l,r,t, A) A = ( {v s,v t }, {discrete values}, {scalar values} ) Discrete values: associated with faces. Discrete values: associated with faces. I.e. material identifier such as texture map. I.e. material identifier such as texture map. Scalar values: associated with corners (vertex, face). Scalar values: associated with corners (vertex, face). E.g color, normal, texture coordinate. E.g color, normal, texture coordinate.

5. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20035 PM Construction 13,546500152 150 faces M0M0M0M0 M1M1M1M1 M 175 ecol 0 ecol i ecol n-1 MnMnMnMn ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’ vspl(v s,v l,v r, A)

6. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20036 Mesh Simplification Which edge to collapse? Minimize the Energy Function: –E(M) = E dist (M) + E spring (M) + E scalar (M) + E disc (M) For each potential edge collapse, calculate ∆E and add to priority queue. Pop edge from queue (with lowest ∆E) and collapse. Update affected edges and every pop next edge. (b) Sampled points X = {x 1, x 2, …, x n } (a) Object to be sampled Sample Points X

7. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20037 Distance Energy Surface of M

8. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20038 Spring Energy

9. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20039 Distance and Spring Where to collapse to have local minimum energy? Mesh Optimization (Hoppe ’93) creates non-linear equations and solves using iterative method. PM chooses 3 locations out of the infinite set: {0, 0.5, 1} vtvtvtvt vsvsvsvs vsvsvsvs ’ vsvsvsvs ? ’

10. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200310 Scalar Energy

11. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200311 Discontinuity Energy Sharp Edge (in yellow) 1.Boundary edge 2.Two adjacent faces have different discrete attributes 3.Adjacent corners have different scalar attributes. xixi

12. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200312 Using PM – LOD13,546500152 150 faces M0M0M0M0 M1M1M1M1 M 175 MnMnMnMn Each intermediate representation of the mesh can be considered a LOD

13. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200313 Using PM – Transmission and Compression Transmission –Transmit M 0, then transmit sequence of vsplit records Compression –Use connectivity coding and efficient use of bits –Use delta-encoding to reduce storage of scalar attributes –Coherence in mesh attributes can be exploited

14. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200314 Geomorph Alpha blend between different resolutions to avoid “snapping” Blending occurs between each pair of vertices related by edge collapses performed (ancestor map)

15. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200315 Selective Refinement M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1

16. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200316 Selective Refinement Perform vspl( s i, l i, r i, A i ) if: (1) vertices {s i,l i,r i } exist (2) REFINE(s i ) is true REFINE(s i ) is defined per application Relax constraint (1’) vertex s i and A’(l i ) and A’(r i ) exist Perform vspl( s i, A’(l i ), A’(r i ), A i ) A’() is an ancestor map similar to that used by geomorphin

17. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200317 Previous Work - MRA Multiresolution Analysis (MRA) Analysis produces base mesh with wavelet coefficients (B) using filter A Synthesis produces mesh of desired resolution using a refining filter and a perturbing filter Figure courtesy of Lounsbery, et al. (`94)

18. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200318 PM vs. MRA Advantages of MRA –encodes geometry & color independently –supports multiresolution editing –guarantees maximum error bound Advantages of PM –lossless –can be more accurate –captures discrete attributes –captures discontinuities (creases)

19. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200319 Results – PM vs. MRA

20. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200320 Results – E scalar

21. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200321 Results – Radiosity Solution

22. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200322 Conclusion Contribution: PM data structure Advantages –Solves a variety of problems (LOD, Progressive Transmission, Selective Refinement, etc.) –Deals with various mesh attributes aside from geometry Disadvantages –Mesh parameterization can be non-intuitive –Energy function is complex

23. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200323 Sharing Mesh Attributes wedge vertex face corner

24. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200324 Vertex Correspondence MnMnMnMn M0M0M0M0 McMcMcMc MfMfMfMf v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 v1v1v1v1 v2v2v2v2 v3v3v3v3 M f-1 v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 ecol M f-2 v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 ecol ecol

25. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200325 Select refine b a a b

26. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200326 Misc MRA vs PM? Review of PM –Selective refinement as primary contribution. –What improvements have been made from this paper. i.e. who refers to this paper?

27. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200327 Figures

28. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200328 vertex corner face

29. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200329 {f 1 } : { v 1, v 2, v 3 } {f 2 } : { v 3, v 2, v 4 } … connectivity geometry {v 1 } : (x,y,z) {v 2 } : (x,y,z) … face attributes {f 1 } : “skin material” {f 2 } : “brown hair” …

30. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200330 {v 2,f 1 } : (n x,n y,n z ) (u,v) {v 2,f 2 } : (n x,n y,n z ) (u,v) … corner attrib. {f 1 } : { v 1, v 2, v 3 } {f 2 } : { v 3, v 2, v 4 } … connectivity geometry {v 1 } : (x,y,z) {v 2 } : (x,y,z) … face attributes {f 1 } : “skin material” {f 2 } : “brown hair” …

31. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200331 PM benefit PM VnVnVnVn MnMnMnMn M0M0M0M0 n progressive transmission n continuous-resolution n smooth LOD n geometry compression lossless n single resolution vspl FnFnFnFn attributes

32. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200332 ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’

33. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200333 Vertex Split vsvsvsvs vlvlvlvl vrvrvrvr vspl(v s,v l,v r, v s,v t,…) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs ’’ ’ ’ attributes

34. visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200334 Reconstruction150 M0M0M0M0 M1M1M1M1 vspl 0 152 M 175 500 … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 MnMnMnMn