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Progressive Meshes Hugues Hoppe Computer Graphics Group Microsoft Research SIGGRAPH 96 S.

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Presentation on theme: "Progressive Meshes Hugues Hoppe Computer Graphics Group Microsoft Research SIGGRAPH 96 S."— Presentation transcript:

1 Progressive Meshes Hugues Hoppe Computer Graphics Group Microsoft Research SIGGRAPH 96 S

2 Complex meshes 43,000 faces lots of faces! Challenges: - rendering - storage - transmission

3 Contributions l New mesh simplification procedure n preserve appearance (colors, normals, …) l New representation: progressive mesh n lossless n continuous-resolution n efficient n progressive

4 Traditional mesh representation VF (appearance attributes: normals, colors, textures,... ) mesh M Vertex 1 x 1 y 1 z 1 Vertex 2 x 2 y 2 z 2 … Face Face Face …

5 Previous Work Mesh simplification Mesh simplification 13,000 [Schroeder-etal92][Turk92][Hoppe-etal93][Rossignac-Borrel93][Cohen-etal96]... 1, ?

6 Previous Work Level-of-detail (LOD) Level-of-detail (LOD) [Clark76][Funkhouser93] distance from viewer? distance closefar 10,0002,0001, Concern: transitions may pop would like smooth LOD

7 New mesh simplification procedure l Idea: apply sequence of edge collapses: ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr (optimization) S

8 Simplification process 13, M0M0M0M0 M1M1M1M1 M 175 ecol 0 ecol i ecol n-1 M=M n ^

9 Invertible! Vertex split transformation: vsvsvsvs vlvlvlvl vrvrvrvr vspl(v s,v l,v r, v s,v t,…) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs S attributes

10 Reconstruction process 150 M0M0M0M0 M1M1M1M1 vspl M … vspl i … 13,546 vspl n-1 M n =M ^ progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 M n =M ^S V

11 Application: Continuous-resolution LOD From PM, extract M i of any desired complexity. M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1 MiMiMiMi 3,478 faces? 3,478 M0M0M0M0 M n =M ^ MiMiMiMi 100K faces/sec! 200K faces/sec! (166 MHz Pentium) V

12 Property: 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

13 Application: Smooth transitions Correspondence is a surjection: v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 MfMfMfMf v1v1v1v1 v2v2v2v2 v3v3v3v3 McMcMcMc can form a smooth visual transition: geomorph can form a smooth visual transition: geomorph VF M f c V V

14 Space overhead of PM ?! Application: Mesh compression vsvsvsvs vlvlvlvl vrvrvrvr vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs Record deltas: l v t - v s l v s - v s l … Encoding of vspl records: n connectivity: ~ good triangle strips n attributes: excellent delta-encoding [Deering95] vspl(v s,v l,v r, v s,v t,…)

15 Application: Progressive transmission Transmit records progressively: M0M0M0M0 vspl 0 vspl 1 Receiver displays: time M0M0M0M0 vspl i-1 MiMiMiMi vspl n-1 M ^ (~ progressive JPEG)

16 Application: Selective refinement M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1 (e.g. view frustum) S

17 How to select edge collapses? l Preserve appearance: n geometric shape n scalar fields (e.g. color) n discontinuity curves pointspoints S

18 Selecting edge collapses Greedy algorithm: always collapse edge resulting in smallest E Greedy algorithm: always collapse edge resulting in smallest E Simplification rates: ~ 30 faces/sec n off-line process n could use simpler heuristics

19 Previous Work Multiresolution analysis (MRA) Multiresolution analysis (MRA) [Lounsbery-etal93] [Eck-etal95] [Certain-etal96] base mesh wavelet coefficients (detail) S

20 Comparison with MRA l Advantages of MRA n encodes geometry & color independently n supports multiresolution editing l Advantages of PM n lossless n more accurate n captures discrete attributes n captures discontinuities

21 Summary PM VF M^ M0M0M0M0 vspl n continuous-resolution n smooth LOD n space-efficient n progressive lossless n single resolution SV

22 Demo l 166 MHz Pentium l 3D Labs graphics card (~$250) l Windows 95 + DirectX


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