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Progressive Meshes

Progressive Meshes. Hugues Hoppe Computer Graphics Group Microsoft Research SIGGRAPH 96. S. Complex meshes. 43,000 faces. lots of faces!. Challenges: - rendering - storage - transmission. Contributions. New mesh simplification procedure preserve appearance (colors, normals, …)

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Progressive Meshes

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

  4. Traditional mesh representation mesh M V F Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2 … Face 1 2 3 Face 3 2 4 Face 4 2 7 … (appearance attributes:normals, colors, textures, ...)

  5. PreviousWork Mesh simplification 13,000 [Schroeder-etal92] [Turk92] [Hoppe-etal93] [Rossignac-Borrel93] [Cohen-etal96] ... 1,000 200 ?

  6. PreviousWork Level-of-detail (LOD) [Clark76] [Funkhouser93] distance from viewer? close far 10,000 2,000 1,000 500 250 Concern: transitions may “pop”® would like smooth LOD

  7. (optimization) New mesh simplification procedure • Idea: apply sequence of edge collapses: ecol(vs ,vt , vs) ’ vt vr vl vl vr vs ’ vs S

  8. ^ M=Mn Simplification process 13,546 500 152 150 M175 M1 M0 ecoln-1 ecol0 ecoli

  9. Invertible! Vertex split transformation: attributes vspl(vs ,vl ,vr , vs,vt,…) ’ ’ ’ vt vl vr vl vr vs vs ’ S

  10. 150 152 500 13,546 ^ ^ M0 M1 M175 Mn=M M0 Mn=M vspl0 … vspli … … vspli … vspln-1 vspl0 vspln-1 progressive mesh (PM) representation Reconstruction process V S

  11. 3,478 ^ M0 Mn=M Mi 200K faces/sec! 100K faces/sec! (166 MHz Pentium) Application: Continuous-resolution LOD From PM, extract Mi of any desired complexity. 3,478 faces? M0 vspl0 vspl1 vspli-1 vspln-1 Mi V

  12. Mf-1 Mf-2 v1 v1 v2 v2 ecol ecol v3 v3 v4 v4 ecol v5 v5 v6 v6 v7 Property: Vertex correspondence Mf Mc M0 v1 v1 Mn v2 v2 v3 v3 v4 v5 v6 v7 v8

  13. Application: Smooth transitions Correspondence is a surjection: Mf Mc v1 v1 v2 v2 Mf«c v3 v3 v4 V V F v5 v6 ® can form a smooth visual transition: geomorph v7 v8 V

  14. Application: Mesh compression vspl(vs ,vl ,vr ,vs,vt,…) ’ ’ • Record deltas: • vt - vs • vs - vs • … vt ’ ’ vl vl vr vr vs ’ vs ’ • Encoding of vspl records: • connectivity: ~ good triangle strips • attributes: excellent delta-encoding [Deering95] Space overhead of PM ?!

  15. vspli-1 vspln-1 Mi ^ M (~ progressive JPEG) Application: Progressive transmission Transmit records progressively: time M0 vspl0 vspl1 Receiver displays: M0

  16. Application: Selective refinement vspl0 vspl1 vspli-1 vspln-1 M0 (e.g. view frustum) S

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

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

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

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

  21. ^ M V F M0 Summary PM lossless vspl • single resolution • continuous-resolution • smooth LOD • space-efficient • progressive S V

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

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