View-Dependent Refinement of Progressive Meshes Hugues Hoppe Microsoft Research SIGGRAPH 97

Rendering complex meshes 860,000 faces! VF

Traditional level-of-detail 50,000 faces progressive mesh representation [SIGGRAPH96] 10,000 faces 2,000 faces view-independent LOD linear sequence poppop

View-Independent LOD: Difficulties 100,000 faces outside view frustum distant backfacing S

View-dependent LOD 29,400 faces different LOD’s coexist over surface

Applications & Related work height fields parametric surfaces arbitrary meshes [Cignoni etal 95] [De Floriani etal 96] [Lindstrom etal 96] … [Rockwood etal 89] [Abi Ezzi etal 93] [Kumar etal 95] … [Xia-Varshney 96] S

Contributions l Progressive mesh  vertex hierarchy  selective refinement l Dependencies  consistent framework l View-dependent refinement criteria

base mesh original mesh 150 M0M0M0M0 M1M1M1M1 152 Review of progressive meshes … M 175 … 50013,546 MnMnMnMn vlvlvlvl vrvrvrvr vuvuvuvu vtvtvtvt vsvsvsvs vlvlvlvl vrvrvrvr edge collapse vertex split

150 M0M0M0M0 M1M1M1M1 vspl The PM representation M … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 M0M0M0M0 MnMnMnMn MiMiMiMi MnMnMnMn

Idea: Selective refinement M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1 [SIGGRAPH 96]: incremental update not possible

Parent-child vertex relations vsvsvsvs vtvtvtvt vuvuvuvu vsplit

v2v2v2v2 Vertex hierarchy vspl 0 M0M0M0M0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 vspl 5 v 14 v 15 v6v6v6v6 PM: MnMnMnMn [Xia & Varshney 96] M0M0M0M0

vspl 2 v 11 v1v1v1v1 v2v2v2v2 v4v4v4v4 v8v8v8v8 v9v9v9v9 v3v3v3v3 v7v7v7v7 v5v5v5v5 v 12 v 13 v 10 v 14 v 15 v6v6v6v6 v2v2v2v2 Selective refinement vspl 0 M0M0M0M0 vspl 1 vspl 3 vspl 4 vspl 5 v1v1v1v1 v3v3v3v3 M0M0M0M0 v 10 v 11 vspl 3 v1v1v1v1 v2v2v2v2 v4v4v4v4 v5v5v5v5 vspl 0 v6v6v6v6 v7v7v7v7 vspl 1 v5v5v5v5 v 12 v 13 vspl 4 v 10 selectively refined mesh v8v8v8v8 v9v9v9v9 vspl 2 v3v3v3v3 v8v8v8v8 v9v9v9v9 v3v3v3v3 Restrictions?

Legality conditions? vlvlvlvl vrvrvrvr vuvuvuvu vtvtvtvt vsvsvsvs vlvlvlvl vrvrvrvr vsplit ecol n vsplit legal if: –v s is active –v l and v r are active n ecol legal if: –? problem: consistent? [SIGGRAPH96] [Xia&Varshney96]: legal if identical neighborhood

New vspl/ecol parametrizations vsplit ecol f n1 f n0 vsvsvsvs f n3 f n2 f n1 f n0 vuvuvuvu vtvtvtvt f n3 f n2 n vsplit legal if: –v s is active –f n0,f n1,f n2,f n3 are active n ecol legal if: –v t,v u are active –f n0,f n1,f n2,f n3 are adjacent

previous mesh v5v5v5v5 v 10 v 11 v4v4v4v4 v8v8v8v8 v9v9v9v9 v7v7v7v7 v 12 v 13 v1v1v1v1 v2v2v2v2 v3v3v3v3 Runtime algorithm M0M0M0M0 v6v6v6v6 v 14 v 15 v 12 v 13 v 12 v 10 v 11 v 10 v 11 v4v4v4v4 v4v4v4v4 v6v6v6v6 v 14 v 15 v6v6v6v6 v 14 v 15 v8v8v8v8 v9v9v9v9 v3v3v3v3 v7v7v7v7 v7v7v7v7 v8v8v8v8 v8v8v8v8 v9v9v9v9 v9v9v9v9 new mesh dependency l Algorithm: n incremental (frame coherence) n efficient (~15% of frame time) n amortizable v 11 v 10 v4v4v4v4 v 14 v 15 v7v7v7v7 v8v8v8v8 v9v9v9v9

View-dependent refinement criteria 3 criteria: n view frustum n surface orientation n screen-space geometric error See paper for details. S

(1) View frustum too high too far right view is unchanged

(2) Surface orientation view is unchanged oriented away

(3) Screen-space geometric error refinement near silhouette coarser in distance tolerance=0.5 pixels

All three criteria together 69,473 faces  10,528 faces 1.9 frame/sec  6.7 frame/sec S

Fast rendering: triangle strips Greedy algorithm: n IRIS GL: avg faces/strip n OpenGL: avg. 4.2 faces/strip

32 Bezier patches Application: Parametric surfaces PM M0M0M0M0 pre- process vspl 25,440 VF M v1v1v1v1 M0M0M0M0 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 MnMnMnMn load 10,000 1,800

Geomorphs smooth visual transitions

VIDEO view frustum (2-window terrain) screen-space error (2-window terrain) silhouette refinement (sphere) all 3 criteria including orientation (teapot) arbitrary mesh (gameguy) geomorph flythrough of gcanyon

Summary l Selective refinement framework l View-dependent refinement criteria l Real-time algorithm (fast, amortizable) l Arbitrary progressive meshes  geometrically optimized refinement!

Future work l Memory management for large models l Runtime generation of geomorphs l Refinement criteria for surface shading l Animated models