and Recent Extensions Progressive Meshes Progressive Meshes Multiresolution Surface Modeling Multiresolution Surface Modeling Hugues Hoppe

Transcription

1 Progressive Meshes Progressive Meshes and Recent Extensions Hugues Hoppe Microsoft Research SIGGRAPH 97 Course SIGGRAPH 97 Course Multiresolution Surface Modeling Multiresolution Surface Modeling

2 Meshes in computer graphics Meshes in computer graphics mesh M V F Vertex 1 x 1 y 1 z 1 Vertex 2 x 2 y 2 z 2 Face Face Face (appearance attributes: normals, colors, textures,...)

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

4 Talk outline Talk outline SIGGRAPH 96 Progressive mesh (PM) representation continuous-resolution efficient progressive transmission 97 View-dependent refinement of PM s 97 Progressive simplicial complex (PSC) repr.

5 Mesh simplification techniques Mesh simplification techniques 13,000 [Schroeder-etal92] etal92] [Hoppe-etal93] etal93] [Rossignac-Borrel93] [Cohen-etal96] etal96] [Garland-Heckbert97]... 1, ?

6 Traditional level-of of-detail (LOD) [Clark76] [Funkhouser93] 10,000 distance from viewer? close 1,000 far Concern: transitions may pop would like smooth LOD 250

7 Progressive mesh representation Progressive mesh representation Basic idea: Simplify mesh through sequence of transformations. Record: simplified mesh simplified mesh + sequence of inverse transformations sequence of inverse transformations

8 Edge collapse Simplification v t v l v r v s ecol(v s,v t, v s ) (optimization) v l v r v s 13, M=M ^ n ecol n-1 M 175 M ecol ecol i 0 M 0

9 Invertible! Vertex split transformation Invertible! Vertex split transformation v l v s v r attributes vspl(v s,v l,v r, v s,v t, ) v t v l v r v s

10 150 Reconstruction process ,546 M 0 M 1 M 175 M n =M^ vspl 0 vspl i i vspl n-1 n-1 progressive mesh (PM) representation

11 Application: Continuous-resolution LOD From PM, extract M i of any desired complexity. M 0 vspl 0 vspl 1 vspl i-1 vspln-1 3,478 faces? 3,478 M i M 0 M M n =M^ i 260K faces/sec! 180K faces/sec! (200 MHz Pentium Pro)

12 VIDEO: PM construction and LOD VIDEO: PM construction and LOD gameguy ecol s gameguy vspl s gameguy LOD sandal LOD

13 Property: Vertex correspondence Property: Vertex correspondence M f M f-1 M f-2 M c M n v 1 v 1 v 1 v 1 M 0 v 2 v 2 v v ecol 2 ecol 2 v v v v v 4 v 4 v ecol 4 v v v v 6 v 6 v 6 v 7 v 7 v 8

14 Application: Smooth transitions Application: Smooth transitions M f M c M n v 1 v 1 M 0 v 2 v 2 v 3 v 3 v 4 v 5 v 6 v 7 v 8 M f c V V F can form a smooth visual transition: geomorph

15 VIDEO: PM geomorphs VIDEO: PM geomorphs gameguy 1 geomorph gameguy 12 geomorphs gameguy 6 rotating

16 Application: Mesh compression vspl i (v s,v l,v r,v s,v t, ) v t v l v v s r v l v r v s Analysis: Record: (log 2 i bits) v s (log (~5 bits) v l & v r (~5 bits) v t - v s (delta) v s - v s (delta) predict materials connectivity: n(4+log 2 n) bits vs. n(6log 2 n) bits geometry: ~30n bits vs. 96n bits [Deering95]

17 Application: Progressive transmission Application: Progressive transmission Transmit records progressively: time M 0 vspl 0 vspl 1 vspl i-1 vspln-1 Receiver displays: M 0 M i (~ progressive GIF & JPEG) M^

18 Conversion traditional mesh representation progressive mesh representation V F M 0 vspl Optimization process Various metrics (speed vs. quality) Typically performed off-line

19 How to select edge collapses? How to select edge collapses? Preserve appearance: geometric shape scalar fields (e.g. color, normals) discontinuity curves E e e da e dl = ( shape + scalars ) + ( disc ) face areas disc. edges Σ Σ points points

20 Error metric: point sampling shape discontinuities 1600 faces 1600 faces 300 faces

21 Selecting edge collapses Selecting edge collapses Greedy algorithm: always collapse edge resulting in smallest E. Optimize position and attributes of resulting vertex. Simplification rates: ~ 30 faces/sec off-line process could use faster, simpler metrics e.g. [Garland-Heckbert97]

22 VIDEO/DEMO: PM results VIDEO/DEMO: PM results radiosity 6 geomorphs mandrill image

23 PM Summary PM Summary M^ PM V F lossless M 0 vspl single resolution continuous-resolution smooth LOD space-efficient efficient progressive [Microsoft DirectX 5.0]

24 View-Dependent Refinement of Progressive Meshes [SIGGRAPH 97]

25 Adaptive refinement: motivation Adaptive refinement: motivation

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

27 Using progressive meshes Using progressive meshes M 0 vspl 0 vspl 1 vspl i-1 vspln-1 (e.g. view frustum)

28 Contributions PM vertex hierarchy selective refinement Dependencies consistent framework View-dependent refinement criteria

29 Parent-child vertex relations v s vsplit v t v u

30 Vertex hierarchy PM: M 0 vspl 0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 M 0 v 1 v 2 v 3 v 10 v 11 v 4 v 5 v 8 v 9 M n v 12 v 13 v 6 v 7 [Xia & Varshney 96] v 14 v 15

31 Selective refinement M 0 vspl 0 vspl 1 vspl 2 vspl 3 vspl 4 vspl 5 M 0 v 1 v 2 v 3 v 10 v 11 v 4 v 5 v 8 v 9 v 12 v 13 v 6 v 7 selectively refined mesh Restrictions? v 14 v 15

32 New vspl/ecol parametrizations New vspl/ecol parametrizations f n0 v s f n1 f n2 f n3 vsplit ecol f n0 f n1 v u v t f n3 f n2 v s vsplit f n0 f n1 f n2 f n3 v t v u f l f r ecol f n0 f n1 f n2 f n3 v t v u f l f r v s

33 Runtime algorithm M 0 v 1 v 2 v 3 v 10 v 11 v 4 v 5 v 8 v 9 v 12 v 13 initial mesh initial mesh Algorithm: v 6 v 14 v 15 incremental (frame coherence) efficient (~15% of frame time) amortizable v 7 dependency new mesh

34 View-dependent refinement criteria 3 criteria: view frustum surface orientation screen-space space geometric error

35 View frustum View frustum view is unchanged too high too far right

36 Surface orientation Surface orientation view is unchanged oriented away

37 Screen-space geometric error tolerance=0.5 pixels refinement near silhouette coarser in distance

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

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

40 Selective Refinement Summary Selective Refinement Summary M^ V F M 0 PM vspl continuous-resolution smooth LOD space-efficient efficient progressive M 0 v 1 v 2 M^ v 3 v 4 v 5 v 6 v 7 v 8 view-dependent refinement real-time algorithm

41 Progressive Simplicial Progressive Simplicial Complexes [SIGGRAPH 97] (Joint work with Jovan Popovic)

42 PM restrictions: PM restrictions: Supports only meshes (orientable, 2-dimensional 2 manifolds) 2,522 Preserves topological type M 0 M i M n 8, ,744

43 Progressive Simplicial Complexes Progressive Simplicial Complexes Represent arbitrary triangulations : any dimension, non-orientable, orientable, non-manifold, non-regular, Progressively encode both geometry and topology.

44 Generalization PM PSC edge collapse (ecol) vertex unification (vunify vunify) vertex split (vspl) generalized vertex split (gvspl)

45 LOD sequence M 1 M 22 gvspl 1 M 116 gvspl i gvspl n-1 PSC representation M n =M^

46 VIDEO: PSC VIDEO: PSC drumset schooner comparison of PM and PSC (davidson) geomorphs (cessna) 1-d d non-manifold curve (castle)

47 Space analysis Space analysis connectivity geometry! materials cessna destroyer drumset chandelier schooner castle2d Dataset A D V K(C) K(a) bits per vertex

48 PSC Summary PSC Summary M^ PSC V K lossless M 1 gvspl arbitrary simplicial complex any triangulation single vertex progressive geometry and topology

49 Future Work Future Work LOD on volumes Memory management for large models Refinement criteria for surface shading Animated models Editing using PM/PSC