Multiresolution Meshes. COS 526 Tom Funkhouser, Fall 2016 Slides by Guskov, Praun, Sweldens, etc.

Transcription

1 Multiresolution Meshes COS 526 Tom Funkhouser, Fall 2016 Slides by Guskov, Praun, Sweldens, etc.

2 Motivation Huge meshes are difficult to render store transmit edit Multiresolution Meshes! [Guskov et al.]

3 Multiresolution Meshes Irregular Semi-regular Completely regular [Hoppe]

4 Multiresolution Meshes Irregular Semi-regular Completely regular [Hoppe]

5 Irregular Multiresolution Meshes Encode mesh simplification operations in tree Cut through tree defines a mesh Move cut up/down to simplify/refine Xia96, Hoppe97, Luebke97

6 Progressive Mesh Slide by Hoppe Encode continuous detail as sequence of edge collapses v t ecol(v s,v t, v s ) v l v r v l v s v r v s M N ecol 0 ecol 1 ecol i-1 ecol n-1

7 Progressive Mesh Slide by Hoppe Simplification process 13, M=M ^ n ecol n-1 M 175 M 1 ecol i ecol 0 M 0

8 Progressive Mesh Slide by Hoppe Inversion is possible with vertex split transformation attributes vspl(v s,v l,v r, v s,v t, ) v t v l v s v r v l v r v s

9 Progressive Mesh Slide by Hoppe Reconstruction process ,546 M 0 M 1 M 175 vspl 0 vspl i i vspl n-1 n-1 progressive mesh (PM) representation M n =M^

10 Progressive Mesh Slide by Hoppe From PM, extract M i of any desired complexity (this is multiresolution) M 0 vspl 0 vspl 1 vspl i-1 vspl n-1 M i 3,478 faces? 3,478

11 Progressive Mesh Hoppe

12 Progressive Mesh Hoppe

13 Progressive Mesh Benefits/Applications: Progressive transmission Surface compression Selective refinement

14 Progressive Transmission Slide by Hoppe Transmit records progressively: time M 0 vspl 0 vspl 1 vspl i-1 vspl n-1 Receiver displays: M 0 M i (~ progressive JPEG) M^

15 Progressive Transmission Slide by Southern Details added while user is browsing. Very useful for model repositories. [Certain et al.]

16 Progressive Transmission Hoppe

17 Mesh Compression Slide by Southern Lossy compression

18 Mesh Compression Slide by Southern Lossless compression

19 Mesh Compression vspl(v s,v l,v r, v s,v t, ) v l v v s r v l v r v s v t Slide by Hoppe Record deltas: v t - v s v s - v s Encoding of vspl records: connectivity: ~ good triangle strips attributes: excellent delta-encoding

20 Selective Refinement (VDPM) Slide by Hoppe Refine mesh adaptively based on viewpoint M 0 vspl 0 vspl 1 vspl i-1 vspl n-1 (e.g. view frustum)

21 Selective Refinement (VDPM) Hoppe

22 Selective Refinement (VDPM) Hoppe

23 Progressive Mesh Summary Slide by Hoppe M^ PM V F lossless M 0 vspl single resolution continuous-resolution smooth LOD space-efficient progressive

24 Multiresolution Meshes Irregular Semi-regular Completely regular [Hoppe]

25 Semi-Regular Mesh Arbitrary base mesh + refinement via subdivision [Hoppe]

26 Multiresolution Analysis original mapping remesh Irregular domain Regular [Guskov et al.]

27 Multiresolution Analysis step 1: construct a simple domain mesh K step 2: construct a parametrization r of M over K step 3: remesh

28 Multiresolution Analysis Step 1: construct simple base domain topological type of K = topological type of M small number of triangular regions smooth and straight boundaries mesh M partition domain mesh K [Lounsberry et al.]

29 Multiresolution Analysis Step 2: construct parameterization Map each face of domain mesh to corresponding triangular region local map [Lounsberry et al.]

30 Multiresolution Analysis Step 2: construct parameterization Map each face of domain mesh to corresponding triangular region Local maps must agree on boundaries and introduce small distortions harmonic maps planar triangle triangular region [Lounsberry et al.]

31 Multiresolution Analysis Step 3: remesh Regular subdivision [Hoppe]

32 Multiresolution Representation Wavelet representation base shape M 0 + sum of local correction terms (wavelet terms) [Lounsberry et al.]

33 Multiresolution Representation downsample predict/subdivide details/wavelets [Guskov et al.]

34 Multiresolution Representation Burt-Adelson pyramid coarsen subdivide n-1 vertices n vertices F details [Guskov et al.]

35 Multiresolution Representation wavelets wavelets [Guskov et al.]

36 Multiresolution Representation Two scalar displacement (t,n) One scalar (normal mesh) B A n A B n t t=o C C Normal Mesh [Guskov et al.]

37 Multiresolution Representation Normal mesh [Guskov et al.]

38 Multiresolution Meshes Applications: Adaptive remeshing Compression Filtering Editing Morphing

39 Adaptive Remeshing [Guskov et al.]

40 Adaptive Remeshing [Zorin et al.]

41 Adaptive Remeshing Both 11K triangles Uniform Adaptive [Zorin et al.]

42 Multiresolution Meshes Applications: Adaptive remeshing Compression Filtering Editing Morphing

43 Mesh Compression Effect of wavelet transform changes distribution of coefficients almost all coefficients close to zero 3 scalars 1 scalar Vertex coordinates Wavelet coefficients [Guskov et al.]

44 Mesh Compression Fixed file size Normal Meshes: CPM: [Guskov et al.]

45 Mesh Compression 956B 2004B 4806B 26191B 26K 4 bits/v 1253B 2804B 6482B 14844B 15K 2.5 bits/v [Guskov et al.]

46 Multiresolution Meshes Applications: Adaptive remeshing Compression Filtering Editing Morphing

47 Multiresolution Mesh Processing Smoothing [Guskov et al.]

48 Multiresolution Mesh Processing Enhancing smoothed + 2 * (original - smoothed) = enhanced [Guskov et al.]

49 Multiresolution Mesh Processing Filtering [Guskov et al.]

50 Multiresolution Meshes Applications: Adaptive remeshing Compression Filtering Editing Morphing

51 Multiresolution Mesh Editing Goal: edit surface with operations at various resolutions [Guskov et al.]

52 Multiresolution Mesh Editing When edit at fine resolution, update higher levels of multiresolution hierarchy Input at level 3 Edit on level 3 Effect of edit on level 2 [Zorin et al.]

53 Multiresolution Mesh Editing original coarse edit coarse edit fine [Guskov et al.]

54 Multiresolution Mesh Editing [Guskov et al.]

55 Multiresolution Mesh Editing [Zorin et al.]

56 Multiresolution Mesh Editing [Zorin et al.]

57 Multiresolution Mesh Editing [Zorin et al.]

58 Multiresolution Mesh Editing [Zorin et al.]

59 Multiresolution Meshes Applications: Adaptive remeshing Compression Filtering Editing Morphing

60 Multiresolution Mesh Morphing Goal: interpolate surfaces [Lee et al.]

61 Multiresolution Mesh Morphing Common parameterization If two semi-regular meshes have the same base domain, then they share a common parameterization

62 Multiresolution Mesh Morphing [Lee et al.]

63 Multiresolution Mesh Morphing [Lee et al.]

64 Multiresolution Mesh Morphing [Lee et al.]

65 Multiresolution Mesh Morphing Multiresolution Can morph different multiresolution levels at different rates

66 Multiresolution Mesh Morphing [Lee et al.]

67 Multiresolution Mesh Morphing with Spatial Control [Lee et al.]

68 Multiresolution Mesh Morphing [Lee et al.]

69 Multiresolution Mesh Morphing with Spatial Control [Lee et al.]

70 Multiresolution Meshes Irregular Semi-regular Completely regular [Hoppe]

71 Completely Regular Mesh Slide by Hoppe Regular sampling of parameter domain [r,g,b] = [x,y,z] Geometry Image

72 Multiresolution Meshes Key ideas Multiresolution analysis provides parameterization Different resolutions represent different frequencies Can map operations in parameter domain to operations on mesh (e.g., smoothing, morphing, etc.)

73 Acknowledgements Slides by Igor Guskov Wim Sweldens Peter Schroeder Denis Zorin Aaron Lee Emil Praun Michael Lounsberry Hugues Hoppe