Irregular to Completely Regular Meshing in Computer Graphics

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Irregular to Completely RegularMeshingin
Computer Graphics

• Hugues Hoppe
• Microsoft Research
• International Meshing Roundtable2002/09/17

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Complex meshes in graphics (1994)
70,000 faces
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Complex meshes in graphics (1997)
860,000 faces
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Complex meshes in graphics (2000)
2,000,000,000faces
Challenges - rendering - storage -
transmission - scalability
Digital Michelangelo Project
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Multiresolution geometry
Semi-regular
Irregular
Completely regular
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Multiresolution geometry

• Irregular meshes
• Progressive meshes 1996
• View-dependent refinement 1997
• Texture-mapping PM 2001
• Semi-regular meshes
• Multiresolution analysis 1995
• Completely regular meshes
• Geometry images 2002

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Goals in real-time rendering

• 1 Rendering speed
• 60-85 frames/second
• 2 Rendering quality
• geometric visual accuracy
• temporal continuity
• Not a Goal
• Mesh quality

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Not a goal mesh quality
13,000 faces
? 1,000 faces
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Irregular meshes
Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2
Face 2 1 3 Face 4 2 3
Rendering cost vertex processing
rasterization
vertices
constant
yuck
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Texture mapping
Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2
s1 t1 s2 t2
Face 2 1 3 Face 4 2 3
Visual accuracy using coarse mesh
t
normal map
s
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Goals in real-time rendering

• 1 Rendering speed
• Minimize vertices ? best accuracy using
  irregular meshes
• 2 Rendering quality
• Use texture mapping ? parametrization

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Simplification Edge collapse
ecol
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Invertible vertex split transformation
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Progressive mesh
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Applications

• Continuous LOD
• Geomorphs
• Progressive transmission

demo
demo
demo
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Progressive Mesh Summary
PM
V
F
lossless
M0
vspl

• continuous-resolution
• smooth LOD
• progressive
• space-efficient

• single resolution

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View-dependent refinement of PMs
actual view
overhead view
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Parent-child vertex relations
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Vertex hierarchy
vspl0
M0
vspl1
vspl2
vspl3
vspl4
vspl5
PM
v2
v1
v3
M0
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Selective refinement
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Runtime algorithm
v1
v2
v3
M0
v5
v10
v11
v4
v8
v9
v7
v12
v13
v6
v12
v14
v15

• Algorithm
• incremental
• efficient
• amortizable

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DEMO View-dependent LOD
demo
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Complex terrain model
Puget Sound data 16K x 16K vertices 537 million
triangles
10m spacing, 0.1m resolution
4m demo
simpler 10m demo
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Selective Refinement Summary
PM

• continuous-resolution
• smooth LOD
• space-efficient
• progressive

M0
vspl

• view-dependentrefinement
• real-time algorithm

M0
v1
v2

M
v3
v4
v5
v6
v7
v8
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Texture mapping progressive meshes
Sander et al 2001

• Construct texture atlas valid for all M0Mn.

e.g. 1000 faces
demo
pre-shaded demo
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Multiresolution geometry

• Irregular meshes
• Progressive meshes 1996
• View-dependent refinement 1997
• Texture-mapping PM 2001
• Semi-regular meshes
• Multiresolution analysis 1995
• Completely regular meshes
• Geometry images 2002

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Semi-regular representations
Eck et al 1995 Lee et al 1998 Khodakovsky
2000 Guskov et al 2000 Lee et al 2000
semi-regular
irregular base mesh
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Challenge finding domain
Eck et al 1995 Lee et al 1998 Khodakovsky
2000 Guskov et al 2000 Lee et al 2000
original surface
base domain
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Techniques

• Delaunay partition parametrization

Eck et al. 1995

• Mesh simplification

Lee et al. 1998
Lee et al. 2000
Guskov et al. 2000
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Semi-regular Applications

• View-dependent refinement
• Texture-mapping
• Multiresolution editing
• Compression

Lounsbery et al. 1994
Certain et al. 1995
Zorin et al. 1997
Khodakovsky et al. 1999
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Multiresolution geometry

• Irregular meshes
• Progressive meshes 1996
• View-dependent refinement 1997
• Texture-mapping PM 2001
• Semi-regular meshes
• Multiresolution analysis 1995
• Completely regular meshes
• Geometry images 2002

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Mesh rendering complicated process
Vertex 1 x1 y1 z1 Vertex 2 x2 y2 z2
s1 t1 s2 t2
Face 2 1 3 Face 4 2 3
random access!
random access!
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Current architecture
geometry
random
framebufferZ-buffer
GPU

random

texture
compression
random
compression
2D image compression
40M ?/sec
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New architecture
framebufferZ-buffer
geometry textureimage
GPU
sequential
random
great compression
compression

• Minimize vertices bandwidth, through
  compression.
• Maximize sequential (non-random) access

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Geometry Image
Gu et al 2002
3D geometry
completely regular sampling
geometry image257 x 257 12 bits/channel
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Basic idea
cut
parametrize
demo
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Basic idea
cut
sample
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Basic idea
cut
store
render
r,g,b x,y,z
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Rendering
(65x65 geometry image)
demo
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Rendering with attributes
geometry image 2572 x 12b/ch
normal-map image 5122 x 8b/ch
rendering
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Normal-Mapped Demo
geometry image129x129 12b/ch
normal map512x512 8b/ch
demo
pre-shaded demo
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Advantages for hardware rendering

• Regular sampling ? no vertex indices.
• Unified parametrization ? no texture
  coordinates.
• ? Raster-scan traversal of source data
• ? Run-time decompression?

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Compression
Image wavelet-coder
? 1.5 KB
295 KB
fused cut
topological sideband (12 B)
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Compression results
295 KB ?
1.5 KB
3 KB
12 KB
49 KB
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Semi-regular
Irregular
Completely regular
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(No Transcript)
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Texture Mapping Demo
2,000 faces
demo
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Displaced subdivision surfaces
Lee et al 2000
control mesh
displaced surface
surface
movie
movie
scalar displacements
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Mip-mapping
257x257
129x129
65x65
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Some artifacts
aliasing
anisotropic sampling