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Irregular to Completely Regular Meshing in Computer Graphics. Hugues Hoppe Microsoft Research International Meshing Roundtable 2002/09/17. Complex meshes in graphics (1994). 70,000 faces. Complex meshes in graphics (1997). 860,000 faces. Complex meshes in graphics (2000).

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irregular to completely regular meshing in computer graphics

Irregular to Completely RegularMeshingin Computer Graphics

Hugues Hoppe

Microsoft Research

International Meshing Roundtable2002/09/17

complex meshes in graphics 2000
Complex meshes in graphics (2000)

2,000,000,000faces

Challenges:

- rendering

- storage

- transmission

- scalability

[Digital Michelangelo Project]

multiresolution geometry
Multiresolution geometry

Irregular

Semi-regular

Completely regular

multiresolution geometry6
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]
goals in real time rendering
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”
not a goal mesh quality
Not a goal: mesh quality

13,000 faces

 1,000 faces

irregular meshes
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

texture mapping
Texture mapping

Vertex 1 x1 y1 z1

Vertex 2 x2 y2 z2

Face 2 1 3

Face 4 2 3

s1 t1

s2 t2

“Visual” accuracy

using coarse mesh

t

normal map

s

goals in real time rendering11
Goals in real-time rendering

#1 : Rendering speed

  • Minimize #vertices  best accuracy using irregular meshes

#2 : Rendering quality

  • Use texture mapping  parametrization
simplification edge collapse

13,546

500

152

150 faces

Mn

M175

M1

M0

ecoln-1

ecol0

ecoli

Simplification: Edge collapse

ecol

progressive mesh

150

152

500

13,546

M0

M1

M175

Mn

M0

Mn

vspl0

… vspli …

… vspli …

vspln-1

vspl0

vspln-1

progressive mesh (PM) representation

Progressive mesh
applications
Applications
  • Continuous LOD
  • Geomorphs
  • Progressive transmission

demo

demo

demo

progressive mesh summary

^

M

Progressive Mesh Summary

PM

V

F

lossless

M0

vspl

  • single resolution
  • continuous-resolution
  • smooth LOD
  • progressive
  • space-efficient
view dependent refinement of pm s

coarser

finer

vspl0

vspl1

vspli-1

vspln-1

M0

View-dependent refinement of PM’s

actual view

overhead view

vertex hierarchy

vspl0

vspl1

vspl2

vspl3

vspl4

vspl5

M0

v1

v2

v3

v10

v10

v11

v4

v5

v5

v8

v9

v12

v13

v6

v6

v7

Mn

v14

v15

Vertex hierarchy

M0

vspl0

vspl1

vspl2

vspl3

vspl4

vspl5

PM:

M0

v1

v2

v3

selective refinement

M0

vspl0

vspl0

vspl1

vspl1

vspl2

vspl2

vspl3

vspl3

vspl4

vspl4

vspl5

vspl2

M0

v1

v1

v1

v2

v2

v2

v3

v3

v3

v3

v10

v10

v10

v11

v11

v4

v4

v5

v5

v5

v8

v8

v9

v9

v8

v9

v12

v12

v13

v13

v6

v6

v7

v7

selectively refined mesh

v14

v15

Selective refinement
runtime algorithm

v3

v9

v10

v10

v11

v11

v4

v4

v8

v8

v8

v9

v9

dependency

v12

v13

v6

v6

v7

v7

new mesh

initial mesh

v14

v14

v15

v15

v15

Runtime algorithm

M0

v1

v2

v3

v10

v11

v4

v5

v8

v9

v12

v12

v13

v6

v7

v14

v15

  • Algorithm:
    • incremental
    • efficient
    • amortizable
complex terrain model
Complex terrain model

Puget Sound data

16K x 16K vertices

~537 million triangles

10m spacing, 0.1m resolution

4m demo

simpler 10m demo

selective refinement summary

^

M

V

F

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

texture mapping progressive meshes

[Sander et al 2001]

Texture mapping progressive meshes
  • Construct texture atlas valid for allM0…Mn.

e.g. 1000 faces

demo

pre-shaded demo

multiresolution geometry26
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]
semi regular representations
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

challenge finding domain
Challenge: finding domain

[Eck et al 1995]

[Lee et al 1998]

[Khodakovsky 2000]

[Guskov et al 2000]

[Lee et al 2000]…

base domain

original surface

techniques
Techniques
  • “Delaunay” partition + parametrization

[Eck et al. 1995]

  • Mesh simplification + …

[Lee et al. 1998]

[Lee et al. 2000]

[Guskov et al. 2000]

semi regular applications
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]

multiresolution geometry31
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]
mesh rendering complicated process
Mesh rendering: complicated process

Vertex 1 x1 y1 z1

Vertex 2 x2 y2 z2

Face 2 1 3

Face 4 2 3

s1 t1

s2 t2

random access!

random access!

current architecture
Current architecture

geometry

random

framebufferZ-buffer

GPU

$

random

$

texture

compression

random

compression

2D image compression

~40M Δ/sec

new architecture
New architecture

framebufferZ-buffer

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

geometry & textureimage

GPU

sequential

~random

great compression

compression

geometry image

[Gu et al 2002]

Geometry Image

completely regular sampling

3D geometry

geometry image257 x 257; 12 bits/channel

basic idea
Basic idea

cut

parametrize

demo

basic idea37
Basic idea

cut

sample

basic idea38
Basic idea

cut

store

render

[r,g,b] = [x,y,z]

rendering
Rendering

(65x65 geometry image)

demo

rendering with attributes
Rendering with attributes

geometry image 2572 x 12b/ch

normal-map image 5122 x 8b/ch

rendering

normal mapped demo
Normal-Mapped Demo

geometry image129x129; 12b/ch

normal map512x512; 8b/ch

demo

pre-shaded demo

advantages for hardware rendering
Advantages for hardware rendering
  • Regular sampling  no vertex indices.
  • Unified parametrization  no texture coordinates.

Raster-scan traversal of source data

 Run-time decompression?

compression
Compression

Image wavelet-coder

295 KB

 1.5 KB

fused cut

+ topological sideband (12 B)

compression results
Compression results

295 KB 

1.5 KB

3 KB

12 KB

49 KB

slide45

Irregular

Semi-regular

Completely regular

texture mapping demo
Texture Mapping Demo

2,000 faces

demo

displaced subdivision surfaces
Displaced subdivision surfaces

[Lee et al 2000]

control mesh

surface

displaced surface

movie

movie

scalar displacements

mip mapping
Mip-mapping

257x257

129x129

65x65

some artifacts
Some artifacts

aliasing

anisotropic sampling

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