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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 l.jpg

Irregular to Completely RegularMeshingin Computer Graphics

Hugues Hoppe

Microsoft Research

International Meshing Roundtable2002/09/17




Complex meshes in graphics 2000 l.jpg
Complex meshes in graphics (2000)

2,000,000,000faces

Challenges:

- rendering

- storage

- transmission

- scalability

[Digital Michelangelo Project]


Multiresolution geometry l.jpg
Multiresolution geometry

Irregular

Semi-regular

Completely regular


Multiresolution geometry6 l.jpg
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 l.jpg
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 l.jpg
    Not a goal: mesh quality

    13,000 faces

     1,000 faces


    Irregular meshes l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg

    13,546

    500

    152

    150 faces

    Mn

    M175

    M1

    M0

    ecoln-1

    ecol0

    ecoli

    Simplification: Edge collapse

    ecol


    Invertible vertex split transformation l.jpg

    vspl(vs ,vl ,vr, …)

    ecol

    vl

    vr

    vs

    Invertible: vertex split transformation


    Progressive mesh l.jpg

    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 l.jpg
    Applications

    • Continuous LOD

    • Geomorphs

    • Progressive transmission

    demo

    demo

    demo


    Progressive mesh summary l.jpg

    ^

    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 l.jpg

    coarser

    finer

    vspl0

    vspl1

    vspli-1

    vspln-1

    M0

    View-dependent refinement of PM’s

    actual view

    overhead view


    Parent child vertex relations l.jpg

    vsplit

    vs

    vsplit

    vu

    vt

    Parent-child vertex relations


    Vertex hierarchy l.jpg

    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 l.jpg

    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 l.jpg

    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 l.jpg
    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 l.jpg

    ^

    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 l.jpg

    [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 l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg
    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 l.jpg
    Current architecture

    geometry

    random

    framebufferZ-buffer

    GPU

    $

    random

    $

    texture

    compression

    random

    compression

    2D image compression

    ~40M Δ/sec


    New architecture l.jpg
    New architecture

    framebufferZ-buffer

    • Minimize #vertices bandwidth,through compression.

    • Maximize sequential (non-random) access

    geometry & textureimage

    GPU

    sequential

    ~random

    great compression

    compression


    Geometry image l.jpg

    [Gu et al 2002]

    Geometry Image

    completely regular sampling

    3D geometry

    geometry image257 x 257; 12 bits/channel


    Basic idea l.jpg
    Basic idea

    cut

    parametrize

    demo


    Basic idea37 l.jpg
    Basic idea

    cut

    sample


    Basic idea38 l.jpg
    Basic idea

    cut

    store

    render

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


    Rendering l.jpg
    Rendering

    (65x65 geometry image)

    demo


    Rendering with attributes l.jpg
    Rendering with attributes

    geometry image 2572 x 12b/ch

    normal-map image 5122 x 8b/ch

    rendering


    Normal mapped demo l.jpg
    Normal-Mapped Demo

    geometry image129x129; 12b/ch

    normal map512x512; 8b/ch

    demo

    pre-shaded demo


    Advantages for hardware rendering l.jpg
    Advantages for hardware rendering

    • Regular sampling  no vertex indices.

    • Unified parametrization  no texture coordinates.

      Raster-scan traversal of source data

       Run-time decompression?


    Compression l.jpg
    Compression

    Image wavelet-coder

    295 KB

     1.5 KB

    fused cut

    + topological sideband (12 B)


    Compression results l.jpg
    Compression results

    295 KB 

    1.5 KB

    3 KB

    12 KB

    49 KB


    Slide45 l.jpg

    Irregular

    Semi-regular

    Completely regular


    Texture mapping demo l.jpg
    Texture Mapping Demo

    2,000 faces

    demo


    Displaced subdivision surfaces l.jpg
    Displaced subdivision surfaces

    [Lee et al 2000]

    control mesh

    surface

    displaced surface

    movie

    movie

    scalar displacements


    Mip mapping l.jpg
    Mip-mapping

    257x257

    129x129

    65x65


    Some artifacts l.jpg
    Some artifacts

    aliasing

    anisotropic sampling


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