Progressive Meshes

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Progressive Meshes

• A Talk by Wallner and Wurzer for the overfull
  MathMeth auditorium

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What its all about...
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Overview

• Advantages PMs
• Definition and Basics
• GeoMorphs
• Mesh Compression
• Selective Refinement
• Construction

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Lets start off...
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Advantages of PMs

• Mesh Simplification
• LOD Approximation
• Progressive Transmission
• Mesh Compression
• Selective Refinement

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Definition and Basics (1)

• A corner is a (vertex,face) tuple
• We are speaking of a sharp edge if
• it is a boundary adge
• the adjacent faces have different discrete values
  or
• adjacent corners have different scalar values

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Definition and Basics (2)

• Traditional Mesh
• Progressive Mesh
• (M0,Vsplit0
  Vsplitn-1)

K
V
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Definition and Basics (3)

• ? lossless !

vsplit
vt
vl
vr
vl
vr
vs

vs
ecol
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Definitions and Basics (4)
M0 ... Minimal Detailed Version
13,546
500
152
150
M0
M1
M175
ecol0
ecoli
ecoln-1
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Geomorph

• Smooth visual transition between two meshes Mf, Mc

Mf
Mc
v1
v1
v2
v2
Mfc
v3
v3
v4
V
F
V
v5
v6
v7
PM with geomorph
v8
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Geomorph (2)
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Mesh Compression
vspl(vs ,vl ,vr , vs ,vt ,)

• Record deltas
• vt - vs
• vs - vs

vt


vl
vl
vr
vr
vs

vs

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Selective Refinement

M0
vspl0
vspl1
vspli-1
vspln-1
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Selective Refinement (2)

• Rules for the vertex splits
• All involved vertices are present
• doRefine(v) TRUE ? neighbours should be
  further refined
• vertex is absent ? a previous vertex split was
  not executed, based on the two upper rules

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Selective Refinement (3)
View Frustum
Split not performed...
...because this split wasnot performed...
...which makes this vertex not present
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Selective Refinement (4)
View Frustum
if this would be present
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Construction

• Task
• Construct Mn-1, Mn-2, ... M0
• Naive Algorithm
• select random edge to collapse until
  resolution M0 faces

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Construction (2)

• Problems of naive algorithm
• Geometry is not preserved
• Color, Normals etc. are not preserved
• Discontinuities are not preserved

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Construction (3)

• Better algorithm
• (Re-)Sample object
• Simplify Object
• Use energy function to measure accuracy
• Extend to preserve...
• surface geometry
• color and normals
• discontinuities

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Energy Function

• E(V) Edist(V) Espring(V)
  Escalar(V)Edisc(V)
• ?E negative ? perform split

( less energy used for simplified mesh)
furtherexplanations
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With better algorithm...
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Summary

• PM have many advantages
• lossless
• captures discrete attributes
• captures discontinuities
• continuous-resolution
• smooth LOD
• space-efficient
• progressive

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Links (1)

• Progressive Meshes
• Hoppe
• http//research.microsoft.com/hoppe/(all
  images in this talk except those explicitly
  labeled courtesy of H. Hoppe)

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Links (2)

• quadric error metric scheme
• Garland and Heckbert
• http//graphics.cs.uiuc.edu/garland/papers.html
• memoryless scheme
• Lindstrom and Turk
• http//www.cs.gatech.edu/gvu/people/Phd/Peter.Lin
  dstrom.html

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Thank you for your attention !

• Progressive Meshes
• Wallner and Wurzer

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Discussion Note

• Problem of this approach

pictures courtesy of Markus Gross
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Discussion Note

• Better Approach

picture courtesy of Markus Gross