CS 395: Adv. Computer Graphics

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CS 395 Adv. Computer Graphics

• Week 5Modeling II
• Subdivision and Simplification
• Watt Chapter 2.5
• Jack Tumblin
• jet_at_cs.northwestern.edu

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Shape Manipulation

• How can we
• Simplify a shape? 10Mpoly ? 500 poly?
• Check Visibility? discard many Mpolys never
  seen?
• Make a shape from a cloud of points?
• Warp from Shape A to Shape B?

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Model Simplification

• The idea
• It should look the same, but
• have fewer polys.

Watson 2000

• In general, it works!
• Only limited user control.
• Some surface mappings handled poorly.

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Model Simplification

• Many 3D Models are too big to
• Display interactively
• Display at all (!)
• Sources
• 3D scanning Laser Time-of-Flight Reflectometry
• Visualization of scientific data
• Huge CAD/CAM efforts
• 100 man-years plants, ships and planes
• Procedural models grass, trees, cities, etc.

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Edge Collapse / Vertex Split

• Elemental Simplify Operation (by consensus)

• Edge Collapse
• choose edge
• 2 old ?1 new vertex
• update edges, faces

• Vertex Split
• choose edge pair
• 1 old?2new vertices
• update edges, faces

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Model Simplification

• Basic approach
• Choose a simplifier (e.g. edge collapse)
• Choose a quality measure (a 'cost' for the
  operator)
• Use a greedy algorithm (edge collapse
  example)
• Sort edges by cost
• Loop until simple enough
• Collapse least-cost edge
• Re-sort affected nearby edges

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Combinatoric Explosion

• How many different ways to simplify? TOO MANY!
  
• ( of vertex removal sequences) (valence)
• Recall that valence edges that end at a
  vertex.
• or formally, O(N! N/E)
• Also O(N) new vertex placements
• ?Good Simplification Quality metrics needed!

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Simplification Hierarchy

• What is it?
• Binary Tree of Edge Collapses
• Graph nodevertex, Graph Edgecollapse
• Leaf nodeoriginal mesh vertex
• Parent node new vertex from edge collapse
• Why use it?
• Can pre-compute it
• Load entire graph (cheap)
• Graph Cut quickly selects a pre-computed,locally
  - simplified model

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Local Simplification
Many Polygons (far from the graph root) Few
Polygons (near the graph root)
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Model Simplification Taxonomy I

• Quick Taxonomy of simplifying methods
• Spatial Clustering
• Merge chosen clusters of verts, edges, faces
• Earliest (Rossignac)
• easy, very fast, but poor quality
• Pairwise merge algorithms
• Merge adjacent face pair, edge pair, or vertex
  pair (edge collapse Hoppe,Garland)
• Slower, but often best quality
• Can be tricky for non-triangle faces .

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Model SimplificationTaxonomy II

• Pruning algorithms
• vertex deletion ( delete adjacent edges)
• edge deletion ( delete empty vertices)
• face deletion ( replace with a vertex)
• too crude changes too large!
• Opinion Research community converged on edge
  collapse only edge collapse matters anymore!

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Related Problems

• Level of detail (LOD)
• Simplified models in interactive display
• Measuring visual fidelity
• Which simplifier best preserves the visual
  appearance?
• Surface fitting
• 3D scanner gives a cloud of points
• How do we make a surface model?

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Related Problems

• Mesh Zippering (Turk Levoy 1996)
• Make multiple partial scans
• Fit surface to each scan (fairly simple)
• Choose two partial scans
• Align them using iterated closest points
• Join the surfaces topologically
• Tune the local geometry compare to point cloud
• Critique widely used
• -- didnt address reflectance surface
  properties
• -- what about parametric surfaces?

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Surface fitting

• Surface fitting Find surface from a cloud of
  points

Hoppe 94
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Related Problems

• Shape comparison Problem
• How can we sort and query for shapes?
• Define a shape-labeling function we want...
• Compact, low-dimensional identifier (string?)
• invariant to scaling, rotation, minor
  details
  
  (defined as...?)
  
• (Osada, Funkhouser et al)
• sprinkle model with randomly placed points
• find distance between random point pairs
• collect a histogram of these distances
• E.g. volume of tetrahedron between four model
  points
• Use it to create a shape distribution
• Make a lot of random samples of shape function
• Form a histogram
• Fit a piecewise linear probability distribution
  function
• Result, a vector with N integers
• Compare shape distributions
• Use existing function comparison approaches
• They use Minkowski sum

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Related Problems

• Shape comparison Problem
• How can we sort and query for shapes?
• Define a shape-labeling function we want...
• Compact, low-dimensional identifier (string?)
• invariant to scaling, rotation, minor
  details
  
  (defined as...?)
  
• (Osada, Funkhouser et al. 2001)
• sprinkle model with randomly placed points
• find distance between random point pairs
• collect a histogram of these distances

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Other Shape Manipulations

• Deforming Polygonal Shapes
• Bones and skin
• Space Warp(don't bend object bend space)
• 'Growing Skin (Markosian99)
• Particle System, Force-Field guide mesh growth
• Implicit surfaces (bend space)

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'Growing Skin (Markosian99)

• Start with an underlying skeleton
• Particle System guides skin growth on it
• Skinspring-mass system with drag, stiffness,
  etc.

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'Growing Skin (Markosian99)

• Start with an underlying skeleton
• Particle System, force field guides skin growth
  on it.
• Skinspring-mass system with drag, stiffness,
  etc.

Markosian1999
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3D Morphing

• Change shape A to shape B (Turk/OBrien99)