Controlled Topology Simplification Voxel Based Object Simplification

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Controlled Topology Simplification(Voxel Based
Object Simplification)

• T. He, L. Hong, A. Varshney, S. Wang
• Udeepta Bordoloi

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Why Simplification?

• Levels of Detail
• High frame rate
• Removal of high frequencies (anti-aliasing)
• Moire patterns

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Conceptually

• Simplification can be in two areas
• Geometry
• Reduce the number of geometry primitives
• Topology
• Reduce the number of holes, tunnels etc.

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The factor of Topology

• Simplifying
• Will change the topology!!!
• Preserving
• Will limit the amount of simplification possible
• Will keep certain high frequencies
• Can we take the middle path?

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Pipeline
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Sampling

• Input models
• Polygonal
• Range scanned
• Volume
• Mathematical function
• Sample the 3-d space
• Get a 3-d signal (volume as we know in sci-viz)

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Controlled(?) Filtering

• Use low-pass filtering to create
  frequency-limited versions of the sampled volume
• To create a series of LOD volumes, use a series
  of low-pass filters.
• End result volume pyramid
• Can easily get interpolated volumes for
  in-between levels

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Compare this volume hierarchy with -

• Locality based clustering of geometry
• Mip-maps (which use averaging, also a kind of
  low-pass filtering)

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Pipeline
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Reconstruction

• Volume reconstruction
• Surface reconstruction
• Iso-surface
• Too many faces
• Can output high frequency patterns
• Need to preserve topology of the iso-surface
  while simplifying
• Method of choice improved Splitting Box Algo.

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Splitting Box

• Vertices above/equal iso-value black
• Vertices below iso-value white
• Edge is MC if
• Color changes at most once along the sequence of
  its vertices
• Face is MC if all 4 edges are MC
• Box is MC if all 6 faces are MC

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Splitting Box

• Start with the whole grid as a single box
• Recursive division of the box along its longest
  edge until
• 2x2x2 box
• MC box B with satisfactory approximation
• What is a satisfactory approximation?

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Satisfactory approximation

• Sub-boxes of B, B1 and B2, are MC
• Approximation triangles intersect the common face
  of B1 and B2 in between grid points where there
  is a color change
• Triangle chain of B geometrically coincident with
  that of B1 and B2 (?)
• Thus, approximate surface cannot be more than one
  sampling distance in error

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Adaptive Marching Cubes

• Edge is AMC if
• Color changes at most once along the sequence of
  its vertices
• Face is AMC if all 4 edges are AMC
• Box is AMC if all possible grid lines in the
  encompassed 3d space are AMC

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How is AMC different from Splitting Box?

• Splitting Box can have unnecessary splits
• E.g., non-MC box can get split along an MC edge,
  thus sub-boxes would still be non-MC
• Non-AMC splits are done by finding the axes which
  have non-AMC edges
• Different approximation checking
• Within a user-specified distance from the true
  (MC) surface

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Multi-layered surface rendering

• Render multiple surfaces at different opacities
• Visibility order determination a problem

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Results

• Slides