Decimation%20Of%20Triangle%20Meshes

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Decimation Of Triangle Meshes
Avneesh Sud Special Topics in Computer Graphics
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What Is Decimation ?

• Reduction in the number of triangles in a
  triangle mesh, maintaining the original topology,
  as well as its overall appearance determined by
  discrete and scalar attributes.

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The Basic Mesh

• The Mesh is a collection of triangles in 3-space,
  given by ( V,T(V) ), where V is the list of
  vertices, and T(V) the list of triangle
  definitions

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Requirements for a Good Decimation

• The original topology of the mesh must be
  preserved
• The decimated mesh must be a good approximation
  to the original
• Optional Vertices of the decimated mesh be a
  subset of original set. This allows to preserve
  the appearance attributes

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The algorithm

• Characterize the local vertex geometry and
  topology
• Evaluate decimation criteria
• Triangulate the resulting holes.

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Characterizing Local Geometry

• Determines the vertices which are possible
  candidates for deletion.
• All vertices except complex vertices are
  candidates for deletion.

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Characterizing Local Geometry
Corner Edge
Simple
Boundary
Complex
Interior Edge
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Evaluating Decimation Criteria

• Simple Vertices Distance to average plane

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Evaluating Decimation Criteria

• Boundary and Feature Edges Distance to edge

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Triangulation

• If a vertex is eliminated, the loop created by
  removing the vertex is re-triangulated.
• Every loop is star shaped recursive loop
  splitting triangulation schemes are used.
• If a loop cannot be retriangulated, the vertex
  generating the loop is not removed.

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Recursive Splitting Triangulation

• A split plane orthogonal to average plane is
  determined.
• If two loops do not overlap the split plane is
  acceptable

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Recursive Splitting Triangulation

• Best splitting plane is determined using an
  aspect ratio
• Maximum aspect ratio gives best splitting plane

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Special Cases

• Modification of topology of a closed structure
• Topological holes in the mesh
• These are checked by triangulation to ensure
  duplicate triangles or edges are not created

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Results
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Results