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Transcript
```Decimation Of Triangle
Meshes
Avneesh Sud
Special Topics in
Computer Graphics
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.
Decimation
The Basic Mesh
• The Mesh is a collection of triangles in 3space, given by ( V,T(V) ), where V is the
list of vertices, and T(V) the list of
triangle definitions
Decimation
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
Decimation
The algorithm
• Characterize the local vertex geometry
and topology
• Evaluate decimation criteria
• Triangulate the resulting holes.
Decimation
Characterizing Local
Geometry
• Determines the vertices which are
possible candidates for deletion.
• All vertices except complex vertices are
candidates for deletion.
Decimation
Characterizing Local
Geometry
Simple
Corner Edge
Boundary
Complex
Decimation
Interior Edge
Evaluating Decimation Criteria
• Simple Vertices : Distance to average
plane
Decimation
Evaluating Decimation Criteria
• Boundary and Feature Edges : Distance
to edge
Decimation
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.
Decimation
Recursive Splitting
Triangulation
• A split plane orthogonal to average plane
is determined.
• If two loops do not overlap the split
plane is acceptable
Decimation
Recursive Splitting
Triangulation
• Best splitting plane is determined using
an aspect ratio
Min. distance of loop vertices from split line
Aspect Ratio 
Split line length
• Maximum aspect ratio gives best splitting
plane
Decimation
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
Decimation