1. Decimation Of Triangle Meshes
Avneesh Sud
Special Topics in Computer Graphics

2. Advanced Topics in 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
Advanced Topics in Graphics

3. Advanced Topics in Graphics
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
Decimation
Advanced Topics in Graphics

4. 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
Advanced Topics in Graphics

5. Advanced Topics in Graphics
The algorithm
Characterize the local vertex geometry and topology
Evaluate decimation criteria
Triangulate the resulting holes.
Decimation
Advanced Topics in Graphics

6. Characterizing Local Geometry
Determines the vertices which are possible candidates for deletion.
All vertices except complex vertices are candidates for deletion.
Decimation
Advanced Topics in Graphics

7. Characterizing Local Geometry
Corner Edge
Simple
Boundary
Complex
Interior Edge
Decimation
Advanced Topics in Graphics

8. Evaluating Decimation Criteria
Simple Vertices : Distance to average plane
Decimation
Advanced Topics in Graphics

9. Evaluating Decimation Criteria
Boundary and Feature Edges : Distance to edge
Decimation
Advanced Topics in Graphics

10. Advanced Topics in Graphics
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
Advanced Topics in Graphics

11. Recursive Splitting Triangulation
A split plane orthogonal to average plane is determined.
If two loops do not overlap the split plane is acceptable
Decimation
Advanced Topics in Graphics

12. Recursive Splitting Triangulation
Best splitting plane is determined using an aspect ratio
Maximum aspect ratio gives best splitting plane
Decimation
Advanced Topics in Graphics

13. Advanced Topics in Graphics
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
Advanced Topics in Graphics

14. Advanced Topics in Graphics
Results
Decimation
Advanced Topics in Graphics

15. Advanced Topics in Graphics
Results
Decimation
Advanced Topics in Graphics