1. CS 526 - Computer Graphics II
Decimation
Cristian Luciano

2. Contents Goals of decimation Levels of details
Topology preserving algorithms:
“Decimation of triangle meshes”
Schroeder, Zarge, Lorenzen (General Electric Co.)
“Progressive meshes”
Hugues Hoppe (Microsoft Research)
Topology simplifying algorithm:
“A topology modifying progressive decimation algorithm”
William Schroeder (GE Corporate R&D Center)
Conclusions

3. Goals of Decimation Reduce number of triangles in a triangle mesh
Maintain a good approximation to the original appearance

4. Levels of Detail d1 d2
Two approaches:
Distance LOD
Screen-Size LOD

5. “Decimation of triangle meshes” by Schroeder, Zarge, Lorenzen (SIGGRAPH’92)
For each point in the triangle mesh
Classify point and topology in the neighborhood of the point
If (the point can be deleted) then
Delete point
Triangulate the resulting hole

6. What kind of point is this?
Candidates for deletion
Interior Edge
Simple
Boundary
Complex
Corner

7. What is the error if the point is deleted?
Interior Edge
Simple
Boundary d
Average plane d
boundary
If (distance is less than d) then
Delete point
Delete all triangles using the point

8. What to do after point deletion?
The resulting hole has to be triangulated
Recursive 3D divide-and-conquer technique
Now: three polygons
Before: five polygons

9. Results
Original mesh
90% decimated

10. “Progressive meshes” by Hugues Hoppe (SIGGRAPH’96)
Progressive mesh = series of triangles meshes related by two invertible operations:
Edge collapse
Edge split S

11. Mesh simplification and reconstruction
Edge collapse
13,546
500
152
150
Thus the simplification starts with the original mesh, denoted M^n, and through a sequence of edge collapse transformations, simplifies it down to a very coarse base mesh, M^0.
<click> You can see the effect of the very last edge collapse transforming M^1 into M^0; it removes the last window from the airplane.
Edge split

12. Results

13. Modifies mesh topology to obtain more reduction
“A topology modifying progressive decimation algorithm” by William Schroeder (IEEE Visualization’97)
Basically combines:
“Decimation of triangle meshes”
“Progressing meshes”
Modifies mesh topology to obtain more reduction
Red edges = mesh boundaries
Green edges = manifold or interior edges

14. Vertex split and merge Interior Edge Corner Complex Simple
Vertex merge
Interior Edge
Complex
Corner
Simple

15. Results

16. Conclusions Three techniques to reduce number of polygons
Two preserving topology algorithms
One simplifying topology algorithm
How to classify points for decimation:
Simple, complex, boundary, interior edge, corner
Preserving topology operations:
Edge collapse
Edge split
Simplifying topology operations:
Vertex split
Vertex merge
Results of three algorithms

17. Thanks!
Any questions? Any comments?