Decimation of Triangle Meshes

1. Decimation of Triangle Meshes William J. Schroeder, Jonathan A. Zarge, William E. Lorensen Presented by Alden Chew Serban Porumbescu

2. What is the Problem? • Want to visualize data interactively • Too many triangles • Too little hardware

3. High Level Approach • Characterize the local vertex geometry and topology • Evaluate decimation criteria for vertex removal • Triangulate the resulting hole

4. Vertex Classification • Feature edge: dihedral angle greater than user specified feature angle • An interior edge vertex is a vertex with two feature edges • A corner has one, three, or more feature edges

5. Vertex Removal • Based on user specified distance to plane or distance to edge (boundary vertex)

6. Vertex Removal • Removal of vertex creates a hole in the mesh • Triangulate • Removal of feature edge: • Create a new feature edge • If two non-overlapping loops can be created, triangulate the two loops

7. Triangulate Resulting Hole • Triangulate using a recursive loop splitting procedure • The stencil of the hole is called a loop • Loops are divided into two parts by a split line • Split line • A line between two non-adjacent vertices in the loop

8. Split Plane • Split plane • The plane orthogonal to the average plane through a split line • Used for half space comparisons

9. Loop Splitting Procedure • Need to create two non-overlapping loops • A valid loop is entirely on one side of the split plane …. • If the loop contain more than three vertices, recurse • If the loop has three vertices, form a triangle

10. Split Line Selection • Many split lines to choose from • Choose line that maximizes the aspect ratio • The aspect ratio is the minimum distance of the loop vertices to the split plane divided by the length of the split line

11. Special Cases • Want to preserve topology • Don’t create duplicate triangles and triangle edges

12. Sample Run From VTK (US Patent Number 5,559,388)

13. Skull

14. Blade

15. Hawaii

16. Mars