BOXING VIA VERTEX CLUSTERING

• Simplest application of boxing: cluster vertices (Rossignac-Borrel [3]).
• STEP 1: Grading of Vertices
  • Based on "visual importance"
  • (A) Favor vertices with high probability of being in silhouette
  • (B) Favor vertices that bound large faces
  • (a) Estimated by inverse of maximum angle theta of incident faces.
  • (b) Estimated by maximum length of incident edges.
  • Low [2] argues that cos(theta/2) is a better estimate than 1/theta.
• STEP 2: Triangulation of Faces
  - standard routine
• STEP 3: Clustering of Vertices
  - SIMPLEST: truncate low order bits of coordinates
• STEP 4: Synthesis of Representative Vertices
  - E.g. Center of mass of cluster
  - Choose vertex of maximum weight.
  - SIMPLEST: use truncated coordinates
• STEP 4: Elimination of Vertices, Edges and Faces
  - Eliminate duplicated trianges/edges/vertices
  - Edges or Triangles collapse to points
  - Eliminate point only if non isolated
  - Triangles collapse to edges
  - Eliminate only if the edge bounds a face in simplified model
• STEP 5: CLEANUP
  - result may not be "valid 3D models"
• Evaluation
  - method is fast
  - no need to know surface topology
  - topology not preserved
  - grading of vertices is rather subjective
• REFINEMENTS
  - Local clustering: use vertices of large weight as centers of clustering coordinates