Explosion of digital 3D models 1. reverse engineering: laser scanning 2. interactive software….
Problem: large scale Digital Michelangelo project:
1 billion polygons
Real-time application real-time rendering, real-time interaction…
Motivation
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Input Mesh models Example poses
Output Multi-resolution hierarchy:
Simplified vertices and their skin weights
Method Minimize an error metric using quartic
optimization method
Simplification of Articulated Meshes
2. Vertex clustering method RB[93] Cluster generation Compute a representation Mesh generation Topology changes
Previous work: static mesh
1. break-simplify-stitch[SF99] Break into bones Simplify bones individually Stitch together
Previous work: deformable
2. static simplification-reinterpret[HP01] Do simplification on static model Reinterpret the simplification on deformable
models
Previous work: deformable
3. Bagging method[MG03] Compute simplification for all poses Sum QEF error of all vertices for each pose Use the QEF of vertices to govern the order
of edge collapses
Previous work: deformable
4.improve method #3[DR05] Improve by locally rotating the QEF using
bone transformation and adding the QEF together
Allow QEF to position simplified vertices
Previous work: deformable
5.build multi-resolution hierarchy and search a closest simplification [SPB01,SP01]
Build multiply simplifications For each pose of deformation, find a closest
simplification that has best qualify for that pose
Previous work: deformable
Input: one or more poses of the skeleton
Use edge collapses methods Modify the quadratic error function
Method
Minimize error function
Not quadratic, but quartic with α and v Approach: split into two steps
Fix α, find optimal v --- quadratic!!! Fix v, find optimal α ----quadratic!!!
Method
Fix α, find optimal v due to insufficient pose sampling or small
number of bones. Lead to invertible matrix
Method