Projects

Computational Geometry and Topology in Geometric Modeling and Graphics

Reconstruction

• Curve reconstruction
• Surface reconstruction
• Non-smooth, non-manifold surface reconstruction
• Boundary reconstruction

Meshing

• Polyhedra
• Smooth surface
• Remeshing
• Isosurface
• Piecewise smooth complexes
• Localized Delaunay refinement

Homology features

• Handle and tunnel loops
• Shortest homology bassis
• Optimal homologous cycles

Shape features

• Medial axis
• Curve skeletons
• Dimension detection
• Shape segmentation and matching
• Normal and feature approximation

Data sparsification

• Graph Induced complex

Simplification

Computational and combinatorial geometry

Computational topology (NSF report)