The Geometric and Solid Modeling Group at UNC is investigating techniques to perform efficient and accurate geometric computation. These include computation of Voronoi diagrams, medial axis, swept volumes and complex shapes defined by Boolean operations.

• Model Synthesis
• Fast Distance Field and Voronoi Diagram Computation using Graphics Hardware
  • Interactive 3D Distance Field Computation using Linear Factorization
  • Interactive Computation of Discrete Generalized Voronoi Diagrams using Range Culling
  • DiFi: Fast 3D Distance Field Computation Using Graphics Hardware
  • Fast Computation of Voronoi Diagrams using Graphics Hardware
• Efficient Approximate Algorithms for Boolean Operations, Motion Planning, Sweeps and Minkowski Sum with Geometric and Topological Guarantees
  • Fast Swept Volume Approximation of Complex Polyhedral Models
  • Feature-Sensitive Subdivision and Iso-Surface Reconstruction
  • Efficient Max-Norm Distance Computation and Reliable Voxelization
  • Star-shaped Roadmaps - A Deterministic Sampling Approach for Complete Motion Planning
  • Reliable Implicit Surface Polygonization using Visibility Mapping
  • Topology Preserving Free Configuration Space Approximation
  • Topology Preserving Isosurface Extraction for Geometry Processing
• Medial Axis Computation
  • Homotopy-Preserving Medial Axis Simplification
  • Efficient Computation of a Simplified Medial Axis
  • Exact Computation of the Medial Axis of a Polyhedron
• ESOLID: Accurate Boundary Evaluation

• Ming C. Lin
• Dinesh Manocha

• DARPA
• RDECOM
• Intel
• National Science Foundation
• Army Research Office

• Young J. Kim (EWHA University, Korea)
• Mark Foskey (UNC Radiology)
• Kenneth E. Hoff III (NVidia)
• John Keyser (Texas A&M University)
• Shankar Krishnan (AT&T Labs)
• Tim Culver (Think3)
• Gokul Varadhan (Google)