Geometric

The GAMMA research group 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.

Publications

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VV-NET: Voxel VAE Net with Group Convolutions for Point Cloud Segmentation  2019.
International Conference on Computer Vision 2019

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Interactive simulation of local interactions in dense crowds using elliptical agents  2017.
Journal of Statistical Mechanics: Theory and Experiment

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Multi-contact Frictional Rigid Dynamics using Impulse Decomposition  2017.
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2017)

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CAMA: Contact-Aware Matrix Assembly with Unified Collision Handling for GPU-based Cloth Simulation  2016.
Computer Graphics Forum, (Proceedings of Eurographics 2016)

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GPU Accelerated Convex Hull Computation  2012.
Computers and Graphics (Proc Shape Modeling International)

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Efficient Boundary Extraction of BSP Solids Based on Clipping Operations  2012.
IEEE Transactions on Visualization and Computer Graphics (TVCG)

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GPU-based Offset Surface Computation Using Point Samples  2012.
ACM Solid and Physical Modeling

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Model Synthesis: A General Procedural Modeling Algorithm  2011.
IEEE Transactions on Visualization and Computer Graphics (TVCG)

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Efficient Simplex Computation for Fixture Layout Design  2011.
Computer-Aided Design (CAD)

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Transforming GIS Data into Functional Road Models for Large-Scale Traffic Simulation  2011.
IEEE Transactions on Visualization and Computer Graphics (TVCG)

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Example-based Curve Synthesis  2010.
Computers and Graphics

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Constraint-based Model Synthesis.  2009.
SIAM/ACM Joint Conference on Geometric and Physical Modeling

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Model Synthesis  2009.
Ph.D. Dissertation, University of North Carolina at Chapel Hill

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Example-based Curve Generation  2009.

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A Simple Path Non-Existence Algorithm Using C-obstacle Query  2008.
Algorithmic Foundation of Robotics VII: Selected Contributions of the Seventh International Workshop on the Algorithmic Foundations of Robotics (WAFR), Springer Tracts in Advanced Robotics (STAR)

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D-Plan: Efficient Collision-free Path Computation for Part Removal and Disassembly  2008.
International CAD Conference (Best Paper)

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Continuous Model Synthesis  2008.
ACM Transactions on Graphics (Proc SIGGRAPH Asia)

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Real-time Path Planning for Virtual Agents in Dynamic Environments  2007.
IEEE Virtual Reality (VR)

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C-DIST: Efficient Distance Computation for Rigid and Articulated Models in Configuration Space  2007.
ACM Symposium on Solid and Physical Modeling (SPM)

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Surface Distace Maps  2007.
Graphics Interface

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Cable Route Planning in Complex Environments Using Constrained Sampling  2007.
ACM Symposium on Solid and Physical Modeling (SPM)

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Example-based Model Synthesis  2007.
ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D)

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Interactive 3D Distance Field Computation Using Linear Factorization  2006.
ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D)

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Fast C-obstacle Query Computation for Motion Planning  2006.
IEEE International Conference on Robotics and Automation (ICRA)

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Homotopy-preserving Medial Axis Simplification  2006.
International Journal of Computational Geometry and Applications (IJCGA)

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Generalized Penetration Depth Computation  2006.
ACM Symposium on Solid and Physical Modeling (SPM)

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Fast Proximity Computation Among Deformable Models Using Discrete Voronoi Diagrams  2006.
ACM Transactions on Graphics (Proc ACM SIGGRAPH)

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Surface Distance Maps  2006.

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Homotopy-preserving Approximate Voronoi Diagram of 3D Polyhedron  2006.

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Homotopy-preserving Medical Axis Simplification  2005.
ACM Symposium on Solid and Physical Modeling (SPM)

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Interactive Computation of Discrete Generalized Voronoi Diagrams Using Range Culling  2005.
International Symposium on Voronoi Diagrams in Science and Engineering

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Efficient Collision Culling among Deformable Objects Using Graphics Processors  2005.
Presence: Teleoperators and Virtual Environments

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A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots  2005.
International Journal of Robotics Research (IJRR)

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Accurate Minkowski Sum Approximation of Polyhedral Models  2005.
Graphical Models

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Topology Preserving Surface Extraction Using Adaptive Subdivision  2004.
Eurographics Symposium on Geometry Processing (SGP)

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Geometry-Driven Physical Interaction Between Avatars and Virtual Environments  2004.
Computer Animation and Virtual Worlds (CAVW)

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Efficient Computation of a Simplified Medial Axis  2003.
ACM Symposium on Solid Modeling and Applications (SMA)

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Exact Computation of a Medial Axis of a Polyhedron  2003.
Computer Aided Geometric Design (CAGD)

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Feature-sensitive Subdivision and Iso-surface Reconstruction  2003.
IEEE Visualization (VIS)

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Fast Swept Volume Approximation of Complex Polyhedral Models  2003.
ACM Symposium on Solid Modeling and Applications (SMA)

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A Hybrid Approach for Determinant Signs of Moderate-sized Matrices  2003.
International Journal of Computational Geometry and Applications (IJCGA)

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ESOLID - A System for Exact Boundary Evaluation  2002.
ACM Symposium on Solid Modeling and Applications (SMA)

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Simplified Representations for Modeling Hair  2002.

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PRECISE: Efficient Multiprecision Evaluation of Algebraic Roots and Predicates for Reliable Geometric Computation  2001.
ACM Symposium on Computational Geometry (SCG)

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Reliable Geometric Computations with Algebraic Primitives and Predicates  2001.
Workshop on Uncertainty in Geometric Computations

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BOOLE: A Boundary Evaluation System for Boolean Combinations of Sculptured Solids  2001.
International Journal of Computational Geometry and Applications (IJCGA)

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Efficient and Exact Manipulation of Algebraic Points and Curves  2000.
Computer-Aided Design (CAD)

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Exact Boundary Evaluation for Curved Solids  2000.
Ph.D. Dissertation, University of North Carolina at Chapel Hill

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Partitioning Trimmed Spline Surfaces into Non-Self-Occluding Regions for Visibility  2000.
Graphical Models

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A Hybrid Approach for Evaluating Signs of Moderately-sized Matrices  2000.

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Efficient and Accurate B-rep Generation of Low Degree Sculptured Solids Using Exact Arithmetic  1999.
Computer Aided Geometric Design (CAGD)

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MAPC: A library for Efficient and Exact Manipulation of Algebraic Points and Curves  1999.
ACM Symposium on Computational Geometry (SCG)

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Accurate Computation of the Medial Axis of a Polyhedron  1999.
ACM Symposium on Solid Modeling and Applications (SMA)

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Fast and Accurate Boundary Evaluation of Low-degree Sculptured Solids  1998.
IMA Conference on Mathematics of Surfaces

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Efficient and Accurate B-rep Generation of Low Degree Sculptured Solids Using Exact Arithmetic  1997.
ACM Symposium on Solid Modeling and Applications (SMA)

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Interactive Boundary Computation of Boolean Combinations of Sculptured Solids  1997.
Eurographics

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Efficient and Accurate Boundary Evaluation Algorithms for Boolean Combinations of Sculptured Solids  1997.
Ph.D. Dissertation, University of North Carolina at Chapel Hill

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Incremental Algorithms for Collision Detection Between Solid Models  1997.
IEEE Transactions on Visualization and Computer Graphics (TVCG)

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Algebraic Pruning: A Fast Technique for Curve and Surface Intersection  1997.
Computer Aided Geometric Design (CAGD)

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An Efficient Surface Intersection Algorithm Based on Lower Dimensional Formulation  1997.
ACM Transactions on Graphics

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Efficient and Accurate B-rep Generation of Low Degree Sculptured Solids Using Exact Arithmetic  1996.

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Algebraic Loop Detection and Evaluation Algorithms for Curve and Surface Interrogations  1996.
Graphics Interface

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BOOLE: A System to Compute Boolean Combinations of Sculptured Solids  1996.
CSG

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High Speed and High Fidelity Visualization of Complex CSG Models  1995.
BCS International Conference on Visualization and Modeling

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Numeric-symbolic Algorithms for Evaluating One Dimensional Algebraic Sets  1995.
ACM Symposium on Symbolic and Algebraic Computation (SYMSAC)

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Representation and Computation of Boolean Combinations of Sculptured Models  1995.
ACM Symposium on Computational Geometry (SCG)

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Representation and Fast Display of Complex CSG Models  1995.

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Algorithms for Intersecting Parametric and Algebraic Curves II: Multiple Intersections  1995.
Computer Vision, Graphics and Image Processing

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Hidden Surface Removal Algorithms for Curved Surfaces  1994.

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Algorithms for Intersecting Parametric and Algebraic Curves I: Simple Intersections  1994.
ACM Transactions on Graphics

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Algebraic Pruning: A Fast Technique for Curve and Surface Intersection  1993.

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Detecting Cusps and Inflection Points in Curves  1992.
Computer Aided Geometric Design (CAGD)

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Implicit Representation of Rational Parametric Surfaces  1992.
Journal of Symbolic Computation (JSC)

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Algorithms for Implicitizing Rational Parametric Surfaces  1992.
Computer Aided Geometric Design (CAGD)

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Rational Curves with Polynomial Parametrizations  1991.
Computer-Aided Design (CAD)

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A New Approach for Surface Intersection  1991.
International Journal of Computational Geometry and Applications (IJCGA)

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