Matrix computations (3rd ed.)
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
Fast penetration depth computation for physically-based animation
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Nonconvex rigid bodies with stacking
ACM SIGGRAPH 2003 Papers
Efficient collision detection for animation and robotics
Efficient collision detection for animation and robotics
Impulse-based dynamic simulation of rigid body systems
Impulse-based dynamic simulation of rigid body systems
Six-degree-of-freedom haptic rendering using incremental and localized computations
Presence: Teleoperators and Virtual Environments
Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion
IEEE Transactions on Visualization and Computer Graphics
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
Interactive continuous collision detection for non-convex polyhedra
The Visual Computer: International Journal of Computer Graphics
Generalized penetration depth computation
Computer-Aided Design
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
Covering Minkowski sum boundary using points with applications
Computer Aided Geometric Design
Generalized penetration depth computation based on kinematical geometry
Computer Aided Geometric Design
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
C2A: controlled conservative advancement for continuous collision detection of polygonal models
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Volume contact constraints at arbitrary resolution
ACM SIGGRAPH 2010 papers
Adaptive image-based intersection volume
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
ACM Transactions on Graphics (TOG)
Computer-Aided Design
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We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.