Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Collision Detection for Moving Polyhedra
IEEE Transactions on Pattern Analysis and Machine Intelligence
A geometric investigation of reach
A geometric investigation of reach
The complexity of robot motion planning
The complexity of robot motion planning
Geometric collisions for time-dependent parametric surfaces
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Convex decomposition of polyhedra and robustness
SIAM Journal on Computing
Interval methods for multi-point collisions between time-dependent curved surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
V-COLLIDE: accelerated collision detection for VRML
VRML '97 Proceedings of the second symposium on Virtual reality modeling language
Strategies for polyhedral surface decomposition: an experimental study
Computational Geometry: Theory and Applications
A fast and robust GJK implementation for collision detection of convex objects
Journal of Graphics Tools
Interference detection among solids and surfaces
Communications of the ACM
Obstacle Collision Detection Using Best Ellipsoid Fit
Journal of Intelligent and Robotic Systems
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Fast continuous collision detection for articulated models
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Fast continuous collision detection among deformable models using graphics processors
Computers and Graphics
C-DIST: efficient distance computation for rigid and articulated models in configuration space
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Interactive Continuous Collision Detection Using Swept Volume for Avatars
Presence: Teleoperators and Virtual Environments
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
Velocity-Aligned Discrete Oriented Polytopes for Dynamic Collision Detection
IEEE Transactions on Visualization and Computer Graphics
Kinematic convexity of spherical displacements and its application to collision prediction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Efficient distance computation in configuration space
Computer Aided Geometric Design
Generalized penetration depth computation based on kinematical geometry
Computer Aided Geometric Design
C2A: controlled conservative advancement for continuous collision detection of polygonal models
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Fast continuous collision detection using deforming non-penetration filters
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Fast continuous collision detection using parallel filter in subspace
I3D '11 Symposium on Interactive 3D Graphics and Games
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Computer-Aided Design
Fast continuous collision detection among deformable models using graphics processors
EGVE'06 Proceedings of the 12th Eurographics conference on Virtual Environments
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The prediction of collisions amongst N rigid objects may be reduced to a series of computations of the time to first contact for all pairs of objects. Simple enclosing bounds and hierarchical partitions of the space-time domain are often used to avoid testing object-pairs that clearly will not collide. When the remaining pairs involve only polyhedra under straight-line translation, the exact computation of the collision time and of the contacts requires only solving for intersections between linear geometries. When a pair is subject to a more general relative motion, such a direct collision prediction calculation may be intractable. The popular brute force collision detection strategy of executing the motion for a series of small time steps and of checking for static interferences after each step is often computationally prohibitive. We propose instead a less expensive collision prediction strategy, where we approximate the relative motion between pairs of objects by a sequence of screw motion segments, each defined by the relative position and orientation of the two objects at the beginning and at the end of the segment. We reduce the computation of the exact collision time and of the corresponding face/vertex and edge/edge collision points to the numeric extraction of the roots of simple univariate analytic functions. Furthermore, we propose a series of simple rejection tests, which exploit the particularity of the screw motion to immediately decide that some objects do not collide or to speed-up the prediction of collisions by about 30%, avoiding on average 3/4 of the root-finding queries even when the object actually collide.