SCG '87 Proceedings of the third annual symposium on Computational geometry
Curved surfaces and coherence for non-penetrating rigid body simulation
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Journal of the ACM (JACM)
Incremental algorithms for collision detection between solid models
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
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
Hardware-assisted virtual collisions
VRST '98 Proceedings of the ACM symposium on Virtual reality software and technology
Obstacle Collision Detection Using Best Ellipsoid Fit
Journal of Intelligent and Robotic Systems
Collision Detection for Interactive Graphics Applications
IEEE Transactions on Visualization and Computer Graphics
Incremental Algorithms for Collision Detection Between Polygonal Models
IEEE Transactions on Visualization and Computer Graphics
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Collision Detection of a Moving Polygon in the Presence of Polygonal Obstacles in the Plane
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast and Accurate Collision Detection for Virtual Environments
Dagstuhl '97, Scientific Visualization
Image-Based Techniques in a Hybrid Collision Detector
IEEE Transactions on Visualization and Computer Graphics
Collision prediction for polyhedra under screw motions
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Image-based collision detection
Integrated image and graphics technologies
Continuous path verification in multi-axis NC-machining
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Local Model of Interaction for Haptic Manipulation of Rigid Virtual Worlds
International Journal of Robotics Research
A randomized marking scheme for continuous collision detection in simulation of deformable surfaces
Proceedings of the 2006 ACM international conference on Virtual reality continuum and its applications
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
A Virtual Environment Testbed for Training Laparoscopic Surgical Skills
Presence: Teleoperators and Virtual Environments
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
A new algebraic method for robot motion planning and real geometry
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Precise generalized contact point and normal determination for rigid body simulation
Proceedings of the 2009 ACM symposium on Applied Computing
Fast generation of multiple collision-free and linear trajectories in dynamic environments
IEEE Transactions on Robotics
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 parallel filter in subspace
I3D '11 Symposium on Interactive 3D Graphics and Games
Fast continuous collision detection among deformable models using graphics processors
EGVE'06 Proceedings of the 12th Eurographics conference on Virtual Environments
A collisions evaluation method in virtual environment for collaborativeassembly
Journal of Network and Computer Applications
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We consider the collision-detection problem for a three-dimensional solid object moving among polyhedral obstacles. The configuration space for this problem is six-dimensional, and the traditional representation of the space uses three translational parameters and three angles (typically Euler angles). The constraints between the object and obstacles then involve trigonometric functions. We show that a quaternion representation of rotation yields constraints which are purely algebraic in a seven-dimensional space. By simple manipulation, the constraints may be projected down into a six-dimensional space with no increase in complexity. The algebraic form of the constraints greatly simplifies computation of collision points, and allows us to derive an efficient exact intersection test for an object which is translating and rotating among obstacles.