Topologically sweeping an arrangement
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Incremental computation of planar maps
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Collision Detection for Interactive Graphics Applications
IEEE Transactions on Visualization and Computer Graphics
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Efficient collision detection of complex deformable models using AABB trees
Journal of Graphics Tools
Real-Time Collision Detection and Response for Complex Environments
CGI '00 Proceedings of the International Conference on Computer Graphics
CLODs: dual hierarchies for multiresolution collision detection
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A State Machine for Real-Time Cutting of Tetrahedral Meshes
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Meshless deformations based on shape matching
ACM SIGGRAPH 2005 Papers
Interactive collision detection between deformable models using chromatic decomposition
ACM SIGGRAPH 2005 Papers
A physically-based framework for real-time haptic cutting and interaction with 3D continuum models
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Fast collision detection for deformable models using representative-triangles
Proceedings of the 2008 symposium on Interactive 3D graphics and games
Fast collision detection using the A-buffer
The Visual Computer: International Journal of Computer Graphics
Extension of half-edges for the representation of multiresolution subdivision surfaces
The Visual Computer: International Journal of Computer Graphics
A unified structure for crowd simulation
Computer Animation and Virtual Worlds
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Collision detection in geometrically complex scenes is crucial in physical simulations and real time applications. Works based on spatial hierarchical structures have been proposed for years. If correct performances are obtained for static scenes, these approaches show some limitations when the complexity of the scene increases and particularly in case of deformable meshes. The main drawback is the time needed to update the spatial structures - often trees - when global deformations or topological changes occur in the scene. We propose a method to detect collisions in complex and deformable environments with constant time amortized complexity for small displacements. Our method is based on a convex decomposition of the environment coupled with a forecast mechanism exploiting temporal coherence. We use the topological adjacencies and incidence relationships to reduce the number of geometrical tests. Deformations of the scenes are handled with no cost as far as no topological changes occur. Topological transformations, like cuts and sewings, are handled locally, exploiting the spatial coherence and do not imply global updates. We illustrate our method in two experimental frameworks: a particles flow simulation and a meshless animation system both lying in a deformable mesh. We compare our work with classical optimization based on bounding volumes hierarchies to validate its efficiency on large scenes.