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Mathematics: Collision Detection
Collision Detection Shader Using Cube-Maps |
Sphere Trees for Speedy BSPs |
Using the Covariance Matrix for Better-Fitting Bounding Objects |
Fast Contact Reduction for Dynamics Simulation |
Fast Collision Detection for 3D Bones-Based Articulated Characters |
Considerations for Movement and Physics in MMP Games |
Collision Detection of Deformable Volumetric Meshes |
Recursive Dimensional Clustering: A Fast Algorithm for Collison Detection |
Sphere Trees for Fast Visibility Culling, Ray Tracing, and Range Searching |
Abstract: The article presents an algorithm and demonstration application that manages thousands of objects in motion that are continuously maintained as a collection of hierarchical bounding spheres in a SphereTree. The design goal for this algorithm has been to make the 99-percentile case spend almost no CPU time updating an object in motion within the tree structure. Queries against the SphereTree perform more tests than other data structures, but this is mitigated by the fact that the tree can be maintained using very little CPU time. This data structure is ideally suited for gross culling of massive numbers of moving objects in a large world space. It doesn't matter if the objects are moving at widely disparate speeds, or even if many of them are not in motion at all. It also has a very low cost when objects are inserted and removed from the tree with great frequency.
Compressed Axis-Aligned Bounding Box Trees |
Abstract: The axis-aligned bounding box (AABB) tree structure has proven to be very useful for accelerating intersection queries on sets of geometry. The data structure is easy to implement, the built structure is numerically well conditioned, and like all binary trees, they have O(log n) search time. This article explains several techniques that can be used to lower the overall memory footprint of an AABB tree to 11 bytes per triangle.
Direct Access Quadtree Lookup |
Abstract: This article presents a general-purpose optimization for quadtree access that improves performance in three ways over the traditional implementations: 1) by eliminating node traversal and the unnecessary cache-misses it causes, 2) by requiring fewer instructions and CPU cycles overall vs. a best case traditional approach, and 3) by doing so in a compact amount of time and with minimal memory accesses regardless of what depth in the tree the target node resides in.
Abstract: This article will help lay the groundwork for building an accurate physics simulation by starting with one of the most crucial parts of a real-time physics engine: 3D collision detection. The two basic algorithms this article covers are: Bounding Sphere Collision Detection and Triangle-to-Triangle Collision Detection.
Multi-Resolution Maps for Interaction Detection (Collision Detection) |
Abstract: This article describes a method for reducing the number of proximity tests that must be performed for games with large numbers of game objects of varying sizes.
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