Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
An optimal algorithm for intersecting three-dimensional convex polyhedra
SIAM Journal on Computing
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Solving the Collision Detection Problem
IEEE Computer Graphics and Applications
Spheres, molecules, and hidden surface removal
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
I-COLLIDE: an interactive and exact collision detection system for large-scale environments
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Computer graphics (2nd ed. in C): principles and practice
Computer graphics (2nd ed. in C): principles and practice
Efficient collision detection for moving polyhedra
Proceedings of the eleventh annual symposium on Computational geometry
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 fly-throughs in virtual environments
Proceedings of the twelfth annual symposium on Computational geometry
On the complexity of the union of fat objects in the plane
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An image-based approach to three-dimensional computer graphics
An image-based approach to three-dimensional computer graphics
Analysis of a bounding box heuristic for object intersection
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
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
Linear Size Binary Space Partitions for Fat Objects
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Algorithms for minimum volume enclosing simplex in R3
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
AfriGraph '01 1st International Conference on Virtual Reality, Computer Graphics and Visualization in Southern Africa ( formerly known as SAGA 2001 )
Reporting intersecting pairs of convex polytopes in two and three dimensions
Computational Geometry: Theory and Applications
Merging faces: a new orthogonal simplification of solid models
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
| Hi-index | 0.00 |
Heuristics that exploit bouning boxes are common in algorithms for rendering, modeling, and animation. While experience has shown that bounding boxes improve the performance of these algorithms in practice, the previous theoretical analysis has concluded that bounding boxes perform poorly in the worst case. This paper reconciles this discrepancy by analyzing intersections among n geometric objects in terms of two parameters: &agr; an upper bound on the aspect ratio or elongatedness of each object; and &sgr; an upper bound on the scale factor or size disparity between the largest and smallest objects. Letting Ko and Kb be the number of intersecting object pairs and bounding box pairs, respectively, we analyze a ratio measure of the bounding boxes' efficiency, r=Kb/n+Ko . The analysis proves that r=Oas log2s and r=Was . One important consequence is that if &agr; and &sgr; are small constants (as is often the case in practice), thenKb= O(Ko)+O(n, so an algorithm that uses bounding boxes has time complexity proportional to the number of actual object intersections. This theoretical result validates the efficiency that bounding boxes have demonstrated in practice. Another consequence of our analysis is a proof of the output-sensitivity of an algorithm for reporting all intersecting pairs in a set of n convex polyhedra with constant &agr; and &sgr;. The algorithm takes time O(nlogd−1n+Kologd−1n) for dimension d = 2, 3. This running time improves on the performance of previous algorithms, which make no assumptions about &agr; and &sgr;.