Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Solving the Collision Detection Problem
IEEE Computer Graphics and Applications
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
Real-time collision detection for motion simulation within complex environments
SIGGRAPH '96 ACM SIGGRAPH 96 Visual Proceedings: The art and interdisciplinary programs of SIGGRAPH '96
An image-based approach to three-dimensional computer graphics
An image-based approach to three-dimensional computer graphics
Collision detection in aspect and scale bounded polyhedra
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Analysis of a bounding box heuristic for object intersection
Journal of the ACM (JACM)
Collision Detection and Response for Computer Animation
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
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We consider the use of bounding boxes to detect collisions among a set of convex objects in Rd. We derive tight bounds on the ratio between the number of box intersections and the number of object intersections. Confirming intuition, we show that the performance of bounding boxes improves significantly when the underlying objects are all convex. In particular, the ratio is θ(α1-1/d σbox1/2) if each object has aspect ratio at most α and the set has scale factor σbox. More significantly, the bounding box performance ratio is θ(αavg2(1-1/d/3-1/d σbox1/3-1/d n1-1/d/3-1/d) if only the average aspect ratio αavg of the n objects is known. These bounds are the best possible as we show matching lower bound constructions. The case of convex objects is interesting for several reasons: first, in many applications, the objects are either naturally convex or are approximated by their convex hulls for convenience; second, in some applications, the penetration of convex hulls is interpretedas collision; and finally, the question is interesting from a theoretical standpoint.