Collision Detection Using Bounding Boxes: Convexity Helps
نویسندگان
چکیده
We consider the use of bounding boxes to detect collisions among a set of convex objects in R d. We derive tight bounds on the ratio between the number of box intersections and the number of object intersections. Connrming intuition, we show that the performance of bounding boxes improves signiicantly when the underlying objects are all convex. In particular, the ratio is (1?1=d 1=2 box) if each object has aspect ratio at most and the set has scale factor box. More signiicantly, the bounding box performance ratio is (2(1?1=d) 3?1=d avg 1 3?1=d box n 1?1=d 3?1=d) if only the average aspect ratio avg 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: rst, 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 interpreted as collision; and nally, the question is interesting from a theoretical standpoint. The proofs of our theorems are quite delicate, requiring several new ideas and non-trivial analyses.
منابع مشابه
Bounding box collision detection
In this paper we address the problem of intersection detection between pairs of bounding boxes in three-dimensional space. Our motivation for investigating this problem comes from the need for an efficient collision detection framework applicable in the context of large scale contact analysis. Not considering underlying physics of the mechanical contact problem we focus on purely geometrical se...
متن کاملDynamic Collision Detection using Oriented Bounding Boxes
2 Oriented Bounding Boxes 5 2.1 Separation of OBBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Testing for Intersection of OBBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Stationary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Constant Velocities . . . . . . . . . . . . ...
متن کاملBeyond Bounding Boxes: Precise Localization of Objects in Images
Beyond Bounding Boxes: Precise Localization of Objects in Images
متن کاملA Collision Detection-Based Wandering Method for Equipment Deploy Scene in Land Reclamation Area of Mining Dump
Aiming at developing a simple and efficient collision detection method to support the wandering in equipment deploy scene in land reclamation area of mining dump. This paper presents an efficient algorithm for collision detection in the waste dump land reclamation equipment deploy scene using a bounding volume nestification which consists of an oriented bounding boxes (OBBs) enhanced with axial...
متن کامل