Kinetic Collision Detection for Convex Fat Objects

Abstract

We design compact and responsive kinetic data structures for detecting collisions between n convex fat objects in 3-dimensional space that can have arbitrary sizes. Our main results are:(i) If the objects are 3-dimensional balls that roll on a plane, then we can detect collisions with a KDS of size O(n log n) that can handle events in O(log 2 n) time. This structure processes O(n 2 ) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories.(ii) If the objects are convex fat 3-dimensional objects of constant complexity that are free-flying in R 3 , then we can detect collisions with a KDS of O(n log 6 n) size that can handle events in O(log 7 n) time. This structure processes O(n 2 ) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories. If the objects have similar sizes then the size of the KDS becomes O(n) and events can be handled in O(log n) time.

A review of collision detection for deformable objects

“…Abam et al proposed kinetic algorithms for three-dimensional CD, 113 it is only suitable for broad-phase CD of simple polygonal deformable bodies, and its performance is far worse than other existing methods. The dynamic data structure can be well adapted to deformed bodies and moving objects, but such an approach is vulnerable to oversampling or undersampling, and can also be wasteful of computational resources.…”

Advanced Methods for Robot-Environment Interaction towards an Industrial Robot Aware of Its Volume

“…The theory of collisions between volumes is here studied, in order to detect if a volume is in contact with others; furthermore, in order to correctly implement the methods of volumetric interference regions, a further module to compute the minimum distance between volumes has to be taken into account this study is strictly connected to the one related to collision detection and it will not be described here. For a deeper treatment of this topic, the reader can refer to [15]. The study of such architecture is a step towards the realization of a more intelligent robot and aware of its volume, starting from the tool mounted on its flange and giving the opportunity to extend this model to the whole robot arm.…”

Kinetic Compressed Quadtrees in the Black-Box Model with Applications to Collision Detection for Low-Density Scenes

“…(In addition, if there is a collision the motion equations of the objects involved are changed based on the collision response.) KDSs for collision detection have been proposed for 2D collision detection among polygonal objects [2,15], for 3D collision detection among spheres [14], and for 3D collision detection among fat convex objects [1].…”

“…Such knowledge is not always available. Another disadvantage is that some KDSs are complicated and may not be efficient in practice-the collision-detection KDS for fat objects [1] is an example. We therefore study collision detection in the more practical blackbox model [9,12], where we receive new locations for the objects of S at regular time steps t = 1, 2, .…”