Kinetic collision detection between two simple polygons

AbstractWe design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting

Kinetic and dynamic data structures for convex hulls and upper envelopes

AbstractLet S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n2βs+2(n)logn) critical events, each in O(log2n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, βs(q)=λs(q)/q, and λs(q) is the maximum length of Davenport–Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch, Guibas and Hershberger [J. Basch, L.J. Guibas, J. Hershberger, Data structures for mobile data, J. Algorithms 31 (1999) 1–28], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic

Shooting permanent rays among disjoint polygons in the plane

We present a data structure for ray shooting-and-insertion in the free space among disjoint polygonal obstacles with a total of $n$ vertices in the plane, where each ray starts at the boundary of some obstacle. The portion of each query ray between the starting point and the first obstacle hit is inserted permanently as a new obstacle. Our data structure uses O(n log n) space and preprocessing time, and it supports m successive ray shooting-and-insertion queries in O(n log2 n + m log m) total time. We present two applications for our data structure: (1) Our data structure supports efficient implementation of auto-partitions in the plane i.e. binary space partitions where each partition is done along the supporting line of an input segment. If n input line segments are fragmented into m pieces by an auto-partition, then it can now be implemented in O(n log2n+m log m) time. This improves the expected runtime of Patersen and Yao's classical randomized auto-partition algorithm for n disjoint line segments to O(n log2 n). (2) If we are given disjoint polygonal obstacles with a total of n vertices in the plane, a permutation of the reflex vertices, and a half-line at each reflex vertex that partitions the reflex angle into two convex angles, then the folklore convex partitioning algorithm draws a ray emanating from each reflex vertex in the prescribed order in the given direction until it hits another obstacle, a previous ray, or infinity. The previously best implementation (with a semi-dynamic ray shooting data structure) requires O(n3/2-e/2) time using O(n1+e) space. Our data structure improves the runtime to O(n log2 n)

Scalable collision detection for distributed virtual environments

PhD ThesisDistributed Virtual Environments (DVEs) provide a mechanism whereby dispersed users can interact with one-another within a shared \'irtual world. DVEs commonly allow users to interact with one-another in ways analogous to the real-world, e.g. mimicking Newtonian physics. A scalable DVE should enable large numbers of users to participate simultaneously, regardless of the In geographical location and hardware configurations of individual users. addition, these users should perceive a mutually-consistent virtual world in which each user perceives a consistent series of events in real-time. Collision detection and response is a fundamental requirement of most virtual environments and simulations. It is a computationally-expensive operation which must be perfonned at frequent intervals in all virtual environments which simulate the motion of solid objects. Collision detection has received large amounts of research interest and as a result a number of efficient collision detection algorithms have been proposed. However, these collision detection approaches are designed to detect collisions efficiently in simulations run on a single machine and are not capable of overcoming problems associated with scalability and consistency, which are of paramount importance in DVEs. This thesis presents a new collision detection approach, tenned distributed collision detection, which provides high-levels of scalability, consistency and responsiveness. This thesis presents the algorithms and theory which underpin the distributed collision detection approach and provides experimental results demonstrating its scalability and responsiveness

Kinetic Collision Detection Between Two Simple Polygons

We design a kinetic data structure for detecting collisions between two simple polygons in motion. In order to do so, we create a planar subdivision of the free space between the two polygons, called the external relative geodesic triangulation, which certifies their disjointness. We show how this subdivision can be maintained as a kinetic data structure when the polygons are moving, and analyze its performance in the kinetic setting. 1 Introduction The problem of collision detection between moving objects is fundamental to simulations of the physical world. It has been studied in a number of di#erent communities, including robotics, computer graphics, computeraided design, and computational geometry. Methods have been developed for the case of rigid bodies moving freely in two and three dimensions. Many extant techniques for collision checking on objects of complex geometry rely on hierarchies of simple bounding volumes surrounding each of the objects. For a given placement of two no..