Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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An Animation Speed-independent Collision Detection Algorithm

애니메이션 속도에 무관한 충돌 탐지 알고리즘

  • 김형석 (동의대학교 멀티미디어공학과)
  • Published : 2004.04.01
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Abstract

This paper presents an efficient collision detection algorithm the performance of which is independent of animation speed. Most of the previous collision detection algorithms are incremental and discrete methods, which find out the neighborhood of the extreme vertex at the previous time instance in order to get an extreme vertex at each time instance. However, if an object collides with another one with a high torque, then the angular speed becomes faster. Hence, the candidate by the incremental algorithms may be farther from the real extreme vertex at this time instance. Therefore, the worst time complexity nay be $O(n^2)$, where n is the number of faces. Moreover, the total time complexity of incremental algorithms is dependent on the time step size of animation because a smaller time step yields more frequent evaluation of Euclidean distance. In this paper, we propose a new method to overcome these drawbacks. We construct a spherical extreme vertex diagram on Gauss Sphere, which has geometric properties, and then generate the distance function of a polyhedron and a plane by using this diagram. In order to efficiently compute the exact collision time, we apply the interval Newton method to the distance function.

본 논문에서는 애니메이션 속도에 무관한 충돌 탐지 알고리즘을 제안한다. 현재까지 개발된 대부분의 충들 탐지 알고리즘들은 점진적(incremental) 알고리즘들로서, 현 시점에서의 가까운 점(근점)을 찾기 위하여 이전 시점의 근점 주위를 먼저 찾는다. 그런데 만일 움직이는 물체가 충돌 반응에 의해서 큰 토크를 받게 된다면 회전 속도가 증가하게 되어, 다음 시점에서의 실제 근점은 현 시점에서의 근점과는 매우 동떨어져 있어 엉뚱한 위치에서 근점을 찾게 되는 단점을 가진다. 그러므로, 최악의 경우에는 각 시점에서 $O(n^2)$, 시간이 소요될 수 있다. 또한 애니메이션 속도에 따라 이러한 점진적 계산 회수가 변하게 되어 전체적인 알고리즘의 소요 시간이 변하게 되는 단점을 가지고 있다. 본 논문에서는 이러한 문제점을 근본적으로 해결하고자 새로운 방법을 제안하고자 한다. 먼저, 기하학 특성을 내포하는 구면 근점 다이아그램을 생성하고, 이를 이용하여 두 물체간의 단일 거리 함수를 생성한다. 충돌 시점을 효율적으로 찾기 위해서 구간 뉴튼 방법을 거리함수에 적용한다.

Keywords

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