Approximate and exact collision detection among polyhedral objects in arbitrary motion

• Main Authors: Wang, Jui-Lung, 王瑞龍
• Other Authors: Chin-Shyurng Fahn
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/00259262476980053467

碩士 === 國立台灣工業技術學院 === 電機工程技術研究所 === 85 === This thesis presents the algorithms for collision detection in a 3-Dgraphical environment simulated by a computer system, where all the objectsare represented as polyhedral ones and perform arbitrary translating and/orrotating motions. These algorithms can be directly used for both convex andconcave objects which consist of convex polygons. In the realisticapplications, there require two kinds of solutions: time-interrupted andtime- continuous collision detection; the former can detect the exact positionof a collision event at a fixed time step, and the latter can determine bothapproximate time and position of a collision event. The algorithms first localize the object-to- object collision events by the"space cell" method which divides the 3-D environment into small cells. Inthis manner, only those cells that intersect moving objects are examined inorder to reduce the number of testing a pair of bounding volumes surroundingthe objects. An azimuth-elevation map method is then proposed to quicklyselect the polygons in the overlap region between two candidate objects bypresorting their vertices in the spherical coordinates system. Afterperforming that, a divide- and-conquer method which takes advantage of thebounding box representation is presented to moderate the number of thepolygons needed to be checked by a polygon-to-polygon intersection test. Todeal with the time-interrupted and time- continuous collision detection, twopolygon-to-polygon intersection testing methods based on a hierarchicalscheme are developed to reduce unnecessary computation. All the experiments are made by using the Microsoft Visual C/C++ 4.0compiler under the operation system Microsoft Windows NT 4.0 of a personalcomputer with a Pentium Pro-180 CPU and 64M RAM. As shown in the experiments,the time complexity of the space cell method grows near linearly as theamount of objects increases. When the bounding sphere of an object exactlyembraces its occupied space, the azimuth-elevation map method is moreefficient than the enumerative method for selecting all the polygons withinor across the overlap region. The divide-and- conquer method can economizelots of computing time as the experiments reveal. The time-continuouscollision detection algorithm is successfully verified, and also compared withthe time-interrupted collision detection one to understand its computationloading. So far, all the experimental results from our proposed methods arevery encouraging.