THE PROBLEMS OF ACCURACY AND ROBUSTNESS IN GEOMETRIC COMPUTATION

作     者：HOFFMANN, CM 

作者机构：Comput. Sci. Dept. Purdue Univ. West Lafayette IN 

出 版 物：《COMPUTER》 (IEEE计算机杂志)

年 卷 期：1989年第22卷第3期

页      面：31-&页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：AT&T Foundation National Science Foundation, NSF, (CCR 86-198 17) National Science Foundation, NSF Office of Naval Research, ONR, (014-86-K-0465) Office of Naval Research, ONR 

主　　题：accuracy computational geometry degeneracies avoidance degenerate positions floating-point computation geometric computation geometric operations interacting numeric data interacting symbolic data limited-precision rational arithmetic linear elements model numerical precision perturbation-free methods purely symbolic representations representation robustness symbolic data alteration 

摘      要：Practical implementation of geometric operations remains error-prone, and the goal of implementing correct and robust systems for carrying out geometric computation remains elusive. The problem is variously characterized as a matter of achieving sufficient numerical precision, as a fundamental difficulty in dealing with interacting numeric and symbolic data, or as a problem of avoiding degenerate positions. The author examines these problems, surveys some of the approaches proposed, and assesses their potential for devising complete and efficient solutions. He restricts the analysis to objects with linear elements, since substantial problems already arise in this case. Three perturbation-free methods are considered: floating-point computation, limited-precision rational arithmetic, and purely symbolic representations. Some perturbation approaches are also examined, namely, representation and model, altering the symbolic data, and avoiding degeneracies