Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms

This paper describes a general purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those obtained without using it. We believe that this technique will become a standard tool in writing geometric software.

[1]  A. Charnes.  Optimality and Degeneracy in Linear Programming , 1952 .

[2]  G. Dantzig,et al.  Notes on Linear Programming: Part 1. The Generalized Simplex Method for Minimizing a Linear Form under Linear Inequality Restraints , 1954 .

[3]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[4]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .

[5]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[6]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[7]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[8]  R. Seidel.  A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions , 1981 .

[9]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[10]  Richard Pollack,et al.  Multidimensional Sorting , 1983, SIAM J. Comput..

[11]  L. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi , 1985, TOGS.

[12]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[13]  Raimund Seidel,et al.  Constructing higher-dimensional convex hulls at logarithmic cost per face , 1986, STOC '86.

[14]  Leonidas J. Guibas,et al.  Topologically sweeping an arrangement , 1986, STOC '86.

[15]  Herbert Edelsbrunner,et al.  Computing a Ham-Sandwich Cut in Two Dimensions , 1986, J. Symb. Comput..

[16]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[17]  Franz Aurenhammer,et al.  Geometric Relations Among Voronoi Diagrams , 1987, STACS.

[18]  Chee-Keng Yap,et al.  A geometric consistency theorem for a symbolic perturbation scheme , 1988, SCG '88.