Computational geometry and discrete computations

In this talk we describe some problems arising in practical implementation of algorithms from computational geometry. Going to robust algorithms needs to solve issues such as rounding errors and degeneracies. Most of the problems are closely related to the incompatibility between on one side algorithms designed for continuous data and on the other side the discrete nature of the data and the computations in an actual computer.

[1]  Franco P. Preparata,et al.  A Probabilistic Analysis of the Power of Arithmetic Filters , 1998, Discret. Comput. Geom..

[2]  Kenneth L. Clarkson,et al.  Safe and effective determinant evaluation , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[3]  Jonathan Richard Shewchuk,et al.  Robust adaptive floating-point geometric predicates , 1996, SCG '96.

[4]  Stefan Felsner,et al.  On the Number of Arrangements of Pseudolines , 1996, SCG '96.

[5]  Christopher J. Van Wyk,et al.  Efficient exact arithmetic for computational geometry , 1993, SCG '93.

[6]  Donald E. Knuth,et al.  Axioms and Hulls , 1992, Lecture Notes in Computer Science.

[7]  Kokichi Sugihara,et al.  A robust Topology-Oriented Incremental algorithm for Voronoi diagrams , 1994, Int. J. Comput. Geom. Appl..

[8]  Douglas M. Priest,et al.  Algorithms for arbitrary precision floating point arithmetic , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.

[9]  Christoph Burnikel,et al.  Exact computation of Voronoi diagrams and line segment intersections , 1996 .

[10]  Mariette Yvinec,et al.  Evaluation of a new method to compute signs of determinants , 1995, SCG '95.

[11]  Kurt Mehlhorn,et al.  Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry , 2012, EATCS Monographs on Theoretical Computer Science.

[12]  Giuseppe Liotta,et al.  Robust Proximity Queries in Implicit Voronoi Diagrams , 1996, CCCG.

[13]  Kurt Mehlhorn,et al.  Exact geometric computation in LEDA , 1995, SCG '95.

[14]  D. Michelucci.  Arithmetic Issues in Geometric Computations , 1996 .

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

[16]  Kurt Mehlhorn,et al.  The Implementation of Geometric Algorithms , 1994, IFIP Congress.

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

[18]  Raimund Seidel,et al.  Better lower bounds on detecting affine and spherical degeneracies , 1995, Discret. Comput. Geom..

[19]  Bernard Chazelle,et al.  Better lower bounds on detecting affine and spherical degeneracies , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[20]  Michael B. Dillencourt,et al.  Realizability of Delaunay Triangulations , 1990, Inf. Process. Lett..