Towards implementing robust geometric computations

Computational geometry has the unique opportunity to bridge the sharp gap between theoretical and applied computer science. Indeed, practical computations with geometric objects are of intense interest to a wide range of applied work including computer aided design, robotics, mathematics, engineering, etc. At the same time, these computations pose many challenging problems of considerable theoretical depth and interest.

[1]  Raimund Seidel,et al.  Constructing Arrangements of Lines and Hyperplanes with Applications , 1986, SIAM J. Comput..

[2]  M. Karasick On the representation and manipulation of rigid solids , 1989 .

[3]  Kokichi Sugihara,et al.  On Finite-Precision Representations of Geometric Objects , 1989, J. Comput. Syst. Sci..

[4]  Victor J. Milenkovic,et al.  Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic , 1989, Artif. Intell..

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  Jeffrey C. Lagarias,et al.  The computational complexity of simultaneous Diophantine approximation problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[7]  Raimund Seidel,et al.  Constructing arrangements of lines and hyperplanes with applications , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[8]  John E. Hopcroft,et al.  Robust set operations on polyhedral solids , 1987, IEEE Computer Graphics and Applications.

[9]  Thomas Ottmann,et al.  Numerical stability of geometric algorithms , 1987, SCG '87.

[10]  F. Frances Yao,et al.  Finite-resolution computational geometry , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).