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C. Burnikel, K. Mehlhorn, S. Schirra, How to compute the Voronoi diagram of line segments: theoretical and experimental results. Proc. 2nd Eur. Symp. Alg. (ESA 94), 1994.
C. Burnikel, K. Mehlhorn, S. Schirra, On degeneracy in geometric computations, Proc. Fifth Annual Symp. Discrete Algorithms pp. 16–23, 1994.
K. L. Clarkson, Safe and effective determinant evaluation, 33th Symp. on Found. Comp. Sci. 387–395, 1992.
H. Edelsbrunner, E. Mücke. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics 9(1):66–104, 1990.
S. Fang, B. Bruderlin, X. Zhu, Robustness in solid modelling — a tolerance based, intuitionistic approach, Computer Aided Design, 25:9, 1993.
S. Fortune, Progress in computational geometry, in Directions in Geometric Computing, Ch. 3, pp. 81–128, R. Martin, ed. Information Geometers Ltd, 1993.
S. Fortune, C. Van Wyk, Static analysis yields efficient exact integer arithmetic for computational geometry, to appear, Transactions on Graphics. See also Efficient exact arithmetic for computational geometry, Proc. Ninth Ann. Symp. Comp. Geom, pp. 163–172, 1993.
S. Fortune, Numerical stability of algorithms for 2d Delaunay triangulations, International Journal of Computational Geometry and Applications, 5(1,2), 193–213, 1995.
S. Fortune, Polyhedral modelling with exact arithmetic, Proc. Third Symp. Solid Modeling and Applications, pp. 225–234, 1995.
L. Guibas, D. Marimont, Rounding arrangements dynamically, Proc. Eleventh Ann. Symp. Comp. Geom, pp. 190–199.
C. Hoffmann, The problems of accuracy and robustness in geometric computation. Computer 22:31–42 (1989).
D.J. Jackson, Boundary representation modelling with local tolerances, Proc. Third Symp. on Solid Modeling and Applications, pp. 247–254 (1995).
P. Jaillon, Proposition d'une arithmétique rationnelle paresseuse et d'un outil d'aide à la saisie d'objets en synthèse d'images, Thèse, Ecole Nationale Superieure des Mines de Saint-Etienne, 1993.
S. Näher, The LEDA user manual, Version 3.1, January 16, 1995. LEDA is available by anonymous FTP from ftp.mpi-sb.mpg.de in directory /pub/LEDA.
Victor Milenkovic, Verifiable implementations of geometric algorithms using finite precision arithmetic. Artificial Intelligence, 37:377–401, 1988.
A. Rege, J. Canny, Fast point location for two-and three-dimesional real algebraic geometry, to appear, 1995.
J. R. Shewchuk, Robust adaptive floating-point geometric predicates, Proc. 12th Ann. Symp. Comp. Geom, pp. 141–150.
K. Sugihara, M. Iri, Construction of the Voronoi diagram for one million generators in single precision arithmetic, First Can. Conf. Comp. Geom., 1989.
C. Yap, T. Dubé, The exact computation paradigm, 452-492, Computing in Euclidean geometry, D.Z. Du, F. Hwang, eds, World Scientific, 1995, second edition.
J. Yu, Exact arithmetic solid modeling, Ph.D. Thesis, Purdue University, 1992, available as CSD-TR-92-037.
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© 1996 Springer-Verlag Berlin Heidelberg
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Fortune, S. (1996). Robustness issues in geometric algorithms. In: Lin, M.C., Manocha, D. (eds) Applied Computational Geometry Towards Geometric Engineering. WACG 1996. Lecture Notes in Computer Science, vol 1148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014476
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DOI: https://doi.org/10.1007/BFb0014476
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