Robustness in Geometric Computations*

[+] Author and Article Information
Christoph M. Hoffmann

Computer Science, Purdue University, West Lafayette, IN 47907

J. Comput. Inf. Sci. Eng 1(2), 143-155 (Mar 01, 2001) (13 pages) doi:10.1115/1.1375815 History: Received February 01, 2001; Revised March 01, 2001
Copyright © 2001 by ASME
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Lakos, J., 1996, Large-Scale C++ Software Design, Addison-Wesley, Reading, MA.
Hoffmann, C. M., Hopcroft, J., and Karasick, M., 1988, “Towards Implementing Robust Geometric Computations,” Proc. 4th ACM Symp. on Comp. Geometry, pp. 106–117.
Hoffmann, C. M., 1989, Geometric and Solid Modeling, An Introduction, Morgan Kaufman, San Mateo, CA.
Gavrilova, M., and Rokne, J. G., 2000, “Reliable Line Segment Intersection Testing,” CAD 32, pp. 737–746.
Ratschek,  H., and Rokne,  J., 1999, “Exact Computation of the Sign of a Finite Sum,” Appl. Math. Comp. , pp. 99–127.
de Berg, M., van Kreveld, M., Overmars, M., and Schwarzkopf, O., 1997, Computational Geometry, Algorithms and Applications, Springer-Verlag, New York.
Sugihara,  K., and Iri,  M., 1989, “A Solid Modeling System Free From Topological Inconsistency,” J. of Inf. Proc., 12, pp. 380–393.
Fortune, S., 1995, “Polyhedral Modeling with Exact Arithmetic,” Proc. 3rd Symp. Solid Modeling, ACM Press, NY, pp. 225–234.
Fortune,  S., and Van Wyk,  C., 1993, “Efficient Exact Arithmetic for Computational Geometry,” Proc. 9th Symp. Comp. Geometry, ACM Press, NY, pp. 163–172.
Yu, J., 1991, “Exact Arithmetic Solid Modeling,” Ph.D Thesis, CS, Purdue University.
Sugihara,  K., 1992, “A Simple Method for Avoiding Numerical Error and Degeneracy in Voronoi Diagram Construction,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 75-A, pp. 468–477.
Hopcroft,  J. E., and Kahn,  P. J., 1992, “A Paradigm for Robust Geometric Algorithms,” Algorithmica, 7, pp. 339–380.
Golub, G., and van Loan, C., 1983, Matrix Computations, Johns Hopkins University Press.
Hammer, R., Hocks, M., Kulisch, U., and Ratz, D., 1995, C++ Toolbox for Verified Computing, Basic Numerical Problems, Springer Verlag, New York.
Jenkins,  M., and Traub,  J., 1970, “A Three Stage Variable-Shift Iteration for Polynomial Zeros and Its Relation to Generalized Rayleigh Iteration,” Numer. Math., 14, pp. 252–263.
Press, W., Teukolsky, S., Wetterling, W., and Flannery, B., 1992, Numerical Recipes in C, 2nd edition, Cambridge University Press.
Neumaier, A., 1990, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, England.
Sederberg,  T., and Farouki,  R., 1992, “Approximation by Interval Bézier Curves,” IEEE Comput. Graphics Appl., 87–95.
Hu,  C-Y., Patrikalakis,  N., and Ye,  X., 1996, “Robust Interval Solid Modeling,” CAD, pp. 807–817 and 819–830.
Wallner,  J., Krasauskas,  R., and Pottmann,  H., 2000, “Error Propagation in Geometric Computations,” CAD 32, pp. 631–641.
Farin, G., 1992, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, Boston; 3rd ed.
Farouki,  R., and Rajan,  V., 1987, “On the Numerical Condition of Polynomials in Bernstein Form,” Comp. Aided Geom., Design, 4, pp. 191–216.
Keyser,  J., Culver,  T., Manocha,  D., and Krishnan,  S., 2000, “Efficient and Exact Manipulation of Algebraic Points and Curves,” CAD, pp.649–662.
Kortenkamp, U., 1999, “Foundations of Dynamic Geometry,” Ph.D Thesis, Informatik, Swiss Fed. Inst. of Technology.
Agrawal, A., 1995, “A General Approach to the Design of Robust Algorithms for Geometric Modeling,” Ph.D Thesis, Comp. Science, University of Southern California.


Grahic Jump Location
Intersection of a cube with a tetrahedron
Grahic Jump Location
Possible inconsistent face partitions
Grahic Jump Location
The intersection of representable segments need not be representable
Grahic Jump Location
The grid of floating-point numbers
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The planes are perturbed towards each other, giving an improper polyhedron
Grahic Jump Location
The core of the improper polyhedron is extracted
Grahic Jump Location
“Nearness” that implies coincidence is not transitive
Grahic Jump Location
Tolerance zone for linear combinations of rectangles
Grahic Jump Location
Bézier curve with toleranced control points in extended domain
Grahic Jump Location
Bézier curve with toleranced control points
Grahic Jump Location
Tolerance zones for linear combinations of disks
Grahic Jump Location
DeCasteljau algorithm for a Bézier curve
Grahic Jump Location
Support lines of a convex set
Grahic Jump Location
Interval Newton step when 0∉f([x](k), adapted from Hammer et al. 14)
Grahic Jump Location
Interval Newton step when 0∊f([x](k), adapted from Hammer et al. 14, where c(k)=m([x](k)))
Grahic Jump Location
Can v be on both faces but not on the connecting edge?




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