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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Grahic Jump Location
Bézier curve with toleranced control points
Grahic Jump Location
Bézier curve with toleranced control points in extended domain
Grahic Jump Location
Tolerance zone for linear combinations of rectangles
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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
Can v be on both faces but not on the connecting edge?
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
Interval Newton step when 0∉f([x](k), adapted from Hammer et al. 14)
Grahic Jump Location
Support lines of a convex set
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DeCasteljau algorithm for a Bézier curve
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Tolerance zones for linear combinations of disks
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Intersection of a cube with a tetrahedron



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