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




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