Parameterization in Finite Precision |
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Authors: | C L Bajaj A V Royappa |
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Affiliation: | (1) Department of Computer Sciences and TICAM, University of Texas at Austin, Austin, TX 78712, USA., US;(2) Department of Computer Sciences, Millsaps College, Jackson, MS 39210, USA., US |
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Abstract: | Certain classes of algebraic curves and surfaces admit both parametric and implicit representations. Such dual forms are
highly useful in geometric modeling since they combine the strengths of the two representations. We consider the problem of
computing the rational parameterization of an implicit curve or surface in a finite precision domain. Known algorithms for
this problem are based on classical algebraic geometry, and assume exact arithmetic involving algebraic numbers. In this work
we investigate the behavior of published parameterization algorithms in a finite precision domain and derive succinct algebraic
and geometric error characterizations. We then indicate numerically robust methods for parameterizing curves and surfaces
which yield no error in extended finite precision arithmetic and, alternatively, minimize the output error under fixed finite
precision calculations.
Received January 8, 1997; revised August 27, 1998. |
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Keywords: | , Curves and surfaces, Geometric modeling, Numerical methods, Computational algebraic geometry, |
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