Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations

Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a $$\mathcal{O}(n)$$ algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floating-point arithmetic is adequate. We describe IASolver, a Java applet (http://www.cs.brandeis.edu/~tim) that serves as testbed for this idea. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009950630139
Publisher site
See Article on Publisher Site

Abstract

Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a $$\mathcal{O}(n)$$ algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floating-point arithmetic is adequate. We describe IASolver, a Java applet (http://www.cs.brandeis.edu/~tim) that serves as testbed for this idea.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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