Correct Delaunay Triangulation in the Presence of Inexact Inputs and Arithmetic

Correct Delaunay Triangulation in the Presence of Inexact Inputs and Arithmetic The construction of the Delaunay triangulation depends on the correct determination of whether or not a fourth point is inside the circle determined by three other points. By modeling the data points as disks and examining the associated mutual tangent circles, we show how to construct an incircle test that is reliable and sharp, one that is not corrupted by round-off error, one that can deal with inexact input data, avoids rational and big integer arithmetic, and brings geometry to the forefront instead of error analysis or arithmetic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Correct Delaunay Triangulation in the Presence of Inexact Inputs and Arithmetic

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Publisher
Kluwer Academic Publishers
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:1009977923779
Publisher site
See Article on Publisher Site

Abstract

The construction of the Delaunay triangulation depends on the correct determination of whether or not a fourth point is inside the circle determined by three other points. By modeling the data points as disks and examining the associated mutual tangent circles, we show how to construct an incircle test that is reliable and sharp, one that is not corrupted by round-off error, one that can deal with inexact input data, avoids rational and big integer arithmetic, and brings geometry to the forefront instead of error analysis or arithmetic.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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