Residual Iteration and Accurate Polynomial Evaluation for Shape-interrogation Applications

Hoffmann, C.; Park, with G.; Simard, J-R.; Stewart, N. F.

Residual Iteration and Accurate Polynomial Evaluation for Shape-interrogation Applications

Files

009-014_hoffmann.pdf (99.85 KB)

Date

2004

Authors

Hoffmann, C.
Park, with G.
Simard, J-R.
Stewart, N. F.

Publisher

The Eurographics Association

Abstract

Surface interrogation and intersection depend crucially on good root-finding algorithms, which in turn depend on accurate polynomial evaluation. Conventional algorithms for evaluation typically encounter difficulties near multiple roots, or roots that are very close, and this may lead to gross errors in the geometric computation, or even catastrophic failure. In this paper we study the cost and accuracy of several approaches to polynomial evaluation, explaining the reasons for non-convergence of certain methods, and supporting our subsequent conclusions with the results of benchmarking experiments.

        @inproceedings{10.2312:sm.20041371
,
booktitle = {Solid Modeling
},
editor = {Gershon Elber and Nicholas Patrikalakis and Pere Brunet
},
title = {{Residual Iteration and Accurate Polynomial Evaluation for Shape-interrogation Applications
}},
author = {Hoffmann, C. and 
Park, with G. and 
Simard, J-R. and 
Stewart, N. F.
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7783
},
ISBN = {3-905673-55-X
},
DOI = {10.2312/sm.20041371
}
}