Stewart, Neil ;
Zidani, Malika
Transfinite interpolation for welldefinition in error analysis in solid modelling
Abstract
An overall approach to the problem of error analysis in the context of solid modelling, analogous to the standard forward/backward error analysis of Numerical Analysis, was described in a recent paper by Hoffmann and Stewart. An important subproblem within this overall approach is the welldefinition of the sets specified by inconsistent data. These inconsistencies may come from the use of finiteprecision realnumber arithmetic, from the use of lowdegree curves to approximate boundaries, or from terminating an infinite convergent (subdivision) process after only a finite number of steps.
An earlier paper, by Andersson and the present authors, showed how to resolve this problem of welldefinition, in the context of standard trimmedNURBS representations, by using the Whitney Extension Theorem. In this paper we will show how an analogous approach can be used in the context of trimmed surfaces based on combinedsubdivision representations, such as those proposed by Litke, Levin and SchrÃƒÂ¶der.
A further component of the problem of welldefinition is ensuring that adjacent patches in a representation do not have extraneous intersections. (Here, "extraneous intersections" refers to intersections, between two patches forming part of the boundary, other than prescribed intersections along a common edge or at a common vertex.) The paper also describes the derivation of a bound for normal vectors that can be used for this purpose. This bound is relevant both in the case of trimmedNURBS representations, and in the case of combined subdivision with trimming.
BibTeX  Entry
@InProceedings{stewart_et_al:DSP:2006:719,
author = {Neil Stewart and Malika Zidani},
title = {Transfinite interpolation for welldefinition in error analysis in solid modelling},
booktitle = {Reliable Implementation of Real Number Algorithms: Theory and Practice},
year = {2006},
editor = {Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
number = {06021},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2006/719},
annote = {Keywords: Forward/backward error analysis, robustness, welldefinition, trimmed NURBS, combined subdivision, trimming, bounds on normals}
}
Keywords: 

Forward/backward error analysis, robustness, welldefinition, trimmed NURBS, combined subdivision, trimming, bounds on normals 
Seminar: 

06021  Reliable Implementation of Real Number Algorithms: Theory and Practice

Issue date: 

2006 
Date of publication: 

13.09.2006 