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Transfinite interpolation for well-definition in error analysis in solid modelling Stewart, Neil Zidani, Malika Forward/backward error analysis robustness well-definition trimmed NURBS combined subdivision trimming bounds on normals 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 well-definition of the sets specified by inconsistent data. These inconsistencies may come from the use of finite-precision real-number arithmetic, from the use of low-degree 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 well-definition, in the context of standard trimmed-NURBS 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 combined-subdivision representations, such as those proposed by Litke, Levin and Schröder. A further component of the problem of well-definition 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 trimmed-NURBS representations, and in the case of combined subdivision with trimming. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Neil Stewart and Malika Zidani 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 6021, Reliable Implementation of Real Number Algorithms: Theory and Practice (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.06021.9 urn:nbn:de:0030-drops-7195 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06021.9 eng https://creativecommons.org/licenses/by/4.0/legalcode