The NURBS book
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A transfinite form of Sibson's interpolant
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Combined subdivision schemes for the design of surfaces satisfying boundary conditions
Computer Aided Geometric Design
Normal bounds for subdivision-surface interference detection
Proceedings of the conference on Visualization '01
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Heterogeneous material modeling with distance fields
Computer Aided Geometric Design
Accuracy and semantics in shape-interrogation applications
Graphical Models - Solid modeling theory and applications
Error Analysis for Operations in Solid Modeling in the Presence of Uncertainty
SIAM Journal on Scientific Computing
Trimming for subdivision surfaces
Computer Aided Geometric Design
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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.