Rational Bézier Guarding

We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and featu...

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Bibliographic Details
Published in:Computer graphics forum Vol. 41; no. 5; pp. 89 - 99
Main Authors: Khanteimouri, P., Mandad, M., Campen, M.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.08.2022
Subjects:
Applied computing → Computer‐aided design
CCS Concepts
Computing methodologies → Computer graphics
Mathematical analysis
Mathematics of computing → Mesh generation
Mesh geometry models
Mesh models
Polynomials
Rational functions
Shape modeling
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14605