Rational Bézier Guarding

Khanteimouri, Payam; Mandad, Manish; Campen, Marcel

Rational Bézier Guarding

Files

v41i5pp089-099.pdf (14.15 MB)

Date

2022

Authors

Khanteimouri, Payam
Mandad, Manish
Campen, Marcel

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

Abstract

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.

CCS Concepts: Computing methodologies --> Computer graphics; Mesh models; Mesh geometry models; Shape modeling; Applied computing --> Computer-aided design; Mathematics of computing --> Mesh generation

        @article{10.1111:cgf.14605
,
journal = {Computer Graphics Forum},
title = {{Rational Bézier Guarding
}},
author = {Khanteimouri, Payam and 
Mandad, Manish and 
Campen, Marcel
},
year = {2022
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.14605
}
}