The invariant functions and invariant-image conditions of the rational Bézier triangles
type: Item
instance of: scholarly article
title: The invariant functions and invariant-image conditions of the rational Bézier triangles
zbMATH Open document ID: 1276.65011
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2012-12-13T00:00:00Z
full work available at URL: https://dspace.lboro.ac.uk/2134/14693
review text: The paper focuses on determining the invariant functions and the invariant-image conditions of rational Bézier triangles of arbitrary degree with arbitrary non-zero weights. The author shows that \(\frac{1}{2} (n+1)(n+2)-3\) real-valued invariants, and one discrete-valued invariant determine a complete set the triangles of degree \(n\). The required image-invariance conditions are expressed in a functional equation, which is solved. The explicit form of a complete set of real-valued invariants is computed and shown, when augmented by a single discrete-valued invariant, to determine a complete set. The author uses in his demonstrations the fundamental theorem on invariants of Lie groups and techniques similar to those elaborated for the biquadratic and bicubic Bézier functions.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 26C15
Mathematics Subject Classification ID: 54H15
zbMATH DE Number: 6115366
zbMATH Keywords: rational parametrisation
zbMATH Keywords: geometric modeling
zbMATH Keywords: transformation groups
zbMATH Keywords: invariant functions
zbMATH Keywords: rational Bézier triangles
zbMATH Keywords: functional equation
zbMATH Keywords: invariants of Lie groups
author: H. E. Bez
MaRDI profile type: Publication
OpenAlex ID: W2086669259
cites work: Projective transformations of the parameter of a Bernstein-Bézier curve
cites work: Q4244323
cites work: Minimizing the maximal ratio of weights of a rational Bézier curve
cites work: Minimizing the maximal ratio of weights of rational Bézier curves and surfaces
cites work: Invariant-geometry conditions for the rational bi-quadratic Bézier surfaces
cites work: The Invariant Functions of the Rational Bi-cubic Bézier Surfaces
cites work: Q4849745
DOI: 10.1007/S00200-012-0174-8
description: scientific article; zbMATH DE number 6115366