Contouring a bivariate quadratic polynomial over a triangle
type: Item
instance of: scholarly article
title: Contouring a bivariate quadratic polynomial over a triangle
zbMATH Open document ID: 0726.65014
DOI: 10.1016/0167-8396(90)90041-O
published in: Computer Aided Geometric Design
publication date: 1990-01-01T00:00:00Z
review text: The authors consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bézier patch. The problem of contouring a quadratic polynomial over a triangle has been earlier considered by \textit{S. Marlow} and \textit{M. J. D. Powell} [A Fortran subroutine for plotting the part of a conic that is inside a given triangle. Report No.R8336, Atomic Energy Res. Establishment, Harwell, England (1976)] and the second author [Comput. Aided Geom. Des. 3, 83-127 (1986; Zbl 0633.65007)]. The algorithms given by these authors have some deficiencies. In this paper an algorithm for solving this problem is presented which is more efficient and accurate than that of Marlow and Powell and far more robust than that of the second author. The authors use the Bernstein- Bézier form for quadratic polynomials defined over a triangle, and also for describing conic sections. Recent results show that the Bernstein basis for polynomials is more stable for numerical computations than the monomial basis.
reviewed by: Dimitrie D. Stancu
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 4199447
zbMATH Keywords: contouring
zbMATH Keywords: bivariate quadratic polynomial
zbMATH Keywords: triangular Bézier patch
zbMATH Keywords: conic sections
zbMATH Keywords: Bernstein basis
author: Andrew J. Worsey
author: Gerald Farin
MaRDI profile type: Publication
cites work: A survey of curve and surface methods in CAGD
cites work: Q4178157
cites work: On the numerical condition of polynomials in Bernstein form
cites work: Algorithms for polynomials in Bernstein form
cites work: On the numerical condition of algebraic curves and surfaces. I: Implicit equations
cites work: Adaptive contouring of three-dimensional surfaces
cites work: A 'taut string algorithm' for straightening a piecewise linear path in two dimensions
cites work: Piecewise Quadratic Approximations on Triangles
full work available at URL: 0167-8396(90)90041-o
OpenAlex ID: W2038179089
description: scientific article; zbMATH DE number 4199447