Contouring a bivariate quadratic polynomial over a triangle

A. J. Worsey; G. Farin

doi:10.1016/0167-8396(90)90041-O

Contouring a bivariate quadratic polynomial over a triangle

A. J. Worsey, G. Farin

Computing and Augmented Intelligence, School of (IAFSE-SCAI)

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bézier patch. The important cases where the contour has disjoint sections or is a closed curve are considered in detail. Our results lead to a simple, yet completely robust algorithm for describing contours as piecewise rational quadratic Bézier curves.

Original language	English (US)
Pages (from-to)	337-351
Number of pages	15
Journal	Computer Aided Geometric Design
Volume	7
Issue number	1-4
DOIs	https://doi.org/10.1016/0167-8396(90)90041-O
State	Published - Jun 1990

Keywords

Contouring
conic sections
quadratic Bézier patch

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/0167-8396(90)90041-O

Cite this

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title = "Contouring a bivariate quadratic polynomial over a triangle",

abstract = "We consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular B{\'e}zier patch. The important cases where the contour has disjoint sections or is a closed curve are considered in detail. Our results lead to a simple, yet completely robust algorithm for describing contours as piecewise rational quadratic B{\'e}zier curves.",

keywords = "Contouring, conic sections, quadratic B{\'e}zier patch",

author = "Worsey, {A. J.} and G. Farin",

note = "Funding Information: We are indebted to Brett Bloomquist for many detailed comments on this paper and for his help in correcting flaws in a preliminary release of code. This piece of work has benefitted greatly from his input. Thanks also to Rida Farouki for his careful review of the manuscript. This research was supported in part by the National Science Foundation grant DMS-8803257, awarded to the University of North Carolina at Wilmington, and also by the National Science Foundation grant DCR-8502858 and Department of Energy contract DE-FGO2-87ER25041, both awarded to Arizona State University.",

year = "1990",

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doi = "10.1016/0167-8396(90)90041-O",

language = "English (US)",

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AU - Worsey, A. J.

AU - Farin, G.

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PY - 1990/6

Y1 - 1990/6

N2 - We consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bézier patch. The important cases where the contour has disjoint sections or is a closed curve are considered in detail. Our results lead to a simple, yet completely robust algorithm for describing contours as piecewise rational quadratic Bézier curves.

AB - We consider the problem of contouring a bivariate quadratic polynomial, defined as a triangular Bézier patch. The important cases where the contour has disjoint sections or is a closed curve are considered in detail. Our results lead to a simple, yet completely robust algorithm for describing contours as piecewise rational quadratic Bézier curves.

KW - Contouring

KW - conic sections

KW - quadratic Bézier patch

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Contouring a bivariate quadratic polynomial over a triangle

Abstract

Keywords

ASJC Scopus subject areas

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