The octant of a sphere as a non-degenerate triangular Bézier patch

G. Farin; B. Piper; A. J. Worsey

doi:10.1016/0167-8396(87)90007-0

The octant of a sphere as a non-degenerate triangular Bézier patch

G. Farin, B. Piper, A. J. Worsey

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

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

41 Scopus citations

Abstract

We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all Bézier points are distinct and their associated weights are positive.

Original language	English (US)
Pages (from-to)	329-332
Number of pages	4
Journal	Computer Aided Geometric Design
Volume	4
Issue number	4
DOIs	https://doi.org/10.1016/0167-8396(87)90007-0
State	Published - Dec 1987

Keywords

Octant
rational Bézier triangles
stereographic projection

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(87)90007-0

Cite this

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title = "The octant of a sphere as a non-degenerate triangular B{\'e}zier patch",

abstract = "We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all B{\'e}zier points are distinct and their associated weights are positive.",

keywords = "Octant, rational B{\'e}zier triangles, stereographic projection",

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

note = "Funding Information: The work of G. Farin and B. Piper was supportedin part by the Departmenotf Energy contractD E-FG02-87ER25041a nd the National Science Foundationg rant DCR-8502858; both awardedto Arizona State UniversityT. he researchw as conductedw hileA.J, Worsey was visitingt heD epartmenotf ComputerS ciencea t Arizona State University.",

year = "1987",

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doi = "10.1016/0167-8396(87)90007-0",

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AU - Farin, G.

AU - Piper, B.

AU - Worsey, A. J.

N1 - Funding Information: The work of G. Farin and B. Piper was supportedin part by the Departmenotf Energy contractD E-FG02-87ER25041a nd the National Science Foundationg rant DCR-8502858; both awardedto Arizona State UniversityT. he researchw as conductedw hileA.J, Worsey was visitingt heD epartmenotf ComputerS ciencea t Arizona State University.

PY - 1987/12

Y1 - 1987/12

N2 - We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all Bézier points are distinct and their associated weights are positive.

AB - We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all Bézier points are distinct and their associated weights are positive.

KW - Octant

KW - rational Bézier triangles

KW - stereographic projection

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The octant of a sphere as a non-degenerate triangular Bézier patch

Abstract

Keywords

ASJC Scopus subject areas

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