Link between Bézier and Lagrange curve and surface schemes

Gerald Farin; Phillip J. Barry

doi:10.1016/0010-4485(86)90039-4

Link between Bézier and Lagrange curve and surface schemes

Gerald Farin, Phillip J. Barry

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

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

8 Scopus citations

Abstract

A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.

Original language	English (US)
Pages (from-to)	525-528
Number of pages	4
Journal	Computer-Aided Design
Volume	18
Issue number	10
DOIs	https://doi.org/10.1016/0010-4485(86)90039-4
State	Published - Dec 1986

Keywords

Bézier curves
Lagrange interpolation
geometry
mathematics

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

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10.1016/0010-4485(86)90039-4

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title = "Link between B{\'e}zier and Lagrange curve and surface schemes",

abstract = "A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial B{\'e}zier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for B{\'e}zier curves. A geometric derivation of this scheme is given, and the connection to P{\'o}lya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.",

keywords = "B{\'e}zier curves, Lagrange interpolation, geometry, mathematics",

author = "Gerald Farin and Barry, {Phillip J.}",

note = "Funding Information: This research was supportedi n part by Departmento f Energy Contract No. DE-AC02-85ER12046,b y NSF Grant DCR-8502858, and by the CDC Sponsored Research Project 85U101 to The Universityo f Utah. The authors thank D Hansford for creating Figures 4 and 5, N Sapididis for providing the data for Figure 4, and R E Barnhill for many useful comments.",

year = "1986",

month = dec,

doi = "10.1016/0010-4485(86)90039-4",

language = "English (US)",

volume = "18",

pages = "525--528",

journal = "Computer-Aided Design",

issn = "0010-4485",

publisher = "Elsevier Limited",

number = "10",

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TY - JOUR

T1 - Link between Bézier and Lagrange curve and surface schemes

AU - Farin, Gerald

AU - Barry, Phillip J.

N1 - Funding Information: This research was supportedi n part by Departmento f Energy Contract No. DE-AC02-85ER12046,b y NSF Grant DCR-8502858, and by the CDC Sponsored Research Project 85U101 to The Universityo f Utah. The authors thank D Hansford for creating Figures 4 and 5, N Sapididis for providing the data for Figure 4, and R E Barnhill for many useful comments.

PY - 1986/12

Y1 - 1986/12

N2 - A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.

AB - A class of curves that vary continuously between polynomial Lagrange interpolants and polynomial Bézier curves is discussed. An element in this class is specified by a real number which could be used as a shape parameter for Bézier curves. A geometric derivation of this scheme is given, and the connection to Pólya curves is pointed out. A generalization to the case of tensor product and triangular surface patches is also described.

KW - Bézier curves

KW - Lagrange interpolation

KW - geometry

KW - mathematics

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DO - 10.1016/0010-4485(86)90039-4

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AN - SCOPUS:0022879497

SN - 0010-4485

VL - 18

SP - 525

EP - 528

JO - Computer-Aided Design

JF - Computer-Aided Design

IS - 10

ER -

Link between Bézier and Lagrange curve and surface schemes

Abstract

Keywords

ASJC Scopus subject areas

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