de Casteljau's Algorithm Revisited

Jens Gravesen

de Casteljau's Algorithm Revisited

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator.

Original language	English
Title of host publication	Mathematical Methods for Curves and Surfaces II
Place of Publication	Nashville
Publisher	Vanderbilt University Press
Publication date	1998
Pages	221-228
ISBN (Print)	0-8265-1315-8
Publication status	Published - 1998
Event	International Conference on Mathematical Methods for Curves and Surfaces - Lillehammer, Norway Duration: 3 Jul 1997 → 8 Jul 1997

Conference

Conference	International Conference on Mathematical Methods for Curves and Surfaces
Country	Norway
City	Lillehammer
Period	03/07/1997 → 08/07/1997
Sponsor	SINTEF, The Research Council of Norway, University of Oslo

Series	INNOVATIONS IN APPLIED MATHEMATICS

Cite this

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title = "de Casteljau's Algorithm Revisited",

abstract = "It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator. ",

author = "Jens Gravesen",

year = "1998",

language = "English",

isbn = "0-8265-1315-8",

series = "INNOVATIONS IN APPLIED MATHEMATICS",

pages = "221--228",

booktitle = "Mathematical Methods for Curves and Surfaces II",

publisher = "Vanderbilt University Press",

note = "International Conference on Mathematical Methods for Curves and Surfaces ; Conference date: 03-07-1997 Through 08-07-1997",

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TY - GEN

T1 - de Casteljau's Algorithm Revisited

AU - Gravesen, Jens

PY - 1998

Y1 - 1998

N2 - It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator.

AB - It is demonstrated how all the basic properties of Bezier curves can be derived swiftly and efficiently without any reference to the Bernstein polynomials and essentially with only geometric arguments. This is achieved by viewing one step in de Casteljau's algorithm as an operator (the de Casteljau operator) acting on a sequence of points, producing a sequence with one point less. The properties of Bezier curves are then derived by analysing de Casteljau's operator.

M3 - Article in proceedings

SN - 0-8265-1315-8

T3 - INNOVATIONS IN APPLIED MATHEMATICS

SP - 221

EP - 228

BT - Mathematical Methods for Curves and Surfaces II

PB - Vanderbilt University Press

CY - Nashville

T2 - International Conference on Mathematical Methods for Curves and Surfaces

Y2 - 3 July 1997 through 8 July 1997

ER -