Developable rational Bézier and B-spline surfaces

Helmut Pottmann; Gerald Farin

doi:10.1016/0167-8396(94)00031-M

Developable rational Bézier and B-spline surfaces

Helmut Pottmann^*, Gerald Farin

^*Corresponding author for this work

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

121 Scopus citations

Abstract

A constructive geometric approach to developable rational Bézier and B-spline surfaces is presented. It is based on the dual representation in the sense of projective geometry. By the principle of duality, projective algorithms for NURBS curves can be transferred to constructions for developable NURBS surfaces in dual rational B-spline form. We discuss the conversion to the usual tensor product representation of the obtained surfaces and develop algorithms for basic design problems arising in this context.

Original language	English (US)
Pages (from-to)	513-531
Number of pages	19
Journal	Computer Aided Geometric Design
Volume	12
Issue number	5
DOIs	https://doi.org/10.1016/0167-8396(94)00031-M
State	Published - Aug 1995
Externally published	Yes

Keywords

Developable surface
Dual Bézier curve
NURBS
Principle of duality
Rational Bézier representation
projective geometry

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(94)00031-M

Cite this

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abstract = "A constructive geometric approach to developable rational B{\'e}zier and B-spline surfaces is presented. It is based on the dual representation in the sense of projective geometry. By the principle of duality, projective algorithms for NURBS curves can be transferred to constructions for developable NURBS surfaces in dual rational B-spline form. We discuss the conversion to the usual tensor product representation of the obtained surfaces and develop algorithms for basic design problems arising in this context.",

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author = "Helmut Pottmann and Gerald Farin",

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AU - Pottmann, Helmut

AU - Farin, Gerald

PY - 1995/8

Y1 - 1995/8

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AB - A constructive geometric approach to developable rational Bézier and B-spline surfaces is presented. It is based on the dual representation in the sense of projective geometry. By the principle of duality, projective algorithms for NURBS curves can be transferred to constructions for developable NURBS surfaces in dual rational B-spline form. We discuss the conversion to the usual tensor product representation of the obtained surfaces and develop algorithms for basic design problems arising in this context.

KW - Developable surface

KW - Dual Bézier curve

KW - NURBS

KW - Principle of duality

KW - Rational Bézier representation

KW - projective geometry

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U2 - 10.1016/0167-8396(94)00031-M

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JO - Computer Aided Geometric Design

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ER -

Developable rational Bézier and B-spline surfaces

Abstract

Keywords

ASJC Scopus subject areas

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