Computing the Minkowski sum of ruled surfaces

Heidrun Mühlthaler; Helmut Pottmann

doi:10.1016/j.gmod.2003.07.003

Computing the Minkowski sum of ruled surfaces

Heidrun Mühlthaler, Helmut Pottmann^*

^*Corresponding author for this work

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

20 Scopus citations

Abstract

The boundary of the Minkowski sum of two geometric objects is part of the so-called convolution surface of the boundary surfaces of the two input objects. In most cases, convolution surfaces can be computed only by numerical algorithms. The present paper studies convolution surfaces of ruled surfaces. There, explicit parameterizations for the convolution surface can be derived. Moreover, we study the rational convolution surface of two rational ruled surfaces and the connection to rational parameterizations of offsets of rational ruled surfaces.

Original language	English (US)
Pages (from-to)	369-384
Number of pages	16
Journal	Graphical Models
Volume	65
Issue number	6
DOIs	https://doi.org/10.1016/j.gmod.2003.07.003
State	Published - Nov 2003
Externally published	Yes

Keywords

Convolution surface
General offset
Minkowski sum
Offset surface
Rational parameterization
Ruled surface

ASJC Scopus subject areas

Software
Modeling and Simulation
Geometry and Topology
Computer Graphics and Computer-Aided Design

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10.1016/j.gmod.2003.07.003

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AU - Pottmann, Helmut

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AB - The boundary of the Minkowski sum of two geometric objects is part of the so-called convolution surface of the boundary surfaces of the two input objects. In most cases, convolution surfaces can be computed only by numerical algorithms. The present paper studies convolution surfaces of ruled surfaces. There, explicit parameterizations for the convolution surface can be derived. Moreover, we study the rational convolution surface of two rational ruled surfaces and the connection to rational parameterizations of offsets of rational ruled surfaces.

KW - Convolution surface

KW - General offset

KW - Minkowski sum

KW - Offset surface

KW - Rational parameterization

KW - Ruled surface

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DO - 10.1016/j.gmod.2003.07.003

M3 - Article

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SP - 369

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JF - Graphical Models

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ER -

Computing the Minkowski sum of ruled surfaces

Abstract

Keywords

ASJC Scopus subject areas

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