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Journal for Geometry and Graphics 19 (2015), No. 1, 013--029
Copyright Heldermann Verlag 2015

Classification of Manifolds Resulting as Minkowski Operation Products of Basic Geometric Point Sets

Daniela Velichová
Institute of Mathematics and Physics, Faculty of Mechanical Engineering, Slovak University of Technology, Nám. slovody 17, 812 31 Bratislava, Slovakia

This paper brings a basic classification of possible results of the point set operations 'Minkowski sum' and 'Minkowski product' performed on elementary geometric figures as point subsets in the Euclidean space En, which can be represented analytically by the relevant vector maps. The intrinsic geometric properties of the resulting manifolds are presented with illustrations of various appealing results in E3, and 3-dimensional orthographic views of manifolds from spaces E4 and E6.

Keywords: Minkowski point set operation, vector sum, exterior wedge product of vectors, Minkowski point set combination, Minkowski operator.

MSC: 51N20; 53A05

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