# Minkowski Triples of Curve Segments

• Daniela Velichová
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)

## Abstract

Paper brings classification of manifolds determined as Minkowski mixed triple combinations of three different curve segments represented parametrically by their vector maps. Some intrinsic differential properties of resulting manifolds are derived, namely those based on the properties of original curve segments chosen as operands in the respective Minkowski point set operations. Minkowski mixed triple combination can be determined in more different forms considering equal or not equal parameterization of the three basic curve segments, while resulting manifolds are found to be of dimension 1 to 3 consequently. Parameters of these combinations are powerful shaping tools influencing considerably geometric and aesthetic characteristics of the resulting objects. Various forms of manifolds determined by means of this generating principle are presented, including examples of manifolds determined as various Minkowski triple combinations of three circles positioned into different planes in the Euclidean space, and existence of their singular points is discussed.

## Keywords

Minkowski sum and product Minkowski triple combinations

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