Forms from Minkowski Triples of Circles

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Daniela Velichová: Forms from Minkowski Triples of Circles. In: Bridges 2014. Pages 469–472



This paper deals with the modelling and study of various shapes arising from mathematical objects defined by means of Minkowski point set combinations. The aim is to present spatial objects with complex shapes generated by means of vector operations defined on smooth manifolds in Euclidean space. Examples using space curves that produce surfaces with unusual shapes are presented as flexible mathematical models suitable for various applications in computer aided modelling, design, architecture and art.

Extended Abstract


Used References

[1] Kaul, A., Farouki, R. T., Computing Minkowski sums of Planar Curves, International Journal of Computational Geometry and Applications 5, 1995, pp. 413-432.

[2] Lee, I. K., Kim, M. S., Elber, G, The Minkowski Sum of 2D Curved Objects, Proceedings of Israel- Korea Bi-National Conference on New Themes in Computerized Geometrical Modeling, Tel-Aviv Univ., 1998, pp. 155-164.

[3] Velichová, D., Minkowski Set Operations in Modelling of Manifolds, Proceedings of the GeoGra 2012 International Conference, Budapest 2012, Hungary, ISBN 978-963-08-3162-8, CD-rom, 4 pp.

[4] Velichová, D., The Art of Geometry, Proceedings 2013, 16th Conference Bridges, Enschede, Tesselations, Phoenix, Arizona, USA, pp. 143-150.

[5] Velichová, D., Minkowski Operators in Shape Modelling, Proceedings of ESMA Conference, Cagliari 2014, 8pp.

[6] Velichová D., Minkowski Triples, Proceedings - Aplimat 2013, Slovak University of Technology in Bratislava, ISBN 978-80-227-3865-1, P69 - 7pp.


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