The Art of Geometry

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Daniela Velichová: The Art of Geometry. In: Bridges 2013. Pages 143–150



This paper deals with new methods for modelling and studying shape in mathematics. It aims to show similarities between mathematical and artistic solutions applied in the creation of a piece of work – artistic or mathematical. Minkowski operations on point sets are introduced to create complex forms as point set combinations and used as generating principles for modelling various interesting geometric structures such as point mosaics, flexible curves and smooth surface patches in Euclidean space.

Extended Abstract


Used References

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

[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 Modelling, Tel-Aviv Univ., pp. 155-164. 1998.

[3] Lee, I. K., Kim, M. S., Polynomial/Rational Approximation of Minkowski Sum Boundary Curves, Graphical Models and Image Processing, Vol. 60, No. 2, pp. 136–165. 1998.

[4] Peternel, M., Manhart, F., The Convolution of Paraboloid and a Parameterized Surface, Journal for Geometry and Graphics, Vol. 7, pp. 157-171. 2003.

[5] Velichová, D., Minkowski Sum in Geometric Modelling, Proceedings of the 6th Conference "Geometry and Graphics", Ustroň, Poland, pp. 65-66. 2009.

[6] Velichová, D., Minkowski Set Operations in Geometric Modelling of Continuous Riemannian Manifolds, Scientific Proceedings, STU in Bratislava, SR, ISBN 978-80-227-3326-7, pp. 179-186. 2009.

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


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