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Translation Surfaces and Isotropic Transport Nets on Rational Minimal Surfaces

  • Jan VršekEmail author
  • Miroslav Lávička
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)

Abstract

We will deal with the translation surfaces which are the shapes generated by translating one curve along another one. We focus on the geometry of translation surfaces generated by two algebraic curves in space and study their properties, especially those useful for geometric modelling purposes. It is a classical result that each minimal surface may be obtained as a translation surface generated by an isotropic curve and its complex conjugate. Thus, we can study the minimal surfaces as special instances of translation surfaces. All the results about translation surfaces will be directly applied also to minimal surfaces. Finally, we present a construction of rational isotropic curves with a prescribed tangent field which leads to the description of all rational minimal surfaces. A close relation to surfaces with Pythagorean normals will be also discussed.

Notes

Acknowledgments

The authors were supported by the project LO1506 of the Czech Ministry of Education, Youth and Sports. We thank to all referees for their valuable comments, which helped us to improve the paper.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Applied SciencesUniversity of West BohemiaPlzeňCzech Republic
  2. 2.NTIS – New Technologies for the Information Society, Faculty of Applied SciencesUniversity of West BohemiaPlzeňCzech Republic

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