Line graphics for visualization of surfaces and curves on them

Author:

Velickovic Vesna1ORCID,Dolicanin Edin2

Affiliation:

1. Department of Computer Science, Faculty of Sciences and Mathematics, University of Niš, Serbia

2. Department of Technical Science, State University of Novi Pazar, Serbia

Abstract

In this paper, we describe the main principles of our approach for the visualization of surfaces and curves on them in three-dimensional space by the use of line graphics. We also compare our approach with the standard method of polygon mesh. Mainly, we discuss the representation of surfaces, special lines on surfaces and lines of intersections of surfaces. Furthermore, we address the problems of visibility and finding the contour lines of surfaces. Finally we apply our method for visualizing some selected topic in mathematics.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference23 articles.

1. Cheshkova, M.A. On the geometry of Enneper’s surface. (Russian) Differentsialnaya Geom. Mnogoobraz 2007, 38, 139-142.

2. Dankwort, C. W.; Podehl, G. A new aesthetic design workflow: results from the european project FIORES. In CAD Tools and Algorithms for Product Design; Springer-Verlag, Berlin, Germany, 2000; pp. 16-30.

3. Dumitru, D. Minimal surfaces that generalize the Enneper’s surface. Novi Sad J. Math. 2010, 40, 17-22.

4. Failing M. Entwicklung numerischer Algorithmen zur computergrafischen Darstellung spezieller Probleme der Differentialgeometrie und Kristallographie; Shaker Verlag, Aachen, Germany; Ph.D. Thesis, Giessen, 1996.

5. Failing M.; Malkowsky E. Ein effizienter Nullstellenalgorithmus zur computergrafischen Darstellung spezieller Kurven und Flächen. Mitt. Math. Sem. Giessen 1996, 229, 11-28.

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