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Program for Design of Kirchhoff-Plateau Surfaces

Student: Mikhail Ilchenko

Supervisor: Rimma Akhmetsafina

Faculty: Faculty of Computer Science

Educational Programme: Software Engineering (Bachelor)

Year of Graduation: 2018

This work is dedicated to design and visualization of minimal surfaces that span rigid boundary curve and named Kirchhoff-Plateau surfaces. In this paper I present theoretical basics and implementation of problems such as computational visualization of three-dimensional objects, modelling closed elastic curves and finding surfaces of minimum area for given elastic boundary curve. The result of this work is developed cross platform program-visualizer created with Python 3 programming language and OpenGL graphics library. This program allows to create Kirchhoff-Plateau surfaces. For creation user draws 2D boundaries using Catmull-Rom splines. Then program changes z coordinate of splines knots and forms minimal surface described with additional points. This paper contains 42 pages, 3 chapters, 24 illustrations, 37 bibliography items, 4 appendices. Keywords: Kirchhoff-Plateau problem, Plateau problem, computer graphics, minimal surfaces, Catmull-Rom splines, elastic curves.

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