Computational Geometry

Practical introduction to mathematical methods of geometrical modelling, particularly geodesic curves on surfaces.

This lecture addresses master students and diploma students after their intermediate diploma which have attended the basic lectures of mathematics. In the lecture-accompanying exercise, the participants get the opportunity to deepen the subjects of the lecture.

Contents

Students are supposed to have basic knowledge of differential calculus and linear algebra to be able to follow the lecture.

The lecture should be understood as introduction to the geometrical modelling of curves and surfaces, in particular about shortest ways and geodesics. First a representation of the necessary elements is given with concepts from differential geometry. Focus will be given to applicability of the presented concepts in an engineering context and to a lesser extent to mathematical formulation and criteria.

Literature

Fundamental textbooks, which are suitable as term-accompanying read:

• M. P. do Carmo
  Differential Geometry of Curves and Surfaces
  Vieweg, Braunschweig, 3. Aufl. 1993
• Wolfgang Kühnel
  Differential Geometry
  Vieweg, 3. Aufl. 2005
• G. Farin
  Curves and Surfaces for Computer Aided Geometric Design
  Academic Press, New York, 3. ed. 1993
• J. Hoschek, D. Lasser
  Fundamentals of Geometric Data Processing
  Teubner, Stuttgart, 1989