Curves in differential gemetry and in geometric modeling

Abstract

In this paper I want to discuss my experience with teaching Differential geometry and Geometric modeling at the Charles University. In particular I want to focus on several concrete topics and different ways how to handle them.

The most interesting is connection between the theoretical and applied aspects of these topics. We will thus discuss the reparameterization of curves, curvature, torsion, various frames along the curve, polynomial and rational curves.

Keywords

• differential geometry
• geometric modeling
• curvature
• reparameterization
• rotation minimizing frame