Dynamic differential geometry in an educational augmented reality application

In this thesis a number of geometry software packages leading both to static and dynamic constructions and their particular features will be presented. Afterwards Construct3D a 3D dynamic geometry construction tool will be introduced. It is based on the Augmented Reality System Studierstube. Construct3D's greatest advantage compared to other dynamic geometry software is the possibility for users to see the real environment augmented with virtual content with the aid of a head mounted display. That gives the users, mainly high school and university students, the opportunity to actually construct, explore and interact with three dimensional content in "real" 3D space. The practical part of this thesis was the implementation of a number of new functions for Construct3D. Several tools have been developed to enhance the understanding of the term curvature of curves and surfaces. To complement the already available sweep function of Construct3D helical and general sweeps have been implemented.