The field of geometric modelling or Computer Aided Geometric Design (CAGD), which is mainly based on numerical analysis, analytic, projective and differential geometry as well as computer science, provides the necessary algorithms for the required curve and surface representations. CAGD also supplies the related discipline of Computer Graphics with many of its mathematical and geometrical foundations. Recently there are the first approaches of combining geometric modelling applications with the emerging fields of Virtual and Augmented Reality. The discipline of Virtual Reality (VR) completely immerses users inside a synthetic environment whereas Augmented Reality (AR) allows the user to see three-dimensional virtual objects superimposed upon the real world. The objective of this class is to introduce the mathematical foundations of the field of geometric modelling and computer aided geometric design as well as to give a general overview of the emerging fields of virtual and augmented reality.
Polynomial B\'ezier curves
Analytic versus geometric continuity
B-spline curves, Rational curves (projective geometry, properties, conic sections)
B\'ezier and B-Spline surfaces
Virtual and augmented reality: Introduction and applications,
3D-Viewing, Haptics, VR and AR devices
Geometric Modelling in VR/AR