R. Krasauskas "Geometry by Virtual Reality"

Catalog description:

This course has a goal to give an experience for students to model geometric forms by means of virtual reality. The emphasis is given to interactive vizualization methods. Students are free to choose any VRML, SGML, XML tools to make a vizualization of geometrical objets (objects may be selected according to their wishes).

Current texts:

G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 3 ed., 1992
D. Hilbert, S. Cohn-Vossen, Anschauliche Geometrie, Springer, Berlin, 1932
G.K. Francis, A Topological Picturebook, Springer, 1988
Ames, Nadeau, Moreland, The VRML 2.0 Sourcebook, John Wiley & Sons, 1997

Goals:

The course disclose the link between the geometry and recent technology: the Virtual Reality Modelling Language is a basis to model nontrivial geometric objects. The examples of geometric and topological objects are being discussed: parametrizable algebraic surfaces, Mobius surface, Klein bottle, knots and 3-D varieties, Steiner and Boya's surfaces, the task of sphere conversion. The VRML methods are applied in order to discuss the possibilities and limitations of virtual modelling, as well as problems unsolved. The special emphasis is given on practical implementation of algorithms.

Content:

• VRML;
• Parametrizable algebraic and other surfaces;
• Knots and 3-dimensional varieties;
• Other topological and geometric objects;
• Algorithms for vizualization;
• Implementation and demonstration of solutions.

Typical requirements:

basic courses in calculus, analytic geometry, linear algebra, elements of computer graphics and programming are necessary.