R. Krasauskas "Bézier Surfaces for CAD"

Catalog description:

This course (project) has a goal to give an experience for students in computer aided geometric design. Bzier surfaces are building blocks for NURBS (Non-Uniform Rational B-Splines) which became industrial standard for CAD software. For practice it is important to find their parametrizations which are most suitable for visualization. Students are free to choose any 3D computer graphics software (preferably MAPLE).

Current texts:

G. Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 3 ed., 1992.

Goals:

The course (project) is concerned with visualization of rational Bzier surfaces: TP-surfaces, Bzier triangular patches and more general toric patches. They all are defined as parametric surfaces. The goal is to find a reparametrization of the same degree with the most uniform grid, which does not change shape of the given patch. The emphasis will be on practical implementation of the algorithm.

Content:

• survey of rational Bézier curves, tensor product surfaces, Bézier triangle patches;
• reparametrizations of rational curve arcs and surfaces patches which do not change shape;
• formulation of the optimization problem;
• description of an algorithm for finding the "best" parametrization;
• implementation and demonstration of the solution.

Typical requirements:

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

Helpful background:

experience with MAPLE or other package with simple 3D graphics is desirable.