SUBJECT

Geometric modeling

lecture

master

Faculty of Science

Mathematics MSc

3

Semesters 1-4

Autumn/Spring semester

Solid modeling. Wire frames. Boundary representations. Implicit equations and parameterizations of boundary surfaces. Constructive Solid Geometry, Boolean set operations.

Representing curves and surfaces. Curve interpolation. Cubic Hermite polynomials. Fitting a composite Hermite curve through a set of given points. Curve approximation. Control polygon, blending functions. Bernstein polynomials. Bézier curves. De Casteljau algorithm. B-spline functions, de Boor algorithm. Application of weights, rational B-spline curves. Composite cubic B-spline curves, continuity conditions. Bicubic Hermite interpolation. Fitting a composite Hermite surface through a set of given points. Surface design. Bézier patches. Rational B-spline surfaces. Composite surfaces, continuity conditions.

1. G. Farin: Curves and surfaces for computer aided geometric design. Academic Press, Boston, 1988.
2. I. D. Faux and M. J. Pratt: Computational geometry for design and manufacture. Ellis Horwood Limited, Chichester, 1979.