Syllabus
1. Representation of surface, curve on surface, first and second fundamental form. Gauss curvature
2. Special surfaces - minimal surfaces, ruled surface
3. Translation surfaces, revolve and screw motion of curve, sweep, extrude, path extrude
4. Joining parametric surface patches, geometric continuity
5. Implicit representation, meta balls, blending function
6. Point data interpolation, Langrange polynomial, cubic spline interpolation
7. Point data approximation, polynomial surface methods
8. Approximation with tensor product patches
9. Coons patches, bicubic Hermite patches
10. Bicubic spline interpolation, knot sequence
11. Rectangular and triangular Bezier patches
12. Rational Bezier surfaces, NURBS
13. Subdivision surfaces - subdivision Doo-Sabin, Catmull-Clark, Loop and Butterfly
14. Polygonal mesh and methods of optimization
Annotation
In this course we will concentrate of the subdiscipline of geometric modelling known as computer aided geometric design, which was formed from the mathematical structures and methods used in CAD/CAM systems and subsequently exploited in computer graphics and computer animation. The goal in this course is to examine the basic underlying geometric structures that are used in solving some problems in geometric modelling.