Computer Graphics
Code  Completion  Credits  Range 

W01A009  ZK  45 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Technical Mathematics
 Synopsis:

The subject is focused on theoretical base of classical methods for freeform interpolation and approximation curves and surfaces modelling which are used in CAD/CAM/CAE systems, e.g. Ferguson, Bézier and Coons representation.
 Requirements:
 Syllabus of lectures:

1.Ferguson polynomials, Ferguson cubic curve.
2.Cubic interpolation spline curve, boundary conditions.
3.Bernstein polynomials, Bézier curve.
4.Connection of Bézier cubic curves.
5.Coons polynomials, Coons cubic curve.
6.Relation between Ferguson, Bézier and Coons cubic curve.
7.Connection of Coons cubic curves, Coons cubic Bspline curve.
8.Ferguson 12vector and 14vector patch.
9.Bézier patch.
10.Coons approximation surface.
11.Relation between Ferguson and Bézier patches and Coons approximation surface.
12.Principle of patching.
13.Coons interpolation patches.
14.Special cases of nonuniform rational Bspline (NURBS) representation.
 Syllabus of tutorials:

1.Hermite polynomials, Ferguson cubic curve.
2.Cubic interpolation spline curve, boundary conditions.
3.Bernstein polynomials, Bézier curve.
4.Connection of Bézier cubic curves.
5.Coons polynomials, Coons cubic curve.
6.Relation between Ferguson, Bézier and Coons cubic curve.
7.Connection of Coons cubic curves, Coons cubic Bspline curve.
8.Ferguson 12vector and 14vector patch.
9.Bézier patch.
10.Coons approximation surface.
11.Relation between Ferguson and Bézier patches and Coons approximation surface.
12.Principle of patching.
13.Coons interpolation patches.
14.Special cases of nonuniform rational Bspline (NURBS) representation.
 Study Objective:
 Study materials:

Linkeová, I.: Základy počítačového modelování křivek a ploch, skriptum ČVUT, Praha, 2008.
Linkeová, I.: NURBS křivky (Neuniformní racionální Bspline křivky), monografie ČVUT, Praha, 2007.
Farin, G.: Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1988.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: