Computer Graphics

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

The subject is focused on theoretical base of classical methods for free-form 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 B-spline curve.

8.Ferguson 12-vector and 14-vector 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 non-uniform rational B-spline (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 B-spline curve.

8.Ferguson 12-vector and 14-vector 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 non-uniform rational B-spline (NURBS) representation.

Study Objective:

Study materials:

Linkeová, I.: Základy počítačového modelování křivek a ploch, skriptum ČVUT, Praha, 2008.

Linkeová, I.: NURBS křivky (Neuniformní racionální B-spline křivky), monografie ČVUT, Praha, 2007.

Farin, G.: Curves and Surfaces for Computer Aided Geometric Design, Academic Press, 1988.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: