Description:

The subject is focused on the mathematical theory of the curves and surfaces in computer graphics and their visualisation. The Rhinoceros - NURBS modelling for Windows is used to demonstrate the geometrical properties of the curves and surfaces.

Contents:

1. Ferguson curve - definition, analytical and graphical representation, properties, applications.
2. Bézier curve - definition, analytical, graphical and CAD representation, properties, free form curves modelling, applications.
3. Coons, B-spline and NURBS curve - definition, analytical, graphical and representation, properties, free form curves modelling, applications.
4. Ferguson 12-vector patch - definition, analytical and graphical representation, applications.
5. Bézier surface - definition, analytical, graphical and CAD representation, applications.
6. Coons surface - definition, analytical, graphical and CAD representation, applications.
7. Patching - free form surfaces modelling with required continuity.

Seminar contents:

1. Rhinoceros I - helix and helicoidal surfaces modelling.
2. Free-form curves - analytical and graphical representation.
3. Rhinoceros II - free-form curves modelling.
4. Free-form surfaces - analytical and graphical representation.
5. Free-form surfaces - analytical and graphical representation - continuing.
6. Rhino III - free-form surface modelling.
7. Test. Assessments.

Recommended literature:

Linkeová, I.: Curves and Surfaces for Computer Graphics. CTU in Prague, 2012.

Keywords:

Free-form curve, free-form surface, Rhinoceros, continuity, patching.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar