In diverse applications (automotive industry, shipbuilding, design) freely deformable surfaces need to be designed in CAD environments and processed automatically. The underlying mathematical theory and practical aspects are summarized by the term CAGD (Computer-Aided-Geometric-Design). This lecture presents the most important approaches of modeling curves and surfaces. Geometric properties of these techniques will be discussed along with the practical experiences regarding the design of curves and surfaces.
Note: The first class takes place on Tuesday, October 13th!
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Computer Aided Geometric Design
Lecturer:
Prof. Holger Theisel, Tobias Günther, M.Sc.
Dates:
Tuesday, 15:00 - 17:00, G29-335
Thursday, 11:00 - 13:00, G29-335
Thursday, 11:00 - 13:00, G29-335
Requirements:
Basis knowledge in computer graphics, linear algebra.
Completion:
Oral exam.
Prerequesites:
Correct solution of 2/3 of the assignments.
Certificate/Schein:
Correct solution of 2/3 of the assignments and oral exam.
Additional Information:
Content:
- Differential geometry of curves and surfaces
- Bezier curves
- Bezier spline curves
- B-Spline curves
- Rational curves
- Polar forms
- Tensorproduct Bezier- and B-Spline surfaces
- Bezier surfaces on triangles
- Surface interrogation and fairing
- Subdivision curves and surfaces
Recommended reading:
- G. Farin. Curves and Surfaces for Computer-Aided-Geometric-Design. Morgan Kaufmann, 2002. Fourth edition.
- G. Farin and D. Hansford. The Essentials of CAGD. AK Peters, 2000.
- J. Hoschek and D. Lasser. Grundlagen der Geometrischen Datenverarbeitung. B.G. Teubner, Stuttgart, 1989. (English translation: Fundamentals of Computer-Aided-Geometric-Design, AK Peters.)
- G. Farin. NURB Curves and Surfaces. AK Peters, Wellesley, 1995.
- H.-P. Seidel. An Introduction to Polar Forms. IEEE Computer Graphics and Applications 13, 1, 1993
Lecture Slides
Exercises
Additional Material
