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Computer Aided Geometric Design
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.
Lecturer:
Prof. Holger Theisel, Michael Motejat, M.Sc.
Dates:
German Lecture (Theisel, Motejat):
Tuesday, 15:00 - 17:00 - G29-335
Thursday, 13:00 - 15:00 - G22a-111

first lecture: 11.10.
Classification:
Vorlesung/Übung, 4SWS, ECTS-Credis: 5

WPF CV;B 4-6
WPF IF;B 3-6
WPF IngIF;B 4-6
WPF WIF;B 4-6
IntDesEng;M 2-3
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:
> 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
Files
Alias Ex 1 Ex 2 Ex 3 Ex 4 Ex 5 Ex 6 Ex 7 Sum Percentage
Prism 16 7 9 14.5 9 55.5 38.81
Tyrone 13.5 11 9.5 13.5 47.5 33.22
Memory 25 15 17 21 15 9 102 71.33
Blackbird 10.5 6 2 14 13.5 46 32.17
Nostalgia 24.5 13 19 21 14.5 9 101 70.63
Awakening 21.5 18.5 17 25.5 16 98.5 68.88
Chiquita 22.5 18 15 24.5 16 96 67.13
One 26 18.5 22 16 9 5 96.5 67.48
Firestarter 23.5 14 13 12 13.5 76 53.15
Lazybones 26 22 26 28 16.5 118.5 82.87
Kashmir 25 16 9 27 24 9 110 76.92
Juke 26 22.5 23 24 20 115.5 80.77
Goldfinger 20 20 19.5 26 14.5 12 112 78.32