Vorlesung im SS 2004

Geometric Modelling 1: Kurven und Flächen




Wann & wo?



Mo 10:00-11:30 Raum 36-265
Mi 11:45-13:15 Raum 52-204 Achtung Zeit geändert!
Übung Mo, 13:45 - 15:15 Raum 36-232

Beginn 26.04.2004

Inhalt


Bézier-Kurven

B-Spline-Kurven


G-Spline-Kurven


Unterteilungskurven

Bézier-Dreiecksflächen


Tensorproduktflächen




Ergänzende Literatur

[PBP]
H. Prautzsch, W. Boehm, M. Paluszny: Bézier and B-Spline Techniques, Springer-Verlag, 2002.
[HL]
J. Hoschek, D. Lasser: Grundlagen der geometrischen Datenverarbeitung, B.G. Teubner.
[Far]
G. Farin: Curves and Surfaces for CAGD, Academic Press.
[doC]
M.P. do Carmo: Differentialgeometrie von Kurven und Flächen, vieweg, 1993.
[WW]
J. Warren, H. Weimer: Subdivsion Methods for Geometric Design, Morgan Kaufman Publishers, 2002.



Kapitel 1
1.1-1.3
  • [PBP] Kapitel 1.1-1.3
  • [Far]  Kapitel 2.1, 2.2
1.4
  • [PBP] Kapitel 1.4
  • [doC] Kapitel 1.2
Kapitel 2:
2.1-2.3
  • [PBP] Kapitel 2.1-2.3
  • [Far] Kapitel 3.3, 4.1, 4.2
  • [HL] Kapitel 4.1
2.4

  • [PBP] Kapitel 3.1, 3.2
  • [Far] Kapitel 3.4, 4.7
  • [HL] Kapitel 4.1
  • T. deRose, R. Goldman: A Tutorial Introduction to Blossoming. In: H. Hagen, D. Roller (eds.), Geometric Modelling, Springer, 267-286, 1991 (pdf).
2.5
  • [PBP] Kapitel 3.11, 3.12
  • [Far] Kapitel 5.1, 5.2
  • [HL] Kapitel 4.1.1
2.6+2.7
  • [PBP] Kapitel 3.3-3.6
  • [Far] Kapitel 4.6
  • [HL] Kapitel 4.1
2.8
  • [PBP] Kapitel 3.8
  • [Far] Kapitel 5.3
  • [HL] Kapitel 4.1.1
2.9+2.10
  • [PBP] Kapitel 2.4, 3.10
  • [Far] Kapitel 4.3-4.5, 7.2-7.4
  • [HL] Kapitel 4.1.2, 4.1.3
Kapitel 3:
3.1-3.4
  • [PBP] Kapitel 5.1-5.7 (2.9)
  • [Far] Kapitel 10.3-10.6, 10.9, 10.10
  • [HL] Kapitel 4.3.1-4.3.3
3.5-3.6
  • [PBP] Kapitel 6.1-6.6
  • [Far] Kapitel 10.2, 10.7
  • [HL] Kapitel 4.3.4
Kapitel 4:
4.1+4.2
  • [PBP] Kapitel 7.2, 7.6
  • [Far] Kapitel 11.1-11.3
  • [HL] Kapitel 2.1.1
  • [doC] Kapitel 1.5
4.3-4.5
  • [PBP] Kapitel 7.1, 7.3, 7.4
  • [Far] Kapitel 12, 13
  • [HL] Kapitel 5.1, 5.2, 5.5.1, 5.5.2
4.6+4.7
  • [PBP] Kapitel 7.7-7.9
Kapitel 5:
5.1-5.6
  • [PBP] Kapitel 8
  • [WW] Kapitel 2.1, 3.2
5.7
  • V.L. Rvachev: Compactly supported solutions of functional differential equations and their applications. Russian Math. Surveys, 45: 87-120, 1990.
Kapitel 6:
6.1-6.3
  • [PBP] Kapitel 10.1, 10.2, 10.4
  • [Far] Kapitel 18.1, 18.2, 18.4
  • [HL] Kapitel 6.3.1, 6.3.2
6.4-6.6
  • [PBP] Kapitel 11.1-11.5
  • [Far] Kapitel 18.3, 18.6
6.7-6.9
  • [PBP] Kapitel 10.5, 11.7, 10.6
  • [Far] Kapitel 18.5, 18.7
  • [HL] Kapitel 6.3.3
6.10, 6.11
  • [PBP] Kapitel 12.1-12.4
  • [HL] Kapitel 9.3.2.2-9.3.2.4
Kapitel 7:
7.1-7.6
  • [PBP] Kapitel 9.1, 9.2, 9.5-9.7
  • [Far] Kapitel 16.3, 16.4, 16.6-16.8
  • [HL] Kapitel 6.2.2
7.6
  • [PBP] Kapitel 9.10, 9.11



Weiterführende Literatur

Kapitel 2.6:
  • D. Nairn, J. Peters, D. Lutterkort: Sharp, quantitative boundes on the distance between a polynomial piece and its Bézier polygon, CAGD, 16(7): 613-633, 1999 (pdf).
  • U. Reif: Best bounds on the approximation of polynomials and splines by their control structure,CAGD, 17(6): 579-589, 2000 (pdf).
Kapitel 2.7:
  • D. Filip, R. Magdson, R. Markot: Surface algorithms using bounds on derivatives, CAGD, 3(4): 295-311, 1986 (pdf).
Kapitel 3.1:
  • C. de Boor: On calculating with B-splines. Journal of Approximation Theory, 6: 50-62, 1972 (pdf).
Kapitel 3.5:
  • W. Boehm: On the efficiency of knot insertion algorithms, CAGD, 2: 141-143, 1985 (pdf).
  • E. Cohen, T. Lyche, R.F. Riesenfeld: Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics, Computer Graphics and Image Processing, 14: 87-111, 1980 (pdf).
Kapitel 4.3:
  • W. Degen: Some remarks on Bézier curves, CAGD, 5: 259-268, 1988 (pdf).
  • G. Farin: Visually C2 cubic splines, CAD, 14(3): 137-139, 1982 (pdf).
Kapitel 4.4:
  • W. Boehm: Smooth curves and surfaces. In: G. Farin (ed.), Geometric Modeling: Algorithms and New Trends, SIAM, 175-184, 1987 (pdf).
Kapitel 4.5:
  • J.A. Gregory: Geometric continuity. In: T. Lyche and L.L. Schumaker (eds.), Mathematical Methods in Computer Aided Geometric Design, Academic Press, 353-371, 1989 (pdf).
Kapitel 7.6:
  • U. Reif: TURBS - topologically unrestricted rational B-splines. Constructive Approximation, 14(1):57-78, 1998 (pdf).

© Georg Umlauf 
Last modified: 14th July 2004