Vorlesung im SS 2005

CAGD:
Fortgeschrittene Kurven- und Flächentechnik


Wann & wo?


Montag 10:00-11:30 Raum 36-265
Mittwoch
 11:45 - 13:15
 Raum 46-110
Übung
 Mi, 15:30 - 17:00
 Raum 36-232
Beginn 25.04.2005
Inhalt

1. G-Spline Kurven

2. Geometrisch glatte Flächen

3. Unterteilungskurven

4 .Unterteilungsflächen



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.
[BHR]
C. de Boor, K. Höllig, S. Riemenschneider: Box Splines, Springer-Verlag, 1993.
[WW]
J. Warren, H. Weimer: Subdivison Methods for Geometric Design, Morgan Kaufmann, 2002.




Kapitel 1:
1.1-1.4
  • [PBP] Kapitel 7.2, 7.6
  • [Far] Kapitel 11.1-11.3
  • [HL] Kapitel 2.1.1
  • [doC] Kapitel 1.5
1.5-1.7
  • [PBP] Kapitel 7.1, 7.3, 7.4, 7.5, 7.7
  • [Far] Kapitel 12, 13
  • [HL] Kapitel 5.1, 5.2, 5.5.1, 5.5.2, 5.5.4, 5.5.5
1.8-1.9
  • [PBP] Kapitel 7.8, 7.9
Kapitel 2:
2.1, 2.2
  • [doC] Kapitel 2.4, 2.5, 3.2
  • [Far]  Kapitel 22
2.3-2.6
  • [PBP] Kapitel 13
  • [Far] Kapitel 19.1 + 19.2
  • [HL] Kapitel 7.2, 7.5.2
2.7-2.9
  • [PBP] Kapitel 14.1 - 14.3
2.10
  • [PBP] Kapitel 14.5 + 14.6
Kapitel 3:
3.1-3.6
  • [PBP] Kapitel 8
  • [WW] Kapitel 2.1, 3.2
3.7
  • V.L. Rvachev: Compactly supported solutions of functional differential equations and their applications. Russian Math. Surveys, 45: 87-120, 1990.
Kapitel 4:
4.1-4.5
  • [PBP] Kapitel 15.1 - 15.3, 15.5, 15.7 + 15.8
  • [WW] Kapitel 3.3
4.6-4.10
  • [PBP] Kapitel 16
  • [WW] Kapitel 7.2, 8.1 - 8.3
Weiterführende Literatur

Kapitel 1.5:
  • 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 1.6:
  • W. Boehm: Smooth curves and surfaces. In: G. Farin (ed.), Geometric Modeling: Algorithms and New Trends, SIAM, 175-184, 1987 (pdf).
Kapitel 1.8:
  • 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 1.9:
  • H. Prautzsch: B-Splines with arbitrary connection matrices, Constructive Approximation 20 (2004), 191-205 (pdf).
  • T. DeRose, R. Goldman: A Tutorial Introduction to Blossoming, in Hagen, Roller (eds.), Geometric Modeling, Springer, 267-286, 1991 (pdf).
Kapitel 2.5:
  • B. Piper: Visually smooth interpolation with triangular Bézier patches. In: G. Farin (ed.), Geometric Modelling: Algorithms and New Trends, SIAM, 221-233, 1987 (pdf).
Kapitel 2.9:
  • K. Höllig, H. Mögerle: G-splines, CAGD, 7, 197-207, 1990 (pdf).
Kapitel 2.10:
  • H. Prautzsch: Freeform splines, CAGD, 14, 201-206, 1997 (pdf).
  • J. Peters: C2 free-form surfaces of degree (3,5), CAGD, 19, 113-126, 2002 (pdf).
Kapitel 4.10:
  • U. Reif: A unified approach to subdivision algorithms near extraordinary vertices, CAGD, 12, 153-174, 1995 (pdf).
  • H. Prautzsch, Smoothness of subdivision surfaces at extraordinary points, Adv. Comp. Math., 9, 377-389, 1998 (pdf).
  • H. Prautzsch, U. Reif: Degree estimates for Ck piecewise-polynomial subdivision surfaces, Adv. Comp. Math., 10, 209-217, 1999 (pdf).



© Georg Umlauf 
 Last modified: 13th July 2005