Wann & wo?
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| Mo |
10:00-11:30 |
Raum
36-265 |
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| Mi |
11:45-13:15 |
Raum
52-204 |
Achtung
Zeit geändert!
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| Übung |
Mo,
13:45 - 15:15 |
Raum
36-232
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| Beginn |
26.04.2004 |
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Inhalt
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Bézier-Kurven |
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B-Spline-Kurven
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G-Spline-Kurven
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Unterteilungskurven |
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Bézier-Dreiecksflächen
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Tensorproduktflächen
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| Ergänzende Literatur
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[PBP]
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H. Prautzsch, W.
Boehm, M. Paluszny: Bézier and B-Spline Techniques,
Springer-Verlag,
2002. |
[HL]
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J. Hoschek, D. Lasser:
Grundlagen der geometrischen Datenverarbeitung, B.G. Teubner. |
[Far]
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G. Farin: Curves and
Surfaces for CAGD, Academic Press. |
[doC]
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M.P. do Carmo:
Differentialgeometrie von Kurven und Flächen, vieweg, 1993. |
[WW]
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J. Warren, H. Weimer:
Subdivsion Methods for Geometric Design, Morgan Kaufman Publishers,
2002.
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Kapitel
1
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1.1-1.3
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- [PBP] Kapitel 1.1-1.3
- [Far]
Kapitel
2.1, 2.2
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1.4
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- [PBP] Kapitel 1.4
- [doC] Kapitel 1.2
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Kapitel
2:
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2.1-2.3
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- [PBP] Kapitel 2.1-2.3
- [Far] Kapitel 3.3, 4.1, 4.2
- [HL] Kapitel 4.1
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2.4
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- [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).
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2.5
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- [PBP] Kapitel 3.11, 3.12
- [Far] Kapitel 5.1, 5.2
- [HL] Kapitel 4.1.1
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| 2.6+2.7 |
- [PBP] Kapitel 3.3-3.6
- [Far] Kapitel 4.6
- [HL] Kapitel 4.1
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2.8
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- [PBP] Kapitel 3.8
- [Far] Kapitel 5.3
- [HL] Kapitel 4.1.1
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2.9+2.10
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- [PBP] Kapitel 2.4, 3.10
- [Far] Kapitel 4.3-4.5, 7.2-7.4
- [HL] Kapitel 4.1.2, 4.1.3
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| Kapitel
3: |
3.1-3.4
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- [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
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3.5-3.6
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- [PBP] Kapitel 6.1-6.6
- [Far] Kapitel 10.2, 10.7
- [HL] Kapitel 4.3.4
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Kapitel
4:
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4.1+4.2
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- [PBP] Kapitel 7.2, 7.6
- [Far] Kapitel 11.1-11.3
- [HL] Kapitel 2.1.1
- [doC] Kapitel 1.5
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4.3-4.5
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- [PBP] Kapitel 7.1, 7.3, 7.4
- [Far] Kapitel 12, 13
- [HL] Kapitel 5.1, 5.2, 5.5.1, 5.5.2
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4.6+4.7
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Kapitel
5:
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5.1-5.6
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- [PBP] Kapitel 8
- [WW] Kapitel 2.1, 3.2
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5.7
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- V.L. Rvachev: Compactly supported solutions of
functional differential equations and their applications. Russian Math.
Surveys, 45: 87-120, 1990.
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Kapitel
6:
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6.1-6.3
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- [PBP] Kapitel 10.1, 10.2, 10.4
- [Far] Kapitel 18.1, 18.2, 18.4
- [HL] Kapitel 6.3.1, 6.3.2
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6.4-6.6
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- [PBP] Kapitel 11.1-11.5
- [Far] Kapitel 18.3, 18.6
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6.7-6.9
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- [PBP] Kapitel 10.5, 11.7, 10.6
- [Far] Kapitel 18.5, 18.7
- [HL] Kapitel 6.3.3
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6.10, 6.11
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- [PBP] Kapitel 12.1-12.4
- [HL] Kapitel 9.3.2.2-9.3.2.4
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Kapitel
7:
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7.1-7.6
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- [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
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7.6
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| Weiterführende Literatur |
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Kapitel
2.6:
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- 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).
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Kapitel
2.7:
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- D. Filip, R. Magdson, R. Markot: Surface algorithms
using bounds on derivatives, CAGD, 3(4): 295-311, 1986 (pdf).
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Kapitel
3.1:
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- C. de Boor: On calculating with B-splines. Journal of
Approximation Theory, 6: 50-62, 1972 (pdf).
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Kapitel
3.5:
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- 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).
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Kapitel
4.3:
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- 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).
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Kapitel
4.4:
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- W. Boehm: Smooth
curves and surfaces. In: G. Farin (ed.), Geometric Modeling: Algorithms
and New Trends,
SIAM, 175-184, 1987 (pdf).
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Kapitel
4.5:
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- 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).
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Kapitel
7.6:
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- U. Reif: TURBS - topologically unrestricted rational
B-splines.
Constructive Approximation, 14(1):57-78, 1998
(pdf).
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