Seminar on knots and paths

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Seminar on knots and paths. Yajuan Li Nov. 23, 2005. Outlines. Modifying the knots of B-spline curves. Constrained shape modification of curves and surfaces. Paths of C-B é zier and C-B-spline curves. Future works. References.

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### Seminar on knots and paths

Yajuan Li

Nov. 23, 2005

Outlines
• Modifying the knots of B-spline curves.
• Constrained shape modification of
• curves and surfaces.
• Paths of C-Bézier and C-B-spline curves.
• Future works.
References

http://www.ektf.hu/tanszek/matematika/gemma/gemma.html

Juhász Imre, Hoffmann Miklǒs. JGG= Journal for Geometry and Graphics

[1]The effect of knot modifications on the shape of B-spline curves.JGG, 2001,5, 111–119.

[2]Geometric aspects of knot modification of B-spline surfaces, JGG, , 2002,6, 141-149.

[3]Modifying a knot of B-spline curves，CAGD, 2003, 20, 243- 245.

[4]Constrained shape modification of cubic B-spline curves by means of knots, CAD, , 2004, 36, 437-445.

[5]Symmetric alteration of two knots of B-spline curves.JGG, 2005, accepted.

[6]A limit theorem for one-parameter alteration of two knots of B-spline curves. Annales Mathematicae et Informaticae, 2005, accepted. …

[7] Barnabas Aszodi etc.. Nurbs fairing by knot vector optimization, Journal of WSCG, , 2004. 12.

Future works.

Applying the knots and paths properties into the B-spline fairing

Future works.

Simulated annealing

http://mathworld.wolfram.com/SimulatedAnnealing.html

Future works.

Applying the knots and paths properties into the B-spline fairing

Future works.

Applying the knots and paths properties into the B-spline fairing

Future works.

Applying the knots and paths properties into the B-spline fairing

Future works.

Applying the knots and paths properties into the B-spline fairing

Future works

• How can we Apply the knots and paths properties into the B-spline fairing?
• How can we Apply the knots and paths properties into CAGD?