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# Unifying C-curves and H-curves by extending the calculation to complex numbers - PowerPoint PPT Presentation

Unifying C-curves and H-curves by extending the calculation to complex numbers. Jiwen Zhang, Frank-L. Krause, Huaiyu Zhang. 9(2005)P865-883 Reporter: 张瑞坤. 1.Previous work. *C-curves (Pottmann, 1993; Zhang, 1996, 1997, 1999). {sin t, cos t, t, 1}.

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Unifying C-curves and H-curves by extending the calculation to complex numbers

Jiwen Zhang, Frank-L. Krause, Huaiyu Zhang.

9(2005)P865-883

Reporter:张瑞坤

1.Previous work to complex numbers

*C-curves (Pottmann, 1993; Zhang, 1996, 1997, 1999). {sin t, cos t, t, 1}.

*H-curves (Pottmann, 1993; Lu et al., 2002). {sinh t, cosh t, t, 1}.

2. to complex numbers本文工作

use parameter C﹙0﹤C﹤∞﹚

□CB-splines

C= cos( )( ).

□HB-splines

C= cosh( )( )

Also, use parameter to complex numbers

□CB-splines

□HB-splines

3. Basic identities and to complex numbersprocess

4. FB-spline with uniform to complex numbersparameter C

1) to complex numbers

2)

The subdivision algorithm to complex numbers

Form(8) to complex numbers

5. The curvature of FB- to complex numberssplines

6. F-curves in high orders to complex numbers

2006.2.23