Unifying c curves and h curves by extending the calculation to complex numbers
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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. *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

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Unifying c curves and h curves by extending the calculation to complex numbers

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

1.Previous work

*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}.


Unifying c curves and h curves by extending the calculation to complex numbers

2.本文工作

在复数域上构造参数变换,统一两种曲线,以便能更方便地表示曲线曲面.

use parameter C﹙0﹤C﹤∞﹚

□CB-splines

C= cos( )( ).

□HB-splines

C= cosh( )( )


Unifying c curves and h curves by extending the calculation to complex numbers

Also, use parameter

□CB-splines

□HB-splines


3 basic identities and process

3. Basic identities andprocess


4 fb spline with uniform parameter c

4. FB-spline with uniform parameter C


Unifying c curves and h curves by extending the calculation to complex numbers

1)

2)


The subdivision algorithm

The subdivision algorithm


Unifying c curves and h curves by extending the calculation to complex numbers

Form(8)


5 the curvature of fb splines

5. The curvature of FB-splines


6 f curves in high orders

6. F-curves in high orders


Unifying c curves and h curves by extending the calculation to complex numbers

谢谢!

2006.2.23


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