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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. *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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  1. 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

  2. 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}.

  3. 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( )( )

  4. Also, use parameter □CB-splines □HB-splines

  5. 3. Basic identities andprocess

  6. 4. FB-spline with uniform parameter C

  7. 1) 2)

  8. The subdivision algorithm

  9. Form(8)

  10. 5. The curvature of FB-splines

  11. 6. F-curves in high orders

  12. 谢谢! 2006.2.23

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