The Control Vector Scheme for Design of Planar Primitive PH curves

The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.

Authors:

• Ching-Shoei Chiang
• Sheng-Hsin Tsai
• James Chen

Keywords:

• PH curve
• hodograph
• Bézier curve.

References:

[1] R.T. Farouki, T. Sakkalis, "Pythagrorean Hodographs" IBM J. RES.
DEVELOP. VOL 34, No. 5, September 1990.
[2] Farouki,R.T.,1992.Pythagorean-hodograph Curves in Practical Use.
In:Barnhill,R.E. (Ed.), Geometry Processing For Design and
Manufacturing. SIAM, Philadelphia, p.3-33.
[3] Farouki,R.T.,Neff,1990.Analytic properties of plane offset
curves.Computer Aided Geometric Design,7(1-4):83-99.
[4] Moon, H.P., Farouki, R.T., "Construction and shape analysis of PH
quintic Hermite interpolants", Computer Aided Geometric Design, 2001,
18, 93-115.
[5] W. L├╝ "Rationality of the offsets to algebraic curves and surfaces",
Applied Mathematics, 9 (Ser. B), 265-278.
[6] W. L├╝, "Offset-rational parametric plane curves", Computer-Aided
Geometric Design, 12, 601-616, 1995.
[7] K.K.Kubota, "Pythagorean triples in unique factorization domains",
American Mathematical Monthly, 79, 503-506, 1972.