Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30309
The Control Vector Scheme for Design of Planar Primitive PH curves

Authors: Ching-Shoei Chiang, Sheng-Hsin Tsai, James Chen


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.

Keywords: Bezier curve, PH curve, hodograph

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1151


[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.