Generation of Rational Cubic Bézier Curve Passed through a Given Point

Shengping JIANG  Dingding CHANG  Hiroyuki ANZAI  Mingmin XU  

IEICE TRANSACTIONS on Information and Systems   Vol.E76-D    No.2    pp.307-314
Publication Date: 1993/02/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Image Processing, Computer Graphics and Pattern Recognition
rational Bézier curve,  weight parameter,  given point,  generation method,  

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The research for rational quadratic Bézier curve and its applications for generating conics and curve-fitting have been reported in some papers. But rational cubic Bézier curves, for the complexity of computation of the weight parameters and the difficulty of the shape control, have very rarely been applied up to the present. In this letter, we proposed a new method to generate a rational cubic Bézier curve. For a given point S (assuming the curve pass it) and a given value of the intermediate variable t in the point, we can compute the weight parameters of the rational cubic Bézier curve according to the relation of the control polygon and the given point, and can generate the curve. Then we explained the relation among shape of curve, given point S and intermediate varisble t. As the samples of using the method, we showed the generation of the gear-shape curve, symmetrical curve and spindle-shape curve, etc.. Finally, we discuss the application of this method for curve-fitting.