Generation of Rational Cubic Bezier Curve Passed through a Given Point

概要

論文の詳細を見る
The research for rational quadratic Bezier curve and its applications for generating conics and curve-fitting have been reported in some papers. But rational cubic Bezier curves, for the complexity of computation of the weight parameters and the difficulty of the shape control, have very ralely been applied up to the present. In this letter, we proposed a new method to generate a rational cubic Bezier 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 Bezier 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 variable 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.
社団法人電子情報通信学会の論文
1993-02-25