有理Bézier曲线的权因子计算

COMPUTATION OF THE WEIGHTS IN THE RATIONAL BEZIER CURVES

给出了有理Bézier曲线形状作定量修改时的权因子的计算公式,并且证明了权因子选取的唯一性。

In order to facilitate design of rational Bezier curve, it is necessary to go beyond Piegl's paper and provide solutions for the shape of rational Bezier curve which is adjusted along arbitrary orientation. Tow methods are provided, two-step method and increasing control vertex method, which are used to compute weights of rational Bezier curve. Three groups of computational formulas of the weights in rational Bezier curve are given, which can be adjusted along arbitrary orientation. The groups of formulas are equivalent and revising quantities of weight are the same. The methods proposed in the paper can be used in the interactive system of computer for design of curve.