一個產生雙二次保形曲線的幾何演算法

Abstract

Interpolating algorithm using piecewise biquadratic Bezier curves is developed. The algorithm can automatically generate shape preserving biquadratic curves which faithfully describe the shape implied by the given data points. The curves obtained satisfy the conditions for "visual content". Using this algorithm, the designer is able to control the tension of the interpolating curve at each of the interpolating points. Besides the ease of shape control, the algorithm is conceptually simple and computationally efficient. It can be used to model 2D objects of various shapes. By appropriately adjusting the shape parameters at related interpolating points, the designer can easily change the curve segments' shape without affecting the remaining portions of the curve. From the comparisons of our new interpolating curves with cubic splines, it shows that our method is simple, direct and easy to be implemented.