正则Bézier曲线的广义偏距曲线及其Matlab实现

Generalized Offset Curves of Regular Bézier Curves and Drawing of Them Using Matlab

利用de Casteljau算法求得正则Bézier曲线上各点处的切矢,由此得到x轴到Bézier曲线P(u)上各个点处的切向量的角θ(u),应用于求原始正则Bézier曲线的广义偏距曲线.该方法几何意义明显,算法简洁.同时给出了用Matlab绘制Bézier曲线及其广义偏距曲线的程序,并给出了实例.实践表明,该方法准确快捷,效果较好.

The tangent vector at each point of a Bezier curve is obtained by using de Casteljau algorithm. Then the angle from x-axis to the tangent vector at each point of the original Bezier curve can be got. So we can use this to compute the generalized offset curves of Bezier curves. This method is simple and has obvious geometric meaning. Meanwhile, the Matlab program for drawing Bezier curve and its generalized offset curves are given, the practical examples are also given. From the examples, we can see that this method is exact and quick, and the practical effect is well.