基于拐点分割的Bezier曲线降阶

在Bezier曲线的降阶过程中,要求降阶逼近曲线与被逼曲线的误差满足容许误差条件,当不能满足给定的容许误差时,需要对被逼曲线作分割后再对各段进行降阶逼近.在现行的分割方法中,常常取中点作为其分割点,执行效率较高,但有时还是不能达到容许误差要求,这就需要再次分割.在充分考虑曲线的整体性质和光顺等条件后,提出把中点分割和拐点分割相混合的曲线降阶方式,使逼近曲线既满足一定的精度要求,又有较高的效率,利用尽可能少的分段,满足各段曲线相对光顺.实例分析表明,该方法可以获得较好的Bezier曲线的降阶效果.

One Order-Reduction Approximation of Bezier Curves Based on Inflection Point Division

In the process of one order-reduction approximation of Bezier curve,the error between the reducing curve and the reduced curve must meet the demand of the error bound.Recently using the middle point of the curve as the division point has been applied practically.If division once can not be satisfied,more division must be used.In the presented method,selecting the middle point and the inflection point as the division point is the better way.It not only is efficient,but also can reduce the number of division.Moreover it can also improve the smooth of the Bezier curve.Through the analysis and sample,it is concluded that this method can get a better reduction effect.