Bézier曲线的近似弧长参数化方法
An Approximate Arc-Length Parameterization Method for Bézier Curves
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摘要: 通过求出曲线近似二分之一弧长的点及其相应的参数值,可将曲线分割为2段Bézier曲线,这2段曲线的弧长近似相等,而且都具有单位长度的参数区间;将这2段曲线看作一个整体并对它们的参数进行全局化,可得到一条新曲线,其近似弧长的中点对应于新的全局参数区间的中点;对新生成的Bézier曲线不断重复上述工作,最终得到一条分段Bézier曲线.将该曲线表示为B样条曲线的形式便得到一条近似弧长参数化曲线.Abstract: A method for approximating arc-length parameterization for Bézier curves by using the subdivision techniques is presented.By finding the point of approximately half the arc-length of the curve and subdividing the curve at the corresponding parameter value,we got two Bézier curves,which have approximately equal arc-length and parameter interval of unit length.Viewing the two curves as a whole and globaliz ing their parameters,we got a curve such that the point of the approximately half the arc-length corresponds to the midpoint of the new global parameter interval.Repeatedly doing this to the newly generated Bézier curves and we can finally get a piecewise Bézier curve.Then we can get a curve with approximate arclength parameterization by expressing the curve in B-spline form.
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