Abstract:
Aiming at the existing problems in the computation of planar offset curves such as adaptability and error control,this paper proposes a new algorithm for generating the approximation offset of planar curves based on the Progressive-iteration Approximation(PIA).This algorithm generates line segments approximating the exact offset curve by adaptive sampling on the progenitor curve with tangent vector angle that transfers the problem of approximating curve to that of curve approximating line segments.It reduces the number of sample point as possible at the premise of reflecting the shape feature of the progenitor curve.Then the algorithm selects the characteristic points on the offset curve as the dominant points,and interpolates the dominant points by using the PIA to generate a B-spline curve approximating the line segments.The B-spline curve can approximate the offset curve under the given error by utilizing the method of error control proposed in this paper and the locality of PIA.Experimental result shows that this algorithm is of intuition and easy implementation,which can be used directly for arbitrary planar parameter curve and function curve.It can increase the operating efficiency of the algorithm without solving a global linear equation system.
Key words:
sampling point,
tangent vector,
characteristic point,
offset,
B-spline curve,
Progressive-iteration Approximation(PIA)
摘要： 针对传统平面曲线等距线求解算法在适应性、误差控制等方面存在的问题,基于渐进迭代逼近方法提出一种新的平面曲线等距线算法。通过基曲线上点的切矢转角对基曲线进行自适应采样,得到一条逼近等距线的折线,将曲线与曲线的逼近问题转化为折线与曲线的逼近问题。在充分反映基曲线形状特征的前提下尽可能减少采样点数量。选取等距线上的特征点作为主控制点,利用渐进迭代逼近方法插值所选取的主控制点,得到逼近折线的B样条曲线。给出误差控制方法,同时利用渐进迭代逼近方法的局部性,使所得逼近等距曲线的B样条曲线达到预先给定的精度。实验结果表明,该算法直观简洁,易于实现,可应用于任意平面参数曲线及函数曲线,并且其无需求解线性方程组,运算效率较高。
关键词:
采样点,
切矢,
特征点,
等距线,
B样条曲线,
渐进迭代逼近
CLC Number: