摘要
在计算机绘制地图光滑曲线的方法中，线形插值法计算简单，失真率较大。正轴抛物线平均加权法在一些特殊情况下曲线会偏离节点。斜轴抛物线平均加权法可以获得比较满意的结果，但计算复杂，不利于在微机上运用。本文介绍的张力样条函数插值法，方法严密，计算亦不复杂，对小型的制图系统比较适用。其显著特点是具有一个张力系数σ，当σ→０时，张力样条函数就等同于三次样条函数；当σ→∞时，则退化为分段线形函数。因此，可以选择合适的σ，使得节点间的曲线为最短，既能消除可能出现的多余拐点，又能保持曲线的光滑性。
Among those curve smoothing methods in automatic drawing of maps the linear insertion method is simple but accompanied with obvious distortion.In some special cases,the mean weighted method of main axis parabola would be deviated from the junction points.Mean weighted method of inclined axis parabola can give satisfactory results but the calculation is rather complicated and is favorable to be used in computers. The tension sample strip function insertion method introduced by the author in this paper is strict,less complicated in calculation and suitable for graphic system in a small computer.The remarkable characteristic of which is having a tension factor,when σ→0,the tension sample strip function is equivalent to a third order sample strip function;when σ→∞,it degraded into a segmenting linear function.Therefore,an appropriate value of σ can be selected to minimize the length of curve segment between junction points,which can not only smooth the curve effectively but also remove the unnecessary points of inflection.
出处
《北京地质》
1998年第1期17-24,共8页
Beijing Geology
关键词
计算机
光滑曲线
张力样条函数
插值法
地图
computer,curve smoothing,tension sample strip function,method of insertion.
