复杂曲面上任意方向曲线映射的计算

An algorithm for mapping curves on complex surfaces along any directions

针对在CAD／CAM中经常需要在复杂形体上描绘曲线，提出了自由曲面上映射曲线的计算方法，通过把沿任意方面曲线向曲面映射的问题，转化为一系列等参数曲线与一般柱面的求交问题，减少了工作量，提高了计算效率，由于该方法通过计算参数空间的映射曲线来求出模型空间的映射曲线，使最终结果更加准确，同时采用了NURBS方法，使所有的曲线曲面表示都统一在同一种形式之下，更有利于后续的处理工作。

An algorithm for mapping curves on free form surfaces in CAD/CAM is presented in this paper. In method herein, the issue of mapping curves on a surface is converted to the intersection problem of a series of equal parameter curves with a cylinder, hence calculation becomes more efficient. The mapping curve in model space is calculated by the mapping curve in parameter space, therefore, the result is more accurate. All the curves and surfaces are expressed in the form of NURBS, thus successive use can be made.