空间曲面与平面交线的一种插补算法

An Interpolation Algorithm of Space Intersection Curve of Curved Surface and Plane

针对曲面与平面交线的插补算法进行了研究。直接插补空间曲线是比较复杂的,文章提出一种新方法:首先将原坐标系下的空间平面通过坐标系旋转的方法变换成新坐标系下的等高平面,然后利用等高平面的交线推导插补算法。该算法避免了直接插补空间曲线,降低了计算的复杂度,并且保证了位置误差不超过一步。

There are two kinds of three-dimensional intersection curves： intersection curves of curved surfaces and intersection curves of curved surface and plane. The second kind of intersection curve is made research in this paper. It is complicated to interpolate the space curve directly. This paper proposes a new method. Firstly, a new coordinate is based by rotating the original coordinate. In the new coordinate, the original plane is transformed into a plane of the same height. Secondly, the interpolation algorithm is deduced from the intersection curve of the new plane. The interpolation algorithm which avoids interpolating the intersection curve directly reduce the computational complexity and guarantees a position error of at most one step.