中文摘要：

在这份报纸，我们在场为有在规定忍耐以内的 G1 圆柱的螺旋花键的接近的空间曲线的一个新方法。我们推出一个圆柱的螺旋的一般明确的表达，它有 11 自由。这意味着决定一个圆柱的螺旋需要 11 限制。给一个空间参量的曲线片断，包括起点和这个片断，正切和起点的主要正常的结束点，我们能总是发现一个圆柱的片断插入内推给定的方向和位置向量。以便接近在规定忍耐以内的已知的参量的曲线，我们一步一步地采用试用方法。首先，我们必须保证螺旋片断插入内推给二个结束点和比赛起点的主要正常和正切，然后，我们能到处在规定忍耐以内保留在圆柱的螺旋片断和已知的曲线片断之间的偏差。在第一个片断被形成了以后，我们能构造下一个片断。循环地，我们能构造 G1 接近的圆柱的螺旋花键在规定忍耐以内的整个空间参量的曲线。几个例子也被给显示出这个方法的效率。

英文摘要：

In this paper, we present a new method for approximating spatial curves with a G^1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix, which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G^1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.