国际设备工程与管理（英文版）2007，Vol.12Issue(2)：69-78,10.
Cylindrical Helix Spline Approximation of Spatial Curves
Cylindrical Helix Spline Approximation of Spatial Curves
摘要
Abstract
In this paper, we present a new method for approximating spatial curves with a G1 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 G1 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.关键词
cylindrical helix spline/approximation/spatial curves/methodKey words
cylindrical helix spline/approximation/spatial curves/method分类
建筑与水利引用本文复制引用
..Cylindrical Helix Spline Approximation of Spatial Curves[J].国际设备工程与管理（英文版）,2007,12(2):69-78,10.基金项目
This paper is supported by National Natural Science Foundation of China under Grant No. 50205010 （）
