基于非线性规划解的双圆柱螺线样条的局部构造

LOCALLY CONSTRUCTING DOUBLE CYLINDRICAL HELIX SPLINE BASED ON THE SOLVING NONLINEAR OPTIMIZATION PROBLEMS

给出基于非线性规划解的双圆柱螺线样条局部构造法，把平面几何样条——双圆弧样条推广到常曲率和常挠率的空间几何样条。一对G1拼接的圆柱螺线段可插值空间两端点位矢和单位切矢，且可适应不同的设计要求，如逼近在双圆柱螺线段两端点处的主法矢，使曲线光顺等。本方法在数控加工和显示中有良好的应用前景。

A local construction of double cylindrical helix spline is given based on the solving nonlinear optimization. A planar geometric spline, biarc spline, is generalized to a 3D geometric spline whose curvature and torsion are all constant. A pair of cylindrical helix splines which are G1-jointed can interpolate two given end-points and their tangents, and fit several needs of design, such as to approximate two end-points normal directions of the double cylindrical helix segment, to smooth resulting curves, etc. This method can apply to the NC-manufacture and NC-display.