摘要：圆弧齿轮齿形系数Y_(F2)的计算,通常是把已给的实际齿数Z_2、螺旋角β换算成当量齿数Z_(V2),然后在线图上量测,估算出Y_(F2)的近似值。这种算法误差大,且费时费力。本文将线图放大读数,用三次spline函数S_△(Z)逼近Y_(F2)值,并编写了电算程序框图,给出算例,打印出理想的Y_(F2)值。

摘要：A family of piecewise rational quintic interpolation is presented. Each interpolation of the family, which is identified uniquely by the value of a parameter ai, is of C^2 continuity without solving a system of consistency equations for the derivative values at the knots, and can be expressed by the basis functions. Interpolant is of O（h^r） accuracy when f（x）∈C^r[a,b], and the errors have only a small floating for a big change of the parameter ai, it means the interpolation is stable for the parameter. The interpolation can preserve the shape properties of the given data, such as monotonicity and convexity, and a proper choice of parameter ai is given.

摘要：A new framework for free-form surface design is proposed. Using manifolds can generalize the spline scheme to surfaces of arbitrary topology. Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction. The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physics-based models.

摘要：介绍了根据CATIA软件对VBA(Visual Basic for Application)的支持,利用VBscript脚本语言,开发复杂曲面的造型设计程序的方法。利用数学方法计算生成其截面控制点,利用程序读取控制点坐标,直接在CATIA软件曲面设计环境中,自动生成各剖面的spline曲线,然后采用CATIA高级曲面的"Loft"命令完成复杂曲面的造型设计。