一种用于飞机几何造型的局部曲线、曲面方法

A Local Curve and Surface Scheme for Aircraft Geometric Modelling

本文描述了一种用于 CAD/CAM 系统中的称之为多结点 Hermite 样条的曲线、曲面方法。基于[1][4]的研究,本文得到了关于多结点 Hermite 样条曲线、曲面的一些定量结果。结果表明,多结点 Hermite 样条具有局部修改、节省计算机内存容量以及计算量小等特点。

In existing CAD/CAM systems,the surface modelling method proposed by Coons is widely employed for aircraft geometric configuration design.However, in applying Coons' method,it is inconvenient to control surfaces by means of end conditions.Another well known method,parametric B-spline method,is an approximation scheme.In the sense of interpolation,its inherent advantages, such as local control and convex hull properties,will disappear. A method known as multi-knot Hermite splines was proposed by Qi and Zhou[1],which has extra knots in each curve segment,serving as shape par- ameters.In order to make the formulation given in[1]applicable to aircraft geometric modelling,the author employed different Boolean sum operators to derive a series of multi-knot-based Boolean sum surface schemes[4].In this paper,the author goes beyond Ref.[4]and demonstrates the derivation of the basic function of multi-knot Hermite spline and the cubic expression of the function in matrix form,upon which the matrix representations of multi-knot Hermite curve and surface can thus be established.The method is then readily adaptable in CAD/CAM application.The local and explicit representations of the curve and surface enable local modifications to be made to form a shape desired during the design process.It means that local adjustments can be made without disturbing the rest of the curve or surface. The interactive design program based on the multi-knot Hermite splines has been developed,running on the SIEMENS 7760 and PRIME 9650.Computations are carried out for some parts of an aircraft.The results of the work are very encouraging: (1)The multi-knot Hermite spline is computationally efficient,saving 30% CPU time because of its explicit expression. (2)It provides a significant reduction in the amount of computer space required to represent the surface.If the surface data grid is dimensioned M×N, the amount of memory is reduced by 4×M×N.