一个试验性的辅助外形设计系统

本文介绍了一个用于自由型曲面设计的交互式图象仪系统。该系统是建立在三次、均匀B-样条理论的基础上,为取得更好的拟合效果,选用了两端处具有四重节点的基函数。其主要功能如下: 1.在屏幕或绘图机上显出三维的模型,并允许对模型作出实时的三维坐标变换。 2.通过对离散点圆率序列光顺的方法,达到对所给模型外形的光顺。 3.提供了两种对模型表面作局部修改的方法,且仍保证C²连续。 4.允许对模型作出任意斜截面外形。 在DJS-6计算机及由西安交大设计制造的“751”光笔图象仪上建立了一个辅助外形设计的交互式系统。目前已初具规模,但仍在继续完善和发展。考虑到几何直观,计算简捷,易于控制修改等要求,因此选用了B-样条方法来构成曲线（面）,形象地称之为“曲线（面）的特征多边（面）形设计法”。这里仅简单介绍此系统的主要功能、算法结论及应用图例。

AN EXPERIMENTAL INTERACTIVE COMPUTER GRAPHICS SYSTEM FOR FREE-FORM SURFACE DESIGN

An interactive computer graphics system for free-form surface design is described in this paper, and application of cubic uniform B-splines is suggested as the fundamental method of surface modeling. In order to obtain a better approximation, the basic function with a quadruple knot at each end point is utilized.In respect of curve construction, there are only 18 columns in each of various coefficient matrices for the different numbers of vertexes and the different sequences of curve segments, and the matrix expressions of curves are also given. As a result, real benefit is gained for reducing the storage capacity and increasing the computational speed. In the inverse calculation for the vertexes 26 various composite cases are summarized, which permit to maintain the original straight line segments.It is proposed to fair the given curves by fairing the curvature sequence of the discrete vertexes, and preliminary practical experience is also given.This paper offers a simple and fast engineering algorithm for modifying of the surface data in a local region, while the surface still remains in second order continuity.In the experimental system there are 20 functional buttons （embracing the functions of coordinate transform, 3-dimensional symmetry, construction of an arbitrary section etc. ）. A success has been made in surface modeling of aircraft, automobile and ship.