基于透视投影和曲面法矢的自由曲面造型

提出用控制自由曲面形状的数据点透视投影和曲面在数据点处的法矢进行自由曲面造型的新思想。利用数据点透视投影和曲面法线方向计算数据点的三维坐标，采用参数双三次样条曲面构造自由曲面。这种给定自由曲面数据的方法易于控制自由曲面形状，几何意义明显。

An Easy-to-Apply Method for Modeling Free Curved Surface

In computer aided design, constructing a free curved surface from an image and some of its features is an important but rather difficult task to perform for some designers. We propose a new and easy-to-apply method for modeling a free curved surface from perspective projections and the normal vectors of a free curved surface. Section 1 summarizes very briefly essentials about perspective projections and normal vectors. Section 2 gives the details of our method.Typically we assume four controlling points P 00 ,P 01 ,P 10 and P 11 not on the same plane.The perspective projections of the four controlling points on two planes P 00 P 01 P 10 and P 01 P 10 P 11 are known.Section 2 derives equations for calculating the space coordinates of these four controlling points and thus obtains a small part of the free curved surface to be modeled.We repeat this typical process until we obtain the entire free curved surface.Section 3 gives a numerical example that shows preliminarily that our method is easy-to-apply.