Research on Modeling Free-form Curved Surface Technology

Abstract

In the geometrical design system, there are a lot of methods about how to construct a free-form curved surface. With the development of shipbuilding and aviation, the progress of science and technology, it sets a higher demand for the technology of modeling a free-form curved surface. In this paper, we have elaborated the production, development, application, and the present situation as well as development tendency of the free-form curved surface modeling. In addition, we have proposed a new and easy-to-apply method for modeling a free-form curved surface from its perspective projection and the normal vectors at the controlling points on the free-form curved surface. A briefly essentials about perspective projections and normal vectors is summarized. The details of our method are given as follow. Typically we assume four controlling points P ₀₀, P ₀₁, P ₁₀and P ₁₁ not coplanar. 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. Equations for calculating the three-dimensional coordinates of these four controlling points are derived, and thus a small patch of the free-form curved surface to be constructed is obtained. This typical processing is repeated until the entire free-form curved surface is determined. A numerical example shows preliminarily that our method is easy-to-apply. By using of our modeling method, it is convenient to control the shape of the free-form curved surface to be constructed. The geometrical structure of the modeling free-form curved surface is apparent.