A System Of Visualized Generation And Treatment For Freedom Curves And Surfaces

The study of freedom curves and surfaces was generated and developed as the aerospace, automotive, and other modern industrial's development and the emergence of computer. Despite its study was extended to the four-dimensional surface expression and display, its main target is still on the geometry of the industrial products description. Industrial products can be broadly divided into two categories which industrial products are shaped or formed from these two categories:one categories shape is componented by the primary analytical surfaces such as plane, cylindrical, conical surface, the spherical surface. The second category is which can not be composed of primary analysis surface, and is which be composed of curves and surfaces that changed in complex way and that so-called freedom curves and surfaces. Such as aircraft, automobiles, ship's shape parts.This paper researches the development and implementation of a system of visualized generation and treatment for freedom curves and surfaces. With the development of computer technology, the freedom curve and surface modeling technology is used in the engineering and art design. The designers are urgent for mastering and applicating computer aided geometric design (CAGD) knowledge and technology. Developing a well-function system of visualized generation and treatment for freedom curves and surfaces, helping designers to control and apply CAGD successfully and efficiently, is meaningful.In order to develop a system of visualized generation and treatment for freedom curves and surfaces; and realize the visualization generation of curves and surfaces, and edit and study curves and surfaces; made the following work basee on the analyse of the current circumstances:(1) The realization of the system basic functions. Customize the interface and structure of the system. The system is divided into four modules, that is, parameter-spline, Bezier, B-spline, NURBS. In each module, to different curves and surfaces of their own characteristics, complete the visualization generation of curves and surfaces and their characteristics.(2) After the visualization generation of freedom curves and surfaces, realize the editing part mainly which general CAD systems do not have. Set up an editing region in the system interface's left. Realize dynamic editing through modifying the corresponding parameters of editing region.(3) There are many ways about surface development. But there is no study from the metric relations between the controlling grid and the surface. In this system, make some basic work for the surface development theory on the basis of Bezier. Curve is the basis of a surface. So as the quadratic, qubic Bezier curves examples, study the metric relation between the curve length and controlling polygon's edge and the metric relation between the curve length and the angle of adjacent edges.(4) Making the further study of weight factor's influence to the curves on the basis of NURBS module. Including when modify weight factor, the general influence to the curves. As the ratio between the connection of zero value weight factor with random value weight factor and the connection of zero value weight factor with vector a variable, obtain weight factor formula and study the changing law of weight factor.The above-mentioned functions's realization is as the VC++ software a platform. Through the integrated use of OpenGL graphics library development tools, develop a system of visualized generation and treatment for freedom curves and surfaces.