Classical Methods of Surface Formation: Advantages and Disadvantages

Modern CAD systems that allow the creation of an electronic surface model are generally based on NURBS modeling tools. Classical computational methods of surface design (the methods of Coons, Ferguson, Bezier, etc.) have lost their relevance. However, to prepare the surface as a first approximation, the Coons method can be effectively used, the idea of which is that a portion of the surface is formed as a superposition of three ruled surfaces. This circumstance ensures the computational simplicity of the method. The same applies to surface generation options such as the Ferguson method, the Bezier method, and some nonparametric methods. Each method has its own area of application, its own advantages and disadvantages. The article discusses the distinctive features and practical aspects of implementing these methods on three-dimensional electronic models. Examples of constructing composite surfaces that smoothly fill a mesh frame consisting of quadrangular cells are presented. The presence of triangular cells is allowed. Each cell corresponds to a portion of the surface. It is shown that under certain boundary conditions, portions of the Coons, Ferguson, and Bezier surfaces coincide identically. Criteria for C2-smooth connection of nonparametric bicubic portions of a surface of the form F(x, y) are formulated. An example of calculation and visualization of a C2-smooth surface consisting of six bicubic portions is presented.