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Surfaces and their representation and approximation for technical applications

Abstract Surfaces have a wide use in technical applications, computer graphics, engineering, CAD systems as well as in many other fields. One of the biggest problems is how to represent or approximate surfaces for these applications. In this paper we show that some of them can be obtained as an envelope surface of a one-parametrical set of surfaces. This set of surfaces can be generated by moving and transforming one surface. Then, the envelope is the boundary of the union of a set of surfaces. We present many examples and pictures. Unfortunately, most of the surfaces used in applications are not easy to generate in such an exact form; it is necessary to use some approximations. Skin surfaces and approximations by them is a good choice for some problems. We deal briefly with the theoretical part and then introduce an algorithm for smooth patches generating.