AN ALGORITHM FOR CONSTRUCTING A FACETED SURFACE THAT ENVELOPES A GIVEN CURVED SURFACE

When solving practical problems, on the basis of geometric models in acoustics, optics, etc., to simplify calculations the approximation of curved surfaces by faceted surfaces is performed. When performing this operation, it is necessary that the parameters of the faceted surface and the specified curved surface do not differ much, otherwise the calculation results obtained in solving the problems will not be adequate. One of the most important characteristics of a surface is the direction of the normal vector at a given point on the surface. The position of the normal vector determines the direction of reflected and refracted rays in calculations based on models of geometric optics and acoustics. An algorithm for creating a faceted surface that wraps around a curved surface is proposed. The envelope of the faceted surface is in contact with the curved surface at specified points, therefore, at the points of contact both surfaces have normals that coincide in the direction, at points located in the vicinity of the points of contact, deviations of the normals are insignificant. This method of approximating curved surfaces with faceted ones makes it possible to increase the accuracy of calculations in problems of geometric optics and acoustics.