Геометрическое моделирование каналовых поверхностей в точечном исчислении

Abstract

The article is a continuation of the authors' series of works on the development of the mathematical apparatus "Point Calculus". It introduces the reader to such tools of the point calculus as the metric operator of three points and the definition of the exit point from the plane, which are, respectively, analogs of the scalar and vector product of vectors in the vector calculus. The use of these tools for parametrization of geometrical objects in the point calculus is shown on the example of geometrical modeling of channel surfaces. In particular, the metric operator of three points is used to determine the normal in the tangent, and the definition of the exit point from the plane is used for the binormal. The result is a point algorithm for determining the channel surface in general form. The position and size of the channel surface is determined by simplex points of 3-dimensional space. Any continuous curves, both planar and spatial, can be used as guide lines. In the section plane of the channel surface, any continuous or piecewise lines can be defined, as well as their combinations.