Cyclic and Ruled Surfaces as ∞ 2 Points Equidistant From Two Given Geometric Shapes. Part 1

In this paper, we consider modeling options for linear and cyclic surfaces, which are a two-parameter set (∞2 ) of points equidistant from two given geometric shapes. These figures will be points, lines, circles and some surfaces in certain combinations and positions: planes, spheres, cones, cylinders, and the equidistant method is used to obtain the desired result. The variants of combinations of only two given geometric shapes are considered. In this paper, we study only a small part of the combinations of a point with such simple geometric shapes as a point, a straight line, a circle, a plane, a sphere, a cylinder of rotation, a cone of rotation. That is, 7 options. This is part one of the study. Other options, starting with number 8, will be considered in other parts of the work. Only linear and cyclic surfaces are highlighted; others, more complex, are not considered. Both analytical and synthetic evidence is used. A table is proposed to indicate the ordinal number of the task under consideration, as well as a table of the final result. It is clear that the number of surfaces is many times greater, even now they are receiving all new ways of designing with the release of Ph.D. and doctoral theses, so it is simply impossible to consider them all in a small volume of the article. So this work on cyclic and ruled surfaces, modeled as ∞ 2 points equidistant from two geometric shapes, should be considered only a foundation for the development of many other options.