Surfaces of the congruence of equi-affine images of circle

Abstract

Surfaces of the congruence of equi-affine images of circle

Ivanov I.I., Petrov P.P.

Incoming article date: 08.12.2016

The process of forming the surfaces is the first step in designing of a physical model of the product. In the article one of ways of formation of surfaces, which lines are lines of congruence, is considered. In the article the model of the first order’s congruence of the equi-affine images of the circles, which are received by elliptic rotation of the plane, is developed. This congruence does not have focal lines. Equi-affine images of the circle are ellipses, which are equal on the area. Structural elements of the received congruence are specified, types of coordinate lines of curvilinear coordinates are considered. The parametrical equations of u-congruence and its surfaces, formed by immersion of any line in congruence, are synthesized. Constraints for the inputting parameters of the equations are specified. Examples of surfaces at immersion of a straight line, ellipse and the spiral line with the image of the immersed line on the received surface are given.

Keywords: Congruence, equi-affine transformation, elliptic rotation, parametrical equations, generatrix, circle