Automation of layout design of spiral conical scans

In this paper the authors solve the problem of dense layout on the infinite plane of the spiral scans of the side surface of a straight circular truncated cone. The boundaries of the spiral scans are arcs of circles and spirals of Archimedes. A full scan of the side surface of the cone is a single part. The approach of finding a dense layout by means of implementation of transformations of rotation of figures and their parallel transfer in the Maple 2015 is offered. As an example of the surface, the surface of a conical spiral antenna or the surface of a woman's skirt can be considered. It is shown that for the proposed layout of the spiral scan the proportion of cuttings is equal to 5.3%, and for straight conical scans of the same lateral surface is 10.2%. Thus, the proposed method of layout of the spiral scans in the plane allows to reduce the proportion of cuttings by almost 5%.