Method of Forming Paths for Uniform Surface Treatment for Objects of Complex Shape

In most cases, tool impact paths for surface treatment (painting, milling, laser hardening, etc.) represent a set of continuous spatial curves lying on the surface to be treated. For uniform processing, adjacent curves from this set must be equidistant from each other. This paper presents a new method for covering a given polygonal mesh with equidistant lines based on given initial lines (in the form of a set of vertices on this mesh) and a given distance between adjacent lines, that is measured by Euclidean distance. The method is based on constructing spheres from each vertex of the initial line and removing the vertices of the mesh that fall into at least one of the spheres: the desired equidistant line will be represented by not removed vertices lying on the spheres. To construct each subsequent equidistant line, the last constructed line is used as the initial one: thus, the entire mesh is covered along the surface, despite the fact that the distance between adjacent lines is measured in space. Due to this, the proposed method, unlike the existing ones, works with surfaces of any complexity and requires less computing resources. Ordering the points of the constructed lines, to obtain the reference points of the paths that can be executed by the manipulator, is also presented.