Mathematical Model and Solution Algorithm for Virtual Localization Problem

Introduction. The optimization placement problem refereed to virtual localization is studied. This motivated by the need optimize production of parts from near-net shape blanks using CNC machines. known algorithms for solving come down determining location parameters part CAD model inside point cloud obtained scanning workpiece surface. main disadvantage such use criteria that are insensitive intersection surfaces and workpiece. In order prevent errors in conditions, it necessary involve a human operator conducting operations based on localization. this way, complex objects paramount importance. purpose paper propose new approach problem. Results. A mathematical phi-function technique proposed. We developed solution strategy combines algorithm generating feasible starting points with non-linear procedure. testing proposed was carried out two-dimensional case. computational results illustrated graphical illustrations provided show efficiency algorithm. Conclusions. phi-functions prevents occurrence erroneous solutions surfaces. An formulation case when convex polygons has been developed. For considered test problems, time did not exceed 2.5 sec, which fully meets requirements industrial use. future, planned extend method cases an arbitrary formed Boolean geometric primitives. Keywords: polygonal domain, technique, localization, machining.