Unobstructed shortest paths in polyhedral environments (Q1102729)

The solution of the problem of minimum paths is very important for many questions in engineering, economics, etc. The reviewed book presents some new algorithms, based on extensions of the so called Voronoi diagram. The book consists of six chapters. The first in an introduction, and includes an overview, prerequisites and notation, the statement of the FINDPATH-problem, some methodological and historical remarks and a presentation of related research on motion planning. The second chapter presents a solution of the general instance of FINDPATH, and the third chapter - solutions of two specific instances of FINDPATH. In the fourth chapter two Voronoi-based techniques for FINDPATH are discussed, and in the fifth chapter - some desiderable functionalities of a geometer's workbench. The sixth chapter includes the conclusions, results, proposals of future research, and open problems. One should emphasize valuable references to robotics and computer graphics.