Optical Computational Geometry

Geometric problems can be solved in two ways, by calculating the solution or by its construction. The classical means of geometric constructions, the straight edge/ruler and the compass, are very limited in their capabilities. Most geometric problems cannot be solved by constructing the solution with their help. That is why until recently they were solved numerically with the help of algorithms of Computational Geometry. However advances in optical technology allowed solving them by the step-by-step formation of an optical image of the solution. Such image formation is nothing else but its step-by-step construction by optical means. Just not a ruler and a compass are used to draw the solution on a sheet of paper, but optical devices are used to step-by-step transform the images of the given figures (represented as optical transparencies) into an image of the solution to a problem. This book is an introduction to the theory of such geometric constructions with the help of optical devices. It presents step-by-step procedures for transforming the light wave images of the given figures into images of solutions to various geometric problems. Such procedures are dubbed optical algorithms in the book. The book is thereby the first presentation of the theory of optical algorithms.