The aim is to bring together under one cover the latest advances in the application of computational geometry to the most important areas related to efforts to build a system of action perception: computer vision, robotics, image processing and understanding, pattern recognition, computer graphics, quantum computers, and brain theory neural network. There has been given to increase efforts to overcome various problems in this field using the geometric method is promising. To help overcome this situation, we decided that the time has come to introduce a geometric method that is strong in an integrated to a much larger community of scientists and engineers who are looking for new mathematical tools to solve their problems more complicated.