An overview on distance and pseudo distance functions and their applications

The fast and accurate collision detection and distance calculation between geometric models is fundamental in robotics, manufacturing and computer-simulated environments. This paper surveys the state of the art in the theory and algorithms of distance and pseudo distance functions between convex sets. An overview on the existing results, including fast algorithms for distance calculation, definitions and properties of various pseudo distance functions (the J-function, the growth distance, and the pseudo minimum translational distance), is presented. The distance and pseudo distance functions are versatile in a wide range of areas. Their applications in robot motion planning, grasp analysis/synthesis, form error evaluation, and engineering optimization is demonstrated.