This book demonstrates that classical problems of computational geometry can be solved when the input and output data are on surfaces other than the plane, but that planar techniques cannot always be adapted successfully, and new techniques must be considered. Well-known problems from computational geometry are adapted to cases where the objects are on surfaces, and an attempt is made to answer questions that arise in the growing list of areas in which the results of computational geometry are applicable. These areas are, among others, engineering, computer aided design, manufacturing, geographic information systems, operations research, robotics, computer graphics, and solid modelling. Audience: This volume will be of interest to postgraduate students and researchers whose work involves computational geometry, algorithms, combinatorics, and graph theory.