The computer interpretation of line drawings is a classic problem in artificial intelligence and has inspired the development of some fundamental AI tools, including constraint propagation, probabilistic relaxation, tractable constraints, and (most recently) local simplification of optimisation problems. Based on the author’s considerable research experience, this book looks at line drawing interpretation and constraint satisfaction, covering several landmark results in the field. It contains state-of-the-art reviews of work in both drawing interpretation and discrete optimisation, and is not just restricted to drawings of polyhedral objects, but also covers complex curved objects. Its novel approach to drawing interpretation combines new constraints with recent advances in soft constraint programming. The book will become a standard reference in the field with its coverage of many theoretical results with formal proofs, particularly concerning necessary-and-sufficient conditions for realizability, simplification operations for combinatorial problems and tractability of drawing interpretation. Martin Cooper makes this fascinating topic accessible not only to computer scientists, but also to mathematicians, psychologists and cognitive scientists – indeed to anyone intrigued by optical illusions and impossible or ambiguous figures.