The computer interpretation of line drawings is a classic problem in AI and has inspired the development of some fundamental AI tools. This novel approach to drawing interpretation combines new constraints with recent advances in soft constraint programming, Based on the author's considerable research experience, this book contains state-of-the-art reviews of work in drawing interpretation and discrete optimisation and is not just restricted to drawings of polyhedral objects, but also covers complex curved objects.The book will become a standard reference in the field with its coverage of many theoretical results with formal proofs, and is written in an accessible style making it attractive to any one intrigued by optical illusions and impossible or ambiguous figures, including computer scientists, mathematicians, cognitive scientists and psychologists.