If I was only allowed one computational geometry book then it would undoubtedly be this one.
The first edition of this book is recognised as one of the definitive sources on the subject of Computational Geometry. In fact, O'Rourke has a long history in the field, has published many papers on the subject and is responsible for the computer graphics algorithms newsgroup which is where all computer geometers meet to discuss their ideas and problems.
Typical problems discussed include how a polygon can be represented, how to calculate its area, how to detect if two polygons intersect and how to calculate the convex hull of a polygon. This leads onto more complex issues such as motion planning and seeing if a robot is able navigate from point x to point y without bumping into objects. The algorithms for these (and other) problems are discussed and many are implemented. In addition, many of the ideas are also discussed from the point of view of three and more dimensions.
The only disappointment is that many problems are posed as questions at the end of the chapters and, as far as I could see, you cannot get the answers in the forms of a lecturer's supplement. This is fine in academia but not a lot of use for the commercial world.
Due to the range of problems that incorporate computational geometry this book cannot be expected to answer every problem you might have. You will undoubtedly need access to other textbooks but I have been using the first edition of this book for many years and the second edition is a welcome addition to my bookshelf. If I was only allowed one computational geometry book then it would undoubtedly be this one.