Overview At the beginning of 1999, Springer-Verlag published the book Open Geo- try OpenGL +Advanced Geometry. There, the authors Georg Glaeser and Hellmuth Stachel presented a comprehensive library of geometric me- odsbasedonOpenGLroutines.AnaccompanyingCD-ROMprovidedthesource code and many sample—les. Many diverse topics are covered in this book. The theoretical background is carefully explained, and many examples are given. Since the publication of Open Geometry, the source code has been improved andmanyadditionalfeatureshavebeenaddedtotheprogram.Contributorsfrom allovertheworldhavecomeupupwithnewideas,questions,andproblems.This process has continued up to the present and Open Geometry is growing from daytoday. In order to make all of these improvements accessible to the public, and also in order to give deeper insight into Open Geometry, we decided to write this new Handbook on Open Geometry GL 2.0. It will—ll certain gaps ofOpen Geometry 1.0 and explain new methods, techniques, and examples. On the accompanying CD-ROM the new source code and the sample—les are included. The Handbook now contains 101 well-documented examples and the reader is able to learn about Open Geometry by working through them. In addition, we present a compendium of all important Open Geometry classes and their methods. vi Preface However, we did not intend to write a new tutorial for Open Geometry. The Handbook is rather a sequel, written for the readers of the first book and for advancedprogrammers.Furthermore,itisasourceofcreativeandgoodexamples from diverse fields of geometry, computer graphics, and many other related fields like physics, mathematics, astronomy, biology, and geography.