Until now, all interactions between objects in a virtual 3D world has been based on calculations performed by using linear algebra. linear algebra is very dependent on the coordinates, however, that can make a lot of programming tasks are very specific geometric and complex-often a lot of effort is needed to bring about even modest performance improvement. While linear algebra is an efficient way to determine low-level calculation, not a high-level language suitable for geometric programming. algebraic geometry, or GA, is a compact, effective time, and improve performance to represent the geometry of 3D objects in computer programs. Explaining the GA as a natural extension of linear algebra and convey the importance of geometry in 3D graphics programming, vision, and robotics. Companion web site includes links to GAViewer, a program that will allow you to interact with many characters in 3D books, and Gaigen 2, a platform for the instructive programming exercises that conclude each chapter.