The goal of this book is nothing less than to revolutionize the theoretical foundations and practical implementations of Computer Graphics and Geometric Modeling. The authors propose to thoroughly transform the way Computer Scientists think about and employ algebra and geometry by replacing the standard coordinate based linear algebra common in most textbooks with a coordinate free geometric algebra. Their geometric algebra is a restriction of Clifford Algebra to sums and products that have natural geometric interpretations. These formulas include expressions for classical geometric objects such as vectors, points, lines, planes, circles and spheres as well as conformal transformations such as rotations, reflections, translations, uniform scalings and spherical inversions. This geometric algebra allows one to perform algebra directly with these entities without resorting to their coordinate or matrix representations.
The book is divided into three parts. The first part is devoted to an extended introduction to geometric algebra in ndimensions. All the major products of the geometric algebraouter product, inner product, contraction, meet and join -as well as representations for orthogonal transformations -rotors and versors -are presented here. The second part of the book is devoted to the details of three models of the geometric algebra that are particularly useful for Computer Graphics: the classical vector space model in 3-dimensions, the standard homogeneous model in 4-dimensions, and the relatively new conformal model in 5-dimensions. Implementation issues are discussed at length in the third part of the book.
The authors do an excellent job of motivating and explaining geometric algebra with clearly written text, careful illustrations, a range of pedagogic exercises, and lots of interactive