This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.The inner and outer products of two elements a and b are defined respectively by the following expressions: 1 a Am b = 2(ab+ba), 1 a as b = 2(ababa). ... Elements of the form Ip + I²e 12, where Ip and I² are scalars, form a subset isomorphic to the complex numbers with e12 taking the role of the square root of a1. In this case ... There may even be 358 G. Mullineux and L. Simpson 17.3 Geometry and Transforms.
|Title||:||Guide to Geometric Algebra in Practice|
|Author||:||Leo Dorst, Joan Lasenby|
|Publisher||:||Springer Science & Business Media - 2011-08-28|