Geometric Algebra for Computer Science An Object-Oriented Approach to Geometry

Name: Geometric Algebra for Computer Science An Object-Oriented Approach to Geometry
Availability: OutOfStock
ISBN: 9780123694652

ISBN-10: 0123694655

ISBN-13: 9780123694652

Edition: 2007

Authors: Leo Dorst, Daniel Fontijne, Stephen Mann

List price: $80.95

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Description:

In fields such as robotics, computer graphics, and computer games, it is necessary to compute complex interactions of objects in virtual 3D worlds. In a virtual world, there may be thousands of these objects interacting with each other in real-time. Linear algebra (vector math) is traditionally used to perform these calculations, but linear algebra requires long and complex computer programs to implement and can create very difficult programming challenges. Developers of real-time applications spend a lot of time trying to squeeze the last ounce of performance out of them. Geometric algebra (GA) is a new and compact way of representing the geometry of these objects that makes the…

Book details

List price: $80.95
Copyright year: 2007
Publisher: Elsevier Science & Technology Books
Publication date: 4/19/2007
Binding: Hardcover
Pages: 664
Size: 7.75" wide x 9.50" long x 1.50" tall
Weight: 3.542
Language: English




Why geometric algebra?



Geometric algebra



Spanning oriented subspaces



Metric products of subspaces



Linear transformations of subspaces



Intersection and union of subspaces



The fundamental product of geometric algebra



Orthogonal transformations as versors



Geometric differentiation



Models of geometries



Modeling geometries



The vector space model : the algebra of directions



The homogeneous model



Applications of the homogeneous model



The conformal model : operational Euclidean geometry



New primitives for Euclidean geometry



Constructions in Euclidean geometry



Conformal operators



Operational models for geometries



Implementing geometric algebra



Implementation issues



Basis blades and operations



The linear products and operations



Fundamental algorithms for nonlinear products



Specializing the structure for efficiency



Using the geometry in a ray-tracing application



Appendices



Metrics and null vectors



Contractions and other inner products



Subspace products retrieved



Common equations