• Corpus ID: 62753726

Geometric algebra for computer science - an object-oriented approach to geometry

@inproceedings{Dorst2007GeometricAF,
  title={Geometric algebra for computer science - an object-oriented approach to geometry},
  author={Leo Dorst and Daniel Fontijne and Stephen Mann},
  booktitle={The Morgan Kaufmann series in computer graphics},
  year={2007}
}
Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and reference to the subject for students and experts alike. As a textbook, it provides a thorough grounding in the fundamentals of GA, with many illustrations, exercises and applications. Experts will delight in the refreshing perspective GA gives to… 

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References

SHOWING 1-10 OF 39 REFERENCES

Geometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with

The design of linear algebra and geometry

Conventional formulations of linear algebra do not do justice to the fundamental concepts of meet, join, and duality in projective geometry. This defect is corrected by introducing Clifford algebra

The making of GABLE: a geometric algebra learning environment in Matlab

Geometric algebra extends Clifford algebra with geometrically meaningful operators with the purpose of facilitating geometrical computations. Present textbooks and implementation do not always convey

Geometric Algebra for Subspace Operations

A short computation shows that the meet (∩) and join (∪) are resolved in a projection operator representation with the aid of one additional product beyond the standard geometric algebra products.

On the algebraic and geometric foundations of computer graphics

It is established that unlike projective spaces, Grassmann spaces do support all the algebra and geometry needed for contemporary computer graphics, including the graphics pipeline, shading algorithms, texture maps, and overcrown surfaces.

New Geometric Methods for Computer Vision: An Application to Structure and Motion Estimation

A coordinate-free approach to the geometry of computer vision problems is discussed, believing the present formulation to be the only one in which least-squares estimates of the motion and structure are derived simultaneously using analytic derivatives.

Oriented projective geometry

It is argued here that oriented projective geometry — and its analytic model, based on signed homogeneous coordinates — provide a better foundation for computational geometry than their classical counterparts.

Geometric algebra: A computational framework for geometrical applications (Part I: Algebra)

An introduction to the elements of geometric algebra, which contains primitives of any dimensionality (rather than just vectors), and an introduction to three of the products of geometricgebra, the geometric product, the inner product, and the outer product.

Uncertain Geometry with Circles, Spheres and Conics

Spatial reasoning is one of the central tasks in Computer Vision. It always has to deal with uncertain data. Projective geometry has become the working horse for modelling multiple view geometry,

Clifford Algebras with Numeric and Symbolic Computations

This survey of Clifford algebra covers its applications in quantum mechanics, field theory, spinor calculations, projective geometry, hypercomplex algebra, function theory and crystallography. It