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={L. Dorst and D. 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… Expand
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433 Citations
Highly Influential Citations
44
Background Citations
173
Methods Citations
77
Results Citations
3

433 Citations

Citation Type

Citation Type

Geometric algebra for computer graphics
TLDR
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Geometric Algebra: A Powerful Tool for Solving Geometric Problems in Visual Computing
TLDR
This tutorial aims at introducing the fundamental concepts of GA as a powerful mathematical tool to describe and solve geometric problems in visual computing. Expand
Algorithmic structure for geometric algebra operators and application to quadric surfaces
TLDR
The proposed method is a hybrid solution that includes precomputed code with fast execution for low dimensional vector space, which is somehow equivalent to the state of the art method and for high dimensional vector spaces, a new recursive scheme is introduced and it is proved that associated algorithms are efficient both in terms of computationnal and memory complexity. Expand
Geometric Algebra
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Introduction to Clifford's Geometric Algebra
TLDR
This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model. Expand
Doing Euclidean Plane Geometry Using Projective Geometric Algebra
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize… Expand
Geometric computing in computer graphics and robotics using conformal geometric algebra
TLDR
The main contribution of this thesis is the geometrically intuitive and - nevertheless - efficient algorithm for a computer animation application, namely an inverse kinematicsgorithm for a virtual character based on an embedding of quaternions in Conformal Geometric Algebra. Expand
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References

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