Tutorial Appendix: Structure Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra
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Tutorial: Structure-Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra
A new and useful set of homogeneous coordinates has been discovered for the treatment of Euclidean geometry. They render Euclidean motions not merely linear (as the classical homogeneous coordinates do), but even turn them into orthogonal transformations, through a clever choice of metric in two (not one) additional dimensions. To take full advantage of this new possibility, a good representati...
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This tutorial focuses on describing the implementation and use of reflections in the geometric algebras of three-dimensional (3D) Euclidean space and in the five-dimensional (5D) conformal model of Euclidean space. In the latter reflections at parallel planes serve to implement translations as well. Combinations of reflections allow to implement all isometric transformations. As a concrete exam...
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Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this approach to elementary representations of arbitrary points, point pairs, lines, circles, planes and spheres. Apart from including curved objects, conformal geometri...
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