Guide to Geometric Algebra in Practice pp 329-352 | Cite as

# A Homogeneous Model for Three-Dimensional Computer Graphics Based on the Clifford Algebra for ℝ^{3}

## Abstract

We construct a homogeneous model for Computer Graphics using the Clifford Algebra for ℝ^{3}. To incorporate points as well as vectors within this model, we employ the odd-dimensional elements of this graded eight-dimensional algebra to represent mass-points by exploiting the pseudoscalars to represent mass. The even-dimensional elements of this Clifford Algebra are isomorphic to the quaternions, which operate on the odd-dimensional elements by sandwiching. Along with the standard sandwiching formulas for rotations and reflections, this paradigm allows us to use sandwiching to compute perspective projections.

## Notes

### Acknowledgements

I would like to thank Leo Dorst and Steve Mann for reading a preliminary draft of this manuscript and providing valuable comments, criticisms, and suggestions. I would also like to thank the anonymous referees for their constructive criticisms. This work is much improved as a result of the observations of these people. Any mistakes that still remain are, of course, entirely my own.

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