Computations of 3D Euclidean geometry can be performed using various computational models of different effectiveness.
We wrote a paper (to be published) that compares five alternatives: 3D linear algebra, 3D geometric algebra, a mix of 4D homogeneous coordinates
and Pluecker coordinates, a 4D homogeneous model using geometric algebra, and the 5D Conformal model using
geometric algebra. Higher dimensional models and models using geometric algebra can express geometric
primitives, computations and constructions more elegantly, but this elegance may come at a performance penalty.
This website accompanies the paper on that subject.
Ray tracer performance
To find out more about Gaigen, our geometric algebra implementation, visit:
For more information and tutorials on geometric algebra, visit:
Leo Dorst's Geometric Algebra site.