This chapter describes an approach to efficiently implementing geometric algebra. By “efficient” we mean that if you write a program that uses geometric algebra to do some geometry, it should be about as fast as a similar program that uses a traditional optimized method to do the same geometry. For example, the homogeneous model in geometric algebra (Chapter 11) should perform on par with a traditional implementation of homogeneous coordinates in linear algebra. We will demonstrate that this is possible with benchmarks of a ray tracer. The ray tracer itself is described in the next chapter.

We assume that you have read the preceding implementation chapters, as our goal here is to implement efficiently ...

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