Building an Orthonormal Basis from a 3D Unit Vector Without Normalization

@article{Frisvad2012BuildingAO,
  title={Building an Orthonormal Basis from a 3D Unit Vector Without Normalization},
  author={Jeppe Revall Frisvad},
  journal={J. Graphics Tools},
  year={2012},
  volume={16},
  pages={151-159}
}
I present two tools that save the computation of a dot product and a reciprocal square root in operations that are used frequently in the core of many rendering programs. The first tool is a formula for rotating a direction sampled around the z-axis to a direction sampled around an arbitrary unit vector. This is useful in Monte Carlo rendering techniques… CONTINUE READING