Fast and accurate normalization of vectors and quaternions

TL;DR

This paper introduces a fast and precise method for normalizing vectors and quaternions, improving computational efficiency in geometric and design applications by adapting LAPACK techniques.

Contribution

It presents a novel adaptation of LAPACK-based methods for rapid and accurate normalization of vectors and quaternions, a fundamental operation in computational geometry.

Findings

Significantly faster normalization compared to traditional methods

Maintains high accuracy in vector and quaternion length calculations

Applicable to 2D and 3D geometric computations

Abstract

We present fast and accurate ways to normalize two and three dimensional vectors and quaternions and compute their length. Our approach is an adaptation of ideas used in the linear algebra library LAPACK, and we believe that the computational geometry and computer aided design communities are not aware of the possibility of speeding up these fundamental operations in the robust way proposed here.