Matching 2D Polygonal Arcs by Using a Subgroup of the Unit Quaternions

摘要

A subgroup of the unit quaternions is used to calculate 2D rotations. Benefits of using quaternions over the more common methods include the ability to use the algebra of quaternions to find closed-form solutions and the ability to use the same approach for both 2D and 3D algorithms. The subgroup is applied to matching polygonal arcs of equal length with the resulting solution being the smallest eigenvalue of a2×2matrix. This result is then used to match a short arc to locations on a long arc.