ft_ZYZR Struct Reference

Every orthogonal matrix \(Q \in \mathbb{R}^{3\times3}\) can be decomposed as a product of \(ZYZ\) Euler angles and, if necessary, a reflection \(R\) about the \(xy\)-plane. More...

#include <fasttransforms.h>

Data Fields
double	s [3]
double	c [3]
int	sign

Detailed Description

Every orthogonal matrix \(Q \in \mathbb{R}^{3\times3}\) can be decomposed as a product of \(ZYZ\) Euler angles and, if necessary, a reflection \(R\) about the \(xy\)-plane.

\[ Q = ZYZR, \]

where the \(z\)-axis rotations are:

\[ Z = \begin{pmatrix} c & -s & 0\\ s & c & 0\\ 0 & 0 & 1\end{pmatrix}, \]

the \(y\)-axis rotation is:

\[ Y = \begin{pmatrix} c & 0 & -s\\ 0 & 1 & 0\\ s & 0 & c\end{pmatrix}, \]

and the potential reflection is:

\[ R = \begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & \pm 1\end{pmatrix}. \]

The reflection is stored as an integer sign corresponding to the bottom right entry.

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The documentation for this struct was generated from the following file:

• src/fasttransforms.h