ERotation.hpp File Reference

#include "Enum/AEnum.hpp"

Macros
#define	ENUM_ROTATION

Macro Definition Documentation

ENUM_ROTATION

#define ENUM_ROTATION

Value:

    ERotation, SXYZ, \
    SXYZ, 0, "sxyz", \
    SXYX, 1, "sxyx", \
    SXZY, 2, "sxzy", \
    SXZX, 3, "sxzx", \
    SYZX, 4, "syzx", \
    SYZY, 5, "syzy", \
    SYXZ, 6, "syxz", \
    SYXY, 7, "syxy", \
    SZXY, 8, "szxy", \
    SZXZ, 9, "szxz", \
    SZYX, 10, "szyx", \
    SZYZ, 11, "szyz", \
    RZYX, 12, "rzyx", \
    RXYX, 13, "rxyx", \
    RYZX, 14, "ryzx", \
    RXZX, 15, "rxzx", \
    RXZY, 16, "rxzy", \
    RYZY, 17, "ryzy", \
    RZXY, 18, "rzxy", \
    RYXY, 19, "ryxy", \
    RYXZ, 20, "ryxz", \
    RZXZ, 21, "rzxz", \
    RXYZ, 22, "rxyz", \
    RZYZ, 23, "rzyz"

The documentation comes from the following reference:

https://github.com/matthew-brett/transforms3d/blob/master/transforms3d/euler.py

Rotation axes

Rotations given as a set of three angles can refer to any of 24 different ways of applying these rotations, or equivalently, 24 conventions for rotation angles. See http://en.wikipedia.org/wiki/Euler_angles. The different conventions break down into two groups of 12. In the first group, the rotation axes are fixed (also, global, static), and do not move with rotations. These are called extrinsic axes. The axes can also move with the rotations. These are called intrinsic, local or rotating axes. Each of the two groups (intrinsic and extrinsic) can further be divided into so-called Euler rotations (rotation about one axis, then a second and then the first again), and Tait-Bryan angles (rotations about all three axes). The two groups (Euler rotations and Tait-Bryan rotations) each have 6 possible choices. There are therefore 2 * 2 * 6 = 24 possible conventions that could apply to rotations about a sequence of three given angles. This module gives an implementation of conversion between angles and rotation matrices for which you can specify any of the 24 different conventions.

Specifying angle conventions

You specify conventions for interpreting the sequence of angles with a four character string. The first character is 'r' (rotating == intrinsic), or 's' (static == extrinsic). The next three characters give the axis ('x', 'y' or 'z') about which to perform the rotation, in the order in which the rotations will be performed. For example the string 'szyx' specifies that the angles should be interpreted relative to extrinsic (static) coordinate axes, and be performed in the order: rotation about z axis; rotation about y axis; rotation about x axis. This is a relatively common convention, with customized implementations in :mod:taitbryan in this package. The string 'rzxz' specifies that the angles should be interpreted relative to intrinsic (rotating) coordinate axes, and be performed in the order: rotation about z axis; rotation about the rotated x axis; rotation about the rotated z axis. Wolfram Mathworld claim this is the most common convention : http://mathworld.wolfram.com/EulerAngles.html.