2.3 3D Rotation

If you were to draw a line between two markers that line would have multi-axis rotation as you move the object. That 3D rotation can be measured through three angles. The most common way to measure these angles is through Euler Angles. Typically the first angle is a rotation around the Z axis and then a rotation around the X axis with the third being a Z rotation around the current axis of rotation or Z-X-Z angles.

We are going to use a slightly different set of angles that just measures the rotation around each cardinal plane: X, Y, and Z. Similar to the rotation of a plane: pitch, yaw, and roll. This is a bit easier for us to measure and keep track of. Ultimately we are more concerned with “change” in rotation per frame rather than precise location because we already have that. The above definition shows the rotation of the line between two markers around each cartesian plane.

In this definition we are deconstruct the vector of each marker and then remaking a 2D line with only two of its coordinates for instance just X and Y or X and Z. This allows to get the angle of rotation between that 2D line and a line along the cardinal planes. You can download the above definition here: 3D Rotational Data