Using the 3D orthogonal decomposition exploration tool

Interface notes

This tool can compute and display the orthogonal decomposition of "my vector" (yellow by default) with respect to the direction specified by a "direction vector" (black by default). The lengths and orientations of "my vector" and the "direction vector" can be controlled with sliders (and checkboxes) under the Vector control menu. The orthogonal decomposition will *not* be drawn until the show orthogonal decomposition checkbox under the Decomposition display options menu is selected. There are three (mutually exclusive) options for how the decomposition is displayed controlled by the --tip to tail: proj + orth, --tip to tail: orth + proj, and --show "parallelogram" checkboxes.

As the 3D objects are of course rendered on a flat display, visual cues that may help you interpret the 3D scene properly may be obtained using the Rotational controls or the auto_rotate option under the Additional options menu.

Note that while in many contexts it may be advisable to refer only to unit vectors as direction vectors, here the "direction vector" is simply a vector that has a direction [of interest]. Thus any non-zero vector is suitable for the role.