Generate an Orthogonal Set of Unit Vectors

Given a vector, a set of orthogonal unit vectors is calculated to use as rotated coordinate axes.

Ex 1:
z_in = [0 0 5]';
[x, y, z] = orthogonal_set(z_in);

Supplied with the z axis, two perpendicular unit vectors are created in the xy plane.

Ex 2:
n = [1 -2 5]';
[x, y, z] = orthogonal_set(n);

Supplied with a normal vector, the returned orthogonal set of unit vectors will have a z vector parallel to the normal and an x and y vector that can be used to describe the plane that has n as a normal.

Test Scripts:

t_orthogonal_set.m - unit test the function and ensure the resulting vectors are a correct orthogonal set

t_show_me.m - A quick script that generates the screenshot image