Attitude

The attitude function, denoted by $$\operatorname{att}$$, extracts the attitude of a geometry and returns a purely directional object. The attitude function is defined as


 * $$\operatorname{att}(\mathbf x) = \mathbf x \vee \overline{\mathbf e_4}$$.

The attitude of a line is the line's direction as a vector, and the attitude of a plane is the plane's normal as a bivector.

The following table lists the attitude for the main types in the 4D rigid geometric algebra $$\mathcal G_{3,0,1}$$.