Centers

The center of a round object (a round point, dipole, circle, or sphere) is the round point having the same center and radius. The center of an object $$\mathbf x$$ is denoted by $$\operatorname{cen}(\mathbf x)$$, and it is given by the meet of $$\mathbf x$$ and its own anticarrier:


 * $$\operatorname{cen}(\mathbf x) = -\operatorname{car}(\mathbf x^*) \vee \mathbf x$$.

(The negative sign is not strictly necessary, but is included so the function always produces a result having a positive weight.) The squared radius of an object's center has the same sign as the squared radius of the object itself. That is, a real object has a real center, and an imaginary object has an imaginary center.

The following table lists the centers for the round objects in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$.