Line

In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a line $$\boldsymbol l$$ is a trivector having the general form


 * $$\boldsymbol l = v_x \mathbf e_{415} + v_y \mathbf e_{425} + v_z \mathbf e_{435} + m_x \mathbf e_{235} + m_y \mathbf e_{315} + m_z \mathbf e_{125}$$.

A line can be viewed as an infinitely large circle that contains the point at infinity. A line in conformal geometric algebra is the precise analog of a line in rigid geometric algebra, with the only difference being that the representation of a line in the conformal model contains an additional factor of $$\mathbf e_5$$ in each term.