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Eric Lengyel (talk | contribs) (Created page with "400px|thumb|right|'''Figure 1.''' The various properties of a 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...") |
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Latest revision as of 03:14, 6 August 2023
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.