From Conformal Geometric Algebra
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Any geometric object $$\mathbf x$$ can be projected onto another geometric object $$\mathbf y$$ of higher grade by first calculating the connect of $$\mathbf x$$ with $$\mathbf y$$ and then using the meet operation to intersect the result with $$\mathbf y$$. That is, the projection of $$\mathbf x$$ onto $$\mathbf y$$ is given by

$$(\mathbf y^* \wedge \mathbf x) \vee \mathbf y$$ .

This formula is general and works for flat points, lines, planes, round points, dipoles, circles, and spheres.

See Also