Projections: Difference between revisions
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Eric Lengyel (talk | contribs) (Created page with "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, r...") |
Eric Lengyel (talk | contribs) No edit summary |
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Any geometric object $$\mathbf | Any geometric object $$\mathbf a$$ can be projected onto another geometric object $$\mathbf b$$ of higher grade by first calculating the [[expansion]] of $$\mathbf a$$ onto $$\mathbf b$$ and then using the [[meet]] operation to intersect the result with $$\mathbf b$$. That is, the projection of $$\mathbf a$$ onto $$\mathbf b$$ is given by | ||
:$$(\mathbf | :$$\mathbf b \vee (\mathbf a \wedge \mathbf b^\unicode["segoe ui symbol"]{x2606})$$ . | ||
This formula is general and works for [[flat points]], [[lines]], [[planes]], [[round points]], [[dipoles]], [[circles]], and [[spheres]]. | This formula is general and works for [[flat points]], [[lines]], [[planes]], [[round points]], [[dipoles]], [[circles]], and [[spheres]]. | ||
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== See Also == | == See Also == | ||
* [[ | * [[Expansion]] | ||
Latest revision as of 03:17, 23 October 2023
Any geometric object $$\mathbf a$$ can be projected onto another geometric object $$\mathbf b$$ of higher grade by first calculating the expansion of $$\mathbf a$$ onto $$\mathbf b$$ and then using the meet operation to intersect the result with $$\mathbf b$$. That is, the projection of $$\mathbf a$$ onto $$\mathbf b$$ is given by
- $$\mathbf b \vee (\mathbf a \wedge \mathbf b^\unicode["segoe ui symbol"]{x2606})$$ .
This formula is general and works for flat points, lines, planes, round points, dipoles, circles, and spheres.