Eric Lengyel at 03:17, 23 October 2023

2023-10-23T03:17:07Z

← Older revision		Revision as of 03:17, 23 October 2023
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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		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

	:$$(\mathbf y^* \wedge \mathbf x) ~~\vee \mathbf y~~$$ .		:$$\mathbf b \vee (\mathbf a \wedge \mathbf b^\unicode["segoe ui symbol"]{x2606})$$ .

	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 ==

	* [[~~Connect~~]]		* [[Expansion]]

Eric Lengyel: 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..."

2023-08-06T03:19:16Z

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..."

New page

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 ==

* [[Connect]]

Projections - Revision history

Eric Lengyel at 03:17, 23 October 2023