Difference between revisions of "Plane"

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[[Image:plane.png|400px|thumb|right|'''Figure 1.''' A plane is the intersection of a 4D trivector with the 3D subspace where $$w = 1$$.]]
 
In the 4D projective geometric algebra $$\mathcal G_{3,0,1}$$, a ''plane'' $$\mathbf f$$ is a trivector having the general form
 
In the 4D projective geometric algebra $$\mathcal G_{3,0,1}$$, a ''plane'' $$\mathbf f$$ is a trivector having the general form
  

Revision as of 21:05, 23 April 2021

File:Plane.png
Figure 1. A plane is the intersection of a 4D trivector with the 3D subspace where $$w = 1$$.

In the 4D projective geometric algebra $$\mathcal G_{3,0,1}$$, a plane $$\mathbf f$$ is a trivector having the general form

$$\mathbf f = f_x \mathbf e_{234} + f_y \mathbf e_{314} + f_z \mathbf e_{124} + f_w \mathbf e_{321}$$ .

All planes possess the geometric property.

A plane is unitized when $$f_x^2 + f_y^2 + f_z^2 = 1$$.

When used as an operator in the sandwich product, a unitized plane is a specific kind of flector that performs a reflection through itself.

See Also