# InfinitePlane

InfinitePlane[{p1,p2,p3}]

represents the plane passing through the points p1, p2, and p3.

InfinitePlane[p,{v1,v2}]

represents the plane passing through the point p in the directions v1 and v2.

# Examples

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## Basic Examples(3)

An InfinitePlane in 3D:

Different styles applied to an infinite plane:

Determine if points belong to a given infinite plane:

## Scope(17)

### Graphics(7)

#### Specification(2)

Define an infinite plane in 3D using three points:

Define the same plane using a single point and two tangent vectors:

An infinite plane varying in direction:

#### Styling(2)

Color directives specify the color of the infinite plane:

FaceForm and EdgeForm can be used to specify the styles of the faces and edges:

#### Coordinates(3)

Specify coordinates by fractions of the plot range:

Specify scaled offsets from the ordinary coordinates:

Points and vectors can be Dynamic:

### Regions(10)

Embedding dimension is the dimension of the coordinates:

Geometric dimension is the dimension of the region itself:

Point membership test:

Get the conditions for membership:

An infinite plane has infinite measure and undefined centroid:

Distance from a point:

Signed distance from a point:

Nearest point in the region:

Nearest points:

An infinite plane is unbounded:

Find the region range:

Integrate over an infinite plane:

Optimize over an infinite plane:

Solve equations over an infinite plane:

## Applications(7)

Find the plane in which a triangle is embedded:

InfinitePlane can use the same parametrization as Triangle:

Find the plane in which a polygon is embedded:

To find the plane, take the first three points (or any three points not on a line):

The tangent plane to a parametric surface f[u,v] is given by InfinitePlane[f[u,v],{uf[u,v],vf[u,v]}]. Find the tangent plane to the parametric surface :

Find the tangent plane to the surface :

Find the intersection points of a sphere, a plane, and a surface defined by :

Visualize intersection points:

Partition space in a BubbleChart:

Combine the graphics:

Visualize a reflection plane:

Define a reflection plane:

Define a ReflectionTransform using a point on the plane and its normal vector:

Visualize the reflection of a unit cube about the plane:

## Properties & Relations(6)

InfinitePlane[{p1,p2,p3}] is equivalent to InfinitePlane[p1,{p2-p1,p3-p1}]:

InfinitePlane[p,{v1,v2}] is equivalent to Hyperplane[Cross[v1,v2],p] in 3D:

ParametricRegion can represent any InfinitePlane:

ImplicitRegion can represent any InfinitePlane:

InfinitePlane is a special case of ConicHullRegion:

Any InfinitePlane can be represented as a union of two HalfPlane regions:

## Neat Examples(2)

A random collection of planes:

Sweep an infinite plane around an axis:

Wolfram Research (2014), InfinitePlane, Wolfram Language function, https://reference.wolfram.com/language/ref/InfinitePlane.html (updated 2016).

#### Text

Wolfram Research (2014), InfinitePlane, Wolfram Language function, https://reference.wolfram.com/language/ref/InfinitePlane.html (updated 2016).

#### CMS

Wolfram Language. 2014. "InfinitePlane." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/InfinitePlane.html.

#### APA

Wolfram Language. (2014). InfinitePlane. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InfinitePlane.html

#### BibTeX

@misc{reference.wolfram_2022_infiniteplane, author="Wolfram Research", title="{InfinitePlane}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/InfinitePlane.html}", note=[Accessed: 09-December-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2022_infiniteplane, organization={Wolfram Research}, title={InfinitePlane}, year={2016}, url={https://reference.wolfram.com/language/ref/InfinitePlane.html}, note=[Accessed: 09-December-2022 ]}