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InfinitePlane
✖
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.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

An InfinitePlane in 3D:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-c6r2pf
Out[1]=1

Different styles applied to an infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-ft3i2t
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-p3gug
Out[2]=2

Determine if points belong to a given infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-pxgsel
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-bpzg0x
Out[2]=2

Scope  (17)Survey of the scope of standard use cases

Graphics  (7)

Specification  (2)

Define an infinite plane in 3D using three points:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-e7r7wx
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-gjh11t
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-71xkk
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-gdpbsj
Out[4]=4

An infinite plane varying in direction:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-f4rlws
Out[1]=1

Styling  (2)

Color directives specify the color of the infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-bes1w
Out[1]=1

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

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-ykmdb
Out[1]=1

Coordinates  (3)

Specify coordinates by fractions of the plot range:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-e3u77e
Out[1]=1

Specify scaled offsets from the ordinary coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-f8i2ip
Out[1]=1

Points and vectors can be Dynamic:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-9cjx7z
Out[1]=1

Regions  (10)

Embedding dimension is the dimension of the coordinates:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-txg5x2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-5q2jur
Out[2]=2

Geometric dimension is the dimension of the region itself:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-bin9zy
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-xze387
Out[2]=2

Point membership test:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-ddq0ru
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-cjj0wh
Out[2]=2

Get the conditions for membership:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-bb4qcz
Out[3]=3

An infinite plane has infinite measure and undefined centroid:

In[1]:=1
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https://wolfram.com/xid/0d6gir0xq7-lu8hn1
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-jkby32
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-ehj3hm
Out[3]=3

Distance from a point:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-3uqq9s
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-pii3zc
Out[2]=2

Signed distance from a point:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-5s0v3r
Out[3]=3

Nearest point in the region:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-pfynp3
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-kjql3z
Out[2]=2

Nearest points:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-36yfy7
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-hg4qin
Out[4]=4

An infinite plane is unbounded:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-j36bgo
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-eqof9h
Out[2]=2

Find the region range:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-ky39j1
Out[3]=3

Integrate over an infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-0ldrux
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-gtyh05
Out[2]=2

Optimize over an infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-6j7164
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-q29ws0
Out[2]=2

Solve equations over an infinite plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-xja6yq
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-1ok044
Out[2]=2

Applications  (7)Sample problems that can be solved with this function

Find the plane in which a triangle is embedded:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-qorsx0

InfinitePlane can use the same parametrization as Triangle:

In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-ekrm22
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-di9hob
Out[4]=4

Find the plane in which a polygon is embedded:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-dtm6ls
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-1iwvv

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

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-dcknpw
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-hwu8us
Out[4]=4

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 :

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-6naqy
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-b7bna3
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-fccxvn
Out[3]=3

Find the tangent plane to the surface :

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-bc3htq
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-d2oryg
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-eelf0
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-gnofuq
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-h539x7
Out[2]=2

Visualize intersection points:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-ozql0o
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-0jr7hl
In[5]:=5
✖
https://wolfram.com/xid/0d6gir0xq7-0hkhnu
In[6]:=6
✖
https://wolfram.com/xid/0d6gir0xq7-lnw1r2
In[7]:=7
✖
https://wolfram.com/xid/0d6gir0xq7-3hs7ij
Out[7]=7

Partition space in a BubbleChart:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-1fm7gd
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-6f1j4w

Combine the graphics:

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-p04vrs
Out[3]=3

Visualize a reflection plane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-4dos5m

Define a reflection plane:

In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-5iqivl

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

In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-2a3gms
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-b8wgcq

Visualize the reflection of a unit cube about the plane:

In[5]:=5
✖
https://wolfram.com/xid/0d6gir0xq7-gy2hm0
In[6]:=6
✖
https://wolfram.com/xid/0d6gir0xq7-idy2gi
Out[6]=6

Properties & Relations  (6)Properties of the function, and connections to other functions

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

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-0thsh1
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-2n7iy4
In[5]:=5
✖
https://wolfram.com/xid/0d6gir0xq7-rnlbun
Out[5]=5

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

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-drk8j3
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-bd4z4o
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-bvzoek
Out[3]=3

ParametricRegion can represent any InfinitePlane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-do6kf2
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-b3dt7k
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-4mog7n
Out[3]=3

ImplicitRegion can represent any InfinitePlane:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-foufor
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-qanq37
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-psdt60
Out[3]=3

InfinitePlane is a special case of ConicHullRegion:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-dbhzyr
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-1dyyl4
Out[2]=2

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

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-k0uwjw
In[2]:=2
✖
https://wolfram.com/xid/0d6gir0xq7-ysphzg
In[3]:=3
✖
https://wolfram.com/xid/0d6gir0xq7-zcbprr
In[4]:=4
✖
https://wolfram.com/xid/0d6gir0xq7-qdp25v
Out[4]=4

Neat Examples  (2)Surprising or curious use cases

A random collection of planes:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-iuc3q
Out[1]=1

Sweep an infinite plane around an axis:

In[1]:=1
✖
https://wolfram.com/xid/0d6gir0xq7-0z8va1
Out[1]=1
Wolfram Research (2014), InfinitePlane, Wolfram Language function, https://reference.wolfram.com/language/ref/InfinitePlane.html (updated 2016).
✖
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).

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_infiniteplane, author="Wolfram Research", title="{InfinitePlane}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/InfinitePlane.html}", note=[Accessed: 15-May-2025 ]}

✖
@misc{reference.wolfram_2025_infiniteplane, author="Wolfram Research", title="{InfinitePlane}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/InfinitePlane.html}", note=[Accessed: 15-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_infiniteplane, organization={Wolfram Research}, title={InfinitePlane}, year={2016}, url={https://reference.wolfram.com/language/ref/InfinitePlane.html}, note=[Accessed: 15-May-2025 ]}

✖
@online{reference.wolfram_2025_infiniteplane, organization={Wolfram Research}, title={InfinitePlane}, year={2016}, url={https://reference.wolfram.com/language/ref/InfinitePlane.html}, note=[Accessed: 15-May-2025 ]}