WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

RegionEmbeddingDimension
✖
RegionEmbeddingDimension

✖

gives the dimension of the space in which the region reg is embedded.

Details

  • RegionEmbeddingDimension is also known as space dimension.
  • The embedding dimension gives the dimension of the ambient space in which reg is embedded.
  • Example cases with rows corresponding to RegionEmbeddingDimension and columns to geometric dimension:

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Find the dimension of the space in which a region is embedded:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-tbxlt
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ce30w
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-k8j2rw
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-basyjj
Out[4]=4

Scope  (14)Survey of the scope of standard use cases

Special Regions  (4)

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-cgwczk
Out[1]=1

Interval:

In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-dj73or
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-eoamtr
Out[4]=4

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ff95qq
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-c9j8dd
Out[2]=2

Line:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bjgri3
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-cvkhkk
Out[4]=4

Circle:

In[5]:=5
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-kyyvln
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ca5l2m
Out[6]=6

Disk:

In[7]:=7
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-b1cbms
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-cdv8fs
Out[8]=8

Regions in including Point:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hnubnh
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-eeut6h
Out[2]=2

Line:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hoqrd8
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-mkjlej
Out[4]=4

Polygon:

In[5]:=5
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-brf9tr
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ln36yy
Out[6]=6

Cylinder:

In[7]:=7
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-c3xs9v
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-u9k2e
Out[8]=8

Regions in including Simplex in :

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-kukhfy
Out[1]=1

Cuboid in :

In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-kojw4f
Out[2]=2

Ball in :

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hhrdfi
Out[3]=3

Formula Regions  (2)

The embedding dimension of a disk represented as an ImplicitRegion:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hb93go
Out[1]=1

A cylinder:

In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-eqicyf
Out[2]=2

A disk embedded in 3D:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-gid4fr
Out[3]=3

The embedding dimension of a disk represented as a ParametricRegion:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hhggr5
Out[1]=1

Using a rational parametrization of the disk:

In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-cjxlq
Out[2]=2

A cylinder:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hgxune
Out[3]=3

A disk embedded in 3D:

In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-lum6g
Out[4]=4

Mesh Regions  (3)

The embedding dimension of a BoundaryMeshRegion:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-lw2y8l
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-fv7un8
Out[2]=2

In 3D:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-c0qyr0
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bufvah
Out[4]=4

The embedding dimension of a MeshRegion in 1D:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-b5wl7w
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-grv26b
Out[2]=2

2D:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-c68v8v
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hbkpya
Out[4]=4

In 3D:

In[5]:=5
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-csiz0o
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ofc6p
Out[6]=6

A 1D mesh embedded in 2D:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-cz1zni
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-h9qzl7
Out[2]=2

Derived Regions  (3)

The embedding dimension of a RegionIntersection:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-286d2
In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-irl1hp
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-fi781v
Out[4]=4

The embedding dimension of a TransformedRegion:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ik7bss
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-f1e58y
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-fbdi4a
Out[3]=3

The embedding dimension of a RegionBoundary:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-84m82
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-emf8i2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-gz1w2t
Out[3]=3

Geographic Regions  (2)

Polygons with GeoPosition:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-1lk1dy
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-8vjhh8
Out[2]=2

Polygons with GeoPositionXYZ:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-4dy58p
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-pzmsx0
Out[4]=4

Polygons with GeoPositionENU:

In[5]:=5
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-sz3fv8
In[6]:=6
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-pjpdg1
Out[6]=6

Polygons with GeoGridPosition:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ipsiqu
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-yjciq7
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Select only full-dimensional primitives:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-5n771t
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-6npg2s
Out[2]=2

Generate random points with the same embedding dimension as a given region:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-2iweco
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-rp2eye

Visualize regions with random points:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-id5eh6
Out[3]=3

Properties & Relations  (8)Properties of the function, and connections to other functions

RegionEmbeddingDimension is the dimension of the space in which a region is embedded:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-keq3fv
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-mckpz
Out[2]=2

RegionDimension is the dimension of the point set that the region represents:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-eieytl
Out[3]=3

RegionEmbeddingDimension is always greater than or equal to RegionDimension:

In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-ievhdr
Out[4]=4

RegionEmbeddingDimension is the number of variables needed for a point in the region:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-dbljxt
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-kdoxzk
Out[2]=2

Since the embedding dimension is 3, three variables are needed:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bojrr5
Out[3]=3

Since the embedding dimension is 3, the point p is taken to have length 3:

In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-edadcf
Out[4]=4

RegionEmbeddingDimension for MeshRegion corresponds to the length of points:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-hfoqwq
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-gmalef
Out[2]=2

Similarly for BoundaryMeshRegion:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-df868p
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-o47whs
Out[4]=4

For an ImplicitRegion, RegionEmbeddingDimension is the number of variables:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-c7nr7r
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bsxfnv
Out[2]=2

For a ParametricRegion, RegionEmbeddingDimension is the number of equations:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-b22zdr
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bi58y8
Out[2]=2

Boolean operations are defined for regions of the same RegionEmbeddingDimension:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-isvwwt
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-famngs
Out[2]=2

With the same embedding dimension, the operation is well defined:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-74ltb
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-jczshf
Out[4]=4

Boolean operations do not change the RegionEmbeddingDimension:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-bouzlo
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-b21j11
Out[2]=2

Various Boolean operations all have the same embedding dimension:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-dv5oms
Out[3]=3

The RegionEmbeddingDimension of a RegionProduct is the sum of the input dimensions:

In[1]:=1
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-pn6prk
In[2]:=2
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-dt0hy1
Out[2]=2

The resulting embedding dimension is the sum:

In[3]:=3
✖
https://wolfram.com/xid/01lsa6i4qy01q2v8i-lkf02a
Out[3]=3
Wolfram Research (2014), RegionEmbeddingDimension, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html.
✖
Wolfram Research (2014), RegionEmbeddingDimension, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html.

Text

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

✖
Wolfram Research (2014), RegionEmbeddingDimension, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html.

CMS

Wolfram Language. 2014. "RegionEmbeddingDimension." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html.

✖
Wolfram Language. 2014. "RegionEmbeddingDimension." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html.

APA

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

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

BibTeX

@misc{reference.wolfram_2025_regionembeddingdimension, author="Wolfram Research", title="{RegionEmbeddingDimension}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}", note=[Accessed: 29-March-2025 ]}

✖
@misc{reference.wolfram_2025_regionembeddingdimension, author="Wolfram Research", title="{RegionEmbeddingDimension}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_regionembeddingdimension, organization={Wolfram Research}, title={RegionEmbeddingDimension}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}, note=[Accessed: 29-March-2025 ]}

✖
@online{reference.wolfram_2025_regionembeddingdimension, organization={Wolfram Research}, title={RegionEmbeddingDimension}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}, note=[Accessed: 29-March-2025 ]}