# 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

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## Basic Examples(1)

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

## Scope(14)

### Special Regions(4)

Regions in including Point:

Regions in including Point:

Line:

Disk:

Regions in including Point:

Line:

Regions in including Simplex in :

Cuboid in :

Ball in :

### Formula Regions(2)

The embedding dimension of a disk represented as an ImplicitRegion:

A cylinder:

A disk embedded in 3D:

The embedding dimension of a disk represented as a ParametricRegion:

Using a rational parametrization of the disk:

A cylinder:

A disk embedded in 3D:

### Mesh Regions(3)

The embedding dimension of a BoundaryMeshRegion:

In 3D:

The embedding dimension of a MeshRegion in 1D:

2D:

In 3D:

A 1D mesh embedded in 2D:

### Derived Regions(3)

The embedding dimension of a RegionIntersection:

The embedding dimension of a TransformedRegion:

The embedding dimension of a RegionBoundary:

### Geographic Regions(2)

Polygons with GeoPosition:

Polygons with GeoPositionXYZ:

Polygons with GeoPositionENU:

Polygons with GeoGridPosition:

## Applications(2)

Select only full-dimensional primitives:

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

Visualize regions with random points:

## Properties & Relations(8)

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

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

RegionEmbeddingDimension is always greater than or equal to RegionDimension:

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

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

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

RegionEmbeddingDimension for MeshRegion corresponds to the length of points:

Similarly for BoundaryMeshRegion:

For an ImplicitRegion, RegionEmbeddingDimension is the number of variables:

For a ParametricRegion, RegionEmbeddingDimension is the number of equations:

Boolean operations are defined for regions of the same RegionEmbeddingDimension:

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

Boolean operations do not change the RegionEmbeddingDimension:

Various Boolean operations all have the same embedding dimension:

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

The resulting embedding dimension is the sum:

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.

#### CMS

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

#### BibTeX

@misc{reference.wolfram_2021_regionembeddingdimension, author="Wolfram Research", title="{RegionEmbeddingDimension}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}", note=[Accessed: 19-May-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2021_regionembeddingdimension, organization={Wolfram Research}, title={RegionEmbeddingDimension}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}, note=[Accessed: 19-May-2022 ]}