RegionEmbeddingDimension

RegionEmbeddingDimension[reg]

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:

Interval:

Regions in including Point:

Line:

Circle:

Disk:

Regions in including Point:

Line:

Polygon:

Cylinder:

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.

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: 17-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_regionembeddingdimension, organization={Wolfram Research}, title={RegionEmbeddingDimension}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionEmbeddingDimension.html}, note=[Accessed: 17-June-2021 ]}

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