# RegionUnion

RegionUnion[reg1,reg2,]

gives the union of the regions reg1, reg2, .

# Examples

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## Basic Examples(2)

Union of two disks:

Visualize it:

Union of two MeshRegion objects:

## Scope(12)

### Special Regions(6)

For some regions, the union is computed explicitly:

Visualize the union:

A union of Line regions:

Visualize it:

With overlap:

Visualize it:

A union of Polygon regions:

Visualize it:

A union of two Disk regions:

Visualize it:

A union of two Cuboid regions:

Visualize it:

A union of regions with different RegionDimension:

Visualize it:

### Formula Regions(2)

A union of ImplicitRegion objects is an ImplicitRegion:

2D:

3D:

nD:

A union of ParametricRegion objects:

Visualize it:

### Mesh Regions(2)

A union of BoundaryMeshRegion objects is a BoundaryMeshRegion:

2D:

3D:

A union of full-dimensional MeshRegion objects is a MeshRegion:

2D:

3D:

### Derived Regions(2)

A union of BooleanRegion objects:

Visualize it:

A union of TransformedRegion objects:

Visualize it:

## Applications(6)

Union of regions:

Union of all South America countries to get the map:

Country regions:

South America map:

Define a stadium as the union of disks and a rectangle:

The area is the sum of disk and quadrilateral areas:

Define a capsule as the union of balls and a cylinder:

The volume is the sum of the ball and cylinder volumes:

By taking a RegionUnion of many disks, dilation of a mesh can be approximated:

Create disks of the dilation radius around the mesh boundary:

Then simply take the union of all disks plus the original mesh:

By removing a RegionUnion of many disks, erosion of a mesh can be approximated:

Create disks of the erosion radius around the mesh boundary:

Then subtract the union of the disks from the original mesh:

## Properties & Relations(5)

A point p belongs to RegionUnion[reg1,reg2,] if it belongs to some regi:

Use RegionMember to test membership:

RegionUnion is a Boolean combination Or of regions:

RegionSymmetricDifference can be found using RegionUnion and RegionDifference:

The RegionDimension of a union is the max of all input dimensions:

If two regions are disjoint, the RegionMeasure of their union is a sum:

If they overlap, you must subtract the measure of the RegionIntersection:

## Possible Issues(2)

RegionUnion is defined only for regions with the same RegionEmbeddingDimension:

RegionUnion may include overlapping lower-dimensional components:

The connected mesh components:

## Neat Examples(1)

The union of two spiral polygons:

Wolfram Research (2014), RegionUnion, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionUnion.html (updated 2017).

#### Text

Wolfram Research (2014), RegionUnion, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionUnion.html (updated 2017).

#### CMS

Wolfram Language. 2014. "RegionUnion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/RegionUnion.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_regionunion, author="Wolfram Research", title="{RegionUnion}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/RegionUnion.html}", note=[Accessed: 19-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regionunion, organization={Wolfram Research}, title={RegionUnion}, year={2017}, url={https://reference.wolfram.com/language/ref/RegionUnion.html}, note=[Accessed: 19-July-2024 ]}