Union of two disks:

Visualize it:

Union of two MeshRegion objects:

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:

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

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:

RegionUnion is defined only for regions with the same RegionEmbeddingDimension:

RegionUnion may include overlapping lower-dimensional components:

The connected mesh components:

The union of two spiral polygons: