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RegionIntersection—Wolfram Language Documentation

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• See Also
  • RegionUnion
  • RegionDifference
  • RegionSymmetricDifference
  • BooleanRegion
• Related Guides
  • Derived Geometric Regions
  • Polygons
  • Polyhedra
  • Geometric Computation

Intersection of two disks:

Visualize it:

Intersection of two MeshRegion objects:

For some regions, intersection is computed explicitly:

Visualize the intersection:

An intersection of an infinite line and a ball:

Visualize the intersection:

An intersection of Line regions:

Visualize it:

An intersection of Polygon regions:

Visualize it:

An intersection of two Disk regions:

Visualize it:

An intersection of a cuboid a cone:

Visualize it:

An intersection of regions with different RegionDimension:

Visualize it:

Intersection of regions:

Define a disk segment as an intersection of a disk and a half-plane:

Define a new basic region diskSegment that uses the same notation as Disk does for disk sectors, so that diskSegment[{x,y},r,{θ₁,θ₂}] represents the disk segment from θ₁ to θ₂. Do it by writing it as a RegionIntersection of a Disk and a HalfPlane:

This evaluates an object that is RegionQ and can be used as any other region:

Visualize the disk segment together with the disk:

A point p belongs to RegionIntersection[reg₁,reg₂,…] if it belongs to all reg_i:

Use RegionMember to test membership:

RegionIntersection is a Boolean combination And of regions:

The RegionMeasure of an intersection obeys a simple formula:

Subtract the measure of the RegionUnion from the sum of the measures:

The RegionDimension of an intersection is at most the minimum of all input dimensions:

It can be lower, however:

These regions overlap only at a point, so the dimension of the intersection is 0:

The intersection of two spiral polygons:

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