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RegionMember—Wolfram Language Documentation

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• See Also
  • Element
  • RegionMemberFunction
  • RegionDistance
  • SignedRegionDistance
  • RegionEqual
  • RegionWithin
  • MemberQ
  • Between
  • GeometricScene
• Related Guides
  • Region Properties and Measures
  • Polygons
  • Solid Geometry
  • Plane Geometry
  • Polyhedra
  • Synthetic Geometry
  • Interval Arithmetic

RegionMember[reg,{x,y,…}]

gives True if the numeric point {x,y,…} is a member of the constant region reg and False otherwise.

RegionMember[reg,{x,y,…}]

gives conditions for the point {x,y,…} to be a member of reg.

Test whether a particular point is in a region:

Get conditions for point membership:

Create RegionMemberFunction to apply to different points:

Directly test whether a point is in a region:

Directly test whether a list of points is in a region:

Get conditions for point membership by using variables {x,y}:

Create RegionMemberFunction to apply to different points:

Regions in :

Regions in :

Visualize region membership in :

Get the region bounds:

Uniformly sample over the bounding box for the region:

Regions in :

Visualize region membership in :

Regions in :

Implicit regions:

Visualize region membership in :

Get the region bounds:

Uniformly sample over the bounding box for the region:

Parametric regions:

Convert polygon data for the given country to a MeshRegion:

Determine membership of a city:

For a parameterized region, RegionMember can give conditions on the parameters to determine when a given point is a member:

Find an instance where the region includes the point:

Visualize it:

Generate points on a region by filtering a uniform set of points:

Get the region bounds:

Uniformly sample over the bounding box of the region:

Select member points:

Visualize member points:

Convert polygon data for the given country to a MeshRegion:

Get the region bounds:

Uniformly sample over the bounding box of the region:

Perform Monte Carlo integration to estimate the area of a unit disk:

Get the region bounds:

Uniformly sample over the bounding box of the region:

Count the number of samples inside the region:

Get the ratio of samples inside the region to the total number of sample points:

Get the bounding area:

Get the approximate area of the region:

Use random points in a region to perform Monte Carlo integration:

Evaluate a function at each sample point and take their average:

Compare with the exact value:

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