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:

MeshRegion in 2D:

In 3D:

BoundaryMeshRegion in 2D:

BoundaryMeshRegion in 3D:

RegionIntersection of two regions:

Get the region bounds:

Uniformly sample over the bounding box for the region:

RegionUnion of mixed-dimensional regions:

TransformedRegion:

RegionBoundary:

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: