Generate a point in a unit ball region:

Generate a list of points for a triangle region:

Generate multiple lists of points for a unit disk region:

Generate points on an unbounded region within given bounds:

The random points are restricted to :

Generate points on an unbounded region within given bounds in :

Regions in :

Regions in :

Visualize region points in :

Regions in :

Visualize region points in :

Regions in :

Implicit regions:

Visualize region points in :

Parametric regions:

MeshRegion in 2D:

In 3D:

BoundaryMeshRegion in 2D:

BoundaryMeshRegion in 3D:

RegionIntersection of two regions:

RegionUnion of mixed-dimensional regions:

Points are generated for the maximum dimensional component:

TransformedRegion:

RegionBoundary:

Generate a list of uniform random unit vectors in :

Visualize a parametric heart curve:

Parametric butterfly curve:

Implicit trifolium curve:

Graphics scene:

Implicit Lissajous region:

Mixed implicit and parametric region:

Country polygon:

Text primitive:

Generate a list of uniform random unit vectors in :

Parametric helix curve:

Implicit Viviani's curve:

Parametric torus surface:

Implicit eight solid:

Graphics3D scene:

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:

Visualize the Minkowski sum (orange) of two regions:

Sum of points from two regions gives points of the Minkowski sum region:

Compute an approximate bounding box for a region from random samples. The resulting bounding will be a subset of the true bounding box:

Compare with its region bounds:

Show that a region is not a subset of another:

Check if any point from a set of random points in the disk are not in the square:

Visualize the random points in the disk that are not in the square:

Determine that two regions are not equal:

Check if any point from a set of random points in the disk is not in the square, or vice versa:

Determine that a region is not convex by sampling, and show that there is a convex combination of the samples that is not a member of the original region:

Generate pairwise convex combinations of random points within the region:

If a point on a pairwise convex combination is not in the region, then the region is not convex:

Alternatively generate and test points in a convex hull of points:

Compute the approximate convex hull of a region from random points within the region:

Find an approximate nearest point in a region by sampling the region and computing the nearest point to the samples. This gives an upper bound for the distance to the region:

Find the nearest point from a set of random points in the region:

Compare the resulting distance to the true minimum distance to the region:

Define a function that finds an approximate farthest point in a region:

Find the farthest point on a region from a given point: