Test whether a region is contained within another:

Visualize them:

Generate conditions for which a region is contained within another:

All convex combinations of points lie within their convex hull:

Find the largest disk contained in a given triangle:

Approximate the largest axes-aligned ellipse contained in the triangle:

Find the smallest disk that contains a given triangle:

Find the smallest axes-aligned ellipse that contains the triangle:

Find all countries that lie completely within the Caribbean Sea:

The polygons of each country:

Select the countries whose polygons lie within the Caribbean Sea:

Verify the results:

View these countries on a map:

Find and visualize all positions where a unit rectangle lies within an annulus:

Perform a random walk inside a region:

Define a function to walk a point in a random direction, staying inside a region:

Simulate a random walk from an initial point:

Visualize the walk:

Use RegionWithin as a partial ordering to visualize concentric disks:

Disks with larger radii can completely cover other disks:

Sort the regions according to membership:

Visualize the rearranged disks:

Use RegionMember to test the membership of a point:

Use RegionWithin to test the membership of a region:

When ℛ₂ is within ℛ₁, all points in ℛ₂ are members of ℛ₁:

Check if two regions are equal:

For non‐empty regions, RegionDisjoint returns False when RegionWithin returns True:

Use FindInstance to find points that violate the subset condition:

Use RandomPoint to find a uniform sampling of points that violate the subset condition:

Use Reduce to find where the subset condition is violated: