Test whether two regions are disjoint:

Visualize them:

Generate conditions for which regions are disjoint:

Estimate by simulating Buffon's needle problem:

Create randomly orientated line segments of length :

Select line segments that overlap the grid of lines:

Visualize overlapping line segments (red):

Estimation of :

Detect collisions between an object and a collection of walls:

Color walls that do not collide with the cow green, and red otherwise:

Find all countries that share a border with France:

The polygons of each country:

Select the countries whose polygons are not disjoint from France's polygon:

Verify the results:

View these countries on a map:

Find and visualize all positions where a unit rectangle is disjoint from an annulus:

Perform a random walk outside of a region:

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

Simulate a random walk from an initial point:

Visualize the walk:

Create a network that connects two US states if they share a border:

Two state's polygons share a border when RegionDisjoint returns False:

Style this network atop a map of the United States:

The largest disconnect is between Maine and the westernmost states:

Find and highlight a path from Maine to California:

A region and its complement are always disjoint:

Disjoint regions share no common point:

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

Use FindInstance to find points that lie in the intersection of two regions:

Use RandomPoint to find a uniform sampling of points that lie in the intersection of two regions:

Use Reduce to find where two regions overlap:

Create a scene of randomly placed, disjoint balls:

In 2D:

In 3D: