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RegionDisjoint—Wolfram Language Documentation

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• See Also
  • RegionEqual
  • RegionWithin
  • RegionMember
  • RegionNearest
  • RegionDistance
  • RandomPoint
• Related Guides
  • Region Properties and Measures
  • Polygons
  • Polyhedra

RegionDisjoint[reg₁,reg₂,reg₃,…]

returns True if the regions reg₁, reg₂, reg₃, … are pairwise disjoint.

Test whether two regions are disjoint:

Visualize them:

Generate conditions for which regions are disjoint:

Show two regions are disjoint:

Visualize them:

Show two regions intersect:

Find conditions that make regions disjoint:

Show multiple regions are pairwise disjoint:

Show multiple regions are not pairwise disjoint:

Implicit regions:

Parametric regions:

Compare two formula regions:

Nonconstant formula regions:

Find all radii where a concentric disk and annulus are disjoint:

Find only the positive radii:

Find when the unit disk is disjoint with an implicitly described annulus:

Show the conditions for which the result is valid:

Explicitly allow for degenerate cases:

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:

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