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RegionDistance—Wolfram Language Documentation

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• See Also
  • RegionDistanceFunction
  • RegionNearest
  • SignedRegionDistance
  • Norm
  • MinValue
  • NMinValue
  • RegionMember
  • RegionWithin
  • DistanceTransform
  • GeometricScene
• Related Guides
  • Region Properties and Measures
  • Polygons
  • Polyhedra
  • Solid Geometry
  • Geometric Computation
  • Calculus
  • Plane Geometry
  • Synthetic Geometry
  • Solvers over Regions

RegionDistance[reg,p]

gives the minimum distance from the point p to the region reg.

RegionDistance[reg₁,reg₂]

gives the minimum distance between points in the regions reg₁ and reg₂.

Find the distance from a point to the unit disk:

Plot the distance as a function of position:

Find the distance from a point to a MeshRegion:

With one argument, you get a RegionDistanceFunction:

Apply the distance function lists of points to compute many distances:

Points:

Plot the distance from a three-point set:

Lines:

Plot it:

Boxes:

Plot the distance to a rectangle:

Simplices:

Plot the distance to a 2D simplex:

Balls:

Plot the distance to a disk:

Ellipsoids:

Plot the distance to a 2D ellipsoid:

Circles and ellipses:

Plot the distance to a circle:

Cylinders and cones:

Equidistance contours for a cylinder:

Regions in :

The distance to a disk represented as an ImplicitRegion:

A cylinder:

The distance to a disk represented as a ParametricRegion:

Using a rational parametrization of the disk:

A cylinder:

Compute the height of a triangle:

Visualize the triangle:

Create a region that is a distance from a circle:

Visualize the region and circle:

Compute the dilation of a region:

The directed Hausdorff distance from region to is defined as . Use RegionDistance to compute the directed Hausdorff distance from =Triangle[{{0,0},{2,0},{0,1}}] to ℬ=Triangle[{{0,0},{1,0},{0,3/2}}]:

Find the nearest distance to any point in :

As expected, the distance is zero for points in that overlap with :

Find the directed Hausdorff distance by maximizing over :

If , you can conclude that where is the closure of and . Show that for the regions in this example:

The Hausdorff distance between region and is defined as where is the directed Hausdorff distance in the previous example. Use RegionDistance to compute the Hausdorff distance between =Triangle[{{0,0},{2,0},{0,1}}] and ℬ=Triangle[{{0,0},{1,0},{0,3/2}}]:

Find the directed Hausdorff distances:

If , you can conclude that and , as in the previous example. Show that and for the regions in this example:

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