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SignedRegionDistance—Wolfram Language Documentation

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• See Also
  • RegionDistanceFunction
  • RegionDistance
  • RegionNearest
  • Norm
  • MinValue
  • NMinValue
  • GeometricScene
• Related Guides
  • Region Properties and Measures
  • Synthetic Geometry
  • Polygons
  • Polyhedra

SignedRegionDistance[reg,p]

gives the minimum distance from the point p to the region reg if p is outside the region and the minimum distance to the complement of reg if p is inside the region.

Find the signed distance from a point inside to the unit disk:

For a point outside:

Plot the distance as a function of position:

Find the signed distance from a point to a MeshRegion:

With one argument, you get a RegionDistanceFunction:

The signed distance to a Point is always non-negative, as it has no interior:

Plot the signed distance from a three-point set:

The signed distance to a Line can be negative in 1D:

But in 2D and above, it is always non-negative:

Plot the signed distance from a line in 2D:

Rectangle:

The signed distance from a Cuboid can be negative in any dimension:

Plot the signed distance to a rectangle:

The signed distance from a full-dimensional Simplex can be negative:

But the signed distance to a lower-dimensional simplex cannot:

Plot the signed distance to a 2D simplex:

The signed distance to a Disk can be negative:

Ball generalizes Disk to any dimension:

Plot the signed distance to a disk:

The signed distance to an Ellipsoid can be negative in any dimension:

Plot the signed distance to an ellipsoid in 2D:

The distance to a Circle is always non-negative, as it has no interior:

The same goes for Sphere in any dimension:

Plot the signed distance to a circle:

Cylinder:

Cone:

The signed 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:

If is a region that is full-dimensional, then the depth of a point is the negative signed region distance. Find the depth of {1,1} in Disk[{0,0},5]:

To illustrate it, you need to compute the nearest point in :

Plot it:

Find the depth of the point {1,1,1} in Cuboid[{0,0,0},{2,2,2}]:

To illustrate it, you need to compute the nearest point in :

Plot it:

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