SignedRegionDistance

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.

SignedRegionDistance[reg]

gives a RegionDistanceFunction[] that can be applied repeatedly to different points.

Details

Examples

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Basic Examples  (2)

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:

Scope  (17)

Special Regions  (8)

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:

Formula Regions  (2)

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:

Mesh Regions  (4)

The signed distance to a BoundaryMeshRegion can be negative in any dimension:

In 2D:

In 3D:

Signed distance cannot be negative to a 0D MeshRegion in 1D:

But it can for a 1D MeshRegion:

Signed distance cannot be negative to a 0D MeshRegion in 2D:

Nor for a 1D MeshRegion:

But it can for a 2D MeshRegion:

Signed distance cannot be negative to a 0D MeshRegion in 3D:

Nor for a 1D MeshRegion:

Nor for a 2D MeshRegion:

But it can for a 3D MeshRegion:

Derived Regions  (3)

The signed distance to a RegionIntersection:

The signed distance to a TransformedRegion:

The signed distance to a RegionBoundary is always non-negative:

Applications  (2)

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:

Properties & Relations  (5)

A point is a RegionMember if the signed distance to the region is non-positive:

A point on the RegionBoundary has signed distance 0:

A point is in the interior of the region if the signed distance to the region is negative:

Abs of SignedRegionDistance is the MinValue of the distance to the RegionBoundary:

For a point outside the region, RegionDistance and SignedRegionDistance are the same:

Wolfram Research (2014), SignedRegionDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/SignedRegionDistance.html.

Text

Wolfram Research (2014), SignedRegionDistance, Wolfram Language function, https://reference.wolfram.com/language/ref/SignedRegionDistance.html.

BibTeX

@misc{reference.wolfram_2020_signedregiondistance, author="Wolfram Research", title="{SignedRegionDistance}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SignedRegionDistance.html}", note=[Accessed: 03-December-2020 ]}

BibLaTeX

@online{reference.wolfram_2020_signedregiondistance, organization={Wolfram Research}, title={SignedRegionDistance}, year={2014}, url={https://reference.wolfram.com/language/ref/SignedRegionDistance.html}, note=[Accessed: 03-December-2020 ]}

CMS

Wolfram Language. 2014. "SignedRegionDistance." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SignedRegionDistance.html.

APA

Wolfram Language. (2014). SignedRegionDistance. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SignedRegionDistance.html