# RegionDistanceFunction

RegionDistanceFunction[reg,]

represents a function whose values give the distance from a point to the region reg.

# Examples

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## Basic Examples(1)

Generate a region distance function for a unit disk:

Apply the distance function to multiple points:

Plot it:

## Scope(17)

### Special Regions(8)

Point sets:

Plot the distance from a three-point set:

Line:

Plot it:

Rectangle can be used in 2D:

Cuboid generalizes it to any dimension:

Equidistance surfaces of a cuboid in 3D:

Simplex can be used in any dimension:

Plot the distance to a 2D simplex:

Disk can be used in 2D:

Ball generalizes a disk to any dimension:

Plot the distance to a disk:

Disk can be an ellipse in 2D:

Ellipsoid generalizes this to any dimension:

Plot the distance to an ellipse:

Circle can be elliptical:

Plot the distance to a circle:

Cylinder and Cone:

Equidistance contours for a cylinder:

### Formula Regions(2)

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:

### Mesh Regions(4)

The distance to a 1D BoundaryMeshRegion:

2D:

The distance to a 0D MeshRegion in 1D:

A 1D region:

The distance to a 0D MeshRegion in 2D:

A 1D region:

A 2D region:

A 0D MeshRegion in 3D:

A 1D region:

A 2D region:

A 3D region:

### Derived Regions(3)

The distance to a RegionIntersection:

The distance to a TransformedRegion:

The distance to a RegionBoundary:

## Applications(3)

Create a region that is a distance from a Triangle:

Visualize the region and triangle:

Create a region that is a distance from the given points:

Create a region that is a distance from a Cuboid:

## Properties & Relations(1)

RegionDistanceFunction gives the same value when applied to a point as RegionDistance:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_regiondistancefunction, author="Wolfram Research", title="{RegionDistanceFunction}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionDistanceFunction.html}", note=[Accessed: 20-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regiondistancefunction, organization={Wolfram Research}, title={RegionDistanceFunction}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionDistanceFunction.html}, note=[Accessed: 20-July-2024 ]}