RegionDistanceFunction [reg,…]
represents a function whose values give the distance from a point to the region reg.
RegionDistanceFunction
RegionDistanceFunction [reg,…]
represents a function whose values give the distance from a point to the region reg.
Details
- RegionDistanceFunction is also known as distance function, distance transform, signed distance function and signed distance transform.
- RegionDistanceFunction works like Function .
- RegionDistanceFunction is generated by RegionDistance [reg] or SignedRegionDistance [reg].
- If generated by RegionDistance , RegionDistanceFunction [reg,…][p] gives RegionDistance [reg,p].
- If generated by SignedRegionDistance , RegionDistanceFunction [reg,…][p] gives SignedRegionDistance [reg,p].
Examples
open all close allBasic 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:
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)
Properties & Relations (1)
RegionDistanceFunction gives the same value when applied to a point as RegionDistance :
Related Guides
History
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_2025_regiondistancefunction, author="Wolfram Research", title="{RegionDistanceFunction}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/RegionDistanceFunction.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_regiondistancefunction, organization={Wolfram Research}, title={RegionDistanceFunction}, year={2014}, url={https://reference.wolfram.com/language/ref/RegionDistanceFunction.html}, note=[Accessed: 17-November-2025]}