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RegionMinCurvature[reg,p]

gives the minimum curvature of the region reg at the point p.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Special Regions  
Formula Regions  
Mesh Regions  
See Also
Related Guides
History
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RegionMinCurvature

RegionMinCurvature[reg,p]

gives the minimum curvature of the region reg at the point p.

Details and Options

  • RegionMinCurvature is also known as a principal curvature.
  • RegionMinCurvature is typically used to measure how the surface bends in a normal direction at point.
  • RegionMinCurvature[reg,p] gives the minimum value of the curvature of the surface reg at p in a normal direction.

Examples

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Basic Examples  (1)

Find the minimum curvature of the unit sphere at the point:

Wolfram Language code: RegionMinCurvature[Sphere[], {1, 0, 0}]

Find the minimum curvature of a mesh region at vertex index 1:

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {20, 3}]]
Wolfram Language code: RegionMinCurvature[ℛ, 1]

At the point:

Wolfram Language code: MeshCoordinates[ℛ][[1]]
Wolfram Language code: RegionMinCurvature[ℛ, %]

Scope  (9)

Special Regions  (6)

The minimum curvature of a Cuboid at the point:

Wolfram Language code: ℛ = Cuboid[{0, 0, 0}, {3, 2, 1}]; RegionMinCurvature[ℛ, {3, 2, 1}]
Wolfram Language code: Region[ℛ]

Parallelepiped:

Wolfram Language code: ℛ = Parallelepiped[{0, 0, 0}, {{1, 0, 0}, {1, 1, 0}, {0, 1, 1}}]; RegionMinCurvature[ℛ, {1, 0, 0}]
Wolfram Language code: Region[ℛ]

Simplex in 3D:

Wolfram Language code: RegionMinCurvature[Simplex[3], {0, 1, 0}]
Wolfram Language code: Region[Simplex[3]]

Ball:

Wolfram Language code: RegionMinCurvature[Ball[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, r], {x, y, z}]
Wolfram Language code: ℛ = Ball[{0, 0, 0}, 1]; RegionMinCurvature[ℛ, {0, 1, 0}]
Wolfram Language code: Region[ℛ]

Ellipsoid:

Wolfram Language code: RegionMinCurvature[Ellipsoid[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, {Subscript[r, x], Subscript[r, y], Subscript[r, z]}], {x, y, z}]
Wolfram Language code: ℛ = Ellipsoid[{0, 0, 0}, {3, 2, 1}]; RegionMinCurvature[ℛ, {3, 0, 0}]
Wolfram Language code: Region[ℛ]

CapsuleShape:

Wolfram Language code: RegionMinCurvature[CapsuleShape[{{Subscript[x, 1], Subscript[y, 1], Subscript[z, 1]}, {Subscript[x, 2], Subscript[y, 2], Subscript[z, 2]}}, r], {x, y, z}]
Wolfram Language code: ℛ = CapsuleShape[]; RegionMinCurvature[ℛ, {2, 0, 0}]
Wolfram Language code: Region[ℛ]

Formula Regions  (1)

The minimum curvature of a sphere represented as an ImplicitRegion:

Wolfram Language code: RegionMinCurvature[ImplicitRegion[x^2 + y^2 + z^2 == 1, {x, y, z}], {x, y, z}]

A hyperboloid:

Wolfram Language code: RegionMinCurvature[ImplicitRegion[x ^ 2 + y ^ 2 - z ^ 2 == 1, {x, y, z}], {x, y, z}]

Mesh Regions  (2)

The minimum curvature of a MeshRegion:

Wolfram Language code: ℛ = ResourceData["Cow"]
Wolfram Language code: RegionMinCurvature[ℛ, 10]

Use "MeshCoordinates" to compute the minimum curvature at each vertex of the mesh:

Wolfram Language code: RegionMinCurvature[ℛ, "MeshCoordinates"]//Short

The minimum curvature of a BoundaryMeshRegion:

Wolfram Language code: ℛ = BoundaryDiscretizeRegion[Ellipsoid[{0, 0, 0}, {4, 3, 2}]]
Wolfram Language code: RegionMinCurvature[ℛ, 1]

Use "MeshCoordinates" to compute the minimum curvature at each vertex of the boundary mesh:

Wolfram Language code: RegionMinCurvature[ℛ, "MeshCoordinates"]//Short
Wolfram Research (2025), RegionMinCurvature, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionMinCurvature.html.

Text

Wolfram Research (2025), RegionMinCurvature, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionMinCurvature.html.

CMS

Wolfram Language. 2025. "RegionMinCurvature." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMinCurvature.html.

APA

Wolfram Language. (2025). RegionMinCurvature. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionMinCurvature.html

BibTeX

@misc{reference.wolfram_2026_regionmincurvature, author="Wolfram Research", title="{RegionMinCurvature}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/RegionMinCurvature.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_regionmincurvature, organization={Wolfram Research}, title={RegionMinCurvature}, year={2025}, url={https://reference.wolfram.com/language/ref/RegionMinCurvature.html}, note=[Accessed: 13-June-2026]}