RegionMeanCurvature
RegionMeanCurvature[reg,p]
gives the mean curvature of the region reg at the point p.
Details and Options
- RegionMeanCurvature is also known as average curvature.
- RegionMeanCurvature is typically used to characterize the local shape and curvature of surfaces.
- RegionMeanCurvature[reg,p] gives the mean curvature of reg at p.
- RegionMeanCurvature[reg,p] is effectively equivalent to (RegionMinCurvature[reg,p] + RegionMaxCurvature[reg,p])/2.
Examples
open all close allBasic Examples (1)
Find the mean curvature of the unit sphere at the point:
RegionMeanCurvature[Sphere[], {1, 0, 0}]Find the mean curvature of a mesh region at vertex index 1:
ℛ = ConvexHullMesh[RandomReal[1, {20, 3}]]RegionMeanCurvature[%, 1]MeshCoordinates[ℛ][[1]]RegionMeanCurvature[ℛ, %]Scope (9)
Special Regions (6)
The mean curvature of a Cuboid at the point:
ℛ = Cuboid[{0, 0, 0}, {3, 2, 1}];
RegionMeanCurvature[ℛ, {3, 2, 1}]Region[ℛ]ℛ = Parallelepiped[{0, 0, 0}, {{1, 0, 0}, {1, 1, 0}, {0, 1, 1}}];
RegionMeanCurvature[ℛ, {1, 0, 0}]Region[ℛ]Simplex in 3D:
RegionMeanCurvature[Simplex[3], {0, 1, 0}]Region[Simplex[3]]Ball:
RegionMeanCurvature[Ball[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, r], {x, y, z}]ℛ = Ball[{0, 0, 0}, 1];
RegionMeanCurvature[ℛ, {0, 1, 0}]Region[ℛ]RegionMeanCurvature[Ellipsoid[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, {Subscript[r, x], Subscript[r, y], Subscript[r, z]}], {x, y, z}]ℛ = Ellipsoid[{0, 0, 0}, {3, 2, 1}];
RegionMeanCurvature[ℛ, {3, 0, 0}]Region[ℛ]RegionMeanCurvature[CapsuleShape[{{Subscript[x, 1], Subscript[y, 1], Subscript[z, 1]}, {Subscript[x, 2], Subscript[y, 2], Subscript[z, 2]}}, r], {x, y, z}]ℛ = CapsuleShape[];
RegionMeanCurvature[ℛ, {2, 0, 0}]Region[ℛ]Formula Regions (1)
The mean curvature of a sphere represented as an ImplicitRegion:
RegionMeanCurvature[ImplicitRegion[x^2 + y^2 + z^2 == 1, {x, y, z}], {x, y, z}]RegionMeanCurvature[ImplicitRegion[x ^ 2 + y ^ 2 - z ^ 2 == 1, {x, y, z}], {x, y, z}]Mesh Regions (2)
The mean curvature of a MeshRegion:
ℛ = ResourceData["Cow"]RegionMeanCurvature[ℛ, 10]Use "MeshCoordinates" to compute the mean curvature at each vertex of the mesh:
RegionMeanCurvature[ℛ, "MeshCoordinates"]//ShortThe mean curvature of a BoundaryMeshRegion:
ℛ = BoundaryDiscretizeRegion[Ellipsoid[{0, 0, 0}, {4, 3, 2}]]RegionMeanCurvature[ℛ, 1]Use "MeshCoordinates" to compute the mean curvature at each vertex of the boundary mesh:
RegionMeanCurvature[ℛ, "MeshCoordinates"]//ShortText
Wolfram Research (2025), RegionMeanCurvature, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionMeanCurvature.html.
CMS
Wolfram Language. 2025. "RegionMeanCurvature." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionMeanCurvature.html.
APA
Wolfram Language. (2025). RegionMeanCurvature. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionMeanCurvature.html