gives the concave hull mesh from the points p1,p2,.


gives the concave hull mesh of the specified parameter α.


  • ConcaveHullMesh is also known as αshapes.
  • A concave hull mesh is typically used to construct regions from points as well as a method of point clustering.
  • ConcaveHullMesh[{p1,p2,},α] is generated from DelaunayMesh[{p1,p2,}] by selecting lines (2D) or triangles (3D) that are contained in a ball of diameter at least α without including other points pi.
  • ConcaveHullMesh takes the same options as MeshRegion.


open allclose all

Basic Examples  (2)

A concave hull from random points:

A concave hull from vertex data:

Scope  (3)

ConcaveHullMesh takes a set of points:

Use a Point list:

ConcaveHullMesh will try to find an α value that creates a tight fit:

Use an explicit α value:

Use smaller α values to capture more details:

Applications  (4)

Basic Applications  (1)

Approximate a parametric surface:

Surface Reconstruction  (3)

ConcaveHullMesh can reconstruct 2D surfaces embedded in 3D:

ConcaveHullMesh can reconstruct non-orientable surfaces:

ConcaveHullMesh can reconstruct closed surfaces in 3D:

Properties & Relations  (2)

ConcaveHullMesh gives a MeshRegion of dimension less than the embedding dimension of the point set:

ConvexHullMesh is equivalent to ConcaveHullMesh with a sufficiently large α:

The convex hull is a full-dimensional region:

Possible Issues  (2)

Small values for α can result in disconnected or empty meshes:

Use a larger value for α:

Automatically choose an α value for the input points:

ConcaveHullMesh works only on 3D points:

Wolfram Research (13), ConcaveHullMesh, Wolfram Language function,


Wolfram Research (13), ConcaveHullMesh, Wolfram Language function,


Wolfram Language. 13. "ConcaveHullMesh." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (13). ConcaveHullMesh. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2021_concavehullmesh, author="Wolfram Research", title="{ConcaveHullMesh}", year="13", howpublished="\url{}", note=[Accessed: 24-January-2022 ]}


@online{reference.wolfram_2021_concavehullmesh, organization={Wolfram Research}, title={ConcaveHullMesh}, year={13}, url={}, note=[Accessed: 24-January-2022 ]}