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


gives the concave hull mesh of the specified parameter α.


gives the concave hull mesh of cells of dimension d.

Details and Options

  • 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,d] is generated from DelaunayMesh[{p1,p2,}] by selecting cells of dimension d that are contained in a ball of radius at most α without including other points pi.
  • ConcaveHullMesh[{p1,p2,},α] selects cells of dimension d where d is the embedding dimension of the points pi.
  • ConcaveHullMesh takes the same options as MeshRegion.


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Basic Examples  (2)

A concave hull mesh of points randomly sampled from an Annulus:

Find its area:

Reconstruct a 3D model from its vertices:

Scope  (6)

Basic Uses  (3)

A concave hull mesh in 1D:

A concave hull mesh in 2D:

A concave hull mesh in 3D:

Specifications  (3)

ConcaveHullMesh takes a set of points:

Use a Point list:

Specify the maximum radius of simplices:

Specify the dimension of simplices:

Use All to get the full -complex for the point set:

Applications  (7)

Curve Reconstruction  (1)

ConcaveHullMesh can reconstruct 1D curves in 1D:



Surface Reconstruction  (4)

ConcaveHullMesh can reconstruct surfaces in 1D:



ConcaveHullMesh can reconstruct 3D models:

ConcaveHullMesh can approximate parametric surfaces:

ConcaveHullMesh can reconstruct non-orientable surfaces:

Solid Reconstruction  (1)

ConcaveHullMesh can reconstruct solids in 1D:



Point Clustering  (1)

Generate normally distributed data and visualize it:

Find the concave hull of the data:

Use ConnectedMeshComponents to separate points into clusters:

Visualize the separate clusters:

Properties & Relations  (4)

ConcaveHullMesh gives a MeshRegion of the same dimension as 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:

Concave hull meshes may have multiple connected components:

The convex hull:

ConcaveHullMesh gives a subset of cells from the DelaunayMesh:

Interactive Examples  (1)

Create an interactive example with draggable points to view the concave hull in real time:

Wolfram Research (2021), ConcaveHullMesh, Wolfram Language function, (updated 2022).


Wolfram Research (2021), ConcaveHullMesh, Wolfram Language function, (updated 2022).


Wolfram Language. 2021. "ConcaveHullMesh." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022.


Wolfram Language. (2021). ConcaveHullMesh. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_concavehullmesh, author="Wolfram Research", title="{ConcaveHullMesh}", year="2022", howpublished="\url{}", note=[Accessed: 22-May-2024 ]}


@online{reference.wolfram_2024_concavehullmesh, organization={Wolfram Research}, title={ConcaveHullMesh}, year={2022}, url={}, note=[Accessed: 22-May-2024 ]}