ConcaveHullMesh [{p1,p2,…}]
gives the concave hull mesh from the points p1,p2,….
ConcaveHullMesh [{p1,p2,…},α]
gives the concave hull mesh of the specified parameter α.
ConcaveHullMesh [{p1,p2,…},α,d]
gives the concave hull mesh of cells of dimension d.
ConcaveHullMesh
ConcaveHullMesh [{p1,p2,…}]
gives the concave hull mesh from the points p1,p2,….
ConcaveHullMesh [{p1,p2,…},α]
gives the concave hull mesh of the specified parameter α.
ConcaveHullMesh [{p1,p2,…},α,d]
gives the concave hull mesh of cells of dimension d.
Details and Options
- ConcaveHullMesh is also known as α‐shapes.
- 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 .
Examples
open all close allBasic 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)
Surface Reconstruction (4)
ConcaveHullMesh can reconstruct surfaces in 1D:
2D:
3D:
ConcaveHullMesh can reconstruct 3D models:
ConcaveHullMesh can approximate parametric surfaces:
ConcaveHullMesh can reconstruct non-orientable surfaces:
Solid Reconstruction (1)
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:
Related Guides
Text
Wolfram Research (2021), ConcaveHullMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ConcaveHullMesh.html (updated 2022).
CMS
Wolfram Language. 2021. "ConcaveHullMesh." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/ConcaveHullMesh.html.
APA
Wolfram Language. (2021). ConcaveHullMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConcaveHullMesh.html
BibTeX
@misc{reference.wolfram_2025_concavehullmesh, author="Wolfram Research", title="{ConcaveHullMesh}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ConcaveHullMesh.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_concavehullmesh, organization={Wolfram Research}, title={ConcaveHullMesh}, year={2022}, url={https://reference.wolfram.com/language/ref/ConcaveHullMesh.html}, note=[Accessed: 04-January-2026]}