# 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 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.

# Examples

open allclose all

## 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 to get the full -complex for the point set:

## Applications(7)

### Curve Reconstruction(1)

ConcaveHullMesh can reconstruct 1D curves in 1D:

2D:

3D:

### 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)

ConcaveHullMesh can reconstruct solids in 1D:

2D:

3D:

### 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, https://reference.wolfram.com/language/ref/ConcaveHullMesh.html (updated 2022).

#### 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_2024_concavehullmesh, author="Wolfram Research", title="{ConcaveHullMesh}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ConcaveHullMesh.html}", note=[Accessed: 05-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_concavehullmesh, organization={Wolfram Research}, title={ConcaveHullMesh}, year={2022}, url={https://reference.wolfram.com/language/ref/ConcaveHullMesh.html}, note=[Accessed: 05-August-2024 ]}