ConvexHullMesh [{p1,p2,…}]
gives a BoundaryMeshRegion representing the convex hull from the points p1, p2, ….
ConvexHullMesh [mreg]
gives the convex hull of the mesh region mreg.
ConvexHullMesh
ConvexHullMesh [{p1,p2,…}]
gives a BoundaryMeshRegion representing the convex hull from the points p1, p2, ….
ConvexHullMesh [mreg]
gives the convex hull of the mesh region mreg.
Details and Options
- ConvexHullMesh is also known as convex envelope or convex closure.
- The convex hull mesh is the smallest convex set that includes the points pi.
- The convex hull boundary consists of points in 1D, line segments in 2D, and convex polygons in 3D.
- ConvexHullMesh takes the same options as BoundaryMeshRegion .
Examples
open all close allBasic Examples (3)
A 1D convex hull mesh:
The region is the smallest convex region that includes the points:
A 2D convex hull mesh:
The region is the smallest convex region that includes the points:
A 3D convex hull mesh:
The region is the smallest convex region that includes the points:
Scope (3)
Create a 1D convex hull mesh from a set of points:
Basic properties:
Convex hull meshes are bounded:
Convex hull meshes are full dimensional:
Find its area and centroid:
Test for point membership:
Find the nearest point and its distance:
Create a 2D convex hull mesh from a set of points:
Basic properties:
Convex hull meshes are bounded:
Convex hull meshes are full dimensional:
Find its area and centroid:
Test for point membership:
Find the nearest point and its distance:
Create a 3D convex hull mesh from a set of points:
Basic properties:
Convex hull meshes are bounded:
Convex hull meshes are full dimensional:
Find its volume and centroid:
Find its surface area:
Find the nearest point and its distance:
Options (13)
MeshCellHighlight (3)
MeshCellHighlight allows you to specify highlighting for parts of a ConvexHullMesh :
By making faces transparent, the internal structure of a 3D ConvexHullMesh can be seen:
Individual cells can be highlighted using their cell index:
Or by the cell itself:
MeshCellLabel (2)
MeshCellLabel can be used to label parts of a ConvexHullMesh :
Individual cells can be labeled using their cell index:
Or by the cell itself:
MeshCellMarker (1)
MeshCellMarker can be used to assign values to parts of a ConvexHullMesh :
Use MeshCellLabel to show the markers:
MeshCellShapeFunction (2)
MeshCellShapeFunction allows you to specify functions for parts of a ConvexHullMesh :
Individual cells can be drawn using their cell index:
Or by the cell itself:
MeshCellStyle (3)
MeshCellStyle allows you to specify styling for parts of a ConvexHullMesh :
By making faces transparent, the internal structure of a 3D ConvexHullMesh can be seen:
Individual cells can be highlighted using their cell index:
Or by the cell itself:
PlotTheme (2)
Use a theme with grid lines and a legend:
Use a theme to draw a wireframe:
Applications (2)
The convex hull of a compound of five tetrahedra is a dodecahedron:
Compute the convex hull of a cow:
Visualize convex hull and cow:
Properties & Relations (3)
ConvexHullMesh is effectively the BoundaryMesh of a DelaunayMesh :
In 3D:
Use DelaunayMesh to get a Delaunay triangulation of the interior of the convex hull:
Use TriangulateMesh to control the triangulation of the interior:
Possible Issues (1)
ConvexHullMesh returns full–dimensional mesh regions only:
Use ConvexHullRegion to get the convex hull:
See Also
ConvexHullRegion ConcaveHullMesh DelaunayMesh VoronoiMesh BoundaryMeshRegion
Function Repository: NonConvexHullMesh ConvexLayers2D IntegerConvexHullMesh PowerDiagram PowerTriangulation
Related Guides
Text
Wolfram Research (2014), ConvexHullMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/ConvexHullMesh.html (updated 2020).
CMS
Wolfram Language. 2014. "ConvexHullMesh." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/ConvexHullMesh.html.
APA
Wolfram Language. (2014). ConvexHullMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConvexHullMesh.html
BibTeX
@misc{reference.wolfram_2025_convexhullmesh, author="Wolfram Research", title="{ConvexHullMesh}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/ConvexHullMesh.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_convexhullmesh, organization={Wolfram Research}, title={ConvexHullMesh}, year={2020}, url={https://reference.wolfram.com/language/ref/ConvexHullMesh.html}, note=[Accessed: 05-December-2025]}