Wolfram Research

Function Repository Resource:

NonConvexHullMesh

Source Notebook

Generate a mesh geometry from points without including exterior concave perimeter areas or holes

Contributed by: Jon McLoone  |  Jon McLoone

ResourceFunction["NonConvexHullMesh"][points,sensitivity]

generates a MeshRegion from points excluding triangles that are larger than sensitivity.

Details and Options

If the data is not reasonably dense over the whole region, it may not be possible to choose a suitable sensitivity that prevents holes but also represents small exterior nonconvex areas.

Examples

Basic Examples (2) 

NonConvexHullMesh generates a mesh from points while preserving the result’s nonconvex shape:

In[1]:=
points = CompressedData["
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"];
In[2]:=
ListPlot[points]
Out[2]=
In[3]:=
ResourceFunction["NonConvexHullMesh"][points, 0.07]
Out[3]=

Increasing the sensitivity value causes small nonconvex regions to be included:

In[4]:=
ResourceFunction["NonConvexHullMesh"][points, 0.1]
Out[4]=

Scope (1) 

Three-dimensional data is supported:

In[5]:=
points3D = CompressedData["
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"];
ListPointPlot3D[points3D]
Out[6]=
In[7]:=
ResourceFunction["NonConvexHullMesh"][points3D, 0.07]
Out[7]=

Properties and Relations (1) 

For large sensitivity values, the result is equivalent to ConvexHullMesh:

In[8]:=
points = CompressedData["
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"];
In[9]:=
ResourceFunction["NonConvexHullMesh"][points, 1]
Out[9]=
In[10]:=
ConvexHullMesh[points]
Out[10]=

Possible Issues (3) 

Setting the sensitivity value too low will result in holes in the MeshRegion:

In[11]:=
points = CompressedData["
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ResourceFunction["NonConvexHullMesh"][points, 0.05]
Out[12]=

If the sensitivity is very small, then all triangles will be excluded:

In[13]:=
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"];
ResourceFunction["NonConvexHullMesh"][points, 0.00005]
Out[14]=

Sensitivity is measured in the coordinate system of the region, so very large geometries will require large sensitivity values:

In[15]:=
points = 1000000 CompressedData["
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"];
ResourceFunction["NonConvexHullMesh"][points, 75000]
Out[16]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

License Information