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MaxCellMeasure
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MaxCellMeasure

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is an option for DiscretizeRegion and related functions that specifies the maximum cell measure for the result.

Details

  • Possible settings for a region of dimension include:
  • mconstrain the -dimensional measure to be at most m
    {…,dimi,…}constrain the -dimensional measure to be at most mi
  • The names "Volume", "Area", and "Length" may be used in place of the dimensions 3, 2, and 1.
  • When only a few cell measure constraints are given, other constraints are automatically computed to be compatible with mesh cells of reasonable quality.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Discretize a unit disk into triangles with area at most 0.5:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-4n2g0t
Out[1]=1

Restrict the area to 0.01:

In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-kae0xe
Out[2]=2

Scope  (7)Survey of the scope of standard use cases

Discretize a unit disk into triangles with area at most 0.1:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-9ldahw
Out[1]=1

Restrict the area to 0.01:

In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-h6e92g
Out[2]=2

This gives the areas of the triangles:

In[3]:=3
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https://wolfram.com/xid/0dqt848dvp2-h09fmy

Specify a maximum length for line segments:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-r3wks9
Out[1]=1

A Histogram of the line segment lengths:

In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-elrnss
Out[2]=2

In 3D, specify a maximum area for faces:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-mgagd5
Out[1]=1

A Histogram of the face areas:

In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-c6dkoj
Out[2]=2

Discretize a Graphics scene with a maximum cell area of 0.1:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-od9574
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-kbjrf2
Out[2]=2

Discretize a Graphics3D scene with a maximum cell volume of 0.1:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-rxviz5
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-bcyrmf
Out[2]=2

Compare different length settings:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-k3uvx2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-tqxl8o
Out[2]=2

Compare different face area settings:

In[1]:=1
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https://wolfram.com/xid/0dqt848dvp2-6bwxok
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqt848dvp2-5ctri2
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqt848dvp2-kcd78z
Out[3]=3
Wolfram Research (2014), MaxCellMeasure, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxCellMeasure.html.
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Wolfram Research (2014), MaxCellMeasure, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxCellMeasure.html.

Text

Wolfram Research (2014), MaxCellMeasure, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxCellMeasure.html.

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Wolfram Research (2014), MaxCellMeasure, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxCellMeasure.html.

CMS

Wolfram Language. 2014. "MaxCellMeasure." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaxCellMeasure.html.

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Wolfram Language. 2014. "MaxCellMeasure." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaxCellMeasure.html.

APA

Wolfram Language. (2014). MaxCellMeasure. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxCellMeasure.html

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Wolfram Language. (2014). MaxCellMeasure. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxCellMeasure.html

BibTeX

@misc{reference.wolfram_2025_maxcellmeasure, author="Wolfram Research", title="{MaxCellMeasure}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MaxCellMeasure.html}", note=[Accessed: 09-July-2025 ]}

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@misc{reference.wolfram_2025_maxcellmeasure, author="Wolfram Research", title="{MaxCellMeasure}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MaxCellMeasure.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_maxcellmeasure, organization={Wolfram Research}, title={MaxCellMeasure}, year={2014}, url={https://reference.wolfram.com/language/ref/MaxCellMeasure.html}, note=[Accessed: 09-July-2025 ]}

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@online{reference.wolfram_2025_maxcellmeasure, organization={Wolfram Research}, title={MaxCellMeasure}, year={2014}, url={https://reference.wolfram.com/language/ref/MaxCellMeasure.html}, note=[Accessed: 09-July-2025 ]}