MaxCellMeasure

MaxCellMeasure

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

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Basic Examples  (1)

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

Restrict the area to 0.01:

Scope  (8)

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

Restrict the area to 0.01:

This gives the areas of the triangles:

Specify a maximum length for line segments:

A Histogram of the line segment lengths:

In 3D, specify a maximum area for faces:

A Histogram of the face areas:

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

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

Compare different length settings:

Compare different area settings:

Compare different face area settings:

Applications  (1)

More accurately approximate a curved boundary by reducing MaxCellMeasure:

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.

CMS

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

BibTeX

@misc{reference.wolfram_2022_maxcellmeasure, author="Wolfram Research", title="{MaxCellMeasure}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/MaxCellMeasure.html}", note=[Accessed: 01-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_maxcellmeasure, organization={Wolfram Research}, title={MaxCellMeasure}, year={2014}, url={https://reference.wolfram.com/language/ref/MaxCellMeasure.html}, note=[Accessed: 01-June-2023 ]}