# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# DiscretizeRegion

DiscretizeRegion[reg]
discretizes a region reg into a MeshRegion.

DiscretizeRegion[reg,{{xmin,xmax},}]
restricts to the bounds .

## Details and OptionsDetails and Options

• DiscretizeRegion is also known as mesh generation and grid generation.
• DiscretizeRegion discretizes the interior and boundaries of the region reg.
• In particular, DiscretizeRegion will attempt to discretize lower dimensional parts of reg.
• The region reg can be anything that is RegionQ and at embedding and geometric dimension .
• The following options may be given:
•  AccuracyGoal Automatic digits of accuracy sought MaxCellMeasure Automatic maximum cell measure MeshQualityGoal Automatic quality goal for mesh cells Method Automatic method to use MeshRefinementFunction None function that returns True if a mesh cell needs refinement PerformanceGoal \$PerformanceGoal whether to consider speed or quality PrecisionGoal Automatic digits of precision sought
• With , the function is applied to each simplex created, where vlist is a list of the vertices and m is the measure. If returns True, the simplex will be refined.
• With AccuracyGoal->a and an attempt will be made to keep the maximum distance between the region reg or the discretized region dreg and any point in RegionSymmetricDifference[reg,dreg] to less than where is the length of the diagonal of the bounding box.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Discretize 1D embedded regions:

 Out[4]=

Restrict to :

 Out[8]=

Mixed dimension region:

 Out[10]=

Discretize 2D embedded regions:

 Out[1]=

Restrict to the first quadrant:

 Out[2]=

Mixed dimension region:

 Out[3]=

Discretize 3D embedded regions:

 Out[1]=

Restrict to the first orthant:

 Out[2]=

Restrict to :

 Out[3]=

## See AlsoSee Also

Introduced in 2014
(10.0)