# DiscretizeRegion

DiscretizeRegion[reg]

discretizes a region reg into a MeshRegion.

DiscretizeRegion[reg,{{xmin,xmax},}]

restricts to the bounds .

# Details 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 ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3.
• • DiscretizeRegion has the same options as MeshRegion, with the following additions and changes:
•  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 f[vlist,m] is applied to each simplex created, where vlist is a list of the vertices and m is the measure. If f[vlist,m] 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.

# Examples

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## Basic Examples(3)

Discretize 1D embedded regions:

 In:= Out= Restrict to :

 In:= Out= Mixed-dimension region:

 In:= Out= Discretize 2D embedded regions:

 In:= Out= In:= Out= Mixed-dimension region:

 In:= Out= Discretize 3D embedded regions:

 In:= Out= Restrict to the first orthant:

 In:= Out= Restrict to :

 In:= Out= ## Neat Examples(2)

Introduced in 2014
(10.0)
|
Updated in 2015
(10.2)