ConstantRegionQ

ConstantRegionQ[reg]

gives True if the reg is a constant region and False otherwise.

Details

  • ConstantRegionQ is also known as parameter-free region.
  • A region is considered constant if it does not depend on symbolic parameters.
  • Only constant regions can be discretized using DiscretizeRegion or rendered using Graphics etc.

Examples

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Basic Examples  (3)

A constant region:

A nonconstant region:

A nonconstant region representing a whole family of regions, with random instances below:

Some operations require constant regions:

Some operations can give results for nonconstant regions:

Scope  (16)

Special Regions  (4)

Regions in including Point:

This region is not constant because it contains a symbolic parameter:

Interval:

Regions in including Point:

Line:

Disk:

Circle with symbolic parameters is not constant:

Regions in including Point:

Line:

Polygon:

Cylinder:

Regions in including Simplex in :

Cuboid in :

Ball in :

With parameters it is no longer constant:

Formula Regions  (3)

A disk represented as an ImplicitRegion:

A cylinder:

Since is not one of the variables, the region is no longer constant:

A disk represented as a ParametricRegion:

Using a rational parametrization of the disk:

A cylinder:

Since is not one of the variables, the region is no longer constant:

ImplicitRegion can have several components of different dimension:

Mesh Regions  (4)

MeshRegion is always constant, including 1D:

2D:

3D:

BoundaryMeshRegion in 1D:

2D:

2D:

MeshRegion that represents a curve in 2D:

A MeshRegion can have components of different dimension:

Derived Regions  (5)

RegionIntersection of two regions:

RegionUnion of mixed-dimensional regions:

TransformedRegion with a parameterized transformation function is not constant:

Replace the symbolic parameters to make the region constant:

RegionBoundary:

RegionUnion of a nonconstant region is a nonconstant region:

Applications  (2)

Create a definition that only applies to constant regions:

Select only constant regions from a list of regions:

Only constant regions can be discretized:

Properties & Relations  (3)

If ConstantRegionQ is True, then RegionQ is also True:

MeshRegionQ and BoundaryMeshRegionQ can be used to check more specialized region types:

Mesh regions are always ConstantRegionQ:

BoundedRegionQ can be used to check if a region is bounded:

Possible Issues  (2)

Some functions require constant regions:

Replace the symbolic parameters to make the region constant:

RegionMember returns True or False if the region is constant:

RegionMember returns conditions if the region is not constant:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_constantregionq, author="Wolfram Research", title="{ConstantRegionQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ConstantRegionQ.html}", note=[Accessed: 25-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_constantregionq, organization={Wolfram Research}, title={ConstantRegionQ}, year={2014}, url={https://reference.wolfram.com/language/ref/ConstantRegionQ.html}, note=[Accessed: 25-September-2021 ]}

CMS

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

APA

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