WOLFRAM

gives True if reg is a bounded region and False otherwise.

Details

  • A region is bounded if it can be included in a box with finite ranges.

Examples

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Basic Examples  (2)Summary of the most common use cases

A bounded region:

Out[1]=1
Out[1]=1

An unbounded region:

Out[1]=1
Out[2]=2

Scope  (18)Survey of the scope of standard use cases

Special Regions  (4)

Regions in including Point:

Out[1]=1

Interval:

Out[3]=3
Out[4]=4

A HalfLine is unbounded:

Out[5]=5

Regions in including Point:

Out[1]=1
Out[2]=2

Line:

Out[3]=3
Out[4]=4

Polygon:

Out[5]=5
Out[6]=6

Circle:

Out[7]=7
Out[8]=8

Disk:

Out[9]=9
Out[10]=10

An InfiniteLine is unbounded:

Out[11]=11
Out[12]=12

Regions in including Point:

Out[1]=1
Out[2]=2

Line:

Out[3]=3
Out[4]=4

Cylinder:

Out[5]=5
Out[6]=6

A HalfPlane is unbounded:

Out[7]=7
Out[8]=8

Regions in including Simplex in :

Out[1]=1

Cuboid in :

Out[2]=2

Ball in :

Out[3]=3

Formula Regions  (3)

A parabolic region as an ImplicitRegion:

Out[3]=3
Out[4]=4

A cylinder:

Out[2]=2

A parabola represented as a ParametricRegion:

Out[2]=2
Out[3]=3

Using a rational parametrization of the disk:

The region is bounded, but the parameter is unbounded:

Out[5]=5

ImplicitRegion can have several components of different dimension:

Out[2]=2
Out[3]=3

Mesh Regions  (4)

MeshRegion in 1D:

Out[1]=1
Out[2]=2

2D:

Out[1]=1
Out[2]=2

3D:

Out[12]=12
Out[8]=8

BoundaryMeshRegion in 1D:

Out[1]=1
Out[2]=2

2D:

Out[3]=3
Out[4]=4

3D:

Out[5]=5
Out[6]=6

MeshRegion that represents a curve in 2D:

Out[1]=1
Out[2]=2

A MeshRegion can have components of different dimension:

Out[1]=1
Out[2]=2

Derived Regions  (4)

RegionIntersection of two regions:

Out[4]=4
Out[3]=3

RegionUnion of mixed-dimensional regions:

Out[2]=2
Out[3]=3

TransformedRegion:

Out[2]=2
Out[3]=3

RegionBoundary:

Out[1]=1
Out[2]=2
Out[3]=3

Geographic Regions  (3)

A polygon with GeoPosition:

Out[2]=2

Polygons with GeoPositionXYZ:

Out[4]=4

Polygons with GeoPositionENU:

Out[6]=6

A polygon with GeoGridPosition:

Out[2]=2

BoundedRegionQ works on polygons with geographic entities:

Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Create a definition that only applies to bounded regions:

Out[7]=7

Find an enclosing Sphere for a region:

Compute bounds:

Compute enclosing sphere:

Visualize it:

Out[7]=7

Properties & Relations  (5)Properties of the function, and connections to other functions

RegionIntersection is bounded if at least one region is BoundedRegionQ:

Out[4]=4

Since there is one bounded region, the intersection is bounded:

Out[5]=5

TransformedRegion will be bounded if the regions and transformation are bounded:

Since the transformation is bounded, the resulting region is bounded:

Out[2]=2
Out[3]=3

RegionBounds finds a bounding box that includes the region:

Out[2]=2

The bounds are finite for a bounded region:

Out[3]=3

The bounds are infinite for an unbounded region:

Out[4]=4

The RegionMeasure of a bounded region is finite:

Out[2]=2

The RegionMeasure of an unbounded region is infinite:

Out[4]=4

The RegionCentroid of a bounded region is finite:

Out[2]=2

The RegionCentroid of an unbounded region is Indeterminate:

Out[4]=4
Wolfram Research (2014), BoundedRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/BoundedRegionQ.html.
Wolfram Research (2014), BoundedRegionQ, Wolfram Language function, https://reference.wolfram.com/language/ref/BoundedRegionQ.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_boundedregionq, author="Wolfram Research", title="{BoundedRegionQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BoundedRegionQ.html}", note=[Accessed: 03-May-2025 ]}

@misc{reference.wolfram_2025_boundedregionq, author="Wolfram Research", title="{BoundedRegionQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BoundedRegionQ.html}", note=[Accessed: 03-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_boundedregionq, organization={Wolfram Research}, title={BoundedRegionQ}, year={2014}, url={https://reference.wolfram.com/language/ref/BoundedRegionQ.html}, note=[Accessed: 03-May-2025 ]}

@online{reference.wolfram_2025_boundedregionq, organization={Wolfram Research}, title={BoundedRegionQ}, year={2014}, url={https://reference.wolfram.com/language/ref/BoundedRegionQ.html}, note=[Accessed: 03-May-2025 ]}