BoundedRegionQ

BoundedRegionQ[reg]

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)

A bounded region:

An unbounded region:

Scope  (18)

Special Regions  (4)

Regions in including Point:

Interval:

A HalfLine is unbounded:

Regions in including Point:

Line:

Polygon:

Circle:

Disk:

An InfiniteLine is unbounded:

Regions in including Point:

Line:

Cylinder:

A HalfPlane is unbounded:

Regions in including Simplex in :

Cuboid in :

Ball in :

Formula Regions  (3)

A parabolic region as an ImplicitRegion:

A cylinder:

A parabola represented as a ParametricRegion:

Using a rational parametrization of the disk:

The region is bounded, but the parameter is unbounded:

ImplicitRegion can have several components of different dimension:

Mesh Regions  (4)

MeshRegion in 1D:

2D:

3D:

BoundaryMeshRegion in 1D:

2D:

3D:

MeshRegion that represents a curve in 2D:

A MeshRegion can have components of different dimension:

Derived Regions  (4)

RegionIntersection of two regions:

RegionUnion of mixed-dimensional regions:

TransformedRegion:

RegionBoundary:

Geographic Regions  (3)

A polygon with GeoPosition:

Polygons with GeoPositionXYZ:

Polygons with GeoPositionENU:

A polygon with GeoGridPosition:

BoundedRegionQ works on polygons with geographic entities:

Applications  (2)

Create a definition that only applies to bounded regions:

Find an enclosing Sphere for a region:

Compute bounds:

Compute enclosing sphere:

Visualize it:

Properties & Relations  (5)

RegionIntersection is bounded if at least one region is BoundedRegionQ:

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

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

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

RegionBounds finds a bounding box that includes the region:

The bounds are finite for a bounded region:

The bounds are infinite for an unbounded region:

The RegionMeasure of a bounded region is finite:

The RegionMeasure of an unbounded region is infinite:

The RegionCentroid of a bounded region is finite:

The RegionCentroid of an unbounded region is Indeterminate:

Introduced in 2014
 (10.0)