Wolfram Language & System 10.4 (2016)|Legacy Documentation

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BoundingRegion

BoundingRegion[{pt1,pt2,}]
gives the minimal axis-aligned bounding box for the points ,, .

BoundingRegion[{pt1,pt2,},form]
gives a bounding region of type form.

BoundingRegion[mesh,]
gives a bounding region for a MeshRegion or BoundaryMeshRegion.

Details and OptionsDetails and Options

  • BoundingRegion is also known as enclosing region or circumscribed region.
  • A bounding region for a set of points is a region such that .
  • Optimal bounding regions typically minimize some property for the bounding region, such as the minimum area oriented rectangle. They generally take longer to compute.
  • Fast bounding regions typically provide a bounding region quickly for a large number of points but may not provide the optimal bounding region, such as the minimum area oriented rectangle.
  • Possible form specifications in 1D:
  • "MinInterval"min length interval
  • Possible form specifications in 2D:
  • "MinRectangle"min area axis-aligned rectangle
    "MinOrientedRectangle"min area oriented rectangle
    "MinConvexPolygon"min area convex polygon
    "MinDisk"min area disk
    "FastOrientedRectangle"fast bounding oriented rectangle
    "FastDisk"fast bounding disk
    "FastEllipse"fast bounding ellipse
    "FastStadium"fast bounding stadium
  • Possible form specifications in 3D:
  • "MinCuboid"min volume axis-aligned cuboid
    "MinOrientedCuboid"min volume oriented cuboid
    "MinConvexPolyhedron"min volume convex polyhedron
    "MinBall"min volume ball
    "FastOrientedCuboid"fast oriented cuboid
    "FastBall"fast ball
    "FastEllipsoid"fast ellipsoid
    "FastCylinder"fast cylinder
    "FastCapsule"fast capsule
  • Possible form specifications in nD:
  • "MinCuboid"min measure axis-aligned cuboid
    "MinBall"min measure ball
    "FastOrientedCuboid"fast oriented cuboid
    "FastBall"fast ball
    "FastEllipsoid"fast ellipsoid
  • The following options can be given:
  • WorkingPrecisionMachinePrecisionprecision to use in computations

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

The minimal area Disk that contains a set of points:

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The minimal area Rectangle that contains a set of points:

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The minimal area, arbitrarily oriented rectangle:

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The minimal volume Ball that contains a set of points:

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The minimal volume Cuboid that contains a set of points:

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The minimal volume, arbitrarily oriented cuboid:

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Introduced in 2016
(10.4)