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# BoundingRegion

BoundingRegion[{pt1,pt2,}]

gives the minimal axis-aligned bounding box for the points pt1, pt2, .

BoundingRegion[{pt1,pt2,},form]

gives a bounding region of type form.

BoundingRegion[mesh,]

gives a bounding region for a MeshRegion or BoundaryMeshRegion.

# Details 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 option can be given:
•  WorkingPrecision MachinePrecision precision to use in computations

# Examples

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## 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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