System'

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:
  • WorkingPrecisionMachinePrecisionprecision to use in computations

Examples

open allclose all

Basic Examples  (4)

The minimal area Disk that contains a set of points:

In[5]:=
Click for copyable input
In[6]:=
Click for copyable input
Out[6]=
In[3]:=
Click for copyable input
Out[3]=

The minimal area Rectangle that contains a set of points:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

The minimal area, arbitrarily oriented rectangle:

In[4]:=
Click for copyable input
Out[4]=
In[5]:=
Click for copyable input
Out[5]=

The minimal volume Ball that contains a set of points:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

The minimal volume Cuboid that contains a set of points:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

The minimal volume, arbitrarily oriented cuboid:

In[4]:=
Click for copyable input
Out[4]=
In[5]:=
Click for copyable input
Out[5]=

Scope  (28)

Options  (5)

Applications  (4)

Properties & Relations  (9)

Possible Issues  (1)

See Also

Rectangle  Cuboid  Parallelogram  Parallelepiped  Disk  Ball  Ellipsoid  Cylinder  StadiumShape  CapsuleShape  ArcLength  Area  Volume  RegionMeasure  RegionBounds  ConvexHullMesh  RegionWithin

Introduced in 2016
(10.4)