AffineSpace

AffineSpace[{p1,,pk+1}]

represents the affine space passing through the points pi.

AffineSpace[p,{v1,,vk}]

represents the affine space passing through p in the directions vi.

Details

  • AffineSpace is also known as a point, line, plane, -flat, -plane, etc.
  • AffineSpace can be used as a geometric region and a graphics primitive.
  • AffineSpace represents the region or . The dimension is k if the pi are affinely independent or the vi are linearly independent.
  • AffineSpace can be used in Graphics and Graphics3D.
  • AffineSpace will be clipped by PlotRange when rendering.
  • Graphics rendering is affected by directives such as Opacity and color as well as:
  • PointSize0-dimensional ()
    Thickness,Dashing1-dimensional ()
    FaceForm2-dimensional ()
  • For a two-dimensional AffineSpace, FaceForm[front,back] can be used to specify different styles for the front and back, where the front is defined to be in the direction of the normal Cross[v1,v2] or Cross[p2-p1,p3-p1], depending on which input form is used.

Examples

open allclose all

Basic Examples  (3)

An AffineSpace in 2D:

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

And in 3D:

In[11]:=
Click for copyable input
Out[11]=

Different styles applied to an affine space region:

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

Determine if points belong to a given affine space region:

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

Scope  (17)

Applications  (24)

Properties & Relations  (6)

Neat Examples  (4)

See Also

Hyperplane  InfinitePlane  InfiniteLine  HalfPlane  HalfLine

Introduced in 2015
(10.2)