GeometricTransformation

represents the result of applying the transformation function tfun to the geometric objects corresponding to the primitives g.

transforms geometric objects in g by effectively replacing every point r by m.r.

effectively replaces every point r by m.r+v.

represents multiple copies of g transformed by a collection of transformations.

Details and Options

GeometricTransformation[g,…] remains unchanged under evaluation, but affects how g is rendered.
GeometricTransformation works on lists of graphics primitives and directives in 2D and 3D.
GeometricTransformation[g,{m,v}] effectively applies an affine transform to g.
GeometricTransformation[g,{{m_xx,m_yx},{m_xy,m_yy}}] transforms the unit vectors and to {m_xx,m_xy} and {m_yx,m_yy}, respectively.
For different spec, GeometricTransformation[g,{m,spec}] leaves fixed the following special points on the bounding box of g:

For objects specified with scaled coordinates Scaled[{x,y}], GeometricTransformation effectively applies its transformation to the corresponding ordinary coordinates.
Normal[expr] if possible replaces all GeometricTransformation[g_i,…] constructs by versions of the g_i in which the coordinates have explicitly been transformed.
The following option can be given:
ContentSelectable Automatic whether to allow contents to be selected
For matrices m₁ and m₂, GeometricTransformation[GeometricTransformation[g,m₁],m₂] is equivalent to GeometricTransformation[g,m₂.m₁].