Also known as:
central dilation,
uniform scaling.
A central dilatation is sort of like mapping a shape on a plane onto a plane parallel to it.on a plane maps a shape to another shape like a lens would.
A mapping
δ on a
euclidian plane is a
central dilatation iff δ is a
dilatation with a
fixed point, known as the
dilatation center C.
Since
δ is a dilatation,
it maps any line to a line parallel to it, and a vector changes by a nonzero constant
r called the
dilatation ratio.
A central dilatation can be expressed as:
δC,r(X) = r(X - C) + C = rX + (1-r)C
Hence
δC,r(
X) is a
linear combination of
X and
C.
When the dilatation center happens to be on the
origin (
C = 0), the simpler expression is:
δr(X) = rX
Source:
"Vectors and Transformations in Plane Geometry" by Philippe Tondeur, Publish or Perish, Inc. 1993