Also known as: dilation
A mapping T
on a euclidian plane
is a dilatation iff
it is a similarity transformation
every line to another line parallel to the original.
A similarity transformation
maps any shape to another that is similar to the original.
The set of all dilatations form a group
with composition of dilatations as the group operator.
The composition of dilatations is associative
but not commutative
, hence not abelian
If a dilatation has a fixed point C
, the dilatation is known as a central dilatation
and the point is known as the dilatation center
. The scale factor r
of a dilatation measures the change in perimeter length, and is known as the dilatation ratio
If a dilatation has a dilatation ratio of 1, then it is known as a translation
While the set of all translations form a group, the set of all central dilatations are not a group.
Equation for translation
) = x
Equation for central dilatation
) = r
(x - C
) + C
+ (1 - r
"Vectors and Transformations in Plane Geometry" by Philippe Tondeur, Publish or Perish, Inc. 1993