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
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