Homothetic transformation
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In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin. The number c by which distances are multiplied is called the dilation factor or similitude ratio. Such a transformation is also called an enlargement.
More generally c can be negative; in that case it not only multiplies all distances by [|c|], but also inverses all points with respect to the fixed point.
Choose an origin or center A and a real number [c] (possibly negative). The homothety [h_] maps any point M to a point [M'] such that
- [A-M'=c(A-M)]
A homothety is an affine transformation (if the fixed point is the origin: a linear transformation) and also a similarity transformation. It multiplies all distances by [|c|], all surface areas by [c^2], etc.
See also: dilation (mathematics).
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