Search results
Results from the WOW.Com Content Network
In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number k called its ratio, which sends point X to a point X ′ by the rule, [1]
Dilation is commutative, also given by = =. If B has a center on the origin, then the dilation of A by B can be understood as the locus of the points covered by B when the center of B moves inside A. The dilation of a square of size 10, centered at the origin, by a disk of radius 2, also centered at the origin, is a square of side 14, with ...
The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry . In mathematics, scale invariance usually refers to an invariance of individual functions or curves .
Dilation (affine geometry), an affine transformation; Dilation (metric space), a function from a metric space into itself; Dilation (operator theory), a dilation of an operator on a Hilbert space; Dilation (morphology), an operation in mathematical morphology; Scaling (geometry), including:
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system .
In mathematics, transformation geometry (or transformational geometry) ... Another transformation introduced to young students is the dilation. However, ...
Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France.Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and ...