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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using ...
2D affine transformation matrix: Image title: Illustration of the effect of applying various 2D affine transformation matrices on a unit square by CMG Lee. Note that the reflection matrices are special cases of the scaling matrix. Width: 100%: Height: 100%
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images. This method is often used to measure full-field displacement and strains , and it is widely applied in many areas of science and engineering.
It is also known as Principal Coordinates Analysis (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain, [2] which is given by (,,...,) = (, (),) /, where denote vectors in N-dimensional space, denotes the scalar product between ...
Such a scaling changes the diameter of an object by a factor between the scale factors, the area by a factor between the smallest and the largest product of two scale factors, and the volume by the product of all three. The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors ...
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μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians.