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The stretch factor of the whole mapping is the supremum of the stretch factors of all pairs of points. The stretch factor has also been called the distortion [disputed – discuss] or dilation of the mapping. The stretch factor is important in the theory of geometric spanners, weighted graphs that approximate the Euclidean distances between a ...
A t-path is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner. [1] In computational geometry, the concept was first discussed by L.P. Chew in 1986, [2] although the term "spanner" was not used in the original ...
Both graphs show an identical exponential function of f(x) = 2 x. The graph on the left uses a linear scale, showing clearly an exponential trend. The graph on the right, however uses a logarithmic scale, which generates a straight line. If the graph viewer were not aware of this, the graph would appear to show a linear trend.
A flow is a process in which the points of a space continuously change their locations or properties over time. More specifically, in a one-dimensional geometric flow such as the curve-shortening flow, the points undergoing the flow belong to a curve, and what changes is the shape of the curve, its embedding into the Euclidean plane determined by the locations of each of its points. [2]
with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.
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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).
Relations () valid for biaxial (plane) stress states show that in such a case, the values of the triaxiality factor must always remain in the range <, >, while in the general case of three-dimensional multiaxial tests, the triaxiality factor can take any value from the range <, >.