The term "stretch factor" can refer to different concepts depending on the context in which it is used. Here are a few interpretations of "stretch factor": 1. **Mathematics and Geometry**: In the context of geometric transformations, the stretch factor refers to the ratio by which a shape is stretched or scaled. For example, if a line segment is stretched to twice its original length, the stretch factor is 2.
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For an injective function that does not increase distances, one stretch-factor convention measures the largest compression that must be undone:If the sharp Lipschitz constant of is one, this equals bi-Lipschitz distortion. Fixing the scale matters: uniform compression has stretch factor two in this convention, but bi-Lipschitz distortion one. In a geometric spanner, the corresponding stretch factor is the largest graph-route distance divided by direct Euclidean distance; the graph-to-Euclidean identification does not increase distances. [ref]
https://people.scs.carleton.ca/~michiel/encyc_geometric_spanners.pdf. Gudmundsson, Narasimhan and Smid, Geometric Spanners, §1: the stretch-factor convention
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