I will survey a variety of algorithmic settings in which one would like to compute (or at least use) distances between points that are induced by local scaling of space. I will track this idea through topics in mesh generation, surface reconstruction, and robotics. Then, I will discuss some recent results on exact computation of such distances for the special case where the local scaling of space is proportional to the distance to the input. This gives the first example of an exact computation for a so-called density-based distance.