Fundamentals of the problem
Edgar Chávez, Gonzalo Navarro · SIGSPATIAL Special · 2010
Spatial distance has been for decades a natural concept in applications such as computational geometry, geomatics, meshing, and others. There are several other applications, however, where a more general notion of proximity is necessary. To reuse the large body of knowledge built around spatial distances, researchers have tried to map non-spatial proximity measures to those. This approach is not always successful, and fails in some emblematic cases. Instead, a flexible model, called "metric spaces", captures in a natural way more general proximity concepts. We will briefly present its fundamentals; exhaustive books and surveys exist [2, 3, 1].