I am going to assume that I am working in a Euclidean plane using ONLY the Euclidean metric to measure distances.
12.
Topologically Constrained Isometric Embedding ( TCIE ) is an algorithm based approximating geodesic distances after filtering geodesics inconsistent with the Euclidean metric.
13.
However, not every countable set is discrete, of which the rational numbers under the usual Euclidean metric are the canonical example.
14.
Euclidean metric distance calculation to compute the " branch metric " may be performed with a simple add / subtract operation.
15.
In the case the metric of the space being the Euclidean metric, and using standard notation, it becomes the classical Liouville equation
16.
It is a pseudo-Euclidean metric, or more generally a " constant " pseudo-Riemannian metric in Cartesian coordinates.
17.
Without further specifications, the term " unit disk " is used for the open unit disk about the standard Euclidean metric.
18.
Without appeal to an auxiliary metric, consider the effect of the pullback under " f " of the usual Euclidean metric.
19.
Oftentimes, the familiar Euclidean metric is not directly applicable because the patterns of shapes and images don't form a vector space.
20.
For example, in with Euclidean metric, a sphere of radius is nonempty only if can be written as sum of squares of integers.
