Radial Metric
Radial Metric
The radial metric is defined on as if and lie on the same line through the origin, and otherwise. It looks like a centralized train network, and has been called the French railroad metric.
ρ
×
ρ(x,y)=|x-y|
x
y
|x|+|y|
A neighborhood of a point of radius , , is either a line segment through on the ray from the origin through or the union of a segment from the origin through and a disk centered at the origin.
x
r
{y|ρ(x,y)<r}
x
x
x