I made up the measure (and its name) and I wonder if it is officially defined (and named!)? I need a name, because when I call it "Manhattan visibility" nobody will understand me unless I explain how it is measured.
Having two points in 2d space, those points are less distance if the angle is closer to 0, and far distance if the angle is close to 45°. Comparing two cases, if angle is the same, the second factor is radius -- the bigger, the more distant two points are.
And thus, I coined term visibility, because if the axis is the same, the points can "see" each other, if the radius (real distance) between is greater, the harder to "see" each other.
Please note, it is not Manhattan distance measure. Points (0,0) and (1,1) are closer than (0,0) and (0,10000), while with my measure the latter pair is closer than the former.
Update 1 to give some background, maybe this will help. I am writing the program which generates analog clocks (visually). Next I need to compute how 2 clocks are similar to each other. So let's say 12:00 and 24:00 are identical, 12:15 and 13:15 are pretty similar, less, but still similar are 12:15 and 16:15. 12:00 and 18:30 are completely different.
Update 2 (not verified yet)
This is the code I came up with to compute it:
var dx = Math.abs(a.x-b.x); var dy = Math.abs(a.y-b.y); var min = Math.min(dx,dy); var max = Math.max(dx,dy); if (max==0) // same point return 0; else return min*1.0/max+1-1.0/(1+dx*dx+dy*dy);