A 2D distance measure that gives weightage to the angle between the two points?

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       n1     n8     n7


    n2        c         n6



       n3     n4     n5

Assume that all neighbors ni are (Euclidean) equidistant to candidate c.

Is there a distance measure that would yield a smaller distance between a candidate and a neighbor if the angle between them (w.r.t y-axis) approaches either 0 or 90 degrees? (n2 and n6 would be at 0 degrees and n8 and n4 would be at 90 degrees)

In the example above, the distances need to be like:

[ dist(c, n2) = dist(c, n4) = dist(c, n6) = dist(c, n8) ] < [ dist(c, n1) = dist(c, n3) = dist(c, n5) = dist(c, n7) ]