We difine N(x,y,) to be the intersection of the two circles of radius d(x,y)/2 centered at the points (1- /2)x+(/2)y and (/2)x + (1- /2)y, respectively.
When =1, N(x,y,) corresponds exactly to the Gabriel neighbourhood of x and y. When =2, we get the ``relative neighbourhood'' of the RNG. As approaches , the neighbourhood of x and y approximates the infinite strip formed by translating the line segment (x, y) normal to itself.
We difine N(x,y,) to be the intersection of the two circles of radius d(x,y)/(2) passing through both x and y. When =1, this is consistent with the definition abvove. As approaches 0, N(x,y,) approximates the line segment joining x and y. Thus, except in degenerate situations (three or more points colinear), all point pairs are -neighbours under this scheme for sufficiently small.