I want to do soft-binning for a distance-based histogram. For example a point X lies somewhere between the center points of 4 bins, A,B,C,D. These four points A,B,C,D can be treated as the vertices of a square.
I would like to assign each of these vertex points a certain weightage (between 0-1) based how much the point X is closer to that vertex with two conditions:
* Sum of vertex weights should be 1.
* If X lies on the line between two vertices, only those two vertices should get the share in weightage.
Currently I calculate the weightage as:
WA =(1 - distance of A from X/sum of distances of all vertices from X )/3
Define a coordinate system so that a unit square has vertices:
P_1 = (0,0), P_2 = (1,0), P_3 = (1,1), and P_4 = (0,1).
For i = 1,2,3,4, let W_i be the weight assigned at P_i.
Let the point X have coordinates (x,y), so 0
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