Thursday, July 28, 2011

Sign of 180 Resolution

This is for the case when maxDistance (the distance between maximally separated nodes is 180).

Then there arises an ambiguity is choosing the globalMaxAngle as +180 or -180 in the transformed positions. And it does make a difference to the answer.

Consider for example the case of 3 positions. 10, -170 and -110.

The maximally separated nodes are 10 and -170. Suppose 10 is chosen as origin and clockwise direction is positive. Then

Case 1: -170 ----> 180         (where ----> denotes transformation)

mean = (-120 + 180 + 0 )/3 = 20


Case 2: -170 ----> -180

mean = (-120 + -180 + 0)/3 = -100

-100 seems to be a better choice because migration distances are smaller this way and it adheres to my policy of "keep the parent node at a position within the bounds of the end nodes"

To achieve this effect, I can count which hemisphere has more number of nodes. If the negative hemisphere has more nodes then its -180 and vice versa.

How to find whether a point is in the +ive or -ive hemisphere, that is given in the last post.

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