Transformation Rules

Once I find the two positions which are maximally separated namely globalAngleZero and globalAngleMax, I need to transform the origin to globalAngleZero with positive sense towards the shortest path direction towards globalAngleMax.

maxDistance is the distance between these two positions.

Case 1: maxDistance = 180

For all position in posVector

         let L = minimumAngularDistance(position, globalAngleZero)
        
         if (position >= globalAngleZero OR position <=globalAngleMax)
                do nothing              

         if(position < globalAngleZero OR position > globalAngleMax)
               L = -L (invert the sign)

         sigma += L

meanPos = sigma/n (where n is the length of posVector)

The actual mean position is obtained by adding meanPos to globalAngleZero in a positive sense.


Case 2: maxDistance < 180

For all position in posVector

        let L1 = minimumAngularDistance(position, globalAngleZero)
        let L2 = minimumAngularDistance(position, globalAngleMax)
         
        if (L1 + L2 = maxDistance) (if this point lies inside the region bounded by end points)
              sigma = sigma + L1

        else
             sigma = sigma - L1

meanPos = sigma/n (where n is the length of posVector)

The actual mean position can be obtained by adding meanPos to globalAngleZero in clockwise and anti-clockwise sense and that position is choosen for which L1+L2= maxDistance condition is satisfied.