Finding the center of mass on a 2D bitmap

Question

I\'m coding a game, and I\'d like to be able to find the center of mass of an arbitrary shape on a black and white bitmap such as this:

 012345678
0.XX......
1..X         


        

Answer 1

How about this algorithm (psuedo-code) based on a boolean matrix like in your example :

xSum = 0
ySum = 0
points = 0

for point in matrix
    if point is marked
        xSum += pointX
        ySum += pointY
        points++

return (xSum/points, ySum/points)

Nothing too complicated, calculate where X is the most present, same for Y, divide by number of points you counted, and you got the center of mass. You can further complicate this by giving certain points different weight in the averaging, but this should be your main direction.

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This question got me thinking about an expansion to this question which I could not find a good answer to. I posted the question here: Finding clusters of mass in a matrix/bitmap