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

Depending on the nature of your actionscript interpreter and the pre-processing done on the shapes, you may see a speed improvement (over the direct approach pointed out by Yuval) by initially creating a second copy of the bitmap/array mirrored diagonally, then using row or string manipulation functions to sum the points on each row and column in single steps. This would be O(2mn) instead of O(nn) [see below], but with more overhead.

xSum = 0
ySum = 0
points = 0

for row in matrix
  ySum += rowX * countpoints(row)
  points += countpoints(row)
for row in mirroredmatrix
  xSum += rowX * countpoints(row)

return (xSum/points, ySum/points)

Where countpoints() counts the on-points in a row. This relies on countpoints (which has O(n) runtime) having a lower constant multiplier than the naive approach's runtime (hence above, 'm' being the runtime of countpoints and 'n' being the time for the interpreter to loop through a row). The nature of countpoints() depends on your storage method, which may involve counting characters in a string, or bits in a bitfield.