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

You could count the number of adjoining cells, then center on the cells with the highest neighbor count.

 012345678
0 XX      |
1  XXX    |
2   XXX   |
3  XXXXXXX|
4   XXX   |

 012345678
0 23      |
1  454    |
2   775   |
3  3686421|
4   454   |

In this example you could use the only cell with an 8, as the center point.

If you came up with multiple cells with the same number of neighbors, you would just run the counting routine again, but this time just with the high number cells.

For example, lets pretend that the cells that had 6, 7, and 8, instead all had eight neighbors.

 012345678
0 23      |
1  454    |
2   885   |
3  3888421|
4   454   |

 012345678
0 --      |
1  ---    |
2   XX-   |
3  -XXX---|
4   ---   |

 012345678
0 --      |
1  ---    |
2   34-   |
3  -342---|
4   ---   |

 012345678
0 --      |
1  ---    |
2   -X-   |
3  --X----|
4   ---   |

In the case of a simple tie, I would go with the one that was nearer the center. In this case it would be the upper one of the two.

Note: I'm assuming your not using this for an accurate physics simulation.