Question

I have a 2D distribution of a data set, and I would like to find its gravitation center of these points.

What I would like to do is like the code below,

#include <stdio.h>

#define SIZE 4

struct point {
 short x;
 short y;
};

point find_gravitation(struct point set[], unsigned char size)
{
  point ret;
  .
  .
  .
  ?
  .
  .
  .
  return ret;
}

int
main(int argc, char **argv)
{
 struct point dataset[SIZE];
 struct point ret;

 dataset[0].x = 12;
 dataset[0].y = 24;

 dataset[1].x = 3;
 dataset[1].y = 5;

 dataset[2].x = 71;
 dataset[2].y = -6;

 dataset[3].x = -185;
 dataset[3].y = -26;

 ret = find_gravitation(dataset, SIZE);

 printf("gravitation center is: %d, %d\n", ret.x, ret.y);

 return 0;
}

How can I calculate the gravitation center of this set?

Answer 1

If I am interpreting this correctly:

Because your points are unweighted, the center point would be: (avg(x), avg(y)).

To calculate the average x point, add all x values and divide by the number of points.
To calculate the average y point, add all y values and divide by the number of points.