demo of sample size and vector types.

vector.c

#include "stdio.h"

/* a size type */
typedef struct 
{
  int width;
  int height;
} size;

/* create a new size */
size new_size(int width, int height) 
{
  size s;
  s.width = width;
  s.height = height;
  return s;
}

/* a coordinate vector type */
typedef struct 
{
  int x;
  int y;
} vector;

/* create a new vector */
vector new_vector(int x, int y) 
{
  vector v;
  v.x = x;
  v.y = y;
  return v;
}

/* convert vector to index, given size of grid */
int vector_to_index(size s, vector v) 
{
  return v.y * s.width + v.x;
}

/* convert index to vector, given size of grid */
vector index_to_vector(size s, int index) 
{
  return new_vector(index % s.width, index / s.width);
} 


int main(void) 
{
  /* size with width 15, height 15 */
  size s = new_size(10, 10);
  printf("created size with width %d, height %d\n", s.width, s.height);

  /* convert index 15 to vector */
  vector xy_at_15 = index_to_vector(s, 15);
  printf("index 15 is coordinate %d, %d\n", xy_at_15.x, xy_at_15.y);

  /* convert vector to index */
  int index_at_xy = vector_to_index(s, xy_at_15);
  printf("index of coordinate %d, %d is %d\n", xy_at_15.x, xy_at_15.y, 
    index_at_xy);
  return 0;
}