double fermat_point(Point pt[], int n, Point& ptres){
Point u, v;
double step = 0.0, curlen, explen, minlen;
int i, j, k, idx;
bool flag;
u.x = u.y = v.x = v.y = 0.0;
for(i = 0; i < n; ++i){
step += fabs(pt[i].x) + fabs(pt[i].y);
u.x += pt[i].x;
u.y += pt[i].y;
}
u.x /= n;
u.y /= n;
flag = 0;
while(step > 1e-10){
for(k = 0; k < 10; step /= 2, ++k)
for(i = -1; i <= 1; ++i)
for(j = -1; j <= 1; ++j){
v.x = u.x + step*i;
v.y = u.y + step*j;
curlen = explen = 0.0;
for(idx = 0; idx < n; ++idx){
curlen += pt_distance(u, pt[idx]);
explen += pt_distance(v, pt[idx]);
}
if(curlen > explen){
u = v;
minlen = explen;
flag = 1;
}
}
}
ptres = u;
return flag ? minlen : curlen;
}
/**
* Calculate the box->box distance.
*/
static double box2df_distance(const BOX2DF *a, const BOX2DF *b)
{
/* Check for overlap */
if ( box2df_overlaps(a, b) )
return 0.0;
if ( box2df_left(a, b) )
{
if ( box2df_above(a, b) )
return pt_distance(a->xmax, a->ymin, b->xmin, b->ymax);
if ( box2df_below(a, b) )
return pt_distance(a->xmax, a->ymax, b->xmin, b->ymin);
else
return b->xmin - a->xmax;
}
if ( box2df_right(a, b) )
{
if ( box2df_above(a, b) )
return pt_distance(a->xmin, a->ymin, b->xmax, b->ymax);
if ( box2df_below(a, b) )
return pt_distance(a->xmin, a->ymax, b->xmax, b->ymin);
else
return a->xmin - b->xmax;
}
if ( box2df_above(a, b) )
{
if ( box2df_left(a, b) )
return pt_distance(a->xmax, a->ymin, b->xmin, b->ymax);
if ( box2df_right(a, b) )
return pt_distance(a->xmin, a->ymin, b->xmax, b->ymax);
else
return a->ymin - b->ymax;
}
if ( box2df_below(a, b) )
{
if ( box2df_left(a, b) )
return pt_distance(a->xmax, a->ymax, b->xmin, b->ymin);
if ( box2df_right(a, b) )
return pt_distance(a->xmin, a->ymax, b->xmax, b->ymin);
else
return b->ymin - a->ymax;
}
return MAXFLOAT;
}