void calcBoundingSphere(double *center, double *radius, FaceList *fl){
double maxDistance = 0.0;
for( int i = 0; i < fl->vc-1; i++ ){
for(int j = i + 1; j < fl->vc; j++){
double *a = fl->vertices[i];
double *b = fl->vertices[j];
double distance = vecSquaredDistanceBetween3d(a, b);
if( distance > maxDistance){
midpoint(center, a, b);
*radius = sqrt(distance) * 0.5;
maxDistance = distance;
}
}
}
}
void calcRitterBoundingSphere(double* center, double* radius, FaceList *fl){
/*
An Efficient Bounding Sphere
by Jack Ritter
from "Graphics Gems", Academic Press, 1990
p. 301-303, code: p. 723-725
*/
int count = 0;
double x_min, x_max, y_min, y_max, z_min, z_max;
int px_min, px_max, py_min, py_max, pz_min, pz_max;
double *p;
// Intialize
// Select a point in the mesh as an arbitrary starting point.
p = fl->vertices[0];
px_min = px_max = py_min = py_max = pz_min = pz_max = 0;
x_min = x_max = p[0];
y_min = y_max = p[1];
z_min = z_max = p[2];
// Find 6 minima & maxima points
for( int i = 0; i < fl->vc; i++ ){
p = fl->vertices[i];
if( p[0] < x_min ){
x_min = p[0];
px_min = i;
}
if( p[0] > x_max ){
x_max = p[0];
px_max = i;
}
if( p[1] < y_min ){
y_min = p[1];
py_min = i;
}
if( p[1] > y_max ){
y_max = p[1];
py_max = i;
}
if( p[2] < z_min ){
z_min = p[2];
pz_min = i;
}
if( p[2] > z_max ){
z_max = p[2];
pz_max = i;
}
} // end for
// Find the distance between the extremal values
double x_span_dist = vecSquaredDistanceBetween3d(fl->vertices[px_max], fl->vertices[px_min]);
double y_span_dist = vecSquaredDistanceBetween3d(fl->vertices[py_max], fl->vertices[py_min]);
double z_span_dist = vecSquaredDistanceBetween3d(fl->vertices[pz_max], fl->vertices[pz_min]);
// Find the maximally separated pair; dia1 & dia2
double max_span_dist = x_span_dist;
int dia1, dia2;
dia1 = px_min;
dia2 = px_max;
if( y_span_dist > max_span_dist ){
max_span_dist = y_span_dist;
dia1 = py_min;
dia2 = py_max;
}
if( z_span_dist > max_span_dist ){
dia1 = pz_min;
dia2 = pz_max;
}
// dia1 and dia2 define the diameter of the intial sphere
// calculate the center of the sphere
double _center[3];
midpoint(_center, fl->vertices[dia1], fl->vertices[dia2]);
// Calculate the length of the radius
double radius_sq_dist = vecSquaredDistanceBetween3d(fl->vertices[dia2], _center);
double radius_dist = sqrt(radius_sq_dist);
// Incrementally grow the sphere to include all points
for( int i = 0; i < fl->vc; i++ ){
double test_sq_dist = vecSquaredDistanceBetween3d(fl->vertices[i], _center);
if( test_sq_dist > radius_sq_dist ){
// the current (ith) point is outside the sphere
double test_dist = sqrt(test_sq_dist);
// calculate the radius of the new sphere
radius_dist = (radius_dist + test_dist) * 0.5;
radius_sq_dist = SQR(radius_dist);
// calculate the center of the new sphere
double old_to_new_dist = test_dist - radius_dist;
for(int j = 0; j < 3; j++){
_center[j] = (radius_dist * _center[j] + old_to_new_dist * fl->vertices[i][j]) / test_dist;
}
count++;
}
} // end for
*radius = radius_dist;
for(int j = 0; j < 3; j++){
center[j] = _center[j];
}
//printf("Grew the sphere %d times\n", count);
}
