double polygonCellVolume(const Vector<Point>& points,
const Point& face_centroid,
const Point& cell_centroid)
{
double tot_volume = 0.0;
int num_points = points.size();
for (int i = 0; i < num_points; ++i) {
Point tet[4] = { cell_centroid, face_centroid, points[i], points[(i+1)%num_points] };
double small_volume = std::fabs(simplex_volume(tet));
assert(small_volume > 0);
tot_volume += small_volume;
}
assert(tot_volume>0);
return tot_volume;
}
Point polygonCellCentroid(const Vector<Point>& points,
const Point& face_centroid,
const Point& cell_centroid)
{
Point centroid(0.0);
double tot_volume = 0.0;
int num_points = points.size();
for (int i = 0; i < num_points; ++i) {
Point tet[4] = { cell_centroid, face_centroid, points[i], points[(i+1)%num_points] };
double small_volume = std::fabs(simplex_volume(tet));
assert(small_volume > 0);
Point small_centroid = tet[0];
for(int j = 1; j < 4; ++j){
small_centroid += tet[j];
}
small_centroid *= small_volume/4.0;
centroid += small_centroid;
tot_volume += small_volume;
}
centroid /= tot_volume;
assert(tot_volume>0);
return centroid;
}
inline T volume(const Point<T, 3>* c)
{ return simplex_volume(c); }
inline T area(const Point<T, 2>* c)
{ return simplex_volume(c); }