Vector3 Winding::centroid(const Plane3& plane) const
{
Vector3 centroid(0,0,0);
float area2 = 0, x_sum = 0, y_sum = 0;
const ProjectionAxis axis = projectionaxis_for_normal(plane.normal());
const indexremap_t remap = indexremap_for_projectionaxis(axis);
for (std::size_t i = size() - 1, j = 0; j < size(); i = j, ++j)
{
const float ai = (*this)[i].vertex[remap.x]
* (*this)[j].vertex[remap.y] - (*this)[j].vertex[remap.x]
* (*this)[i].vertex[remap.y];
area2 += ai;
x_sum += ((*this)[j].vertex[remap.x] + (*this)[i].vertex[remap.x]) * ai;
y_sum += ((*this)[j].vertex[remap.y] + (*this)[i].vertex[remap.y]) * ai;
}
centroid[remap.x] = x_sum / (3 * area2);
centroid[remap.y] = y_sum / (3 * area2);
{
Ray ray(Vector3(0, 0, 0), Vector3(0, 0, 0));
ray.origin[remap.x] = centroid[remap.x];
ray.origin[remap.y] = centroid[remap.y];
ray.direction[remap.z] = 1;
centroid[remap.z] = ray.getDistance(plane);
}
return centroid;
}
/// \brief Calculate the \p centroid of the polygon defined by \p winding which lies on plane \p plane.
void Winding_Centroid(const Winding& winding, const Plane3& plane, Vector3& centroid)
{
double area2 = 0, x_sum = 0, y_sum = 0;
const ProjectionAxis axis = projectionaxis_for_normal(plane.normal());
const indexremap_t remap = indexremap_for_projectionaxis(axis);
for(std::size_t i = winding.numpoints-1, j = 0; j < winding.numpoints; i = j, ++j)
{
const double ai = winding[i].vertex[remap.x] * winding[j].vertex[remap.y] - winding[j].vertex[remap.x] * winding[i].vertex[remap.y];
area2 += ai;
x_sum += (winding[j].vertex[remap.x] + winding[i].vertex[remap.x]) * ai;
y_sum += (winding[j].vertex[remap.y] + winding[i].vertex[remap.y]) * ai;
}
centroid[remap.x] = static_cast<float>(x_sum / (3 * area2));
centroid[remap.y] = static_cast<float>(y_sum / (3 * area2));
{
Ray ray(Vector3(0, 0, 0), Vector3(0, 0, 0));
ray.origin[remap.x] = centroid[remap.x];
ray.origin[remap.y] = centroid[remap.y];
ray.direction[remap.z] = 1;
centroid[remap.z] = static_cast<float>(ray_distance_to_plane(ray, plane));
}
}
