Real Polygon3D::areaConvex() const
{
Real sum=0;
Triangle3D temp;
for(size_t i=1;i+1<vertices.size();i++) {
temp.set(vertices[0],vertices[i],vertices[i+1]);
sum += temp.area();
}
return sum;
}
Vector3 Polygon3D::centroidConvex() const
{
const static Real Third = 1.0/3.0;
Vector3 c(Zero);
Real sum=0;
Triangle3D temp;
for(size_t i=1;i+1<vertices.size();i++) {
temp.set(vertices[0],vertices[i],vertices[i+1]);
Real area = temp.area();
c.madd((temp.a+temp.b+temp.c),area*Third);
sum += area;
}
if(sum == 0) return c;
return c/sum;
}