feat: volume integration based on double integrator_t::calculate

frontend/src/implicit_surface_network_solver.cpp

@@ -22,6 +22,7 @@ void implicit_network_solver::generate_polymesh(stl_vector_mp<Eigen::Vector3d>&
     auto integrator = internal::integrator_t(m_blobtree->subfaces, output_parameteric_planes); 
     
     double area = integrator.calculate(4, internal::area_integrand);
+    double volume =  integrator.calculate(4, internal::volume_integrand);
 
     std::cout << "Generated mesh area: " << area << std::endl;
     

surface_integral/interface/subface_integrator.hpp

@@ -85,5 +85,12 @@ double area_integrand(double u, double v, const Eigen::Vector3d& p, const Eigen:
     return 1.0;
 }
 
+// Integrate (1/3) * r · n dA over all subfaces
+double volume_integrand(double u, double v, const Eigen::Vector3d& p, const Eigen::Vector3d& dU, const Eigen::Vector3d& dV)
+{
+    Eigen::Vector3d cross = dU.cross(dV);
+    return (p.dot(cross)) / 3.0; // (1/3) * (x dydz + y dzdx + z dxdy)
+};
+
 
 } // namespace internal