MFEP, by definition, wishes the normal forces on the MFEP, f ⊥ (φ MFEP ) to be zero. To achieve this, the points on the string should first evolve using numerical methods such as the steepest descent or Newton-Raphson. Then it should be re-parameterized to redistribute the nodes along the string after each evolution step so that they are uniformly distributed on the arc. This can be done by defining the parameterization density, ρ(s) and a constant c that satisfy the integral,