# Deformable meshes based on torsional spring

I am trying to learn physics-based animation thanks to the book "Foundation of Physically-Based Modelling and Animation". They introduce the mass-spring model for deformable meshes. Although making each pair of vertices a mass-spring system would give good results, it would be too heavy to compute. So, the authors introduce another technique : between each pair of adjacent triangles, the evolution of the angle is based on a torsional spring model. I don't know if you can read it on the Google preview. It's on page 161 : https://books.google.fr/books?id=vaqdDQAAQBAJ&printsec=frontcover&dq=torsional+spring+foundation+of+physics+based+animation&hl=fr&sa=X&ved=0ahUKEwj-oPTkvobcAhVDtBQKHfj2AaYQ6AEIKzAA#v=onepage&q&f=false

I struggle to understand this model.

For instance, let's imagine we have two adjacent triangles $ABC$ and $BCD$. Let's $\theta$ be the angle between both triangles. The torque is $\tau = k(\theta - \theta_0)$. We want to compute the equivalent forces $f_{A}$,$f_{B}$,$f_{C}$,$f_{D}$, and torques $\tau_{A}$, $\tau_{B}$, $\tau_{C}$, $\tau_{D}$ relatively to $B$.

They state that all sums must be equal to zero : $$f_{A} + f_{B} + f_{C} + f_{D} = 0$$ $$\tau_{A} +\tau_{B} + \tau_{C} + \tau_{D} = 0$$

I don't understand why. Can you give me some help ?

Thanks.