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 ?



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