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 ?


Your Answer


By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.