I think you might be a bit to concentrated on the term 'Lagrange Multiplier'. The important part here is that you know the direction of the constraint force is the gradient of the constraint function and you only need to find a scalar multiplier to determine the constraint force. The reason for this is that constraint forces doesn't do work. IIRC you can show this using virtual displacements. Maybe concentrate a bit more on the physical meaning rather than trying to be overly mathematical abstract.

Thanks! I am glad you found it useful!

I haven't watched that video completely, but I see that it follows Baraff's literature to solve for constraint *forces* (impulses / time_step). He uses essentially the same method as found in the constraint-based literature for non-penetration constraints using the LCP formulation. However, he uses quadratic programming (a global solver) to solve for the multipliers.

As Dirk said, you'll need to define your gradients (normals from the SAT for the collision case), each of which will be inserted into a Jacobian matrix for a general constraint-based system. From there you compute the lagrange multipliers as showed in Catto's slides. I think it is important to understand constraints geometrically when implementing these things. So yeah, we do look for a collision normal and point and only then we can find the force magnitude by relating it to the impulse-momentum law in Euler form and then we find the new relative velocities of each body after the collision/contact.

BTW, different authors use the term impulse and force interchangeble, but assuming the force is constant during the time step then impulse = force * time_step. Therefore the lagrange multipliers both refer to the same thing.

(Do not take this too theoretical but here is an example without using Catto's simplification to solve for the multipliers (impulses) for a distance constraint.)

I think you might be a bit to concentrated on the term 'Lagrange Multiplier'. The important part here is that you know the direction of the constraint force is the gradient of the constraint function and you only need to find a scalar multiplier to determine the constraint force. The reason for this is that constraint forces doesn't do work. IIRC you can show this using virtual displacements. Maybe concentrate a bit more on the physical meaning rather than trying to be overly mathematical abstract.

Thanks! I am glad you found it useful!

I haven't watched that video completely, but I see that it follows Baraff's literature to solve for constraint *forces* (impulses / time_step). He uses essentially the same method as found in the constraint-based literature for non-penetration constraints using the LCP formulation. However, he uses quadratic programming (a global solver) to solve for the multipliers.

As Dirk said, you'll need to define your gradients (normals from the SAT for the collision case), each of which will be inserted into a Jacobian matrix for a general constraint-based system. From there you compute the lagrange multipliers as showed in Catto's slides. I think it is important to understand constraints geometrically when implementing these things. So yeah, we do look for a collision normal and point and only then we can find the force magnitude by relating it to the impulse-momentum law in Euler form and then we find the new relative velocities of each body after the collision/contact.

BTW, different authors use the term impulse and force interchangeble, but assuming the force is constant during the time step then impulse = force * time_step. Therefore the lagrange multipliers both refer to the same thing.

(Do not take this too theoretical but here is an example without using Catto's simplification to solve for the multipliers (impulses) for a distance constraint.)

Hi guys, thank you for answering so far

I've studied a bit of Lagrangian mechanic, I think I begin to see the gist of things now :D