Further Developments to Jakobsen?
Author
Hi, I just recently got back into physics for games, and the most flexible approach for games right now seems to me to be Jakobsen's Verlet Integration Scheme.
Does anyone know of any newer papers that develop upon Jakobsen's idea? Perhaps such as a more efficient alternative than using relaxation to solve interpenetration or a way to incorporate variable elasticities into bodies? So far, Jakobsen's original "Advanced Character Animation" is the only paper I can find that talks about this approach. I know I saw one other once upon a time, but I lost the link.
Thanks a lot for sharing your knowledge.
-Cuppo
hi again skittleo,
the future is here and now ;)
Verlet Integration and Constraints in a Six Degree of Freedom Rigid Body Physics Simulation
is a nice extension to the original paper,
Abstract
At the 1999 Game Developers Conference, Thomas Jakobsen presented a semi-implicit rigid body physics simulation. The simulation could integrate stiff systems at the time steps used in games without the need to compute expensive Jacobian matrices and had very simple constraint implementations. However, the simulation was limited because it did not include a velocity state and it did not integrate the rotational equations of motion, necessitating large numbers of particles and distance constraints to simulate a single rigid body. It was also difficult to set up pin constraints, common in rag-doll simulations.
By extending the simulation to six degrees of freedom through the Verlet-like integration of a state quaternion, joint constraints became simple and straightforward, though a slightly more complicated constraint equation was required. Two methods for implementing the additional degrees of freedom are presented; one that uses the current quaternion and last quaternion as the system states and one that uses the quaternion and the angular rate. The advantages and disadvantages of both methods are discussed. The equations used in pin and angle constraints and the method for resolving collisions are presented. This simulation was developed for the game MX Unleashed, published by THQ.
hope this helps, I used this paper in my 2d physics system and it worked well, though I ended up making a few modifications inline with the nonconvex rigid body with stacking paper to help a few things.
the future is here and now ;)
Verlet Integration and Constraints in a Six Degree of Freedom Rigid Body Physics Simulation
is a nice extension to the original paper,
Abstract
At the 1999 Game Developers Conference, Thomas Jakobsen presented a semi-implicit rigid body physics simulation. The simulation could integrate stiff systems at the time steps used in games without the need to compute expensive Jacobian matrices and had very simple constraint implementations. However, the simulation was limited because it did not include a velocity state and it did not integrate the rotational equations of motion, necessitating large numbers of particles and distance constraints to simulate a single rigid body. It was also difficult to set up pin constraints, common in rag-doll simulations.
By extending the simulation to six degrees of freedom through the Verlet-like integration of a state quaternion, joint constraints became simple and straightforward, though a slightly more complicated constraint equation was required. Two methods for implementing the additional degrees of freedom are presented; one that uses the current quaternion and last quaternion as the system states and one that uses the quaternion and the angular rate. The advantages and disadvantages of both methods are discussed. The equations used in pin and angle constraints and the method for resolving collisions are presented. This simulation was developed for the game MX Unleashed, published by THQ.
hope this helps, I used this paper in my 2d physics system and it worked well, though I ended up making a few modifications inline with the nonconvex rigid body with stacking paper to help a few things.
That one is a GDC classic. :) It's a GDC presentation, and usually, it takes a bit of time to get public. But it's been there for about a year.
Author
Wow thanks for that link. I'll be sure to look through it but I have to admit that my math skills are not quite up-to-par and it will take me some time. Would you mind telling me what advantages this method offers? especially when used in 2D? I noticed that it makes angle contraints much easier but I didn't notice a lot other than that. Mind you, I only had a brief look and I will have to examine it more closely. Thank you very much Structure.
-Cuppo
PS: Is there a website that lists every single paper ever written on this subject in chronological order? Wouldn't that be a godsend?
-Cuppo
PS: Is there a website that lists every single paper ever written on this subject in chronological order? Wouldn't that be a godsend?
Quote:Original post by CuppoJava
PS: Is there a website that lists every single paper ever written on this subject in chronological order? Wouldn't that be a godsend?
*pulls out his magic wand*
enjoy!
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