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3D Engine Animation

November 01, 2006

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I stumbled upon this video while reading auto blogs. Very cool and educational. I have seen it before but couldn't get a copy. I am keeping a link here just for my reference.

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Reminiscence

I started this project at the beginning of this year, and now it is already August!! I don't know how much I can accomplish at this rate. Apparently I am still not qualified to run a open source project and claim myself an expert on multibody dynamics simulations. The current status of the project is Implement Rapid and find the intersection points of triangle meshes. Overlapping of the meshes is allowed instead of finding the first-time contact points. Verify that I have a stable time-stepping scheme that allows overlapping. Review and implement all the novel techniques that can automatically configure time-step size and handle impact and contact seamlessly. In the mean time, fix the box-box collision. The graphics platform has been switched to pure Java 3D eliminating some consistency problems and display irregularities. Incorporate more Physics such as CFD.

Contact Joint Summary

There are three DOF in the contact joint. A generic constraint equation is written as J v = c (1) The first DOF is in the normal direction. The LHS of Eq. ( 1 ) is where r 1 = cp - p 1 and r 2 = cp - p 2 . The RHS of Eq. ( 1 ) is c = erp/ h ⋅depth But c is limited by maxvel, so if (c > maxvel) c = maxvel Since cfm is associated with the constraint DOF, a specific cfm can be entered here. There are 3 possible cfm, which are set up by soft_cfm, slip1, and slip2, respectively. cfm(1) = soft_cfm The impact has a direct effect on c pick the larger value between contact and impact if(c_i > c) c = c_i The lower and upper bounds are lo(1) = 0 hi(1) = infinity The second DOF is the first tangent ...

Equations of Motion

The system equation of motion employed in ODE is which is clearly an explicit time-stepping scheme. However, the constraint equation is expressed implicitly. Eq. (1) and (2) can be combined to be Eq. (3) can be described as a "hybrid" time-stepping scheme. If there are lack of contraints, the equation will be susceptible to instability. Furthermore, cfm is introduced into the LHS of Eq. (3) Eq. (4) is then solved by the LCP subroutine to yield lambda. Finally, update velocities from Eq. (1),

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