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Box stacking in a bowl

September 16, 2006

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Demonstrates collision between convex and concave geometries.

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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

Contact Manifold & Signed Distance Map

A quick review of my work for the past two months: Contact Manifold As I have been struggling with the box-box collision detection, I started to get fascinated by the idea of constructing a contact manifold, which contains a number of selected contact points. My first attempt is to adapt Bullet code from Erwin Coumans, who claims to successfully build correct contact manifolds. Eventually I did not succeed to make the adapted Java code run correctly. Thus I stopped working on the contact manifold idea with frustration. Signed Distance Map Then I bought a book from Christer Ericson with the hope of getting some working box-box collision and/or contact manifold codes. It turned out there was nothing in the book I could use immediately. In the meantime, the idea of signed distance map came to me but I don't understand how it really works. I tried to resolve this problem by adapting PhysicsEngine. So far I have not yet made the adapted Java code work and inevitably the frustration grew

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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