Rigid body game physics 3

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The following article is based on Hubert Eichner’s article on inequality constraints.

Inequality Constraints for Resting Contacts

Contact points (resting contacts) are represented as inequality constraints. In contrast to a joint, a resting contact can only create repellent forces and no attracting forces. Similar to a joint constraint, the resting contact is represented using a function C(y(t)). Here C is one-dimensional and it is basically the distance of the two objects at the contact point. The inequality constraint of the resting contact is latex formula with the matrix J having one row and twelve columns. Instead of anchor points, one uses vectors ri and rj from the center of each object to the contact point. Using the contact normal n the inequality constraint becomes: latex formula The rotational component can be simplified as shown below: latex formula Thus the linear components of J are latex formula And the angular components of J are latex formula The correction term depends on the distance d. I.e. if the distance is negative, a correction is required so that the objects do not penetrate each other any more. latex formula

Sequential Impulses (updated)

The impulses generated by contact constraints and joint constraints are accumulated in a loop. The (cumulative) λ obtained for contact constraint furthermore is clipped to be greater or equal to zero. Note that it has to be the cumulative value which is clipped. The algorithm for solving the joint and contact constraints becomes:

The sequential impulse iterations have to be performed four times when using the Runge-Kutta method. The value λ is stored as Pn for limiting friction impulses lateron.