impulsebased

Impulsebased is a class of numerical methods used to simulate rigid body dynamics by enforcing constraints through instantaneous impulses applied at contacts and joints. In impulse-based simulation, collisions, contacts, and joint limits are treated as events that impart impulses to bodies, rather than applying continuous forces over a time step. The result is a stable resolution of non-penetration and friction across many bodies in contact.

During a time step, the solver determines a set of impulse magnitudes for all active contacts and joints so that the resulting post-impulse velocities satisfy the constraint conditions. The problem is typically formulated as a linear complementarity problem or a related optimization problem and solved iteratively (for example by sequential or projected impulse methods). Normal impulses prevent interpenetration, while friction impulses are constrained by a Coulomb friction model, often approximated to keep the computation efficient. The impulses update velocities, after which positions are advanced.

Advantages of impulse-based methods include robustness to large time steps, good stability for contact-rich scenes, and suitability for real-time simulation in games and interactive applications. They handle many simultaneous contacts gracefully and integrate well with simple collision detection pipelines.

Limitations include potential numerical damping and energy loss depending on the solver configuration, simplified friction and contact models, and limitations in capturing detailed contact dynamics or soft-body effects. Complex scenes may require substepping, warm starts, or hybrid approaches with other numerical schemes.

History and scope: impulse-based constraint solving has roots in constraint-based rigid-body modeling developed in the late 20th century, with notable contributions from researchers in computer graphics. Today the approach underpins many physics engines and simulation toolchains used in animation, robotics, and interactive media.