Stacking Circles and Boxes

Here we see a random assortment of circles and rectangles placed in a uniform rectangular grid. Each wall is an additional immoveable rectangle. Detected collisions are illustrated using a combination of small blue lines pointing along the collision normal, as well as red circles whose radii are proportional to the collision depths.

Visualizing collisions and their properties like this was extremely helpful during debugging, and I strongly recommend doing so to anyone writing their own simulator.

Note that when two rectangles collide along an entire edge, there are a total of two collisions detected at both ends of the colliding region. This design choice, allowing multiple collisions between pairs of bodies, leads to greatly improved stability when using the Sequential Impulses Method. Otherwise, one needs to find a single point along the colliding edges at which to place a correcting impulse, and all my best attempts to do this resulted in unstable oscillations. With multiple collision points, it becomes far more natural to support edge-edge collisions while remaining stable.

The obstacles here eventually fall, not because of instabilities or inaccuracies in the simulation, but because of random initial offsets that were deliberately added during positioning. Without these offsets, the obstacles come to a rest without falling.