When the physics solver has efficiently caught the objects in the mean time of contact, the purpose $m$ is on the floor, as desired.
When the physics solver has not caught the objects in the mean time of contact, the state of affairs just isn’t bodily real looking: one object is partly embedded inside the opposite object, in a method that can’t occur with precise strong our bodies.
Making use of impulses at most deeply penetrated components of those objects does not essentially make the end result extra real looking. Actually, it might make it much less real looking, as a result of in actual physics, the contact level would by no means have gotten that deep inside the opposite object. In actuality, what we would see as a substitute is that the objects deform, compressing within the area of the collision, so we might think about the purpose $m$ is on the quickly deformed floor of the objects, as a substitute. 😉
When the physics simulation is working effectively, practically all interactions might be extra like the primary case: objects solely simply barely touching. So it is smart to optimize for this typical case. If objects are routinely getting so deeply embedded that the centre of the overlapping area is a foul approximation for the floor, then we have to repair that drawback at its supply: decreasing the simulation time step or utilizing steady collision detection algorithms to catch these collisions earlier than they get so deeply embedded. Simply altering the purpose the place we apply the impulses does not repair the issue.
$m$ additionally has some good properties of its personal that make it handy to make use of — we will consider it as a form of handy “common” over the contact patch. Making use of impulses right here for each objects ensures we’re not introducing errors the place one object is gaining extra power/momentum than the opposite is dropping, as we would inadvertently do if every object makes use of its personal most-penetrated level, breaking the symmetry. This $m$ level additionally stays comparatively well-behaved and steady from one time step to a different, or between comparable collisions: a small change within the objects’ positions and orientations tends to provide solely a small change in $m$, whereas the most-penetrated level might change in a sudden, discontinuous method once we’re working with shapes extra advanced than spheres — resulting in noticeably inconsistent behaviour.
So sure, it is an compromise approximation, nevertheless it’s a fairly well-motivated one for sport physics sims, the place we care about consistency, stability, and pace greater than good simulation constancy.
