When the physics solver has efficiently caught the objects in the intervening time of contact, the purpose m is on the floor, as desired.
When the physics solver has not caught the objects in the intervening time of contact, the state of affairs shouldn’t be bodily reasonable: one object is partly embedded inside the opposite object, in a means 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 result extra reasonable. In reality, it may make it much less reasonable, 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 may think about the purpose $m$ is on the quickly deformed floor of the objects, as a substitute. 😉
When the physics simulation is working nicely, almost all interactions shall be extra like the primary case: objects solely simply barely touching. So it is sensible to optimize for this ordinary case. If objects are routinely getting so deeply embedded that the centre of the overlapping area is a nasty approximation for the floor, then we have to repair that drawback at its supply: lowering 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 sort 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 vitality/momentum than the opposite is shedding, 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 related collisions: a small change within the objects’ positions and orientations tends to provide solely a small change in $m$whereas the most-penetrated level may change in a sudden, discontinuous means after we’re working with shapes extra advanced than spheres — resulting in noticeably inconsistent behaviour.
So sure, it is an compromise approximation, but it surely’s a fairly well-motivated one for recreation physics sims, the place we care about consistency, stability, and velocity greater than good simulation constancy.
