Attached is a polynomial-time algorithm that can identify, and then track objects in three-space over time given 3-D point information from a sensor, or other input.

Because the algorithm tracks at the point level, rather than at the object level (i.e., it builds its own objects from point data), it can be used to track objects that have irregular, and even diffuse shapes, like smoke, or steam.

Running on a $200 dollar laptop, it can track 15 Newtonian projectiles at a rate of about 3 frames per second, with an accuracy of about 98% to 100%.

Here’s a plot of one of the sets of projectiles I applied it to:

All of the other functions you need can be found in my full library here.

Projectile_CMNDLINE