How to formulate the equation of the projectile flight curve by points in three-dimensional space?

Question

Programming

There is the value of the projectile flight coordinates in three-dimensional space, calculated with an error, approximately, up to 1-3 cm with a total trajectory length of 4-6 m and a speed of less than 100 km / h. The error in time is insignificant.
I need to get the flight equation of this projectile and interpolate its trajectory and speed when crossing with a target whose coordinates are known, it can be represented as a plane by getting the coordinate and speed. at the moment of impact.
What is the name of such a trajectory? How many points are needed to achieve an acceptable approximation and how to calculate the resulting error.?

Answer 1

www.gamedev.ru/code/forum/?id=131915

Answer 2

Getting two points you must draw a plane in which these points lie. Two points will give a segment, and many planes pass through the segment, but only one of them will be perpendicular to the conditional plane of the earth (conditional, because the Earth is not flat :)). Get the equation for this plane.
That's it, now you have a task in the plane. It already has your parabola.
Well, the transition from three-dimensional coordinates to new two-dimensional ones and back through the equation of the plane.
Don't forget the Coriolis acceleration if you want to solve the problem exactly. Well, to describe the force of friction - here I'm afraid I'm not a hint to you, everything is much more complicated than ordinary mechanics.