Get the trajectory of the rocket-CodePudding

I need to mathematically (or otherwise) get the 3D trajectory of the rocket. I have several variables: starting position, landing position, maximum altitude, flight angle. Here is a demo:

demonstration

And yes, I don't use any popular game engine, I use the Lua language, on the MTA engine (MultiTheftAuto GTA SA). I want to get this trajectory mathematically. I need a set of points. Or if you are familiar with this engine, explain to me how to implement such a flight in the MTA. But you can also show me how this problem can be solved mathematically, or in any other languages and even using the built-in functions of these engines, I will convert the code for Lua and find the implementation of your engine functions on the Internet. Thank you!

EDIT

And yes, I need to change exactly the Y coordinate (height) I have X and Z. I have a loop that every meter of the current trajectory goes through, in this cycle I have a variable X and Z , and I need to get Y based on these variables .

CodePudding user response：

// float x = 0.0 - 1.0

y = sin(x * pi) ^ 0.6