Is there a way to convert that data:
into the 2D point on the screen (X, Y)?
I'm looking for proper math calculations according to this exact set of data.
It's difficult, but it's possible to do it for yourself.
There are lots of libraries that do this for you, but it is more satisfying if you do it yourself:
This problem is possible and I have written my own 3D engine to do this for objects in javascript using the HTML5 Canvas. You can see my code here and solve a 3D maze game I wrote here to try and understand what I will talk about below...
The basic idea is to work in steps. To start, you have to forget about camera angle (yaw, pitch and roll) as these come later and just imagine you are looking down the y axis. Then the basic idea is to calculate, using trig, the pitch angle and yaw to your object coordinate. By this I mean imagining that you are looking through a letterbox, the yaw angle would be the angle in degrees left and right to your coordinate (so both positive and negative) from the center/ mid line and the yaw up and down from it. Taking these angles, you can map them to the x and y 2D coordinate system.
The calculations for the angles are:
pitch = atan((coord.x - cam.x) / (coord.y - cam.y))
yaw = atan((coord.z - cam.z) / (coord.y - cam.y))
with coord.x, coord.y and coord.z being the coordinates of the object and the same for the cam (cam.x, cam.y and cam.z). These calculations also assume that you are using a Cartesian coordinate system with the different axis being: z up, y forward and x right.
From here, the next step is to map this angle in the 3D world to a coordinate which you can use in a 2D graphical representation.
To map these angles into your screen, you need to scale them up as distances from the mid line. This means multiplying them by your screen width / fov. Finally, these distances will now be positive or negative (as it is an angle from the mid line) so to actually draw it on a canvas, you need to add it to half of the screen width.
So this would mean your canvas coordinate would be:
x = width / 2 + (pitch * (width / fov)
y = height / 2 + (yaw * (height / fov)
where width and height are the dimensions of you screen, fov is the camera's fov and yaw and pitch are the respective angles of the object from the camera.
You have now achieved the first big step which is mapping a 3D coordinate down to 2D. If you have managed to get this all working, I would suggest trying multiple points and connecting them to form shapes. Also try moving your cameras position to see how the perspective changes as you will soon see how realistic it already looks.
In addition, if this worked fine for you, you can move on to having the camera be able to not only change its position in the 3D world but also change its perspective as in yaw, pitch and roll angles. I will not go into this entirely now, but the basic idea is to use 3D world transformation matrices. You can read up about them here but they do get quite complicated, however I can give you the calculations if you get this far.