How to find out the coordinates of a two-dimensional projection of a three-dimensional point?

Question

3D

There are 12 lines with which a cube is drawn in two-dimensional space, i.e. each line is indicated by 2 points with coordinates (x;y). You need to rotate this cube along all three axes (x, y, z) using the rotation matrix. I made a rotation along the Z axis (everything works), but for rotations along the X, Y axes, you need to calculate Z. And where to put it next to display new coordinates (x; y), I did not quite understand. Simple equating to 0 doesn't work, or something is wrong with my formula.
Tell me what to do.
PS I have already looked at a lot of information on the Internet and tried different formulas and substitutions, but for some reason it doesn’t work: c
[on the photo is the X-axis rotation code and the rotation matrix used]

and this is what happens during rotation

Answer 1

I think it's because you have line.x=x; line.y=y;. When should be should beline.x=x+dx*z; line.y=y+dy*z;