transform 3D coordinates into 2D coordinates to make a 3D viewer

[half warren]

Hello, i try to make a 3d viewer in lua but for each solution i found, it doesn't work but i don't know if it's cause i'm bad in programming or in math.
to solve this problem i used a lot of manner but today i tried something very different and i know that it's not the best way to solve this problem but i want to know if it might work for you.

here the situation :

a : the cam angle angle whish can change
E : distance with the screen
P : the point whish we know the coordinates
P' : the point perpendicular to the line passing through P
We have also C at the cam's coordinates but we neglect it for the moment

to solve this problem i see the (P'O) line as a linear function and the (PP') line as the reverse of the first function but this one is an affine function.

the first function is determinate by :
f(x) = (sin(a) / cos(a)) × x

and the second one by :
g(x) = -(cos(a) / sin(a)) × x + (cos(a) / sin(a)) × P.z + P.x

then, to find P' z coordinate i used f(x) = g(x)
whish makes :
P'.z = ((cos(a) / sin(a)) × P.z + P.x) ((cos(a) × sin(a)) / sin(a)² + cos(a)²)

i used g(P'.z) to find P'.x :
P'.x = -(cos(a)/sin(a)) (P'.z - P.z) + P.x

then searched [PP'] and [CP'] :
[PP'] = √((P'.z - P.z)² + (P'.x - P.x)²)
[CP'] = √(P'.z+P'.x)

Finally i used thales to find the side PP' of the reduced triangle :
x = CE × PP' / CP'

i know that 0 is a prohibited value for the angle

[pallid hawk]

I've done this using Excel to render 3D images in a 2D chart such as you're doing on paper... I started with some equations I found online... is it not looking correct for you?

Found what I used... dunno if this helps

[half warren]

i want to do without internet i know that we have a lot of solution but when i try mine i see that they don't work and i don't know if it's because i'm not good to write calculation in lua or if it's my calculation whish is bad

[pallid hawk]

*correction: used to plot 3D coordinates (OX, OY, OZ) as a 2D chart (Xr, Xy)

It's a complicated math... hat's off to you to try to solve it from scratch, that's way more involved than I care to assist, sorry!

[half warren]

ok np thank you anyway

[pallid hawk]

Good luck.... found the source video I used too: https://www.youtube.com/watch?v=ou_vAxbTCmo

[half warren]

ok thanks for the help !