How do i draw Lines in a 3D Coordinate system - c

Question

i want to draw lines in a 3D Coordinate System but in 2D in C. I know that i have to do an interpolation
Or can i just draw Vectors?
I read online some facts about interpolation but it didnt work because i have some Coordinates lower than zero. (https://math.stackexchange.com/questions/2305792/3d-projection-on-a-2d-plane-weak-maths-ressources)
Thats why i get so tiny lines.
Here are some of the coordinates of an data i want to draw lines with.
i already read the date and saved the points in an Array (coor).
from x: -10.0
from y: -10.0
from z: -10.0
to x : 200.0
to y: -5.0
to z: 20.0
[#include <windows.h>
#include <windowsx.h>
#include <commctrl.h>
#include <string.h>
#include <stdio.h>
#include <conio.h>
#include "project3res.h"][1]
double coor [4][6];
///////////// KOORDINATENSYSTEM ZEICHNEN//////////////////////
BOOL zeichnen (HWND hwnd)
//double x0=650,y0=350;
//double d= 100; //Hilfsvariable zum Interpolieren von 2D zu 3D
//Vorbereitung
{
double x0=650,y0=350; //KOORDINATENSYSTEM URSPRUNG
double d= 2; //Hilfsvariable für Umwandlung von 3D in 2D
HDC hdc;
PAINTSTRUCT ps;
InvalidateRect (hwnd, NULL, TRUE);
hdc = BeginPaint (hwnd, &ps);
//Zeichenbefehle
//KOORDINATENSYSTEM//
SetViewportOrgEx(hdc,x0,y0,NULL);
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, 100, 0); //X-ACHSE
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, -100, 0);
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, 0, 100); //Y-ACHSE
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, 0, -100);
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, 100, -100); //Z-ACHSE
MoveToEx (hdc, 0, 0, NULL);
LineTo (hdc, -100, 100);
MoveToEx (hdc,coor[0][0]*(d/coor[0][2]), coor[0][1]*(d/coor[0][2]), NULL);
LineTo (hdc, coor[0][3]*(d/coor[0][5]), coor[0][4]*(d/coor[0][5]));
EndPaint (hwnd, &ps);
UpdateWindow(hwnd);
return 0;
}

Answer 1

Recap:
x' = x * d / z;
y' = y * d / z;
Based on your linked post, the positive z-axis points away from you and the center of the projection plane is at (0, 0, d).
Now, if any z-coordinate is less than d (between eye and the plane), as described, clipping will occur.
There are two possibilities to adjust your render output:
move the camera away from the scene
d remains unchanged
add a (positive) distance factor to every z-coordinate (move the objects in the scene along the positive z-axis)
advantage: every point gets projected
disadvantage: scene gets smaller, the more you move away
change the field of view
alter the d value
decrease: wide lens effect
increase: narrow lens, zoom in effect, more clipping will occur
The best approach would be, to find the bounding box of your scene (lines) and fit that box into the frustum of the view (trigonometry required).
The frustum is the cutoff part of the pyramid (the one from your eye to the zfar plane). You need the znear plane (which is d) and the zfar plane, which could be the depth (farthest z-coordinate) of your bounding box.
More Info:
Viewing frustum
The Size of the Frustum at a Given Distance from the Camera
Perspective projection
Camera matrix