My way to do 3D, at least in nCraft, can be sumed up by this :


The camera doesn't move, the vertices can be translated or rotated.

Let's see how we calculate the coordinates of the projection of a vertex on the screen.
The ? represents the horizontal coordinate of the vertex on the screen (from the center). It is calculated with (10/x)*y, with Thales theorem.
The vertical coordinate of the vertex projection is calculated with (10/x)*z.

You calculate this with all the vertices defining your cube, and then, you draw rectangular faces with the coordinates you got. (to draw rectangles, use two triangles)


The result should look like what's on your mind...

No, not necessarily.

Actually, they can be as far as you want, if they are in the field of view cone. (The only restriction is that the x-coordinate can't be negative)
That's why if you want to keep a good speed, you should check if vertices are not too far before drawing them.

Here is the function that I use in nCraft :
-vertices* is an 1D array with 3D coordinates of used vertices. (example : {5,0,0,  5,1,0,  5,1,1  5,0,1})
-pos* is an 1D array when I will store the 2D coordinates of projections (example : {50,50  100,50   50,100  100,100})
-size is the number of vertices

void computeVertices(float *vertices,int *pos,int size)
{
  int i=0;
  float temp=0.0;
  for(i=0;i<size;i++)
  {
    if(vertices[i*3+1]>0)
    {
      temp=OFFSET*vertices[i*3]/vertices[i*3+1]*50.0+160.0;  //offset is an arbitrary value. I use 10.
      pos[i*2]=(int)temp; //screen coordinates have to be integers
      temp=-OFFSET*vertices[i*3+2]/vertices[i*3+1]*50.0+120.0;
      pos[i*2+1]=(int)temp;
    }
    else
    {
      //if vertices are behind the camera, I store arbitrary values to remember not to draw them
      pos[i*2]=-10000;
      pos[i*2+1]=-10000;
    }
  }
}


I made a simple clipped triangle routine. I can share it, if you're interested.
Yeah i*3 is a small but good optimization.