Slowly working my way towards perspective correct 3D dots - references https://lodev.org/cgtutor/raycasting3.html

dotzzz.p8

function init_palette()
 --pal()

 pal(2,141,1)
 pal(7,135,1)
 pal(8,137,1)
 pal(10,140,1)
 pal(11,138,1)
 pal(12,134,1)
 pal(14,131,1)
 pal(15,133,1)
 
 poke(0x5f2e,1)
end

function _init()
 init_palette()

	a=0.25
 
 pt={}
 -- starting dir
 --   -1    0   1
 -- -1 * o      * g 
 -- 0       /\
 -- 1  * r      * b
-- add(pt,point(-1,0,1,8))--red
-- add(pt,point(1,0,-1,3))--green
-- add(pt,point(1,0,1,10))--blue
 add(pt,point(-1,0,-1,9))--orange
 --[[for x=-1,1,1/3 do
  for y=-1,1,1/3 do
   for z=-1,1,1/3 do
    add(pt,point(x,y,z))
   end
  end
 end--]]
 cam={}
 cam.x,cam.z,
 cam.drx,cam.drz,
 cam.cx,cam.cz=
  0,0,
  0,-1,
  0,1
  
 mode=0
end

function point(x,y,z,c)
 local p={}
 p.x,p.y,p.z=x,y,z
 p.col=c or 8+(x*3+y*2)%8
 return p 
end

function _update()
 local da=0
 if(btn(0))da+=0.009
 if(btn(1))da-=0.009
 
 a+=da
 
 local old_camcx,old_plane_x=
  0,cam.cx
  
 cam.drx,cam.drz=
  cos(a),sin(a)

 cam.cx,cam.cz=
  old_plane_x*cos(da)
  +cam.cz*sin(da),
  old_plane_x*sin(da)
  +cam.cz*cos(da)
 
 printh(cam.drx..","..cam.drz.." "..cam.cx..","..cam.cz)
 
 if btn(2) then
  cam.z+=cam.drz/8
  cam.x+=cam.drx/8
 end
 if btn(3) then
  cam.z-=cam.drz/8
  cam.x-=cam.drx/8
 end
 if btnp(4) then
  mode=(mode+1)%4
 end
 
 if(a>1)a-=1
 if(a<0)a+=1
end

modes={
 [0]="2d, no rotation",
 "2d with rotation",
 "3d projected",
 "perspective correct"
}

function _draw()
 cls(0)
 
 --a=0.3622
 if mode==0 then
  draw_2d_no_rot()
 elseif mode==1 then
  draw_2d()
 else
  draw_3d()
 end
 
 print("x= cos("..a..
  ")="..cos(a),0,0,7)
 print("y= sin("..a..")="..-sin(a),0,6,7)
 print("mode: "..modes[mode],0,122)
end

function draw_2d_no_rot()
 local lxe,lye=
  64+cos(a)*8,
  64+sin(a)*8
 line(64,64,lxe,lye,13)
 
 local nxe,nye=
  64-sin(a)*8,
  64+cos(a)*8
  
 line(64,64,nxe,nye,9)
 pset(64,64,7)
 
 for p in all(pt) do
  pset(
   64+(p.x+cam.x)*8,
   64+(p.z+cam.z)*8,p.col)
 end
end

function draw_2d()
 line(64,64,64,56,13)
 line(64,64,72,64,9)
 pset(64,64,7)
 local yaw=a
 
 for p in all(pt) do
 
  local wx=(p.x-cam.x)*8
  local wz=(p.z-cam.z)*8

  local tr_x,tr_z=
   rot(wx,wz,a)

  pset(64-tr_x,64-tr_z,p.col)
 end
end

function draw_3d()
 project(pt)
end

function rot(x,y,a)
 local xd=x
  x=sin(a)*xd-cos(a)*y
  y=cos(a)*xd+sin(a)*y
 
 return x,y
end

function project(pt)
 -->cam space

 for p in all(pt) do
  p.cx,p.cz=rot(
   p.x-cam.x,
   p.z-cam.z,a)
--  p.cy,p.cz=rot(p.y,p.cz,t()/7)
  p.cy=p.y
  
--  p.cz+=2 +cos(t()/6)
 end
 
 -- sort
 for pass=1,3 do
	 for i=1,#pt-1 do
	  if pt[i].cz<pt[i+1].cz then
	   pt[i],pt[i+1]=
	   pt[i+1],pt[i]
	  end
	 end
	 for i=#pt-1,1,-1 do
	  if pt[i].cz<pt[i+1].cz then
	   pt[i],pt[i+1]=
	   pt[i+1],pt[i]
	  end
	 end
 end
 --]]
 -->screen space
 for p in all(pt) do
  -- screen coordinates 
  -- derived only from
  -- the cam coordinates
  -- cz means "further 
  -- from the camera"
  -- goes 3d -> 2d
  
  if mode==2 then
   sx=64-p.cx*64/p.cz
   sy=64+p.cy*64/p.cz
  
   rad=8/p.cz
  else
   local invdet=1/
    (cam.cx*cam.drz-
     cam.drx*cam.cz)
   
   local trx=invdet*(
    cam.drz*p.x-cam.drx*p.y
   )
   local try=invdet*(
    -cam.cz*p.x+cam.cx*p.y
   )
   sx=64*(1+trx/try)
   
 --  local sx_pcnt=
 --   (sx-64)/128 
   rad=abs(8/try)
   --rad=6
   local s_height=abs(128/try)
   
   sy=-s_height/2+64
   printh(try)
  end
  if p.cz>0.1 then

   circfill(sx,sy,rad,p.col)
   circfill(sx+rad/3,sy-rad/3,
    rad/3,7)
  end
 end
 print(stat(1))
end