Add example code for rendering a 3D shape using a Z-buffer

donut.lua

@@ -0,0 +1,93 @@
+#!/usr/bin/env lua5.1
+-- -*- coding: utf-8 -*-
+
+-- 3D “donut” shape rendering using floating-point math
+-- see <https://www.a1k0n.net/2011/07/20/donut-math.html>
+
+-- cargo-culted by erle 2023-09-18
+
+local theta_spacing = 0.1  -- 0.07
+local phi_spacing = 0.002  -- 0.02
+
+local R1 = 1
+local R2 = 2
+local K2 = 5
+
+local screen_height = 256
+local screen_width = 256
+
+local K1 = screen_width * K2 * 3 / ( 8 * ( R1 + R2 ) )
+
+local output = {}
+local zbuffer = {}
+
+local grey = { 120, 120, 120 }
+local gray = { 136, 136, 136 }
+
+for y = 1,screen_height,1 do
+   output[y] = {}
+   zbuffer[y] = {}
+   for x = 1,screen_width,1 do
+      local hori = math.floor( ( (y - 1) / 32 ) % 2 )
+      local vert = math.floor( ( (x - 1) / 32 ) % 2 )
+      output[y][x] = hori ~= vert and grey or gray
+      zbuffer[y][x] = 0
+   end
+end
+
+function render_frame(A, B)
+   -- precompute sines and cosines of A and B
+   local cosA = math.cos(A)
+   local sinA = math.sin(A)
+   local cosB = math.cos(B)
+   local sinB = math.sin(B)
+
+   -- theta goas around the cross-sectional circle of a torus
+   for theta=0, 2*math.pi, theta_spacing do
+      -- precompute sines and cosines of theta
+      local costheta = math.cos(theta)
+      local sintheta = math.sin(theta)
+
+      -- phi goes around the center of revolution of a torus
+      for phi=0, 2*math.pi, phi_spacing do
+        -- precompute sines and cosines of phi
+         local cosphi = math.cos(phi)
+         local sinphi = math.sin(phi)
+
+         -- 2D (x, y) coordinates of the circle, before revolving
+         local circlex = R2 + R1*costheta
+         local circley = R1*sintheta
+
+         -- 3D (x, y, z) coordinates after rotation
+         local x = circlex*(cosB*cosphi + sinA*sinB*sinphi) - circley*cosA*sinB
+         local y = circlex*(sinB*cosphi - sinA*cosB*sinphi) + circley*cosA*cosB
+         local z = K2 + cosA*circlex*sinphi + circley*sinA
+
+         local ooz = 1/z
+
+         -- x and y projection
+         local xp = math.floor(screen_width/2 + K1*ooz*x)
+         local yp = math.floor(screen_height/2 + K1*ooz*y)
+
+         -- calculate luminance
+         local L = cosphi*costheta*sinB - cosA*costheta*sinphi - sinA*sintheta + cosB*( cosA*sintheta - costheta*sinA*sinphi )
+         -- if (L > 0) then
+         if (true) then
+            if (ooz > zbuffer[yp][xp]) then
+                   zbuffer[yp][xp] = ooz
+                   local luminance = math.max( math.ceil( L * 180 ), 0 )
+                   -- luminance is now in the range 0 to 255
+                   r = math.ceil( (luminance + xp) / 2 )
+                   g = math.ceil( (luminance + yp) / 2 )
+                   b = math.ceil( (luminance + xp + yp) / 3 )
+                   output[yp][xp] = { r, g, b }
+            end
+         end
+      end
+   end
+end
+
+dofile('init.lua')
+
+render_frame(-0.7, 0.7)
+tga_encoder.image(output):save("donut.tga")