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

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Nils Dagsson Moskopp 2023-09-18 15:20:21 +02:00
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commit 3029147ed7
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#!/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")