106 lines
3.1 KiB
Lua
106 lines
3.1 KiB
Lua
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#!/usr/bin/env lua5.1
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-- -*- coding: utf-8 -*-
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-- 3D “donut” shape rendering using floating-point math
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-- see <https://www.a1k0n.net/2011/07/20/donut-math.html>
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-- cargo-culted by erle 2023-09-18
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local theta_spacing = 0.01 -- 0.07
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local phi_spacing = 0.002 -- 0.02
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local R1 = 1
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local R2 = 2
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local K2 = 5
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local screen_height = 256
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local screen_width = 256
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local K1 = screen_width * K2 * 3 / ( 8 * ( R1 + R2 ) )
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local output = {}
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local zbuffer = {}
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local grey = { 120, 120, 120 }
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local gray = { 136, 136, 136 }
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for y = 1,screen_height,1 do
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output[y] = {}
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zbuffer[y] = {}
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for x = 1,screen_width,1 do
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local hori = math.floor( ( (y - 1) / 32 ) % 2 )
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local vert = math.floor( ( (x - 1) / 32 ) % 2 )
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output[y][x] = hori ~= vert and grey or gray
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zbuffer[y][x] = 0
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end
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end
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function render_frame(A, B)
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-- precompute sines and cosines of A and B
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local cosA = math.cos(A)
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local sinA = math.sin(A)
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local cosB = math.cos(B)
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local sinB = math.sin(B)
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-- theta goas around the cross-sectional circle of a torus
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local theta = 0
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while theta <= 2*math.pi do
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if ( theta < 2*math.pi * 1/8 ) or ( theta > 2*math.pi * 7/8 ) then
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theta = theta + (theta_spacing * 16)
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else
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theta = theta + theta_spacing
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end
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-- precompute sines and cosines of theta
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local costheta = math.cos(theta)
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local sintheta = math.sin(theta)
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-- phi goes around the center of revolution of a torus
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local phi = 0
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while phi <= 2*math.pi do
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if ( phi > 2*math.pi * 3/8 ) and ( phi < 2*math.pi * 5/8 ) then
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phi = phi + (phi_spacing * 128)
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else
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phi = phi + phi_spacing
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end
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-- precompute sines and cosines of phi
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local cosphi = math.cos(phi)
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local sinphi = math.sin(phi)
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-- 2D (x, y) coordinates of the circle, before revolving
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local circlex = R2 + R1*costheta
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local circley = R1*sintheta
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-- 3D (x, y, z) coordinates after rotation
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local x = circlex*(cosB*cosphi + sinA*sinB*sinphi) - circley*cosA*sinB
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local y = circlex*(sinB*cosphi - sinA*cosB*sinphi) + circley*cosA*cosB
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local z = K2 + cosA*circlex*sinphi + circley*sinA
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local ooz = 1/z
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-- x and y projection
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local xp = math.floor(screen_width/2 + K1*ooz*x)
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local yp = math.floor(screen_height/2 + K1*ooz*y)
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-- calculate luminance
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local L = cosphi*costheta*sinB - cosA*costheta*sinphi - sinA*sintheta + cosB*( cosA*sintheta - costheta*sinA*sinphi )
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-- if (L > 0) then
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if (true) then
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if (ooz > zbuffer[yp][xp]) then
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zbuffer[yp][xp] = ooz
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local luminance = math.max( math.ceil( L * 180 ), 0 )
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-- luminance is now in the range 0 to 255
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r = math.ceil( (luminance + xp) / 2 )
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g = math.ceil( (luminance + yp) / 2 )
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b = math.ceil( (luminance + xp + yp) / 3 )
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output[yp][xp] = { r, g, b }
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end
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end
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end
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end
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end
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dofile('init.lua')
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render_frame(-0.7, 0.7)
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tga_encoder.image(output):save("donut.tga")
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