mandelbulb.lua

   1 require "Vector"
   2 local V = Vector
   3
   4 require "Primitives"
   5 local P = Primitives
   6
   7 require "Operations"
   8 local O = Operations
   9
  10 require "Textures"
  11 local T = Textures
  12
  13 require "Render"
  14
  15 local function make_mandelbulb(max_iter, power, texture)
  16    return function(p)
  17       local z = V.new(p)
  18       local dr = 1.0
  19       local r = 0.0
  20
  21       for i=1,max_iter do
  22          r = V.norm(z)
  23          if r>2.0 then
  24             break
  25          end
  26
  27          -- convert to polar coordinates
  28          theta = math.acos(z[3]/r)
  29          phi = math.atan(z[2],z[1])
  30          dr =  math.pow(r, power-1.0)*power*dr + 1.0
  31
  32          -- scale and rotate the point
  33          zr = math.pow(r ,power)
  34          theta = theta*power
  35          phi = phi*power
  36
  37          -- convert back to cartesian coordinates
  38          z = V.new{math.sin(theta)*math.cos(phi),
  39                    math.sin(phi)*math.sin(theta),
  40                    math.cos(theta)} * zr
  41          z = z + p
  42       end
  43
  44       return {dist = 0.5*math.log(r)*r/dr,
  45               texture = texture}
  46    end
  47 end
  48
  49 local scene = {
  50    -- sdf = make_mandelbulb(T.make_count_texture(0.1)),
  51    sdf = make_mandelbulb(100, 8,
  52                          T.make_phong_texture(
  53                             {V.new{3,-5,3}},
  54                             T.make_solid_pigment{0,0.5,1.0},
  55                             0.1, 1.0, 0.0, 30)),
  56
  57    camera = {location = V.new{0,-5,0},
  58              point_at = V.origin,
  59              right = V.x,
  60              fov = 1}}
  61
  62 Render.eps = 0.001
  63 Render.bg_col = {0,0,0}
  64 Render.render(scene, 640, 480, "out/mandelbulb.ppm")