Drawing an Enderman in LaTeX / sidenote

Drawing an Enderman in LaTeX

Írta: szantaii

2014. július 20. 9:53

alkotunk, játék, szoftver

In the last couple of months I’ve watched some videos of Achievement Hunter’s Let’s Play Minecraft videos where were some encounters with Endermen. I was really fascinated by these creatures since they can teleport, demand respect, mysterious, etc.

I have been “playing” with LaTeX, especially with LuaTeX, recently, and I wanted to make a 3D-like picture. So I have chosen tikz‑3dplot and LuaTeX to draw an Enderman. (I think this is totally drawable with pure TikZ (syntax), therefore compilable with pdflatex, etc., but I found making this using LuaTeX much more simple.)

Image source (left): File:Enderman normal.png – Minecraft Wiki

My drawing (right) is not accurate by many aspects, but I’ve achieved what I wanted.

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% Enderman
% Author: István Szántai (szantaii)
\documentclass{article}

\usepackage{luacode}

\usepackage{xcolor}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\usepackage[active, tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength{\PreviewBorder}{1cm}

\definecolor{endermanblack}{HTML}{000000}
\definecolor{endermangray}{HTML}{161616}
%\definecolor{endermanpurple}{HTML}{CC00FA}
%\definecolor{endermanlightpurple}{HTML}{E079FA}
\definecolor{endermanpurple}{HTML}{FF9EFF}
\definecolor{endermanlightpurple}{HTML}{FFC9FF}
\definecolor{particlecolor}{HTML}{DF4AF8}

\begin{luacode*}
function draw_coordinate_system()
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(3,0,0) node[text=white!50!gray,anchor=north east]{$x$};")
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(0,3,0) node[text=white!50!gray,anchor=west]{$y$};")
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(0,0,3) node[text=white!50!gray,anchor=south]{$z$};")
end

function tikzcube(x, y, z, color)
--[[
\draw[fill=red] (0.5, 0.5, -0.5) -- (-0.5, 0.5, -0.5) -- (-0.5, -0.5, -0.5) -- (0.5, -0.5, -0.5) -- cycle;
\draw[fill=red] (-0.5, 0.5, -0.5) -- (-0.5, 0.5, 0.5) -- (-0.5, -0.5, 0.5) -- (-0.5, -0.5, -0.5) -- cycle;
\draw[fill=red] (-0.5, -0.5, -0.5) -- (0.5, -0.5, -0.5) -- (0.5, -0.5, 0.5) -- (-0.5, -0.5, 0.5) -- cycle;
\draw[fill=red] (0.5, 0.5, -0.5) -- (-0.5, 0.5, -0.5) -- (-0.5, 0.5, 0.5) -- (0.5, 0.5, 0.5) -- cycle;
\draw[fill=red] (0.5, -0.5, -0.5) -- (0.5, 0.5, -0.5) -- (0.5, 0.5, 0.5) -- (0.5, -0.5, 0.5) -- cycle;
\draw[fill=red] (0.5, 0.5, 0.5) -- (-0.5, 0.5, 0.5) -- (-0.5, -0.5, 0.5) -- (0.5, -0.5, 0.5) -- cycle;
]]
local cube = ""

cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- cycle;"
cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- cycle;"
cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- cycle;"
cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- cycle;"
cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", -0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- cycle;"
cube = cube .. "\\draw[ultra thin, fill=" .. color .. "]" ..
"(0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", 0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(-0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- " ..
"(0.5 + " .. x .. ", -0.5 + " .. y .. ", 0.5 + " .. z .. ") -- cycle;"

tex.sprint(cube)
end

function draw_head(x_pos, y_pos, z_pos)
local color
for x = x_pos, x_pos + 7, 1 do
for y = y_pos, y_pos + 7, 1 do
for z = z_pos, z_pos + 6, 1 do
if (x == x_pos or x == x_pos + 7 or
y == y_pos or y == y_pos + 7 or
z == z_pos or z == z_pos + 6) and
not (x == x_pos + 7 and y > y_pos and y < y_pos + 7 and z == z_pos) then

if x == x_pos + 7 and
(y == y_pos or y == y_pos + 2 or
y == y_pos + 5 or y == y_pos + 7) and
z == z_pos + 2 then

tikzcube(x, y, z, "endermanlightpurple")
elseif x == x_pos + 7 and
(y == y_pos + 1 or y == y_pos + 6) and
z == z_pos + 2 then

tikzcube(x, y, z, "endermanpurple")
else
if math.random(0, 8) < 6 then
color = "endermangray"
else
color = "endermanblack"
end
tikzcube(x, y, z, color)
end
end
end
end
end
end

function draw_bodypart(x_pos, y_pos, z_pos, x_length, y_length, z_length)
local color
for x = x_pos, x_pos + x_length - 1, 1 do
for y = y_pos, y_pos + y_length - 1, 1 do
for z = z_pos, z_pos + z_length - 1, 1 do
if x == x_pos or x == x_pos + x_length - 1 or
y == y_pos or y == y_pos + y_length - 1 or
z == z_pos or z == z_pos + z_length - 1 then

if math.random(0, 8) < 6 then
color = "endermangray"
else
color = "endermanblack"
end
tikzcube(x, y, z, color)
end
end
end
end
end

function draw_particles(x_min, x_max, y_min, y_max, z_min, z_max)
local x
local y
local z
local black_amount
local particle_size
local particle_scale
local particle_count = math.random(30, 40)
local particle

for i = 1, particle_count, 1 do

x = math.random(x_min, x_max)
y = math.random(y_min, y_max)
z = math.random(z_min, z_max)

particle_size = math.random(1, 8)
particle_scale = math.random(20, 100) / 100
black_amount = math.random(0, 25)

tex.sprint("\\tdplottransformmainscreen{" .. x .. "}{" .. y .. "}{" .. z .. "}")
for i = 0, particle_size - 1, 1 do
for j = 0, particle_size - 1, 1 do
if math.random(0, 1) == 0 and
((i ~= 0 and j ~= 0) and
(i ~= particle_size - 1 and j ~= 0) and
(j ~= particle_size - 1 and i ~= 0) and
(i ~= particle_size - 1 and j ~= particle_size - 1)) then

particle = "\\filldraw[black!" .. black_amount ..
"!particlecolor, tdplot_screen_coords] (" ..
i * particle_scale * 0.25 .. "+\\tdplotresx, " ..
j * particle_scale * 0.25 .. "+\\tdplotresy) " ..
"rectangle +(" .. particle_scale .. "*0.25, " ..
particle_scale .. "*0.25);"

tex.sprint(particle)
end
end
end
end
end

function draw_enderman(x_rotation, z_rotation)
tex.sprint("\\tdplotsetmaincoords{" .. x_rotation .. "}{" .. z_rotation .. "}")
tex.sprint("\\begin{tikzpicture}[tdplot_main_coords]")

math.randomseed(os.time())

draw_bodypart(3, -2, -30, 2, 2, 30) -- right arm
draw_bodypart(3, 1, -42, 2, 2, 30) -- right leg
draw_bodypart(3, 5, -42, 2, 2, 30) -- left leg
draw_bodypart(2, 0, -12, 4, 8, 12) -- body
draw_bodypart(3, 8, -30, 2, 2, 30)-- left arm
draw_head(0, 0, 0) -- head

draw_particles(-10, 10, -10, 10, -44, 10)
-- draw_coordinate_system()

tex.sprint("\\end{tikzpicture}")
end
\end{luacode*}

\begin{document}
\luadirect{draw_enderman(70, 130)}
\end{document}

Copy the code, save with UTF-8 (without BOM) encoding, and compile using lualatex.

lualatex filename.tex

Update ~16:00 CEST on 21 July 2014:

Yesterday I’ve sent in this code as an example for TeXample.net. I got an answer from the site maintainer including a small improvement suggestion, namely that I should try algorithmize the drawing of a single (TikZ) cube (instead of concatenating a bunch of strings and make the TeX engine do the calculations). So I did, see the code below. (More details below the code.)

% Enderman
% Author: István Szántai (szantaii)
\documentclass{article}

\usepackage{luacode}

\usepackage{xcolor}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\usepackage[active, tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength{\PreviewBorder}{1cm}

\definecolor{endermanblack}{HTML}{000000}
\definecolor{endermangray}{HTML}{161616}
%\definecolor{endermanpurple}{HTML}{CC00FA}
%\definecolor{endermanlightpurple}{HTML}{E079FA}
\definecolor{endermanpurple}{HTML}{FF9EFF}
\definecolor{endermanlightpurple}{HTML}{FFC9FF}
\definecolor{particlecolor}{HTML}{DF4AF8}

\begin{luacode*}
function draw_coordinate_system()
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(3,0,0) node[text=white!50!gray,anchor=north east]{$x$};")
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(0,3,0) node[text=white!50!gray,anchor=west]{$y$};")
tex.sprint("\\draw[white!50!gray,thick,->] (0,0,0) -- " ..
"(0,0,3) node[text=white!50!gray,anchor=south]{$z$};")
end

function matrix_scalar_multiplication(matrix, scalar)
local rows = #matrix
local cols = #matrix[1]
local tmp_matrix = {}

for i = 1, rows do
tmp_matrix[i] = {}
for j = 1, cols do
tmp_matrix[i][j] = matrix[i][j] * scalar
end
end

return tmp_matrix
end

function shift_coordinates(matrix, array)
local matrix_rows = #matrix
local matrix_cols = #matrix[1]
local array_length = #array
local tmp_matrix = {}

if matrix_cols == array_length then
for i = 1, matrix_rows do
tmp_matrix[i] = {}
for j = 1, matrix_cols do
tmp_matrix[i][j] = matrix[i][j] + array[j]
end
end

return tmp_matrix
else
return nil
end
end

function tikzcube(x, y, z, color)
local side_1 = {{1, 1, -1},
{-1, 1, -1},
{-1, -1, -1},
{1, -1, -1}}
local side_2 = {{-1, 1, -1},
{-1, 1, 1},
{-1, -1, 1},
{-1, -1, -1}}
local side_3 = {{-1, -1, -1},
{1, -1, -1},
{1, -1, 1},
{-1, -1, 1}}
local side_4 = {{1, 1, -1},
{-1, 1, -1},
{-1, 1, 1},
{1, 1, 1}}
local side_5 = {{1, -1, -1},
{1, 1, -1},
{1, 1, 1},
{1, -1, 1}}
local side_6 = {{1, 1, 1},
{-1, 1, 1},
{-1, -1, 1},
{1, -1, 1}}
local cube_sides = {side_1, side_2, side_3, side_4, side_5, side_6}
local tex_cube = ""

for i = 1, #cube_sides do
tex_cube = tex_cube .. "\\draw[ultra thin, fill=" .. color .. "] "

local current_side = matrix_scalar_multiplication(cube_sides[i], 0.5)
current_side = shift_coordinates(current_side, {x, y, z})

local current_side_rows = #current_side
local current_side_cols = #current_side[1]

for j = 1, current_side_rows do
for k = 1, current_side_cols do
if k == 1 then
tex_cube = tex_cube .. "("
end

tex_cube = tex_cube .. current_side[j][k]

if k ~= current_side_cols then
tex_cube = tex_cube .. ", "
else
tex_cube = tex_cube .. ") -- "
end
end
end

tex_cube = tex_cube .. "cycle;"

end

tex.sprint(tex_cube)
end

function draw_head(x_pos, y_pos, z_pos)
local color
for x = x_pos, x_pos + 7, 1 do
for y = y_pos, y_pos + 7, 1 do
for z = z_pos, z_pos + 6, 1 do
if (x == x_pos or x == x_pos + 7 or
y == y_pos or y == y_pos + 7 or
z == z_pos or z == z_pos + 6) and
not (x == x_pos + 7 and y > y_pos and y < y_pos + 7 and z == z_pos) then

if x == x_pos + 7 and
(y == y_pos or y == y_pos + 2 or
y == y_pos + 5 or y == y_pos + 7) and
z == z_pos + 2 then

tikzcube(x, y, z, "endermanlightpurple")
elseif x == x_pos + 7 and
(y == y_pos + 1 or y == y_pos + 6) and
z == z_pos + 2 then

tikzcube(x, y, z, "endermanpurple")
else
if math.random(0, 8) < 6 then
color = "endermangray"
else
color = "endermanblack"
end
tikzcube(x, y, z, color)
end
end
end
end
end
end

function draw_bodypart(x_pos, y_pos, z_pos, x_length, y_length, z_length)
local color
for x = x_pos, x_pos + x_length - 1, 1 do
for y = y_pos, y_pos + y_length - 1, 1 do
for z = z_pos, z_pos + z_length - 1, 1 do
if x == x_pos or x == x_pos + x_length - 1 or
y == y_pos or y == y_pos + y_length - 1 or
z == z_pos or z == z_pos + z_length - 1 then

if math.random(0, 8) < 6 then
color = "endermangray"
else
color = "endermanblack"
end
tikzcube(x, y, z, color)
end
end
end
end
end

function draw_particles(x_min, x_max, y_min, y_max, z_min, z_max)
local x
local y
local z
local black_amount
local particle_size
local particle_scale
local particle_count = math.random(30, 40)
local particle

for i = 1, particle_count, 1 do

x = math.random(x_min, x_max)
y = math.random(y_min, y_max)
z = math.random(z_min, z_max)

particle_size = math.random(1, 8)
particle_scale = math.random(20, 100) / 100
black_amount = math.random(0, 25)

tex.sprint("\\tdplottransformmainscreen{" .. x .. "}{" .. y .. "}{" .. z .. "}")
for i = 0, particle_size - 1, 1 do
for j = 0, particle_size - 1, 1 do
if math.random(0, 1) == 0 and
((i ~= 0 and j ~= 0) and
(i ~= particle_size - 1 and j ~= 0) and
(j ~= particle_size - 1 and i ~= 0) and
(i ~= particle_size - 1 and j ~= particle_size - 1)) then

particle = "\\filldraw[black!" .. black_amount ..
"!particlecolor, tdplot_screen_coords] (" ..
i * particle_scale * 0.25 .. "+\\tdplotresx, " ..
j * particle_scale * 0.25 .. "+\\tdplotresy) " ..
"rectangle +(" .. particle_scale .. "*0.25, " ..
particle_scale .. "*0.25);"

tex.sprint(particle)
end
end
end
end
end

function draw_enderman(x_rotation, z_rotation)
tex.sprint("\\tdplotsetmaincoords{" .. x_rotation .. "}{" .. z_rotation .. "}")
tex.sprint("\\begin{tikzpicture}[tdplot_main_coords]")

math.randomseed(os.time())

draw_bodypart(3, -2, -30, 2, 2, 30) -- right arm
draw_bodypart(3, 1, -42, 2, 2, 30) -- right leg
draw_bodypart(3, 5, -42, 2, 2, 30) -- left leg
draw_bodypart(2, 0, -12, 4, 8, 12) -- body
draw_bodypart(3, 8, -30, 2, 2, 30)-- left arm
draw_head(0, 0, 0) -- head

draw_particles(-10, 10, -10, 10, -44, 10)
-- draw_coordinate_system()

tex.sprint("\\end{tikzpicture}")
end
\end{luacode*}

\begin{document}
\luadirect{draw_enderman(70, 130)}
\end{document}

I have added two new functions (matrix_scalar_multiplication, shift_coordinates), and rewrote the tikzcube function, so now the LuaTeX engine makes all necessary calculations instead of the TeX (TikZ?) engine which is considerably slower. Let’s see the numbers.

I’ve measured the compilation time of the original and the improved code. I made 20–20 “dry” compilations (no previous aux, log or pdf files). The average compilation time of the original code was 25.35 seconds while the improved code’s average was only 18.30 seconds. This means that the improved version is 25% faster than the previous one. Stefan, thanks for your suggestion!

sidenote

Drawing an Enderman in LaTeX

Update ~16:00 CEST on 21 July 2014:

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