sidenote

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.)

Enderman Enderman

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.)

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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 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!

Megosztás, like stb.
1 komment
  1. 2014. augusztus 3. 18:17

    […] a follow-up for my last post hereby I present a Creeper (right) in […]

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