sidenote

About a year ago I got a request on GitHub regarding bash-weather, if I intend to make bash-weather print a colored output. I totally forgot about it. But when the other day I was browsing on GitHub I remembered this request, and I have written the “colored output feature”.

bash-weather

bash-weather bash-weather bash-weather

Also, there are some videos about bash-weather and my previous shell scripts (bash-gorillas, bash-life) made by a guy who I think is really into command-line applications (I can understand why).

Check out the description below the videos. ;)

Megosztás, like stb.

I have been working on a project since last (2014) spring. I have been building a mirror inspired by Michael Teeuw’s Magic Mirror and now I have finished it! It is called Mirror π, and it is a “smart mirror”.

Mirror π

What’s this all about? How is it smart? More posts to come (I hope sooner than later), until than you can already browse the source code on GitHub.

Megosztás, like stb.

Múlt héten keresett meg egy kedves barátom, a nap német szava blog szerzője, hogy egy darabig leáll a blog írásával, de szeretné, ha a bejegyzések PDF-ben is elérhetők lennének.

Hát összeálltunk. Ő fogta és lementette az összes posztot. Nagyjából* arra a formára hozta az anyagot, amiben előre megegyeztünk. Én írtam egy parsert LuaTeX-ben. És megszületett a PDF változat.

Ha hibát találtok benne, kérlek jelezzétek!

Az amúgy is zseniális blog bejegyzései mostantól A5-ös méretben, nyomtatásra optimalizáltan** elérhetők:

a nap német szava

* Azért benne hagyott közel kétszáz helytelen idézőjelet, és húsz-harminc rosszul tördelt sort, de sebaj, csak két órát basztam el a kijavításukkal.

** Már ha ki fogsz nyomtatni több, mint hétszáz oldalt. Amúgy képernyőn is jól néz ki.

Megosztás, like stb.

Another font outline animation experiment

In this animation was created using LuaTeX, TikZ, and the glyph “a” from the Linux Libertine font.

The process which this animation resulted in was the following:

  1. Converted the font to SVG to use the path of the glyph.
  2. Split the path into the inner and outer outlines.
  3. Draw the two separate lines with (different) dashed patterns.
  4. Set increasing offset for the dashed patterns for each frame.
  5. Rasterize and create GIF using GIMP.

Sorry, no source code this time.

Megosztás, like stb.

In one of my latest posts I mentioned a question about how to draw individual glyphs with randomized paths on TeX.SX. Today I want to share the answer I posted about two weeks ago, and some related stuff which I’ve made during and after working on the answer.

Let’s see the question first. It is quoting Donald Knuth’s article, Mathematical typography from the Bulletin of the American Mathematical Society.

Knuth: Mathematical typography, Figure 21

Randomization. I’d like to report on a little experiment I did with random numbers. One might complain that the letters I have designed are too perfect, too much like a computer, so they lack “character”. In order to counteract this, we can build a certain amount of randomness into the choices of where to put the pen when drawing each letter, and Figure 21 shows what happens. The coordinates of the key pen positions where chosen independently with a normal distribution and with increasing standard deviation, so that the third example has twice as much standard deviation as the second, the fourth has three times as much, and so on. Note that the two m’s on each line (except the first) are different, and so are the a’s and the t’s, since each letter is drawn randomly.

The question was how to achieve a similar effect in LaTeX without using MetaFont. You can read the answer below, but if you feel tl;dr skip below the long quote for my related works.

I have been thinking about this question for weeks now, and finally I think I came really close to a result you may also like. I have even tried to use Processing to solve this problem, which resulted in a nice animation as a byproduct, but it didn’t lead me closer to the solution. But back to the point…

Unfortunately the solution I’m posting, which is my best and only shot, does not support drawing the distorted glyphs as text but as drawings. Also there is some work to be done outside the context of LaTeX, but most of it is done in LaTeX (LuaTeX + TikZ).

Randomized drawing of individual glyphs

The picture above shows an undistorted glyph (character “a” on the left in the line at the top), a distorted glyph (character “a” on the right in the line at the top), a word consisting of distorted glyphs (middle line), and a special character (Omega), all these can be found in the code at the end of the answer.

Now I will describe the process I have followed to achieve these distortions. I mentioned that there is some work to be done outside of LaTeX, that is to convert a font file into SVG using FontForge. I found the solution how to do this in an answer to the question: Can we extract the points making the character from the font file?

Copy the following into a file named font2svg.pe into your “project” folder.

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#!/usr/bin/env fontforge
Open($1)
Generate($1:t:r + ".svg")

And make a SVG file from the font you want to use (I chose cmr10) with the following command.

fontforge font2svg.pe /usr/local/texlive/2014/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb

Note that the location of the font on the filesystem may vary based on your LaTeX installation and operating system you use, but this will generate an SVG file into your project folder. All is left to process the generated SVG file which contains the data (name, unicode code, width, and outline) of the glyphs, which I will describe below.

The function function read_font_data(file) takes a file name as an argument (the generated SVG file), and extracts the data of the glyphs into an associative array which can be addressed with the unicode code and contains the width and outline data of the specific character. Note that not all glyphs have width or outline data, some basic error checking is done but the code is not foolproof.

The function random_in_interval(lower_boundary, upper_boundary) takes two float arguments, and will return a random float between them. The more the boundaries converge to 1 the smaller the randomization will be. This will be used when the time comes to randomize the outline of a glyph.

The function scale_and_randomize(glyph, scale_factor, lower_boundary, upper_boundary) will take a glyph, a scale factor, a lower and upper boundary, the latter two will be used for the randomization. Scaling is needed because the default measurement unit of TikZ is centimeters (I think) and the outline data of a glyph may contain large values, which TikZ interprets as centimeters. Note that the scale factor may vary depending the font you use, and size you want.

The functions print_glyph(glyph, scale_factor, lower_boundary, upper_boundary) and return_glyph (the latter takes the same arguments) only differ in that print_glyph will pass the TikZ drawing command (using svg.path library) used to print the glyph to LaTeX, while return_glyph only returns the drawing command as a string which can be further used in Lua before passing it to LaTeX.

The remaining functions only use the previously described print_glyph and return_glyph functions to print the picture above.

That’s it. I hope this would fit your needs.

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% Randomized drawing of individual glyphs
% Author: István Szántai (szantaii)
% Original at: http://tex.stackexchange.com/a/197677/8844
\documentclass[10pt, a4paper]{article}

\usepackage[T1]{fontenc}

\usepackage{luacode}

\usepackage{tikz}
\usetikzlibrary{svg.path, positioning}

\pagestyle{empty}

\tikzset{%
    glyph node/.style={%
        inner sep=0pt,%
        outer sep=0pt%
    },%
    glyph outline/.style={%
        line width=0pt%
    }%
}

\begin{luacode*}
    function read_font_data(file)
        local glyphs = {}
        local fd = io.open(file, "r")
        local content = fd:read("*all")
        fd.close()
       
        for glyph in string.gmatch(content, "<glyph[^/>]*") do
            local glyph_tag = string.gsub(glyph, "\n", " ")
            local unicode = string.match(glyph_tag, "unicode="[^"]*")
            local outline = string.match(glyph_tag, "d="[^"]*")
            local width = string.match(glyph_tag, "horiz%-adv%-x="[^"]*")
           
            if unicode ~= nil and #unicode >= 10 then
                unicode = string.sub(unicode, 10, #unicode)
            end
           
            if outline ~= nil and #outline > 4 then
                outline = string.sub(outline, 4, #outline)
            end
           
            if width ~= nil and #width >= 14 then
                width = string.sub(width, 14, #width)
            end
           
            if unicode ~= nil then
                glyphs[unicode] = {width, outline}
            end
        end
       
        return glyphs
    end
   
    -- returns a random float number between the specified boundaries (floats)
    function random_in_interval(lower_boundary, upper_boundary)
        return ((math.random() * (upper_boundary - lower_boundary)) + lower_boundary)
    end
   
    -- note: scaling is applied before randomization
    function scale_and_randomize(glyph, scale_factor, lower_boundary, upper_boundary)
        local width = glyph[1]
        local outline = glyph[2]
       
        local previous_was_number = false
        local processed_outline = ""
        local number = ""
       
        if width ~= nil then
            width = width * scale_factor
        end
       
        if outline ~= nil then
            for i = 1, #outline, 1 do
                local char = string.sub(outline, i, i)
               
                if previous_was_number then
                    if string.match(char, '%d') ~= nil or
                        char == "." then
                        number = number .. char
                    else
                        -- scale and randomize
                        number = number * scale_factor
                        number = number * random_in_interval(lower_boundary, upper_boundary)
                        number = string.format("%.3f", number)
                        processed_outline = processed_outline .. number .. char
                        number = ""
                        previous_was_number = false
                    end
                else
                    if string.match(char, '%d') ~= nil or
                        char == "-" then
                       
                        number = number .. char
                        previous_was_number = true
                    else
                        processed_outline = processed_outline .. char
                        previous_was_number = false
                    end
                end
            end
        end
       
        return {width, processed_outline}
    end
   
    function print_glyph(glyph, scale_factor, lower_boundary, upper_boundary)
        local randomized_glyph = scale_and_randomize(glyph, scale_factor, lower_boundary, upper_boundary)
        local width = randomized_glyph[1]
        local outline = randomized_glyph[2]

        if outline ~= nil then
            tex.sprint("\\filldraw[glyph outline] svg "" .. outline .. "";")
        end
    end
   
    function return_glyph(glyph, scale_factor, lower_boundary, upper_boundary)
        local randomized_glyph = scale_and_randomize(glyph, scale_factor, lower_boundary, upper_boundary)
        local width = randomized_glyph[1]
        local outline = randomized_glyph[2]
       
        if outline ~= nil then
            return "\\filldraw[glyph outline] svg "" .. outline .. "";"
        else
            return ""
        end
    end
   
    function draw_sample_glyphs(glyphs)
        tex.sprint("\\begin{tikzpicture}")
        tex.sprint("\\node[glyph node, matrix, anchor=south west] (a1) {" ..
            return_glyph(glyphs["a"], 0.05, 1, 1) ..
            "\\\\};")
        tex.sprint("\\node[glyph node, matrix, anchor=south west, right=7.5mm of a1] (a2) {" ..
            return_glyph(glyphs["a"], 0.05, 0.8, 1.2) ..
            "\\\\};")
        tex.sprint("\\end{tikzpicture}")
    end
   
    function draw_sample_text(glyphs)
        local horizontal_space = "0.5mm"
        local vertical_space = "1.25mm"
        local scale = 0.05
        local lower_boundary = 0.9
        local upper_boundary = 1.1
       
        tex.sprint("\\begin{tikzpicture}")
        tex.sprint("\\node[glyph node, matrix] (m1) {" ..
            return_glyph(glyphs["m"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of m1] (a1) {" ..
            return_glyph(glyphs["a"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of a1] (t1) {" .. "\\raisebox{" .. vertical_space .. "}{" ..
            return_glyph(glyphs["t"], scale, lower_boundary, upper_boundary) ..
            "}" .. "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of t1] (h1) {" .. "\\raisebox{" .. vertical_space .. "}{" ..
            return_glyph(glyphs["h"], scale, lower_boundary, upper_boundary) ..
            "}" .. "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of h1] (e1) {" ..
            return_glyph(glyphs["e"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of e1] (m2) {" ..
            return_glyph(glyphs["m"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of m2] (a2) {" ..
            return_glyph(glyphs["a"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of a2] (t2) {" .. "\\raisebox{" .. vertical_space .. "}{" ..
            return_glyph(glyphs["t"], scale, lower_boundary, upper_boundary) ..
            "}" .. "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of t2] (i1) {" .. "\\raisebox{" .. vertical_space .. "}{" ..
            return_glyph(glyphs["i"], scale, lower_boundary, upper_boundary) ..
            "}" .. "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of i1] (c1) {" ..
            return_glyph(glyphs["c"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
       
        tex.sprint("\\node[glyph node, matrix, right=" .. horizontal_space ..
            " of c1] (s1) {" ..
            return_glyph(glyphs["s"], scale, lower_boundary, upper_boundary) ..
            "\\\\};")
        tex.sprint("\\end{tikzpicture}")
    end
   
    function draw_sample_glyph(glyphs)
        tex.sprint("\\begin{tikzpicture}")
        print_glyph(glyphs["&#x3a9;"], 0.05, 0.95, 1.05)
        tex.sprint("\\end{tikzpicture}")
    end
   
    function main()
        local cmr10_glyphs = {}
       
        math.randomseed(os.time())
       
        cmr10_glyphs = read_font_data("cmr10.svg")
       
        tex.sprint("\\noindent")
        draw_sample_glyphs(cmr10_glyphs)
        tex.sprint("\\\\[2cm]")
        draw_sample_text(cmr10_glyphs)
        tex.sprint("\\\\[2cm]")
        draw_sample_glyph(cmr10_glyphs)
    end
\end{luacode*}

\begin{document}
\luadirect{main()}
\end{document}

Nice, isn’t it?

I’ve created an animation in LaTeX (clarification later) using this code, which makes the letter “a” wibbly-wobbly. There is also a video which shows the same letter but only the outline is drawn, but in my opinion it doesn’t look that good: Glyph distortion – YouTube.

These videos are also available on Vimeo: Glyph distortion on Vimeo, Glyph distortion #2 on Vimeo.

The second animation (also made in LaTeX) draws a big letter “a” stacking only outlines of it on top of each other which it gives a hollow like look.

This video is also available on Vimeo: Font outline animation #2 on Vimeo.

Only one question remains, how did I made these animations in LaTeX? I just built upon the code above, and rendered a long PDF which’s each page is a frame of the animation. After that I only followed some steps I’ve described before.

Megosztás, like stb.

Az egymást követő nemzedékek külön-külön is nagy tehetségű tipográfusainak teljesítménye a mesterség, a szellemiség és a generációkon keresztül felhalmozódott tudás és tapasztalat öröklése révén gazdagodott. A Kner család örökségét a család harmadik generációjának kiemelkedő egyénisége Haiman György vitte tovább. Kiállításunk a száz éve született könyvtervező művésznek állít emléket.

Petőfi Irodalmi Múzeum

Megosztás, like stb.

The video is also available on Vimeo.

This animation is strongly connected to LaTeX. How come? – you could ask. I’ll come to the point but first I have to confess that this nice piece of video/animation/whatever is “only” a byproduct of a search for a LaTeX related answer.

I’m a LaTeX enthusiast, and I’m trying to be active on TeX.SX, and found a question about how to draw individual glyphs with randomized paths which I could not stop thinking about. I even wanted to learn Metapost, but when I saw what was laying before me I was intimidated. So I thought I should try something easier first, namely Processing, which was very useful for some small projects in the past. I found the Geomerative library written by Ricard Marxer, and when I was looking into the examples which came with the library I found an interesting one, which used the vertices of font outlines. Then came the idea that it would be nice to try to polygonize individual glyphs with different accuracy, draw Bézier curves along/through the vertices, and stack these images on top each other. Just to see how it looks. In the end it turned out to be pretty awesome, I think.

Font outline animation

I’m sharing the source with some notes what and how it does what it does, so others may come up with nice things too. But if you don’t want the “magic” to be debunked, this is where you should stop reading this post.

Note that the following source code comes with no warranty at all, and is under the CC BY-NC-SA 2.5 license.

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/*
Font outline animation
Author: István Szántai (szantaii)
License: CC BY-NC-SA 2.5
*/

import geomerative.*;
import processing.pdf.*;

int frameCount;
float backgroundColor;
float strokeColor;
float strokeOpacity;
float fadeOutOpacity;
float fadeOutOpacityStep;
RShape shape;
RPoint[] points;
int initialPolygonizerLength;
int currentPolygonizerLength;


void setup()
{
  frameCount = 0;
  backgroundColor = 38.25;
  strokeColor = 229.5;
  strokeOpacity = 25.5;
  fadeOutOpacityStep = 10.625;
  fadeOutOpacity = fadeOutOpacityStep;
 
  size(1280, 720, PDF, "frames.pdf");
 
  RG.init(this);

  initialPolygonizerLength = 179;
  currentPolygonizerLength = initialPolygonizerLength;
 
  print("Drawing...");
 
  smooth();
}

void draw()
{
  PGraphicsPDF pdf = (PGraphicsPDF) g;
 
  if (frameCount < 45)
  {
    background(backgroundColor);
    pdf.nextPage();
  }
  else if (frameCount < 399)
  {
    background(backgroundColor);
    noFill();
    strokeCap(ROUND);
    strokeJoin(ROUND);
    stroke(strokeColor, strokeOpacity);
 
    drawBezierVertices("A", width / 2 - 180, 4.95 * height / 6);
    drawBezierVertices("a", width / 2 + 230, 4.95 * height / 6);
   
    if (currentPolygonizerLength > 0)
    {
      --currentPolygonizerLength;
    }
   
    if (frameCount >= 375)
    {
        noStroke();
        fill(backgroundColor, fadeOutOpacity);
        rect(0, 0, 1280, 720);
        fadeOutOpacity += fadeOutOpacityStep;
    }
   
    pdf.nextPage();
  }
  else if (frameCount < 429)
  {
    background(backgroundColor);
    if (frameCount != 428)
    {
      pdf.nextPage();
    }
  }
  else
  {
    println(" done.");
    exit();
  }
 
  frameCount++;
}

void drawBezierVertices(String text, float horizontalPos, float verticalPos)
{
  shape = RG.getText(text, "Palatino-Roman.ttf", 650, CENTER);
  pushMatrix();
  translate(horizontalPos, verticalPos);
 
  for (int i = initialPolygonizerLength; i >= currentPolygonizerLength; i--)
  {
    RG.setPolygonizer(RG.UNIFORMLENGTH);
    RG.setPolygonizerLength(i);
    points = shape.getPoints();
   
    if(points != null && points.length > 3)
    {
      beginShape();
      for(int j = 0; j < points.length - 3; j++)
      {
        if (j == 0)
        {
          vertex(points[j].x, points[j].y);
        }
        else
        {
          bezierVertex(points[j].x, points[j].y,
            points[j + 1].x, points[j + 1].y,
            points[j + 2].x, points[j + 2].y);
        }
      }
      endShape();
    }
  }
  popMatrix();
}

The most important stuff is in the definition of the drawBezierVertices function. This is how it works. It gets a piece of text, which will be “written” with a defined font (note that the chosen font should be in the project’s data folder) making a shape, but it won’t be drawn to the screen. Instead the shape will be polygonized and through the calculated vertices a bezier curve will be drawn. This is iterated a couple times (180 times in this specific example) while vertices are getting closer to each other, so at the end a the true outline of the font would be drawn (more or less).

By reading the source you can also see that every frame of the animation is rendered to pages of a PDF document. Here is why. When rendering to PDF Processing will create a vectorized output. So in the end you can get the frames from the PDF in any resolution you want without losing quality. All is left to rasterize every page of the rendered PDF with the desired resolution into individual raster images (PNG files if you ask me), and make a video from the created image sequence.

Some practical advice. I’ve used Gimp to rasterize the pages of the PDF output (with FullHD, 1920×1080 resolution), and saved them as separate files using the Export Layers plugin. After that I made the image sequence into a video from the command-line using FFmpeg.

ffmpeg -r 30 -i %03d.png -c:v libx264 -preset veryslow -qp 0 -g 1 -bf 2 font_animation.mp4
Megosztás, like stb.

As a follow-up for my last post hereby I present a Creeper (right) in (Lua)LaTeX.

Creeper Creeper

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

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% Creeper
% 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{creeper_white}{HTML}{9AD78E}
\definecolor{creeper_lightgreen}{HTML}{5ED04C}
\definecolor{creeper_green}{HTML}{00A500}
\definecolor{creeper_darkgreen}{HTML}{255522}

\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, colors_array)
        for x = x_pos, x_pos + 7, 1 do
            for y = y_pos, y_pos + 7, 1 do
                for z = z_pos, z_pos + 7, 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 + 7 then
                       
                        local color_index = math.random(1, #colors_array - 1)
                        tikzcube(x, y, z, colors_array[color_index])
                       
                        if x == x_pos + 7 and
                            (z == z_pos + 4 and
                            (y == y_pos + 2 or y == y_pos + 5)) or
                            (z == z_pos + 2 and
                            (y == y_pos + 3 or y == y_pos + 4)) or
                            (z == z_pos + 1 and
                            (y > 1 and y < 6)) then
                           
                            tikzcube(x, y, z, "black")
                        end
                       
                        if x == x_pos + 7 and
                            ((z == z_pos + 5 and
                            ((y > y_pos and y < y_pos + 3) or
                            (y > y_pos + 4 and y < y_pos + 7))) or
                            (z == z_pos + 4 and
                            (y == y_pos + 1 or y == y_pos + 6)) or
                            (z == z_pos + 3 and
                            (y == y_pos + 3 or y == y_pos + 4)) or
                            (z == z_pos + 2 and
                            (y == y_pos + 2 or y == y_pos + 5)) or
                            (z == z_pos and
                            (y == y_pos + 2 or y == y_pos + 5))) then
                           
                            tikzcube(x, y, z, colors_array[#colors_array])
                        end
                    end
                end
            end
        end
    end
   
    function draw_leg(x_pos, y_pos, z_pos, colors_array)
        for x = x_pos, x_pos + 3, 1 do
            for y = y_pos, y_pos + 7, 1 do
                for z = z_pos, z_pos + 5, 1 do
                    if x == x_pos or x == x_pos + 3 or
                        y == y_pos or y == y_pos + 7 or
                        z == z_pos or z == z_pos + 5 then
                       
                        local color_index = math.random(1, #colors_array - 1)
                        tikzcube(x, y, z, colors_array[color_index])
                       
                        if x == x_pos + 3 and
                            ((z == z_pos + 1 and
                            (y == y_pos or y == y_pos + 2 or
                            y == y_pos + 4 or y == y_pos + 6)) or
                            (z == z_pos and
                            (y == y_pos + 1 or y == y_pos + 3 or
                            y == y_pos + 5 or y == y_pos + 7))) then
                           
                            tikzcube(x, y, z, colors_array[#colors_array])
                        end
                       
                        if x == x_pos + 3 and
                            ((z == z_pos + 1 and
                            (y == y_pos + 1 or y == y_pos + 3 or
                            y == y_pos + 5 or y == y_pos + 7)) or
                            (z == z_pos and
                            (y == y_pos or y == y_pos + 2 or
                            y == y_pos + 4 or y == y_pos + 6))) then
                           
                            tikzcube(x, y, z, "black")
                        end
                    end
                end
            end
        end
    end
   
    function draw_bodypart(x_pos, y_pos, z_pos, x_length, y_length, z_length, colors_array)
        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
                       
                        local color_index = math.random(1, #colors_array)
                        tikzcube(x, y, z, colors_array[color_index])
                    end
                end
            end
        end
    end
   
    function draw_creeper(x_rotation, z_rotation)
        local creeper_colors = {"creeper_white",
            "creeper_lightgreen",
            "creeper_green",
            "creeper_darkgreen"}
       
        tex.sprint("\\tdplotsetmaincoords{" .. x_rotation .. "}{" .. z_rotation .. "}")
        tex.sprint("\\begin{tikzpicture}[tdplot_main_coords]")
       
        math.randomseed(os.time())
       
        draw_leg(-2, 0, -18, creeper_colors)
        draw_leg(6, 0, -18, creeper_colors)
        draw_bodypart(2, 0, -12, 4, 8, 12, creeper_colors)
        draw_head(0, 0, 0, creeper_colors)
        -- draw_coordinate_system()
       
        tex.sprint("\\end{tikzpicture}")
    end
\end{luacode*}

\begin{document}
\luadirect{draw_creeper(66, 135)}
\end{document}
Megosztás, like stb.

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.

MISS ME?

Megosztás, like stb.