Test homework drawing PGF error

test-homework.tex

% vim: ft=tex
\RequirePackage{luatex85,shellesc}
\documentclass{scrartcl}

%% I use KOMA-script as I find it gives total control over a document structure.
%% Memoir would probably achieve the same results with marginally less pain, but
%% I'm not entirely sure I want to spend the time learning the other major custom
%% page classes.

%% KOMA options
\KOMAoption{cleardoublepage}{empty}
\KOMAoption{DIV}{10}
\KOMAoption{draft}{false}
\KOMAoption{fontsize}{10pt}
\KOMAoption{headings}{small}
% \KOMAoption{open}{right}
\KOMAoption{paper}{a4}
\KOMAoption{parskip}{half}
\KOMAoption{twoside}{false}
\KOMAoption{captions}{signature}
\KOMAoption{titlepage}{false}
\KOMAoption{abstract}{false}

\usepackage{listings}

%% e-TeX tools
\usepackage{etoolbox}

%% Subfiles for shared preambles
\usepackage{subfiles}

\usepackage{polyglossia}
\setdefaultlanguage[variant=australian]{english}

%% Colours - put this before typography so additional named colours can be defined.
\usepackage[table]{xcolor}
\definecolor{rmitred}{HTML}{DC241F}
\definecolor{rmitblue}{HTML}{341FDC}

\definecolor{red}{HTML}{DC291E}
\definecolor{blue}{HTML}{04588A}
\definecolor{orange}{HTML}{FA6B00}
\definecolor{green}{HTML}{038130}
\colorlet{wood}{brown!80!gray}
\colorlet{steel}{blue!20!gray}

\colorlet{tabledarkrow}{gray!12.5}
% \colorlet{tablelightrow}{gray!0}

%% Typography Settings
\usepackage[protrusion,expansion]{microtype}
\usepackage{fontspec}
\defaultfontfeatures{Ligatures=TeX}
\usepackage{xunicode}
% xltxtra is not used with LuaTeX
% \usepackage{xltxtra}

%% Maths typography — re-enable these if we need maths support
\usepackage{physics}
\usepackage{mathtools}
\usepackage{unicode-math}

%% Use this to set up the headers and footers in the pages later on. 
%% Note that I will need to rework the code for that, as \makeatletter is ugly
\setkomafont{pagehead}{\small\sffamily\color{red}\selectfont}
\setkomafont{pagenumber}{\small\sffamily\color{black}\selectfont}

\usepackage[automark,nouppercase]{scrpage2}
\pagestyle{scrheadings}
\clearscrheadfoot
\lohead{\thetitle}
\rohead{\theauthor}
\cfoot{\pagemark}

\setkomafont{title}{\Huge\sffamily\bfseries\color{red}}
\setkomafont{titlehead}{\color{gray}\large\sffamily}
\setkomafont{author}{\small\itshape}
\setkomafont{publishers}{\usefontofkomafont{author}}
\setkomafont{date}{\small}
\setkomafont{disposition}{\sffamily}
\setkomafont{section}{\sffamily\Large\bfseries}
\setkomafont{subsection}{\sffamily\large\bfseries}
\setkomafont{subsubsection}{\sffamily\bfseries}
\setkomafont{descriptionlabel}{\normalfont\bfseries}

\renewcommand{\sup}[1]{\textsuperscript{#1}}
\newcommand{\sub}[1]{\textsubscript{#1}}

% \usepackage{standalone}
\usepackage{tikz}
% \usepackage{pgfplots}
% \usepackage{pgfplotstable}
% \pgfplotsset{compat=1.13}

% Lua math library seems to clash with tikz decorations
\usepgflibrary{luamath}
\pgfkeys{pgf/luamath=parser}

\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathmorphing}
\usetikzlibrary{intersections}
\usetikzlibrary{positioning}
\usetikzlibrary{external}
\usetikzlibrary{patterns}
\usepgflibrary{arrows.meta}
\usetikzlibrary{bending}
\usetikzlibrary{angles}

% \tikzexternalize[prefix=tikz/,shell escape=-enable-write18]
\tikzset{external/system call={lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"}}
\tikzset{
  % Defines a custom style which generates BOTH, .pdf and .png export
  % but prefers the .png on inclusion.
  %
  % This style is not pre-defined, you may need to copy-paste and
  % adjust it.
  png export/.style={%
    external/system call/.add=%
    {}
    ; convert -density 300 -transparent white "\image.pdf" "\image.png",
  },
  png images/.style={%
    external/system call/.add=%
    {}
    ; convert -density 300 -transparent white "\image.pdf" "\image.png",
    % Don't need this as we're keeping the PDF in the document
    /pgf/images/external info,
    /pgf/images/include external/.code={%
      \includegraphics
      [width=\pgfexternalwidth,height=\pgfexternalheight]
      {##1.png}%
    },
  }
}

\usepackage{siunitx}
\usepackage{cancel}
\sisetup{detect-all, per-mode=symbol}
\DeclareSIPostPower\fourth{4}

\DeclareGraphicsExtensions{.pdf,.png,.jpg}

\makeatletter
\newlength{\questionbeforeskip}
\newlength{\questionafterskip}
\setlength{\questionbeforeskip}{1.0ex plus -1ex minus -0.25ex}
\setlength{\questionafterskip}{1ex plus 0.25ex}
\newlength{\answerskip}
\setlength{\answerskip}{0.25ex plus -0.125ex minus -0.125ex}

\addtotoclist{loq}
\newcommand{\listofloqname}{List of Questions}
\newcommand{\listofquestions}{\listoftoc{loq}}
\setuptoc{loq}{sectionatlist}

\newcounter{question}[section]

\newcommand{\questionautorefname}{question}
\DeclareRobustCommand{\question}[2]{%
  \refstepcounter{question}%
  \addxcontentsline{loq}{section}{Question~#1}
  \pdfbookmark{Question~#1}{question:\thesection.\thequestion}
  {\usekomafont{subsection}{\par\vspace\questionbeforeskip Question~#1.}\par}
  {\itshape #2}\par\vspace\questionafterskip
}%
\newcommand{\answer}{\par\vspace\answerskip{\usekomafont{subsubsection}{Answer}}\par\vspace\answerskip}

\def\toclevel@question{4}
\makeatother

\usepackage[inline]{enumitem}
\setlist[enumerate]{label=(\alph*)}

% \setlist{noitemsep}
% \setlist[1]{labelindent=\parindent}
\newlist{subquestions}{enumerate}{3}
\setlist[subquestions]{leftmargin=*}
\setlist[subquestions,1]{label=\textup{\textbf{(\alph*)}}}
% Inline subquestions
\newlist{subquestions*}{enumerate*}{3}
\setlist[subquestions*]{itemjoin*={{, and }}}
\setlist[subquestions*,1]{label=\textup{\textbf{(\alph*)}}}

\newcommand{\qitem}[1]{\item{\textit{#1}}}
\newcommand{\qitemp}[1]{\qitem{#1}\\[0.5\parskip]}
\newcommand{\qitemq}[1]{\qitem{#1}\quad}

\usepackage{array}
\usepackage{tabulary}
\usepackage{multirow}
\usepackage{multicol}
\usepackage{booktabs}

\newcolumntype{F}{>{\global\let\currentrowstyle\empty}}
\newcolumntype{f}{>{\currentrowstyle}X}
\newcolumntype{-}{>{\currentrowstyle}}
\newcommand{\rowstyle}[1]{\gdef\currentrowstyle{#1}%
  #1\ignorespaces
}
% DEPRECATED
% TODO Find this in all documents and remove it
\newcommand{\SetRowStyle}[1]{\rowstyle #1}

% \newcolumntype{C}{>{\centering\arraybackslash}X}
\newcolumntype{B}{>{\bfseries}} % Bold
\newcolumntype{K}{>{\scshape}}  % Smallcaps (German Kapitälchen)
\newcolumntype{I}{>{\itshape}}  % Italics
\newcolumntype{w}{<{\hspace{0.75em}}}  % Wide column
\renewcommand{\arraystretch}{1.25}
\renewcommand{\tabcolsep}{0.5em}

\usepackage{floatrow}

%% Penalties
\hyphenpenalty=2500
\tolerance=500
\widowpenalty=1500
\clubpenalty=1500

% Metadata goes here
\titlehead{A University}
\subject{The Subject}
\title{Homework 1}
\author{The Author}
\date{\today}

\makeatletter
\let\thetitle\@title
\let\theauthor\@author
\let\thedate\@date
\makeatother

\usepackage{hyperref}
\hypersetup{
  pdfauthor={The Author},
  pdftitle={Homework 1},
  colorlinks=false,
hidelinks}
\usepackage[all]{hypcap}

%% Define all TikZ styles here
\tikzset{%
  information text/.style={xshift=0.30\textwidth, every node/.style={right, text width=0.70\textwidth, inner sep=1ex}},
  %
  my axes/.style={node font=\small, every node/.style={fill=white, fill opacity=0.0, text opacity=1}},
  important line/.style={very thick},
  cross section/.style={draw, line width=0.5pt, blue, fill=blue!40!white, every node/.style={node font=\footnotesize, color=black}},
  shape outline/.style={draw, line width=0.5pt, blue, fill=blue!20!white, every node/.style={node font=\footnotesize, color=black}},
  segment boundary/.style={draw, line width=0.5pt, dashed},
  dim edge/.style={densely dashed, line width=0.5pt, shorten >= -2.5mm, color=black!75!white},
  dim length/.style={draw, line width=0.5pt, arrows={Stealth-Stealth}, every node/.style={anchor=mid, midway, fill=white, node font=\footnotesize, inner sep=1pt},
  },
  translucent node/.style={fill opacity=0.5, text opacity=1},
  translucent shape/.style={fill opacity=0.75},
  rough edge/.style={decorate, decoration={random steps, segment length=2mm, amplitude=0.5mm}},
  % rough edge/.style={decorate, decoration={zigzag}},
  label/.style={every node/.style={anchor=mid, midway, inner sep=2pt, circle, fill=white, fill opacity=0.375, text opacity=1}},
  % png export,
}

\begin{document}

\maketitle

\question{6--20}{Locate the centroid $(\bar x, \bar y)$ for the angle's cross-sectional area:}
\begin{center}
  % \tikzexternaldisable
  \tikzsetnextfilename{homework-1-6-20}
  \begin{tikzpicture}

    \begin{scope}[my axes]
      \draw[->] (0, 0) -- (6, 0) node[right] {$x$} coordinate(x axis);
      \draw[->] (0, 0) -- (0, 5) node[above] {$y$} coordinate(y axis);
    \end{scope}

    \fill [fill=green!50!white]
      (0, 0) -- (4, 0) -- (4, 1) -- (1, 1) -- (1, 3) -- (0, 3) -- cycle;
    \path [fill=green!35!white]
      decorate[rough edge]{(0.75, 4)  -- (1.75, 4)} -- (1, 3) -- (0, 3) -- cycle
      decorate[rough edge]{(1.75, 2)  -- (4.75, 2)} -- (4, 1) -- (1, 1) -- cycle;
    \fill [fill=green!65!white]
      decorate[rough edge]{(1.75, 4)  -- (1.75, 2)} -- (1, 1) -- (1, 3) -- cycle;
    \fill [fill=green!65!white]
      decorate[rough edge]{(4.75, 2)  -- (4.75, 1)} -- (4, 0) -- (4, 1) -- cycle;
    \draw [green!10!white, line width=0.5pt]
      (0, 3) -- (1, 3) -- (1, 1) -- (4, 1) -- (4.75, 2)
      (1, 3) -- (1.75, 4)
      (4, 0) -- (4, 1);
    \draw [green, line width=0.5pt]
      (0.75, 4) -- (0, 3) -- (0, 0) -- (4, 0) -- (4.75, 1)
      (1, 0) -- (1, 1) -- (1.75, 2);

    \begin{scope}[my axes]
      \draw[->] (1.5, 1.9) -- (6, 1.9) node[right] {$x'$};
      \draw[->] (1.5, 1.9) -- (1.5, 5) node[above] {$y'$};
      \fill (1.5, 1.9) circle [radius=0.5mm];
      \node at (1.75, 2.15) {$C$};
    \end{scope}

    \path[label] (0, 0) -- (1, 3) node {1};
    \path[label] (1, 0) -- (4, 1) node {2};

    \draw[dim edge] (0, 0) -- (-0.5, 0);
    \draw[dim edge] (0, 3) -- (-0.5, 3);
    \draw[dim length] (-0.5, 0) -- (-0.5, 3) node {150};

    \draw[dim edge] (0, 0) -- (0, -0.5);
    \draw[dim edge] (1, 0) -- (1, -0.5);
    \draw[dim edge] (4, 0) -- (4, -0.5);
    \draw[dim length] (0, -0.5) -- (1, -0.5) node {50};
    \draw[dim length] (1, -0.5) -- (4, -0.5) node {150};

    \draw[dim edge] (4, 1) -- (5, 1);
    \draw[dim length] (5, 0) -- (5, 1) node {50};

    \draw[dim length] (5.5, 0) -- (5.5, 1.9) node {$\bar y$};
    \draw[dim length] (0, 4.5) -- (1.5, 4.5) node {$\bar x$};

    \node[above right, text width=3cm, node font=\itshape\small] at (2.5, 2.5) {All dimensions in \si{\mm}};


  \end{tikzpicture}
\end{center}
\answer
Divide the area into its composite shapes.
\begin{equation*}
  \begin{array}{l l l l l l}
    \toprule
    \text{Segment} & \text{Area} & \tilde x & \tilde y & \tilde x A & \tilde y A \\
    \midrule
    \multirow{2}{*}{1} 
    & 50 × 150 & \tfrac{1}{2} × 50 
    & \tfrac{1}{2} × 150 
    & 7500 × 25 
    & 7500 × 75 \\

    & =\SI{7500}{\square\mm} 
    & =\SI{25}{\mm} 
    & =\SI{75}{\mm} 
    & =\SI{187500}{\cubic\mm} 
    & =\SI{562500}{\cubic\mm} \\[0.75\parskip]

    \multirow{2}{*}{2} 
    & 50 × 150 
    & \tfrac{1}{2} × 150 + 50
    & \tfrac{1}{2} × 50 
    & 7500 × 125 
    & 7500 × 25 \\

    & =\SI{7500}{\square\mm} 
    & =\SI{125}{\mm} 
    & =\SI{25}{\mm} 
    & =\SI{937500}{\cubic\mm} 
    & =\SI{187500}{\cubic\mm}\\

    \midrule
    \sum & = \SI{15000}{\square\mm} &&& = \SI{1125000}{\mm\cubed} & = \SI{750000}{\mm\cubed} \\
    \bottomrule
  \end{array}
\end{equation*}
\begin{align*}
  \bar x &= \frac{\sum \tilde x A}{\sum A} = \frac{\SI{1125000}{\mm\cubed}}{\SI{15000}{\mm\squared}} = \SI{75}{\mm} \\[\parskip]
  \bar y &= \frac{\sum \tilde y A}{\sum A} = \frac{\SI{750000}{\mm\cubed}}{\SI{15000}{\mm\squared}} = \SI{50}{\mm} 
\end{align*}


\end{document}