Tikzは座標計算もできるぞ
from 2023/08/26
(Gorira Tatsuさんの2023夏休みの自由研究が)自分の前期の実験レポートと同じ指定だtakker.icon
自分もTeXで書いたが、理由は数式をwordで書くのがつらすぎたから
図は最初PGFPlotsで書こうとしたが、挫折してExcelに切り替えた
以降もExcelで済ませようと思ったが、学科唯一の数学系教授にTikzを極めるよう言われて火がついてしまい、データプロット以外はTikzで書ききってしまった
Tikzはいいぞ(洗脳完了)。issac.iconさんもやろう
なんかすごいことはわかるGorira Tatsu.icon
Tikzは数学的な図を書くのが楽しいSummer498.icon
役立つとは言っていない
長期的に価値のあるもの(強弁)だから今すぐ役に立たなくてもいいtakker.icon
奥が深い症候群ではSummer498.icon
というかコンパイルしてるんだから座標位置の計算してほしいんだよな～
できるぞtakker.icon
掌返す準備したSummer498.icon
三角関数使えたっけ
Rotateでなんとかするんかな
使えるtakker.icon
コレは普通に役立つなﾃﾉﾋﾗｸﾙｰSummer498.icon
例
https://gyazo.com/7ca157d644a1e6d091d79eb49d2563ea
code:矩形則.tex
\tikzset{declare function={y(\x)=sqrt(5.5-cos((4/200+0.5)*\x r)-sin((4/200+0.5)*2*\x r));},
plot fill/.style={fill=white},
plot/.style={draw=black!80, thick},
bar/.style={fill=cyan!20,draw=black, thick},
marking/.style={draw=black},
axis/.style={thick, draw=black!65, stealth-stealth}
}
\begin{figure}H
\centering
\begin{tikzpicture}x=0.7cm,y=1.5cm, line cap=round, line join=round
% \path plot fill plot domain=0:5*pi (\x,{y(\x)}) -| cycle;
% 矩形を描く
\foreach \x in {0, 1,2,5*pi-2,5*pi-1}
{
\path bar (\x,0) |- (\x+1, {y(\x)}) |- cycle;
}
% graphを描く
\path plot plot domain=-0.5*pi:(5+0.5)*pi,smooth (\x,{y(\x)}) nodeabove{$y=f(x)$};
% 辺の長さを示す矢印をつける
\path axis (-0.3,0) -- nodeleft{$f(\alpha)$} (-0.3,{y(0)});
\path axis (0,{y(0)+0.3/3}) -- nodeabove{$\Delta x$} (1,{y(0)+0.3/3});
\path axis (5*pi+0.3,0) -- noderight{$f(\beta-\Delta x)$} (5*pi+0.3,{y(5*pi-1)});
\path axis (0,-2/3) -- nodebelow{$N$個} (5*pi,-2/3);
% 座標軸を描く
\path axis (0,3.5) nodeleft{$y$} |- (5*pi+0.8,0) nodebelow{$x$};
% x軸の目盛り線を引く
\path axis, - (0,0) -- ++(0,-3pt) node below {$\alpha$};
\path axis, - (1,0) -- ++(0,-3pt) node below=0.2 {$\alpha+\Delta x$};
\path axis, - (2,0) -- ++(0,-3pt) node below {$\alpha+2\Delta x$};
\path axis, - (5*pi-2,0) -- ++(0,-3pt) node below {$\beta-2\Delta x$};
\path axis, - (5*pi-1,0) -- ++(0,-3pt) node below=0.2 {$\beta-\Delta x$};
\path axis, - (5*pi,0) -- ++(0,-3pt) node below {$\beta$};
% y軸の目盛り線を引く
\path axis, - (0,0) -- ++(0,-3pt);
\foreach \y in {0,3}
{
\path axis, - (0,\y) -- ++(-3pt, 0) node left=0.1 {$\y$};
}
% 途中の矩形を省略したことを表すdotsを入れる
\node(A)scale=2.0 at (2.5*pi,1) {$\ldots$};
\end{tikzpicture}
\caption{矩形測による近似}\label{fig:rect_method}
\end{figure}
code:globalなスタイル設定.tex
\tikzset{
indicator/.style={thick, draw=black!65, stealth-stealth}, % 寸法
subline/.style={thick, draw=black!65, dashed}, % 補助線
strain guage/.style={gray}, % ひずみゲージ
legend/.style={}, % 説明用のラベルとか
beam/.style={thick} % 梁
}
code:上にある部分のコード.tex
\subsection{実験した断面形状}\label{sec:cross-sections}
本実験では、\cref{fig:rect-projection,fig:i-projection,fig:h-projection}に示す矩形断面、I形断面、H形断面の等断面梁と、\cref{fig:rhombus-projection}に示す幅が変化する矩形断面の梁の4本について載荷実験を実施した。
以下、各梁を順に矩形梁、I形梁、H形梁、ひし形梁と呼ぶことにする。
\begin{figure}htbp
\begin{minipage}{0.3\hsize}
\begin{tikzpicture}scale=0.4
\def\width{8.1}
\def\thickness{0.5} % 梁の厚み
\def\margin{1.0} % 寸法を離す距離
\def\barheight{1.4*\margin} % 寸法の両脇の点線の長さ
\coordinate (O) at (0,0);
% 側面図
\draw beam (O) rectangle ++(\width, \thickness);
% 寸法
\draw indicator, stealth- ($(O) + (-\margin,0)$) -- ++(0, -1);
\draw indicator, stealth- ($(O) + (-\margin,\thickness)$) -- ++(0, 1);
\draw subline (O) -- ++(-\barheight, 0);
\draw subline ($(O) + (0,\thickness)$) -- ++(-\barheight, 0);
\path ($(O) + (-\margin,0)$) --node legend, left, rotate=90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
\draw indicator ($(O) + (0, \thickness + 1)$) --node legend, above{$\SI{81}{mm}$} ++(\width, 0);
\draw subline (O) -- ++(0, \barheight);
\draw subline ($(O) + (\width, 0)$) -- ++(0, \barheight);
\end{tikzpicture}
\centering
\caption{矩形断面}\label{fig:rect-projection}
\end{minipage}
\begin{minipage}{0.3\hsize}
\begin{tikzpicture}scale=0.4
\def\l{2.7}
\def\thickness{0.5} % 梁の厚み
\def\margin{1.0} % 寸法を離す距離
\def\barheight{1.2*\margin} % 寸法の両脇の点線の長さ
\coordinate (O) at (0,-\l/2-\thickness/2);
\coordinate (P) at ($(O) + (\l, 0)$);
\coordinate (Q) at ($(P) + (0, \thickness)$);
\coordinate (R) at ($(Q) + (-\l/2 + \thickness/2, 0)$);
\coordinate (S) at ($(R) + (0, \l)$);
\coordinate (T) at ($(Q) + (0, \l)$);
\coordinate (U) at ($(T) + (0, \thickness)$);
\coordinate (V) at ($(U) + (-\l, 0)$);
\coordinate (W) at ($(T) + (-\l, 0)$);
\coordinate (X) at ($(S) + (-\thickness, 0)$);
\coordinate (Y) at ($(R) + (-\thickness, 0)$);
\coordinate (Z) at ($(Q) + (-\l, 0)$);
% 側面図
\draw beam (O) -- (P) -- (Q) -- (R) -- (S) -- (T) -- (U) -- (V) -- (W) -- (X) -- (Y) -- (Z) -- cycle;
% 寸法
% 上部材の厚み
\def\arrowL{0.5}
\draw indicator, stealth- ($(T) + (\margin, 0)$) -- ++(0, -\arrowL);
\draw indicator, stealth- ($(U) + (\margin, 0)$) -- ++(0, \arrowL);
\draw subline (T) -- ++(\barheight, 0);
\draw subline (U) -- ++(\barheight, 0);
\path ($(T) + (\margin, 0)$) --node legend, right, rotate=-90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
% 下部材の厚み
\draw indicator, stealth- ($(P) + (\margin, 0)$) -- ++(0, -\arrowL);
\draw indicator, stealth- ($(Q) + (\margin, 0)$) -- ++(0, \arrowL);
\draw subline (P) -- ++(\barheight, 0);
\draw subline (Q) -- ++(\barheight, 0);
\path ($(P) + (\margin, 0)$) --node legend, right, rotate=-90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
% flangeの幅
\coordinate (M) at ($(Y) + (0, \l/2)$);
\draw indicator, stealth- (M) -- ++(-\arrowL, 0);
\draw indicator, stealth- ($(M) + (\thickness, 0)$) -- ++(\arrowL, 0) node legend, right {$\SI{5}{mm}$};
% webの幅
\draw indicator ($(V) + (0, \margin)$) --node legend, above{$\SI{27}{mm}$} ++(\l, 0);
\draw subline (U) -- ++(0, \barheight);
\draw subline (V) -- ++(0, \barheight);
% flangeの高さ
\draw indicator ($(W) + (-\margin, 0)$) --node legend, left, rotate=90, anchor=south{$\SI{27}{mm}$} ++(0, -\l);
\draw subline (W) -- ++(-\barheight, 0);
\draw subline (Z) -- ++(-\barheight, 0);
\end{tikzpicture}
\centering
\caption{I形断面}\label{fig:i-projection}
\end{minipage}
\begin{minipage}{0.3\hsize}
\rotatebox{90}{
\begin{tikzpicture}scale=0.4
\def\l{2.7}
\def\thickness{0.5} % 梁の厚み
\def\margin{1.0} % 寸法を離す距離
\def\barheight{1.2*\margin} % 寸法の両脇の点線の長さ
\coordinate (O) at (0,-\l/2-\thickness/2);
\coordinate (P) at ($(O) + (\l, 0)$);
\coordinate (Q) at ($(P) + (0, \thickness)$);
\coordinate (R) at ($(Q) + (-\l/2 + \thickness/2, 0)$);
\coordinate (S) at ($(R) + (0, \l)$);
\coordinate (T) at ($(Q) + (0, \l)$);
\coordinate (U) at ($(T) + (0, \thickness)$);
\coordinate (V) at ($(U) + (-\l, 0)$);
\coordinate (W) at ($(T) + (-\l, 0)$);
\coordinate (X) at ($(S) + (-\thickness, 0)$);
\coordinate (Y) at ($(R) + (-\thickness, 0)$);
\coordinate (Z) at ($(Q) + (-\l, 0)$);
% 側面図
\draw beam (O) -- (P) -- (Q) -- (R) -- (S) -- (T) -- (U) -- (V) -- (W) -- (X) -- (Y) -- (Z) -- cycle;
% 寸法
% 上部材の厚み
\def\arrowL{0.5}
\draw indicator, stealth- ($(T) + (\margin, 0)$) -- ++(0, -\arrowL);
\draw indicator, stealth- ($(U) + (\margin, 0)$) -- ++(0, \arrowL);
\draw subline (T) -- ++(\barheight, 0);
\draw subline (U) -- ++(\barheight, 0);
\path ($(T) + (\margin, 0)$) --node legend, right, rotate=-90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
% 下部材の厚み
\draw indicator, stealth- ($(P) + (\margin, 0)$) -- ++(0, -\arrowL);
\draw indicator, stealth- ($(Q) + (\margin, 0)$) -- ++(0, \arrowL);
\draw subline (P) -- ++(\barheight, 0);
\draw subline (Q) -- ++(\barheight, 0);
\path ($(P) + (\margin, 0)$) --node legend, right, rotate=-90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
% flangeの幅
\coordinate (M) at ($(Y) + (0, \l/2)$);
\draw indicator, stealth- (M) -- ++(-\arrowL, 0);
\draw indicator, stealth- ($(M) + (\thickness, 0)$) -- ++(\arrowL, 0) node legend, left, rotate=-90, anchor=south {$\SI{5}{mm}$};
% webの幅
\draw indicator ($(V) + (0, \margin)$) --node legend, above{$\SI{27}{mm}$} ++(\l, 0);
\draw subline (U) -- ++(0, \barheight);
\draw subline (V) -- ++(0, \barheight);
% flangeの高さ
\draw indicator ($(W) + (-\margin, 0)$) --node legend, left, rotate=-90, anchor=north{$\SI{27}{mm}$} ++(0, -\l);
\draw subline (W) -- ++(-\barheight, 0);
\draw subline (Z) -- ++(-\barheight, 0);
\end{tikzpicture}
}
\centering
\caption{H形断面}\label{fig:h-projection}
\end{minipage}
\end{figure}
\begin{figure}htbp
\begin{tikzpicture}scale=0.3
\def\span{34} % スパン長
\def\width{8.1}
\def\widtha{6} % 短い所の長さ
\def\widthb{10.2} % 長い所の長さ
\def\thickness{0.5} % 梁の厚み
\def\margin{1.0} % 寸法を離す距離
\def\barheight{1.2*\margin} % 寸法の両脇の点線の長さ
\coordinate (O) at (0,0);
\coordinate (F) at ($(O) + (3, 1)$); % 正面図の原点
\coordinate (P) at ($(F) + (0, \thickness + 3)$); % 平面図の原点
\coordinate (S) at ($(F) + (\span + 3, 0)$); % 側面図の原点
% 平面図
% なぜか括弧でくくるとエラーになる
\coordinate (P0) at ($(P) + (0, \width/2 - \widtha/2)$);
\coordinate (P1L) at ($(P0) + (\span/2, -\widthb/2 + \widtha/2)$);
\coordinate (P2) at ($(P1L) + (\span/2, \widthb/2 - \widtha/2)$);
\coordinate (P1U) at ($(P1L) + (0, \widthb)$);
\draw beam (P0) -- (P1L) -- (P2) -- ++(0, \widtha) -- (P1U) -- ($(P0) + (0, \widtha)$) -- cycle;
% 寸法
\draw indicator ($(P0) + (-\margin, 0)$) --node legend, left, rotate=90, anchor=south{$\SI{60}{mm}$} ++(0, \widtha);
\draw subline (P0) -- ++(-\barheight, 0);
\draw subline ($(P0) + (0, \widtha)$) -- ++(-\barheight, 0);
\draw indicator (P1L) --node legend, left, rotate=90, anchor=south{$\SI{102}{mm}$} (P1U);
% 補助線
\draw subline ($(F) + (0, \thickness)$) -- (P0);
\draw subline ($(F) + (\span/2, \thickness)$) -- (P1L);
\draw subline ($(F) + (\span, \thickness)$) -- (P2);
% 正面図
\draw beam (F) rectangle ++(\span, \thickness);
\draw beam ($(F) + (\span/2, 0)$) -- ++(0, \thickness);
% 寸法
\draw indicator, stealth- ($(F) + (-\margin, 0)$) -- ++(0, -1);
\draw indicator, stealth- ($(F) + (-\margin, \thickness)$) -- ++(0, 1);
\draw subline (F) -- ++(-\barheight, 0);
\draw subline ($(F) + (0,\thickness)$) -- ++(-\barheight, 0);
\path ($(F) + (-\margin,0)$) --node legend, left, rotate=90, anchor=south{$\SI{5}{mm}$} ++(0,\thickness);
\draw indicator ($(F) + (0, -\margin)$) --node legend, below{$\SI{170}{mm}$} ++(\span/2, 0);
\draw subline (F) -- ++(0, -\barheight);
\draw subline ($(F) + (\span/2, 0)$) -- ++(0, -\barheight);
\draw indicator ($(F) + (\span/2, -\margin)$) --node legend, below{$\SI{170}{mm}$} ++(\span/2, 0);
\draw subline ($(F) + (\span, 0)$) -- ++(0, -\barheight);
% 補助線
\draw subline ($(F) + (\span, 0)$) -- (S);
\draw subline ($(F) + (\span, \thickness)$) -- ($(S) + (0, \thickness)$);
% 側面図
\draw beam (S) rectangle ++(\widthb, \thickness);
\draw beam ($(S) + (\widthb/2 - \widtha/2, 0)$) -- ++(0, \thickness);
\draw beam ($(S) + (\widthb/2 + \widtha/2, 0)$) -- ++(0, \thickness);
% 寸法
\draw indicator ($(S) + (0, -\margin)$) --node legend, below{$\SI{102}{mm}$} ++(\widthb, 0);
\draw subline (S) -- ++(0, -\barheight);
\draw subline ($(S) + (\widthb, 0)$) -- ++(0, -\barheight);
\draw indicator ($(S) + (\widthb/2 -\widtha/2, \thickness + \barheight)$) --node legend, above{$\SI{60}{mm}$} ++(\widtha, 0);
\draw subline ($(S) + (\widthb/2 -\widtha/2, \thickness + \barheight)$) -- ++(0, -\barheight);
\draw subline ($(S) + (\widthb/2 + \widtha/2, \thickness + \barheight)$) -- ++(0, -1);
\end{tikzpicture}
\centering
\caption{ひし形梁の三面図}\label{fig:rhombus-projection}
\end{figure}
\subsection{手順}
使用した材料と器具はひずみゲージを除いて\cref{sec:使用したもの}と同じものを使った。実験方法もひずみを測定しなかったこと以外\cref{sec:載荷実験}と同じなので割愛する。