[Tex/LaTex] How to draw a grid on a shape made of curved lines

diagramstikz-pgf

I am a new user of the Tikz package and I would like to draw the image below using this package for my Thesis.

I think I can create the first grid (left) because the lines are straight, however how could I draw the second grid of the deformed bar? Is there any way to 'deform' the first one or creating a grid from the deformed lines?
Also, regarding the 'zoomed' details: is there any 'automatic' way to draw it using Tikz (I mean like a real zoom of the figure)? Or should I create them separately?
Thanks in advance for any help!

Best Answer

It's a bit fiddly getting the non-linear transformation stuff working in pgf but it can more-or-less do what is required along with the spy library:

\documentclass[tikz,margin=5]{standalone}
\usepgfmodule{nonlineartransformations}
\usepgflibrary{curvilinear}
\usetikzlibrary{spy,calc}
\tikzset{pics/grid/.style={code={%
  \tikzset{x=10pt, y=10pt, step=10pt}
  \draw [thin] (-2, 0) grid ++(4, 20);
  \draw [thick] (-2, 0) rectangle ++(4, 20) (-4, 0) -- (4, 0);
  \draw [thick, fill=gray!50] (0,14) rectangle ++(1,1)
   ++(-.5,-.5) coordinate (-square);
  \draw [<->, thin, gray] (0,14) -- ++(1,1); 
  \coordinate (-corner) at (-2, 20);
}}}
\begin{document}
\begin{tikzpicture}[>=stealth,
  spy using outlines={circle, magnification=3, size=2.5cm, connect spies}]
\pic (a) {grid};
\draw [->, thick, shorten >=5] (a-corner) ++(-1,0)  -- (a-corner);
\spy [red] on (a-square) in node at ($(a-square)+(2.5,0)$);
\scoped{
  \pgfsetcurvilinearbeziercurve
    {\pgfpointxy{5}{0}}{\pgfpointxy{5}{10}}
    {\pgfpointxy{25}{15}}{\pgfpointxy{25}{20}}
  \pgftransformnonlinear{\pgfgetlastxy\x\y%
    \pgfpointcurvilinearbezierorthogonal{\y}{-\x}}%
  \pic (b) {grid};
}
\draw [->, thick, shorten >=5] (b-corner) ++(-1,0) -- (b-corner);
\spy [red] on (b-square) in node at ($(b-square)+(2.5,0)$);
\end{tikzpicture}
\end{document}

Code

\documentclass[tikz,convert=false]{standalone}
\usetikzlibrary{calc,through}
\tikzset{
  m*/.style args={#1:#2}{
    insert path={node [fill=green!50!black, outer sep=+0pt, shape=circle, inner sep=0pt, minimum size=+4pt,#1,label={#2}] {}}
  },
  m/.style={insert path={coordinate (#1)}},
  parLines/.style={draw=red,,shorten <=+-.5cm,shorten >=-.5cm},
  vertLines/.style={draw=purple,shorten >=.5\pgflinewidth},
  @splitLine/.code args={#1 -- #2}{\def\tikztotargetA{#1}\def\tikztotargetB{#2}},
  vert on/.style={
    to path={
      [@splitLine/.expanded={\tikztotarget}]
      -- ($(\tikztotargetA)!(\tikztostart)!(\tikztotargetB)$) node[right angle node,rotate=90*#1] {}\tikztonodes
    }
  },
  vert on/.default=0,
  right angle node/.style={
    at end,sloped,above,allow upside down,
    anchor=south east,
    shape=rectangle,
    inner sep=0pt,
    minimum size=3pt,
    append after command={
      \pgfextra\pgfinterruptpath\draw[right angle node path] (\tikzlastnode.south west) -- (\tikzlastnode.north west) -- (\tikzlastnode.north east);\endpgfinterruptpath\endpgfextra
    }
  },
  right angle node path/.style={draw,thin,black,-,shorten >=.4pt},
  secant/.style={
    to path={
      let \p{@dir}=(\tikztotarget), \n{@dir}={atan2(\x{@dir},\y{@dir})} in
      (node cs: name=\tikztostart, anchor=#1) [m*={name=m#1}:#1] -- (node cs: name=\tikztostart, anchor={2*(\n{@dir}-90)-#1}) [m=m#1'] \tikztonodes
    }
  }
}
\begin{document}
\begin{tikzpicture}[thick]
\clip (-2.5,-2.5) rectangle (2.5,2.5);
\draw[thin, ->] (0,0) [m*={black,minimum size=+3pt,name=O}:] -- node [sloped,above,inner sep=+1pt,font=\scriptsize] {$\vec v$} ++(150:1) coordinate (d);

\draw[thin, ->] (0,0) -- ([rotate=90]d)  [shorten >=-1.3cm];
\draw[thin, ->] (0,0) -- ([rotate=-90]d) [shorten >=-1.3cm];

\node [draw=blue, circle through={(2,0)}] (c) {};

\draw[parLines] (c.50)  [m*={name=m1}:1] -- ++([scale=2] d)    [m=m1'];
\draw[parLines] (c.140) [m*={name=m2}:2] -- ++([scale=-4] d)   [m=m2'];
\draw[parLines] (c.-30) [m*={name=m3}:3] -- ++([scale=4.5] d)  [m=m3'];
\draw[parLines] (c.210) [m*={name=m4}:4] -- ++([scale=-2.5] d) [m=m4'];

\draw[vertLines] (c.center) to[vert on] (m1 -- m1');
\draw[vertLines] (c.center) to[vert on] (m4' -- m4);
\end{tikzpicture}

\foreach \angle in {0,10,...,359}{% Careful, 36 pages!
\begin{tikzpicture}[thick]
\clip (-2.5,-2.5) rectangle (2.5,2.5);
\draw[thin, ->] (0,0) [m*={black,minimum size=+3pt,name=O}:] -- node [sloped,above,inner sep=+1pt,font=\scriptsize] {$\vec v$} ++(\angle:1) coordinate (d);

\draw[thin, ->] (0,0) -- ([rotate=90]d)  [shorten >=-1.3cm];
\draw[thin, ->] (0,0) -- ([rotate=-90]d) [shorten >=-1.3cm];

\node [draw=blue, circle through={(2,0)}] (c) {};

\draw[parLines] (c) to[secant=30]  (d);
\draw[parLines] (c) to[secant=140] (d);
\draw[parLines] (c) to[secant=-30] (d);
\draw[parLines] (c) to[secant=210] (d);


\draw[vertLines] (c.center) to[vert on] (m30 -- m30');
\draw[vertLines] (c.center) to[vert on] (m210' -- m210);
\end{tikzpicture}%
}
\end{document}

Output

enter image description here

[Tex/LaTex] How to draw straight lines between nodes in commutative diagram without using TikZ matrix library

You can use the (p |- q) notation, meaning the intersection of a vertical line through p and a horizontal line through q.

Code

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}[auto]
\node (S1) {$\sigma \cap X_N$};
\node (S2) [below= 2cm and 4cm of S1] {$\sigma \cap X_N$};
\node (S3) [below= 2cm and 4cm of S2] {$\sigma$};
\node (U1) [right= 2cm and 4cm of S1] {$\gamma$};
\node (U2) at (U1 |- S2) {$Y_M$};
\node (U3) at (U2 |- S3) {$R^M$};
\draw[->] (S1) to node {$F_f$} (U1);
\draw[->] (S2) to node {$\widetilde{F}_f$} (U2);
\draw[->] (S3) to node {$\widehat{F}_f$} (U3);
\draw[->] (S1) to node [swap] {$I$} (S2);
\draw[->] (S2) to node [swap] {$\theta_{B_N}$} (S3);
\draw[->] (U1) to node {$P^{\hat{E}{\cdot}{\cdot}}_{Y_M}$} (U2);
\draw[->] (U2) to node {$\theta_{C_M}$} (U3);
\end{tikzpicture}

\end{document}

Output

enter image description here

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