Tikz picture using random number

Question

I am using currently tikz to describe a law used in a Theory. This method describes the construction of sub-Area by breaking point in different lines.

I want to reproduce this picture:

In this one, P1, P2 and P2 are the breaking point created randomly in the Line L1, L2 and L3, respectively.

This is the difficult point for me. I have currently done this part :

\begin{figure}[h]
\begin{center}
\begin{tikzpicture}
\draw (0,0) --++ (3,-3) --++ (3.5,3.5) --++ (-3,3) --cycle;
\draw (0.5,1.5) to[dashed] (1,1) -- (4,-2) to[dashed] (4.5,-2.5)node[below right]{$L_1$} ;
\draw (1.5,2.5) to[dashed] (2,2) -- (5,-1) to[dashed] (5.5,-1.5)node[below right]{$L_2$} ;
\draw (2.5,3.5) to[dashed] (3,3) -- (6,0) to[dashed] (6.5,-0.5)node[below right]{$L_3$} ;
\end{tikzpicture}
\end{center}
\end{figure}

But I don't know exactly how to create the Pn points using random variable. Of course, I think about the interpolation expression of Ln lines and place the breaking point Pn in this line but I don't know how.

The second little problem is about the dashed line, I don't know currently how plotted a line dashed in first time then fulled then dashed.

All line + statement of Area etc is dependent of the random placement of Pn. Can you help me to create this picture please?

Thanks

Answer 1

I managed to draw the entire picture and afterwards rotating it with -45 degrees. This way you can use a random() as your x coordinate:

\documentclass[tikz,margin=5mm]{standalone}

\begin{document}
    \begin{tikzpicture}[line width = .8pt]
        \begin{scope}[rotate=-45]
            \draw (0,0) rectangle (-4,5.5);
            \coordinate (L1) at (0,1.5);
            \coordinate (L2) at (0,3);
            \coordinate (L3) at (0,4.5);
            \coordinate (L4) at (0,6);

            \coordinate (p0) at (-4,0);
            \pgfmathparse{4 * random()}
            \coordinate (p1) at (L1-|-\pgfmathresult,0);
            \pgfmathparse{\pgfmathresult * (1-random())}
            \coordinate (p2) at (L2-|-\pgfmathresult,0);
            \pgfmathparse{\pgfmathresult * (1-random())}
            \coordinate (p3) at (L3-|-\pgfmathresult,0);
            \pgfmathparse{\pgfmathresult * (1-random())}
            \coordinate (p4) at (L4-|-\pgfmathresult,0);

            \foreach \i [remember=\i as \j (initially 0)] in {1,2,3,4}{
                \draw (p\j) -- (p\j|-p\i) edge[dashed] ++ (180:0.75) -- (p\i);
                \draw (p\i) -- (L\i);
                \draw[dashed] (L\i) -- ++(0:0.75) node[pos=1.5]{\( L\i \)};
                \path (p\j) -- (L\i) node[midway]{\( A_\i \)};
                \draw (p\i) circle (0.5mm) node[above=1mm]{\( P_\i \)};
            }

            \draw (p4) -| (0,5.5);

            \draw[<->] (p1) -- node[auto]{\( x \)} (p1|-0,0);
            \draw[<->] ([yshift=-2.5mm]p1) -- node[auto,swap]{\( y \)} ([yshift=-2.5mm]p1-|0,0);
        \end{scope}
    \end{tikzpicture}
\end{document}

It results in (you might need some compilations to get a good result with the random() function):

Small update:
This way one can use a certain part of the previous line without having to wait for random() creating a good value. Also I removed line L4 since that was not drawn in your example image.

\documentclass[tikz,margin=5mm]{standalone}

\begin{document}
    \begin{tikzpicture}[line width = .8pt]
        \begin{scope}[rotate=-45]
            \draw (0,0) rectangle (-4,5.5);
            \coordinate (L1) at (0,1.5);
            \coordinate (L2) at (0,3);
            \coordinate (L3) at (0,4.5);
            \coordinate (L4) at (0,6);

            \coordinate (p0) at (-4,0);
%            \pgfmathparse{4 * random()}
            \pgfmathparse{4 * 0.6}
            \coordinate (p1) at (L1-|-\pgfmathresult,0);
%            \pgfmathparse{\pgfmathresult * (1-random())}
            \pgfmathparse{\pgfmathresult * 0.5}
            \coordinate (p2) at (L2-|-\pgfmathresult,0);
%            \pgfmathparse{\pgfmathresult * (1-random())}
            \pgfmathparse{\pgfmathresult * 0.4}
            \coordinate (p3) at (L3-|-\pgfmathresult,0);
%            \pgfmathparse{\pgfmathresult * (1-random())}
            \pgfmathparse{\pgfmathresult * 0.75}
            \coordinate (p4) at (L4-|-\pgfmathresult,0);

            \foreach \i [remember=\i as \j (initially 0)] in {1,2,3,4}{
                \draw (p\j) -- (p\j|-p\i) edge[dashed] ++ (180:0.75) -- (p\i);
                \path (p\j) -- (L\i) node[midway]{\( A_\i \)};
                \draw (p\i) circle (0.5mm) node[above=1mm]{\( P_\i \)};
            }
            \foreach \i in {1,2,3}{
                \draw (p\i) -- (L\i);
                \draw[dashed] (L\i) -- ++(0:0.75) node[pos=1.5]{\( L\i \)};
            }

            \draw[dashed] (p4) -| (0,5.5);

            \draw[<->] (p1) -- node[auto]{\( x \)} (p1|-0,0);
            \draw[<->] ([yshift=-2.5mm]p1) -- node[auto,swap]{\( y \)} ([yshift=-2.5mm]p1-|0,0);
        \end{scope}
    \end{tikzpicture}
\end{document}