TikZ: Partially dashed curved line

Question

I would like to draw a semi-dashed curved line similar to the line corresponding to \theta_b in the figure below. I used the shorten option there which unfortunately modifies the shape of curved lines. What is the easiest way to do that? Here's my full code (the bit corresponding to the curved line is at the end after % temperature values):

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=2]
  % cell dimensions
  \newcommand{\Dx}{3};
  \newcommand{\Dy}{1};
  \newcommand{\Dz}{2};
  % cell vertices
  \coordinate (O) at (0,\Dy,0);
  \coordinate (A) at (0,\Dy,\Dz);
  \coordinate (B) at (\Dx,\Dy,\Dz);
  \coordinate (C) at (\Dx,0,\Dz);
  \coordinate (D) at (0,0,\Dz);
  \coordinate (E) at (\Dx,\Dy,0);
  \coordinate (F) at (\Dx,0,0);
  \coordinate (G) at (0,0,0);
  % cell faces
  \draw[semithick] (A) -- (B) -- (C) -- (D) -- cycle;  % front face
  \draw[semithick] (B) -- (C) -- (F) -- (E) -- cycle;  % left face
  \draw[semithick] (A) -- (B) -- (E) -- (O) -- cycle;  % top face
  % dashed lines
  \coordinate (P) at (0,-0.77,0);  % bottom of back dashed line
  \draw[dashed,color=gray] (D) -- (G);
  \draw[dashed,color=gray] (G) -- (F);
  \draw[dashed,color=gray] (O) -- (G);
  \draw[dashed,color=gray] (G) -- (P);
  % coordinate lines
  \draw[->] (E) -- ++(0.5,0,0) node[anchor=south west] {$x$};
  \draw[->] (A) -- ++(0,0,1) node[anchor=east] {$y$};
  \draw[->] (P) -- ++(0,-0.5,0) node[anchor=north east] {$z$};
  % dimension lines
  \newcommand{\h}{0.2}
  \draw (O) -- ++(0,\h,0);
  \draw (E) -- ++(0,\h,0);
  \draw (A) -- ++(0,\h,0);
  \draw (A) -- ++(-\h,0,0);
  \draw (D) -- ++(-\h,0,0);
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(E)+(0,\h/2,0)$) node[midway,above] {$2\pi/a_x$};
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(A)+(0,\h/2,0)$) node[xshift=1.5ex, yshift=6.7ex] {$2\pi/a_y$};
  \draw[<->] ($(A)+(-\h/2,0,0)$) -- ($(D)+(-\h/2,0,0)$) node[midway,left] {$d$};
  % temperature values
  \draw (\Dx/2,\Dy,\Dz/2) node {$\theta_s$};
  \filldraw[color=gray] (\Dx/2,0,\Dz/2) circle (0.5pt);
  \draw[dashed,color=gray,shorten >=5]  (0.5*\Dx,0,0.5*\Dz) .. controls (0.6*\Dx,-0.125*\Dy,0.8*\Dz) .. (0.75*\Dx,-0.3*\Dy,1*\Dz);
  \draw[shorten <=25]  (0.5*\Dx,0,0.5*\Dz) .. controls (0.6*\Dx,-0.125*\Dy,0.8*\Dz) .. (0.75*\Dx,-0.3*\Dy,1*\Dz) node[xshift=1.5ex, yshift=-0.7ex] {$\theta_b$};
\end{tikzpicture}
\end{document}

Answer 1

Well, if all you want to do is to have a smooth curve that changes to a dashed pattern inside the box, just draw two curves with the to[in=...,out=...] syntax and make sure that the angles match, i.e. the in of the incoming curve and the out of the outgoing curve have to differ by 180.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=2]
  % cell dimensions
  \newcommand{\Dx}{3};
  \newcommand{\Dy}{1};
  \newcommand{\Dz}{2};
  % cell vertices
  \coordinate (O) at (0,\Dy,0);
  \coordinate (A) at (0,\Dy,\Dz);
  \coordinate (B) at (\Dx,\Dy,\Dz);
  \coordinate (C) at (\Dx,0,\Dz);
  \coordinate (D) at (0,0,\Dz);
  \coordinate (E) at (\Dx,\Dy,0);
  \coordinate (F) at (\Dx,0,0);
  \coordinate (G) at (0,0,0);
  % cell faces
  \draw[semithick] (A) -- (B) -- (C) -- (D) -- cycle;  % front face
  \draw[semithick] (B) -- (C) -- (F) -- (E) -- cycle;  % left face
  \draw[semithick] (A) -- (B) -- (E) -- (O) -- cycle;  % top face
  % dashed lines
  \coordinate (P) at (0,-0.77,0);  % bottom of back dashed line
  \draw[dashed,color=gray] (D) -- (G);
  \draw[dashed,color=gray] (G) -- (F);
  \draw[dashed,color=gray] (O) -- (G);
  \draw[dashed,color=gray] (G) -- (P);
  % coordinate lines
  \draw[->] (E) -- ++(0.5,0,0) node[anchor=south west] {$x$};
  \draw[->] (A) -- ++(0,0,1) node[anchor=east] {$y$};
  \draw[->] (P) -- ++(0,-0.5,0) node[anchor=north east] {$z$};
  % dimension lines
  \newcommand{\h}{0.2}
  \draw (O) -- ++(0,\h,0);
  \draw (E) -- ++(0,\h,0);
  \draw (A) -- ++(0,\h,0);
  \draw (A) -- ++(-\h,0,0);
  \draw (D) -- ++(-\h,0,0);
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(E)+(0,\h/2,0)$) node[midway,above] {$2\pi/a_x$};
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(A)+(0,\h/2,0)$) node[xshift=1.5ex, yshift=6.7ex] {$2\pi/a_y$};
  \draw[<->] ($(A)+(-\h/2,0,0)$) -- ($(D)+(-\h/2,0,0)$) node[midway,left] {$d$};
  % temperature values
  \draw (\Dx/2,\Dy,\Dz/2) node {$\theta_s$};
  \filldraw[color=gray] (\Dx/2,0,\Dz/2) circle (0.5pt);
   \draw[dashed,color=gray]  (0.66*\Dx,0,\Dz) to[out=110,in=-100] (0.5*\Dx,0,0.5*\Dz);
   \draw  (0.66*\Dx,0,\Dz) 
   to[out=-70,in=135] (0.75*\Dx,-0.3*\Dy,1*\Dz) node[xshift=1.5ex, yshift=-0.7ex] {$\theta_b$};
\end{tikzpicture}
\end{document}

Answer 2

Sorry for bumping this topic but, while looking for something else, I found this solution a bit unattractive. One better solution, in my opinion, would be to simply draw the same curve twice, with different clipping options in scopes.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=2]
  % cell dimensions
  \newcommand{\Dx}{3};
  \newcommand{\Dy}{1};
  \newcommand{\Dz}{2};
  % cell vertices
  \coordinate (O) at (0,\Dy,0);
  \coordinate (A) at (0,\Dy,\Dz);
  \coordinate (B) at (\Dx,\Dy,\Dz);
  \coordinate (C) at (\Dx,0,\Dz);
  \coordinate (D) at (0,0,\Dz);
  \coordinate (E) at (\Dx,\Dy,0);
  \coordinate (F) at (\Dx,0,0);
  \coordinate (G) at (0,0,0);
  % cell faces
  \draw[semithick] (A) -- (B) -- (C) -- (D) -- cycle;  % front face
  \draw[semithick] (B) -- (C) -- (F) -- (E) -- cycle;  % left face
  \draw[semithick] (A) -- (B) -- (E) -- (O) -- cycle;  % top face
  % dashed lines
  \coordinate (P) at (0,-0.77,0);  % bottom of back dashed line
  \draw[dashed,color=gray] (D) -- (G);
  \draw[dashed,color=gray] (G) -- (F);
  \draw[dashed,color=gray] (O) -- (G);
  \draw[dashed,color=gray] (G) -- (P);
  % coordinate lines
  \draw[->] (E) -- ++(0.5,0,0) node[anchor=south west] {$x$};
  \draw[->] (A) -- ++(0,0,1) node[anchor=east] {$y$};
  \draw[->] (P) -- ++(0,-0.5,0) node[anchor=north east] {$z$};
  % dimension lines
  \newcommand{\h}{0.2}
  \draw (O) -- ++(0,\h,0);
  \draw (E) -- ++(0,\h,0);
  \draw (A) -- ++(0,\h,0);
  \draw (A) -- ++(-\h,0,0);
  \draw (D) -- ++(-\h,0,0);
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(E)+(0,\h/2,0)$) node[midway,above] {$2\pi/a_x$};
  \draw[<->] ($(O)+(0,\h/2,0)$) -- ($(A)+(0,\h/2,0)$) node[xshift=1.5ex, yshift=6.7ex] {$2\pi/a_y$};
  \draw[<->] ($(A)+(-\h/2,0,0)$) -- ($(D)+(-\h/2,0,0)$) node[midway,left] {$d$};
  % temperature values
  \draw (\Dx/2,\Dy,\Dz/2) node {$\theta_s$};
  
  
  \filldraw[color=gray] (\Dx/2,0,\Dz/2) circle (0.5pt);
  
  %Here is the modified code
  
  \def\pathtodraw{(\Dx/2,0,\Dz/2) to[out=-90,in=160] (0.8*\Dx,-0.3*\Dy,1*\Dz)}
  
  \begin{scope}
        \clip (0,-.78) rectangle (2,0);
        \draw[dashed,color=gray] \pathtodraw;
   \end{scope}
   
   \begin{scope}
        \clip (0,-.78) rectangle (3,-2);
        \draw  \pathtodraw node[xshift=1.5ex, yshift=-0.7ex] {$\theta_b$};
   \end{scope}
   
   
\end{tikzpicture}
\end{document}