how I can draw an skew cylinder (rotate around x axis) and fill it (in 3D tikz)?

Question

I can draw the black part in the picture, but I cant rotate with angle alpha and draw the red part and fill it. Also, it is obvious, two side of figure rotate, and one side is fix, and the other one just shift in the z direction.

my code:

change to:

\documentclass{standalone}
‎\usepackage{tikz,tikz-3dplot}‎‎
\begin{document}‎‎
\begin{tikzpicture}
\draw[->] (0,0,0)--++(5,0,0) node[right]{$x$};
\draw[->] (0,0,0)--++(0,5,0) node[above]{$y$};
\draw[->] (0,0,0)--++(0,0,8) node[below left]{$z$};
\draw[ultra thick] (4,0,0) arc[start angle=0, end angle=60, radius=4] --++(0,0,8.5) arc[start angle=60, end angle=0, radius=4]--cycle;
‎\filldraw[ fill=blue‎, ‎nearly transparent‎, ,‎looseness=.6](4,0,0) arc[start angle=0, end angle=60, radius=4] --++(0,0,8.5) arc[start angle=60, end angle=0, radius=4]--cycle;
\end{tikzpicture}
\end{document}

Answer 1

I'm not sure this will be much help. [But see below for a rotated version which might be more useful, at least.] You need somebody who knows a bit more (read 'anything') about the package tikz-3dplot. This is more by way of my initial experiment than an answer.

As I understand it (which is not very well at all), the package works on the basis of different coordinate systems. So the idea is that to draw an arc in 3d, you need to figure out the right x'y' plane to tell TikZ to draw in, because TikZ can only draw arcs in 2d - not 3. So one thing the package does is provide a command which calculates this plane given an angle.

\tdplotsetthetaplanecoords{30}

This effectively sets up a system of rotated coordinates which lets you draw stuff with the arcs in the appropriate x'y' plane.

... I think ...

To use this, you need to set up the main, non-rotated coordinate system first.

\tdplotsetmaincoords{45}{150}

This choice was somewhat arbitrary. Doubtless you'll want different values. This sets up the main coordinate system which is rotated about the z and x axes by the specified amounts.

\tdplotsetmaincoords{45}{150}
\begin{tikzpicture}[tdplot_main_coords]
  \draw[->] (0,0,0) -- (5,0,0) node[anchor=north east]{$x$};
  \draw[->] (0,0,0) -- (0,5,0) node[anchor=north west]{$y$};
  \draw[->] (0,0,0) -- (0,0,8) node[anchor=south]{$z$};
\end{tikzpicture}

So then we can draw and fill the non-rotated shape.

  \draw [ultra thick, preaction={fill=blue, nearly transparent}] (4,0,0) arc[start angle=0, end angle=60, radius=4] -- ++(0,0,8.5) arc[start angle=60, end angle=0, radius=4] coordinate [pos=.75] (a) -- cycle;

Then we specify the rotated coordinate system using whatever angle e.g. 30.

  \tdplotsetthetaplanecoords{30}

Now if we draw, the coordinates will be relative to the rotated system. I think. So we just need to compensate for the different positions on the circle when we are ending and starting arcs by adding 30 to the values used in the first \draw command.

  \draw [ultra thick, preaction={fill=red, nearly transparent}] (4,0,0) arc[start angle=30, end angle=90, radius=4] -- ++(0,0,8.5) arc[start angle=90, end angle=30, radius=4] coordinate [pos=.75] (b)  -- cycle;

Finally, we can add the angle a bit crudely on top.

  \draw [green, ultra thick, ->] (a) [bend right]to (b)  node [above] {$\alpha$};

Complete code:

\documentclass[border=5pt, multi, tikz]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{45}{150}
\begin{tikzpicture}[tdplot_main_coords]
  \draw[->] (0,0,0) -- (5,0,0) node[anchor=north east]{$x$};
  \draw[->] (0,0,0) -- (0,5,0) node[anchor=north west]{$y$};
  \draw[->] (0,0,0) -- (0,0,8) node[anchor=south]{$z$};
  \draw [ultra thick, preaction={fill=blue, nearly transparent}] (4,0,0) arc[start angle=0, end angle=60, radius=4] -- ++(0,0,8.5) arc[start angle=60, end angle=0, radius=4] coordinate [pos=.75] (a) -- cycle;
  \tdplotsetthetaplanecoords{30}
  \draw [ultra thick, preaction={fill=red, nearly transparent}] (4,0,0) arc[start angle=30, end angle=90, radius=4] -- ++(0,0,8.5) arc[start angle=90, end angle=30, radius=4] coordinate [pos=.75] (b)  -- cycle;
  \draw [green, ultra thick, ->] (a) [bend right]to (b)  node [above] {$\alpha$};
\end{tikzpicture}
\end{document}

EDIT

You might be able to rotate the picture as you wish by rotating the regular TikZ coordinate system using rotate around <axis>=<angle> as shown by Ktree here. For example, if I change the tikz-3d main coordinate transformation to

\tdplotsetmaincoords{-35}{0}

and use

rotate around y=-10

then, making appropriate adjustments for drawing the angle and labelling the axes, the following result can be obtained:

Complete code:

\documentclass[border=5pt, multi, tikz]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{-35}{0}
\begin{tikzpicture}[tdplot_main_coords]
  \begin{scope}[rotate around y=-10]
    \draw[->] (0,0,0) -- (5,0,0) node[anchor=west]{$x$};
    \draw[->] (0,0,0) -- (0,5,0) node[anchor=south]{$y$};
    \draw[->] (0,0,0) -- (0,0,8) node[anchor=north]{$z$};
    \draw [ultra thick, preaction={fill=blue, nearly transparent}] (4,0,0) arc[start angle=0, end angle=60, radius=4] coordinate [pos=.25] (a) -- ++(0,0,8.5) arc[start angle=60, end angle=0, radius=4] -- cycle;
    \tdplotsetthetaplanecoords{30}
    \draw [ultra thick, preaction={fill=red, nearly transparent}] (4,0,0) arc[start angle=30, end angle=90, radius=4] coordinate [pos=.2] (b) -- ++(0,0,8.5) arc[start angle=90, end angle=30, radius=4]  -- cycle;
    \draw [green!75!black, ultra thick, <->] (a) [bend right] to (b);
    \node [green!75!black, yshift=5pt, anchor=south] at (b) {$\alpha$};
  \end{scope}
\end{tikzpicture}
\end{document}

Answer 2

In question1 (duplicate of question here), I show a solution using scopes for the rotations and save path to achieve the filling. This is

• complicated and
• the path is not connected, so the corners might look ugly.

I found a much easier solution when I understood how to apply transformations only to a part of a path:

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    %coordinate system
    \draw[->] (0,0,0)--++(5,0,0) node[right]{$x$};
    \draw[->] (0,0,0)--++(0,5,0) node[above]{$y$};
    \draw[->] (0,0,0)--++(0,0,10) node[below left]{$z$};

    % cylinder:
    \draw[preaction={fill=blue,very  nearly transparent}](4,0,0) 
                arc[start angle=0, end angle=90, radius=4]node[inner sep=0](n11){}
                -- ++(0,0,8.5)node[inner sep=0](n21){}
                arc[start angle=90, end angle=0, radius=4] -- cycle;
    \draw[](n21.center)--(0,0,8.5)--(4,0,8.5);
    \draw[](0,4,0)--(n11.center);

    % skew cylinder
    \draw[ultra thick, preaction={fill=red,nearly transparent}] (4,0,0) 
        {[rotate around x=30]arc[start angle=0, end angle=90, radius=4]node[inner sep=0](n1){}} 
        -- ++(0,0,8.5) node[inner sep=0](n2){}
        {[rotate around x=30]arc[start angle=90, end angle=0, radius=4]} -- cycle;
    % the connections
    \draw[ultra thick](n2.center)--(0,0,8.5)--(4,0,8.5);
    \draw[thick, dashed](0,4,0)--(n1.center);
\end{tikzpicture}
\end{document}