TikZ-3DPlot – How to Draw a Cylinder Above a Cube with Dashed Lines

tikz-3dplot

I am trying to draw this figures with dashed lines

With Mathematica, It easy to draw.

How to draw the second picture with TeX?

I only draw the cube. My code

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
    \tdplotsetmaincoords{70}{100}
\begin{tikzpicture} [tdplot_main_coords,c/.style={circle,fill,inner sep=1pt},line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt},
        declare function={a=3;}]
        \path
        (a,-a,-a) coordinate (A)
        (a,a,-a) coordinate (B)
        (-a,a,-a) coordinate (C)
        (-a,-a,-a) coordinate (D)
        (a,-a,a) coordinate (E)
        (a,a,a) coordinate (F)
        (-a,a,a) coordinate (G)
        (-a,-a,a) coordinate (H)
        (0,0,0)  coordinate (O) ;
    \draw[] (C) -- (F) -- (H) (A) -- (F) (A) -- (B) -- (C) (E) -- (F) -- (G)-- (H)--cycle (A) -- (E) (B) --  (F) (C) -- (G);
        \draw[dashed] (A) -- (D) -- (C) (C) -- (A) -- (H)--cycle (D) -- (H);
        \path foreach \p/\g in {A/-90,B/-90,C/0,D/0,E/90,F/90,G/90,H/90}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}};  
    \end{tikzpicture}
    \end{document}

Best Answer

With the second picture, you can you 3dtools.

 \documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\foreach \Angle in {5, 10, ..., 355}
{   \begin{tikzpicture}[3d/install view={phi=\Angle,theta=70},line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt},
        declare function={a=2.5;},same bounding box=A]
        \path
        (a,-a,-a) coordinate (A)
        (a,a,-a) coordinate (B)
        (-a,a,-a) coordinate (C)
        (-a,-a,-a) coordinate (D)
        (a,-a,a) coordinate (E)
        (a,a,a) coordinate (F)
        (-a,a,a) coordinate (G)
        (-a,-a,a) coordinate (H)
        (0,0,0)  coordinate (O)
        (0,0,a) coordinate (O')
        ;   
        \tikzset{3d/polyhedron/.cd,O={(O)},
            back/.style={3d/polyhedron/complete dashes,fill=none,3d/hidden},
            fore/.style={3d/visible,fill=none},draw face with corners={{(B)},{(C)},{(G)},{(F)}},
            draw  face with corners={{(D)},{(C)},{(G)},{(H)}},
            draw  face with corners={{(A)},{(B)},{(C)},{(D)}},
            draw  face with corners={{(A)},{(B)},{(F)},{(E)}},
            draw  face with corners={{(A)},{(E)},{(H)},{(D)}}}  
        \path (O')  pic[3d/visible/.append style={save named path=cyl}]{3d/frustum={r=a,R=a,h=a}};
        \path[save named path=EFGH] (E) -- (F) -- (G) -- (H) -- cycle;
        \tikzset{3d/ordered paths/.cd,cyl/.style={draw=none}}
        % draw ordered objects  
        \tikzset{3d/draw ordered paths={EFGH,cyl}}
        \path foreach \p/\g in {A/-90,B/180,C/-90,D/-90,E/0,F/90,G/-30,H/0,O'/90}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
    \end{tikzpicture}}
\end{document}

I tried with GeoGebra and put the file at here. You can rotate the figure with mouse.

Related Solutions

[Tex/LaTex] How to draw cylinder inside a sphere like this picture with Tikz

Points (A) (B) (A') and (B') are not the edges of the cylinder, but rather the points where the visible edge of the sphere (circle) and the visible edge of of the cylinder (ellipse) intersect, which depend on the viewing angles.
Points (C) and (D) represent the visible right and left edges.

\documentclass[12pt,border=3mm]{standalone}
\usepackage{fouriernc}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc,backgrounds}
\begin{document}
\def\myangle{70}%
\tdplotsetmaincoords{\myangle}{0}%

\begin{tikzpicture}[scale=1,tdplot_main_coords]
\pgfmathsetmacro{\r}{2*sqrt(3)}% sphere radius=4, cylendar height=4
\path% common coordinates
  (0,0,-2) coordinate (O)
  (0,0,0) coordinate (I)
  (0,0,2) coordinate (O')
  (O) ++(0:\r) coordinate (C)% right edge
  (O) ++(180:\r) coordinate (D);% left edge
\draw[dashed,thick] (C)-- ++(0,0,4) (D)-- ++(0,0,4);
\draw[dashed] (O)--(O');
\begin{scope}[tdplot_screen_coords, on background layer]
      \fill[ball color=orange!70, opacity=1.0] (I) circle (4);
\end{scope}

\pgfmathsetmacro{\mynumer}{2*cos(\myangle)}
\pgfmathsetmacro{\mydenom}{\r*sin(\myangle)}
\pgfmathsetmacro{\quadrant}{ifthenelse(abs(\mynumer)<abs(\mydenom), 0,
  ifthenelse(\mynumer>0, 1, 2))}% 0=side, 1=top, 2=bottom

\ifcase\quadrant
  \pgfmathsetmacro{\intercept}{asin(\mynumer/\mydenom)}
  \path
    (O) ++(-\intercept:\r) coordinate (A)
    (O) ++(-180+\intercept:\r) coordinate (B)
    (O') ++(\intercept:\r) coordinate (A')
    (O') ++(180-\intercept:\r) coordinate (B');
  \draw [thick] (B) arc (-180+\intercept:-\intercept:\r);
  \draw [thick, dashed] (A) arc (-\intercept:180+\intercept:\r);
  \draw [thick] (B') arc (-180-\intercept:\intercept:\r);
  \draw [thick, dashed] (A') arc (\intercept:180-\intercept:\r);

  \foreach \v/\position in {I/left,O/below,O'/above,A/below,B/below,A'/left,B'/left} {
    \draw[draw =black, fill=black] (\v) circle (1.2pt) node [\position=0.2mm] {$\v$};
  }
\or% top
  \path
    (C) coordinate (A)
    (D) coordinate (B)
    (A) ++(0,0,4) coordinate (A')
    (B) ++((0,0,4) coordinate (B');
  \draw [thick] (O') circle (\r);
  \draw [thick, dashed] (O) circle (\r);

  \foreach \v/\position in {I/left,O/below,O'/above,A/below,B/below,A'/left,B'/left} {
    \draw[draw =black, fill=black] (\v) circle (1.2pt) node [\position=0.2mm] {$\v$};
  }
\or% bottom
  \path
    (C) coordinate (A)
    (D) coordinate (B)
    (A) ++(0,0,4) coordinate (A')
    (B) ++((0,0,4) coordinate (B');
  \draw [thick,dashed] (O') circle (\r);
  \draw [thick] (O) circle (\r);

  \foreach \v/\position in {I/left,O/below,O'/above,A/below,B/below,A'/left,B'/left} {
    \draw[draw =black, fill=black] (\v) circle (1.2pt) node [\position=0.2mm] {$\v$};
  }
\fi

\draw[dashed] (O)--(A) (I) --(A);
\tkzMarkRightAngle[size = 0.3](I,O,A);
\end{tikzpicture}
\end{document}

[Tex/LaTex] How to draw a square on cylinder

Consider three points on the square, say B, C and D. Without loss of generality we can assume that they have the coordinates

 C = (r \cos \phi,r \sin\phi,h)
 D = (r \cos (180-\phi),r \sin(180-\phi),h)
 B = (r \cos \phi,-r \sin\phi,0)

The conditions that they form a square mean that

 CD = BC

where

 CD = 2r \cos \phi
 BC = \sqrt{(2r \sin\phi)^2+h^2}

This yields

 \phi = \acos(h^2/(4r^2))/2

This confirms hpechristiansens numerical result:

 CD = 2 r \cos \left(\frac{1}{2} \acos\left(\frac{h^2}{4 r^2}\right)\right)

MWE

\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot} 
\usetikzlibrary{3d,calc,backgrounds,patterns}
\begin{document}
\pgfmathsetmacro{\myr}{3}
\pgfmathsetmacro{\h}{2}
\pgfmathsetmacro{\angA}{acos(\h*\h/(4*\myr*\myr))/2}
\tdplotsetmaincoords{65}{100}
\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,line join=round]
\begin{scope}[canvas is xy plane at z=0]
\draw[dashed] (\tdplotmainphi:\myr) arc(\tdplotmainphi:\tdplotmainphi+180:\myr);
\coordinate (O) at (0,0);
\coordinate (A) at (\angA:\myr);
\coordinate (B) at (180-\angA:\myr);
\draw[thick] (\tdplotmainphi:\myr) coordinate(BR) arc(\tdplotmainphi:\tdplotmainphi-180:\myr)
coordinate(BL);
\end{scope}
\begin{scope}[canvas is xy plane at z=\h]
\coordinate (O') at (0,0);
\coordinate (C) at (-180+\angA:\myr);
\coordinate (D) at (-\angA:\myr);
\draw[thick]  (O') circle[radius=\myr];
\draw [thick](BR) -- (\tdplotmainphi:\myr) (BL) -- (\tdplotmainphi-180:\myr); 
\end{scope}
\fill (A) circle[radius=1pt] node[above] {$A$};
\fill (B) circle[radius=1pt] node[above] {$B$};
\fill (C) circle[radius=1pt] node[above] {$C$};
\fill (D) circle[radius=1pt] node[above] {$D$};
\draw[dashed]  (C) -- (B) --   (A);
\draw[thick] (A) -- (D) -- (C);
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] How to draw cylinder inside a sphere like this picture with Tikz

[Tex/LaTex] How to draw a square on cylinder

Related Question