[Tex/LaTex] How to draw a frustum like this

tikz-3dplot

I am trying to draw a frustum with centers of two bases A, C and two radii SA and CD, height of frustum AC.

I tried

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
    \tdplotsetmaincoords{60}{70}
    \begin{tikzpicture}[tdplot_main_coords,declare function={a=2;
        }]
        \path 
        (0,0,0) coordinate (A)
        (a,0,0) coordinate (B)
        (a,a,0) coordinate (C)
        (0,2*a,0) coordinate (D)
         (0,0,2*a)  coordinate (S)
        ;
\draw (A)--(B)--(C)--(D)--(S) -- cycle (S) -- (B) (S) --(C);
\draw [dashed] (D) -- (A) -- (C);
\path foreach \p/\g in {A/-90,B/-90,C/0,D/0,S/90}{(\p)node{}+(\g:2.5mm) node{$\p$}}; 

\end{tikzpicture}
\end{document}

I got

How can I draw it?

Best Answer

You can use 3dtools

\documentclass[border=3mm,tikz]{standalone}
\usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[3d/install view={phi=55,psi=0,theta=70},
        line join = round, line cap = round,
        c/.style={circle,fill,inner sep=1pt},
        declare function={a=2;r=a*sqrt(2);R=2*a;}]
        \path 
        (0,0,0) coordinate (A) 
        (a,0,0) coordinate (B)
        (a,a,0) coordinate (C) 
        (0,2*a,0) coordinate (D)
        (0,0,2*a) coordinate (S)
        [3d coordinate={(S')=(C)-(D) +(A)}];
            \tikzset{3d/define orthonormal dreibein={A={(A)},B={(S)},C={(S')}}} 
        \path[x={(ex)},y={(ey)},z={(ez)}](A) pic{3d/frustum={r=r,R=R,h=r}};
        \draw[3d/visible](C) -- (D);
    \draw[3d/hidden](S) --(A) -- (B) -- (C) (S) -- (C) (S) -- (D) (A) -- (C) (A) -- (D) (S) -- (B);             
        \path foreach \p/\g in {A/180,B/-90,C/-90,D/0,S/90}
        {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
    \end{tikzpicture}
\end{document}

\documentclass[border=3mm,12pt,tikz]{standalone}
\usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\foreach \Angle in {5,15,...,355}  
{\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70},
        line join = round, line cap = round,same bounding box=A,
        c/.style={circle,fill,inner sep=1pt},
        declare function={a=2;r=a*sqrt(2);R=2*a;}]
        \path 
        (0,0,0) coordinate (A) 
        (a,0,0) coordinate (B)
        (a,a,0) coordinate (C) 
        (0,2*a,0) coordinate (D)
        (0,0,2*a) coordinate (S)
        [3d coordinate={(S')=(C)-(D) +(A)}];
        \pgfmathsetmacro{\myB}{TD("(C)")}   
        \pgfmathtruncatemacro{\itest}{screendepth(\myB)>0?1:0}
        \ifnum\itest=1
        \draw[3d/visible] (C) -- (D);
        \draw[3d/hidden] (S) -- (A);
        \else
        \draw[3d/hidden] (D) -- (C);
        \draw[3d/visible] (S) -- (A);
        \fi   
        \draw[3d/hidden] (A) -- (C)  (A) -- (D) -- (S)
        (A) -- (B) -- (C) (S) -- (B)  -- (C) -- cycle
        ;
        \tikzset{3d/define orthonormal dreibein={A={(A)},B={(S)},C={(S')}}} 
        \path[x={(ex)},y={(ey)},z={(ez)}](A) pic{3d/frustum={r=r,R=R,h=r}};     
        \path foreach \p/\g in {A/180,B/-90,C/-90,D/0,S/90}
        {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; 
    \end{tikzpicture}}
\end{document}

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 dashed lines of this picture

Here is a little tool box that allows you to protect some (closed) path. It is based on the links mentioned in the code (and possibly more). The important pieces are

\begin{scope}
 \tikzset{protect=\rectA}
 \draw[thick,use path=\rectB];
 \draw[thick] (I) -- (M);
 \tikzset{protect=\rectB}
 \draw[thick,use path=\lineA];
\end{scope}

where the paths \rectA, \rectB and \lineA have been used before and saved with save path. \tikzset{protect=\rectA} "protects" the interior of the \rectA path, and likewise for \rectB.

\documentclass[border=2mm,tikz]{standalone} 
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
% based on
% https://tex.stackexchange.com/a/38995/121799
% https://tex.stackexchange.com/a/76216
% https://tex.stackexchange.com/a/59168/194703
% https://tex.stackexchange.com/q/448920/194703
\makeatletter 
\tikzset{
  reuse path/.code={\pgfsyssoftpath@setcurrentpath{#1}}
}
\tikzset{even odd clip/.code={\pgfseteorule},
    protect/.code={
    \clip[overlay,even odd clip,reuse path=#1]
     (-16383.99999pt,-16383.99999pt) rectangle (16383.99999pt,16383.99999pt);
    }}
\makeatother

\tikzset{intersection of line trough/.code args={#1 and #2 with plane containing #3 and normal #4}{%
        \pgfmathsetmacro{\ltest}{abs(TD("#2o#4")-TD("#1o#4"))}%
        \ifdim\ltest pt<0.01pt
        \message{Plane and line are parallel!^^J}
        \pgfmathsetmacro{\myd}{0}
        \else
        \pgfmathsetmacro{\myd}{(TD("#3o#4")-TD("#1o#4"))/(TD("#2o#4")-TD("#1o#4"))}%
        \fi
        \pgfmathsetmacro{\myP}{TD("#1+\myd*#2-\myd*#1")}%
        \pgfkeysalso{insert path={%
                (\myP)
        }}
}}

\begin{document} 
  \tdplotsetmaincoords{60}{65} 
  \begin{tikzpicture}[scale=1,tdplot_main_coords,line join = round, line cap = round, declare function={a = 3;b = 4;}]
    \path
    (0,0,b+2) coordinate (M)
    (0,0,-b) coordinate (N);

    \begin{scope} [canvas is xy plane at z=0] 
      \draw[dashed,save path=\rectB] (-a,-a) rectangle (a,a); 
    \end{scope}

    \begin{scope} [canvas is xy plane at z=a] 
    \draw[thick,save path=\rectA] (-a,-a) rectangle (a,a); 
    \end{scope}
    \draw[dashed,save path=\lineA] (M) -- (N) ;
    \path[overlay][intersection of line trough={(M) and (N) with plane containing (0,0,0) and normal (0,0,1)}] coordinate (I);
    \path[overlay][intersection of line trough={(M) and (N) with plane containing (0,0,a) and normal (0,0,1)}] coordinate (J);
    \begin{scope}
     \tikzset{protect=\rectA}
     \draw[thick,use path=\rectB];
     \draw[thick] (I) -- (M);
     \tikzset{protect=\rectB}
     \draw[thick,use path=\lineA];
    \end{scope}

    \foreach \p in {M,N,I,J}
    \draw[fill=black] (\p) circle (1pt);
    \foreach \p/\g in {M/90,N/-90,I/0,J/0}
    \path (\p)+(\g:3mm) node{$\p$};
    \draw[thick] (M) -- (J);
  \end{tikzpicture} 
\end{document}

It turns out that for some (to me obscure) reasons it can happen in some cases that the insanely large bounding box is too large. However, for most practical applications something more "modest" like

\tikzset{even odd clip/.code={\pgfseteorule}, 
protect/.code={ 
\clip[overlay,even odd clip,reuse path=#1] 
(-6383.99999pt,-6383.99999pt) rectangle (6383.99999pt,6383.99999pt); 
}}

will be more than sufficient.

Best Answer

Related Solutions

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

[Tex/LaTex] How to draw dashed lines of this picture

Related Question