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如何绘制一个由两个区域分隔的圆锥体？

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如何绘制一个由两个区域分隔的圆锥体？

我可以生成一个底部为圆形的圆锥体，但我不知道如何在其中标记另一个圆锥体。我想要的最终结果如下图所示。

在此处输入图片描述

答案1

 \documentclass[tikz]{standalone}
\begin{document}
    \begin{tikzpicture}
\draw(0,0) circle (2cm and 0.5cm);
\draw(2,0) -- (0,6) -- (-2,0) arc (180:360:2cm and 0.5cm);
\draw(-2,0) arc (180:360:2cm and 0.5cm) -- (0,6) -- cycle;
\draw[dashed](-2,0) arc (180:0:2cm and 0.5cm);
\draw[dashed](2,0) -- node[below] {$2r$} (0,0); 
\draw(-1,3)arc (180:360:1cm and 0.25cm);
\draw[dashed](-1,3)arc (180:0:1cm and 0.25cm);
\draw[dashed](1,3) -- node[below=-2pt] {$r$} (0,3) ;

\draw[|-|] (-2.5,6) -- (-2.5,0) node[left,pos=.5]{$2h$};
\draw[|-|] (2.5,6) -- (2.5,3) node[right,pos=.5]{$h$};
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

您可以使用。在此代码中，您可以更改行 的tikz-3dplot值。就您而言，。x\pgfmathsetmacro\myx{\h/2}myx = h/2

\documentclass[border=1mm,tikz,12pt]{standalone} 
\usepackage{tikz-3dplot} 
\begin{document} 
    \pgfmathsetmacro\th{75} 
    \pgfmathsetmacro\az{60} 
    \tdplotsetmaincoords{\th}{\az} 
    \pgfmathsetmacro\a{1} 
    \pgfmathsetmacro\R{3*\a} %radius of base 
    \pgfmathsetmacro\h{5*\a} %hight of cone 
    \pgfmathsetmacro\myx{\h/2}
    \pgfmathsetmacro\myr{(\h-\myx)*\R/\h} 
    \pgfmathsetmacro\cott{{cot(\th)}} 
    \pgfmathsetmacro\fraction{\R*\cott/\h} 
    \pgfmathsetmacro\angle{{acos(\fraction)}} 
    \pgfmathsetmacro\PhiOne{180+(\az-90)+\angle} 
    \pgfmathsetmacro\PhiTwo{180+(\az-90)-\angle} 
    \pgfmathsetmacro\sinPhiOne{{sin(\PhiOne)}} 
    \pgfmathsetmacro\cosPhiOne{{cos(\PhiOne)}} 
    \pgfmathsetmacro\sinPhiTwo{{sin(\PhiTwo)}} 
    \pgfmathsetmacro\cosPhiTwo{{cos(\PhiTwo)}} 
    \begin{tikzpicture} [tdplot_main_coords,line join = round, line cap = round] 
    \path 
    (0,0,0) coordinate (O)
     (0,0,\h) coordinate (S)
    (0,0,\myx) coordinate (O');
    \draw[dashed] (O) -- (O') node[right, midway]{$x$};
    \draw[dashed] (S) -- (O') node[sloped,midway,auto=left]{$h-x$}; 
    \begin{scope}[canvas is xy plane at z=\myx]
    \tdplotdrawarc[thick]{(O')}{\myr}{\PhiOne}{360+\PhiTwo}{anchor=north}{}     \tdplotdrawarc[dashed]{(O')}{\myr}{\PhiTwo}{\PhiOne}{anchor=north}{}
    \draw[dashed] (O') --(\myr*\cosPhiTwo,\myr*\sinPhiTwo,0) node[midway, below] {$ r $}; 
    \end{scope}

        \tdplotdrawarc[thick]{(O)}{\R}{\PhiOne}{360+\PhiTwo}{anchor=north}{}    \tdplotdrawarc[dashed]{(O)}{\R}{\PhiTwo}{\PhiOne}{anchor=north}{}
     \draw[thick] (S) -- (\R*\cosPhiOne,\R*\sinPhiOne,0); 
    \draw[thick] (S) -- (\R*\cosPhiTwo,\R*\sinPhiTwo,0); 
    \draw[dashed] (O) --(\R*\cosPhiTwo,\R*\sinPhiTwo,0) node[midway, below] {$ R = 2r $};
    \foreach \p in {S,O,O'}
    \draw[fill=black] (\p) circle (1.5pt);
    \foreach \p/\g in {S/90,O/-90,O'/180}
    \path (\p)+(\g:3mm) node{$\p$};
    \end{tikzpicture} 
    \end{document}

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有了\pgfmathsetmacro\myx{\h/5}，我们有

在此处输入图片描述

答案3

如果你想要一个正确的 3D 锥体，你可以阅读此科学教学中的数学

代码来自 Aslanbek Naziev (梁赞国立大学)。我改编了代码以适应 v3.02。

 \documentclass{standalone} 
 \usepackage{tkz-euclide}

 \begin{document} 
 \thispagestyle{empty} 
 \begin{tikzpicture} 
 \tkzSetUpPoint[size=3] 
 \begin{scope}[xscale=2] 
 \tkzDefPoint(0,0){O_1}
 \tkzDefPoint(0,1.25){R}
 \tkzDefPoint(0,6){T}
 \tkzDefPoint(-1.25,0){A} 
 \tkzDefPoint(1.25,0){B}
 \tkzDefPoint(0,1.25){C}
 \tkzDefPoint(0,-1.25){D} 
 \tkzDefTangent[from = T](O_1,R)
 \tkzGetPoints{t_1}{t_2} 
 \tkzDrawArc[dashed](O_1,t_2)(t_1) 
 \tkzDrawArc(O_1,t_1)(t_2) 
 \tkzDefPointBy[symmetry=center O_1](t_1)
 \tkzGetPoint{t_3} 
 \tkzDrawSegments[dashed](t_1,t_3 T,O_1 C,D)
 \tkzDrawSegments(T,t_1 T,t_2 T,t_3)
 \tkzLabelPoints[above right](O_1) 
 \end{scope} 
 \tkzDefPoint(-2.5,-1.25){X1}
 \tkzDefPoint(12,-1.25){Y1} 
 \tkzDefPoint(-2.5,0){X}
 \tkzDefPoint(12,0){Y} 
 \tkzDefPoint(-2.5,1.25){X2}
 \tkzDefPoint(12,1.25){Y2} 
 \tkzDefPoint(-2.5,6){X3}
 \tkzDefPoint(12,6){Y3} 
 \tkzDefPoint(3,1.25){C'} 
 \tkzInterLC[R](X1,Y1)(C',5 cm) 
 \tkzGetPoints{D'}{E'} 
 \tkzInterLL(X,Y)(C',D') 
 \tkzGetPoint{O_1'} 
 \tkzDefLine[mediator](C',D') 
 \tkzGetPoints{F'}{G'} 
 \tkzInterLL(X3,Y3)(F',G') 
 \tkzGetPoint{T'} 
 \tkzDefCircle[in](C',T',D') 
 \tkzGetPoint{I} 
 \tkzGetLength{rIN} 
 \tkzDefTangent[from = T'](I,O_1') 
 \tkzGetPoints{G}{H} 
 \tkzInterLL(T',O_1')(G,H) 
 \tkzGetPoint{J} 
 \tkzDefLine[parallel=through J](X,Y) 
 \tkzGetPoint{j} 
 \tkzInterLL(T,O_1)(J,j) 
 \tkzGetPoint{O_2} 
 \tkzDefLine[parallel=through I](X,Y) 
 \tkzGetPoint{i} 
 \tkzDefLine[parallel=through G](X,Y) 
 \tkzGetPoint{g} 
 \tkzInterLL(T,O_1)(G,g) 
 \tkzGetPoint{C_1} 
 \begin{scope}[xscale=2] 
 \tkzDefCircle[radius](O_2,C_1) 
 \tkzDefTangent[from = T](O_2,C_1) 
 \tkzGetPoints{t_4}{t_5}
 \tkzDrawArc[dashed](O_2,t_5)(t_4) 
 \tkzDrawArc(O_2,t_4)(t_5) 
 \end{scope} 
 \tkzInterLL(T,O_1)(I,i) 
 \tkzGetPoint{O} 
 \tkzInterLC[R](T',O_1')(I,\rIN pt) 
 \tkzGetPoints{N'}{Z'} 
 \tkzDefLine[parallel=through N'](X,Y) 
 \tkzGetPoint{n} 
 \tkzInterLL(T,O_1)(N',n) 
 \tkzGetPoint{N} 
 \tkzDrawPoints(O_1,O_2,t_1,t_2,t_3) 
 \tkzLabelPoints[right](O_2) 
 \end{tikzpicture} 
 \end{document}

在此处输入图片描述

带有 5.06 和 5.10（该版本在 ctan 上可用，但尚未在所有服务器上可用）

\documentclass{standalone} 
 \usepackage{tkz-euclide}

 \begin{document} 
 \thispagestyle{empty} 
 \begin{tikzpicture} 
 \tkzSetUpPoint[size=3] 
 \begin{scope}[xscale=2] 
 \tkzDefPoint(0,0){O_1}
 \tkzDefPoint(0,1.25){R}
 \tkzDefPoint(0,6){T}
 \tkzDefPoint(-1.25,0){A} 
 \tkzDefPoint(1.25,0){B}
 \tkzDefPoint(0,1.25){C}
 \tkzDefPoint(0,-1.25){D} 
 \tkzDefTangent[from = T](O_1,R)
 \tkzGetPoints{t_2}{t_1} 
 \tkzDrawArc[dashed](O_1,t_2)(t_1) 
 \tkzDrawArc(O_1,t_1)(t_2) 
 \tkzDefPointBy[symmetry=center O_1](t_1)
 \tkzGetPoint{t_3} 
 \tkzDrawSegments[dashed](t_1,t_3 T,O_1 C,D)
 \tkzDrawSegments(T,t_1 T,t_2 T,t_3)
 \tkzLabelPoints[above right](O_1) 
 \end{scope} 
 \tkzDefPoint(-2.5,-1.25){X1}
 \tkzDefPoint(12,-1.25){Y1} 
 \tkzDefPoint(-2.5,0){X}
 \tkzDefPoint(12,0){Y} 
 \tkzDefPoint(-2.5,1.25){X2}
 \tkzDefPoint(12,1.25){Y2} 
 \tkzDefPoint(-2.5,6){X3}
 \tkzDefPoint(12,6){Y3} 
 \tkzDefPoint(3,1.25){C'} 
 \tkzInterLC[R](X1,Y1)(C',5) 
 \tkzGetPoints{D'}{E'} 
 \tkzInterLL(X,Y)(C',D') 
 \tkzGetPoint{O_1'} 
 \tkzDefLine[mediator](C',D') 
 \tkzGetPoints{F'}{G'} 
 \tkzInterLL(X3,Y3)(F',G') 
 \tkzGetPoint{T'} 
 \tkzDefCircle[in](C',T',D') 
 \tkzGetPoint{I} 
 \tkzGetLength{rIN} 
 \tkzDefTangent[from = T'](I,O_1') 
 \tkzGetPoints{G}{H} 
 \tkzInterLL(T',O_1')(G,H) 
 \tkzGetPoint{J} 
 \tkzDefLine[parallel=through J](X,Y) 
 \tkzGetPoint{j} 
 \tkzInterLL(T,O_1)(J,j) 
 \tkzGetPoint{O_2} 
 \tkzDefLine[parallel=through I](X,Y) 
 \tkzGetPoint{i} 
 \tkzDefLine[parallel=through G](X,Y) 
 \tkzGetPoint{g} 
 \tkzInterLL(T,O_1)(G,g) 
 \tkzGetPoint{C_1} 
 \begin{scope}[xscale=2] 
 \tkzDefTangent[from = T](O_2,C_1) 
 \tkzGetPoints{t_4}{t_5}
 \tkzDrawArc[dashed](O_2,t_5)(t_4) 
 \tkzDrawArc(O_2,t_4)(t_5) 
 \end{scope} 
 \tkzInterLL(T,O_1)(I,i) 
 \tkzGetPoint{O} 
 \tkzInterLC[R](T',O_1')(I,\rIN) 
 \tkzGetPoints{N'}{Z'} 
 \tkzDefLine[parallel=through N'](X,Y) 
 \tkzGetPoint{n} 
 \tkzInterLL(T,O_1)(N',n) 
 \tkzGetPoint{N} 
 \tkzDrawPoints(O_1,O_2,t_1,t_2,t_3) 
 \tkzLabelPoints[right](O_2) 
 \end{tikzpicture} 
 \end{document}

答案4

您可以使用3dtools 这里像这样

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[3d/install view={phi=110,theta=70},line join = round, line cap = round,
    declare function={R=4;v=6;% base radius and height of the cone 
        r=R/2;% radius of the small circle
        h=(R-r)*v/R;%  height of the base of the upper circle
    }] 
    \path pic{3d/cone={r=R,h=v}} (0,0,h) pic{3d/cone={r=r,h/.evaluated=v-h}};
    \draw[3d/hidden] (0,0,0) -- (0,0,v);    
\end{tikzpicture} 

\end{document}

在此处输入图片描述

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