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如何绘制表面的无限小部分？

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如何绘制表面的无限小部分？

我正在尝试使用 TikZ 绘制以下图形，但发现了一些问题：

在此处输入图片描述

这是我的尝试：

    \begin{tikzpicture}
\def\a{2} 
\def\b{1} 
\def\h{6}
\draw[->] (0,0)--(-\a,0) node[midway, above]{$r$};
\filldraw (0,0) circle(1pt); 
\filldraw (0,\h) circle(1pt); 
\draw[dashed, ->] (0,\h)--(0,\h+2) node[left] {$d\vec{S}$};
\draw[blue, thick] (\a,0)--(\a,\h) (-\a,0)--(-\a,\h);
\draw[dashed,blue, thick] (\a,0) arc [x radius=\a, y radius=\b, start angle=0, end angle=180];
\draw[blue, thick] (-\a,0) arc [x radius=\a, y radius=\b, start angle=180, end angle=360];
\draw[blue, thick]  (0,\h) ellipse (\a cm and \b cm);
\draw[->] (0,\h)--(3,\h) node[above, midway] {$\vec{E}$}; 
\draw[ultra thick] (0,0)--(0,\h) node[midway, left] {$\lambda >0$};
\end{tikzpicture}

在此处输入图片描述

我还需要绘制一些其他的图形，例如：

在此处输入图片描述

我的问题总是出在表面部分。有什么想法吗？

答案1

旧符号：circle(1pt)和新符号：circle[radius=1 pt]。当你把它们混在一起时，我就很焦虑。

\documentclass[tikz, border=1 cm]{standalone}
\begin{document}
\begin{tikzpicture}
\def\a{2} 
\def\b{1} 
\def\h{6}
\draw[->] (0,0)--(-\a,0) node[midway, above]{$r$};
\filldraw (0,0) circle[radius=1 pt]; 
\filldraw (0,\h) circle[radius=1 pt]; 
\draw[dashed, ->] (0,\h)--(0,\h+2) node[left] {$d\vec{S}$};
\draw[blue, thick] (\a,0)--(\a,\h) (-\a,0)--(-\a,\h);
\draw[dashed,blue, thick] (\a,0) arc[x radius=\a, y radius=\b, start angle=0, end angle=180];
\draw[blue, thick] (-\a,0) arc[x radius=\a, y radius=\b, start angle=180, end angle=360];
\draw[blue, thick]  (0,\h) ellipse[x radius=\a, y radius=\b];
\draw[->] (0,\h)--(3,\h) node[above, midway] {$\vec{E}$}; 
\draw[ultra thick] (0,0)--(0,\h) node[midway, left] {$\lambda >0$};
\draw[red, thick, fill=pink, opacity=0.5]
  ({\a*cos(-80)},{\b*sin(-80)+4}) arc[x radius=\a, y radius=\b, start angle=-80, end angle=-60] --
  ({\a*cos(-60)},{\b*sin(-60)+3.4}) arc[x radius=\a, y radius=\b, start angle=-60, end angle=-80] -- cycle;
\draw[red, thick, ->] ({\a*cos(-70)},{\b*sin(-70)+3.7}) -- ({2*\a*cos(-70)},{2*\b*sin(-70)+3.7}) node[above right, midway]{$\vec{E}$};
\end{tikzpicture}
\end{document}

表面积较小的圆柱体

答案2

这是不同表面和体积元素的代码

% !TeX encoding = utf8
% !TeX spellcheck = fr

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,positioning,fit}
\usepackage{tikz-3dplot}
\usepackage[french]{babel}
\usepackage[margin=1cm]{geometry}


\usepackage{subfig}
\usepackage{esvect}

\begin{document}



\begin{figure}[!htb]
\centering

\makeatletter
\define@key{x sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{x sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{x sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
    \setkeys{x sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*cos(\mytheta)}{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}}

%along y axis
\define@key{y sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{y sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{y sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
    \setkeys{y sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*cos(\mytheta)}{\myradius*sin(\mytheta)*sin(\myphi)}}


%along z axis
\define@key{z sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{z sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{z sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
    \setkeys{z sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}{\myradius*cos(\mytheta)}}

\makeatother
\subfloat[coordonnées cartésiennes]{
\begin{tikzpicture}[scale=1.2]
\draw[fill=yellow] (0.2,0.2)coordinate(aa)  rectangle (2,3)coordinate(bb);
\draw[-latex] (0,0) -- (2.5,0) node[above](xx){$\vv{x}$};
\draw[-latex] (0,0) coordinate(oo) -- (0,3.3) node[right](yy){$\vv{y}$};

\draw[dashed] (oo-|aa)node[below]{$X_1$} --(aa);
\draw[dashed] (oo|-aa)node[left]{$Y_1$} --(aa);
\draw[dashed] (oo-|bb)node[below](X2){$X_2$} --(aa-|bb);
\draw[dashed] (oo|-bb)node[left](Y2){$Y_2$} --(aa|-bb);
\node[fill=gray] (P) at (1.2,1.3){+};
\node[above=0em of P] {$\mathrm{d}x$};
\node[right=0em of P] {$\mathrm{d}y$};
\draw[dashed] (P.center) --(P.center|-oo)node[below]{$x$};
\draw[dashed] (P.center) --(oo|-P.center)node[left]{$y$};

\node[fit=(xx) (Y2) (X2)](cadre){};
\node[below=0em of cadre]{$\mathrm{d} s= \mathrm{d} x \cdot \mathrm{d} y$};
\end{tikzpicture}
}
\hspace{1em}
\subfloat[coordonnées polaires]{
\begin{tikzpicture}[scale=1.3]
\draw [dashed] (0,0) coordinate(oo) -- (15:1.5cm)coordinate(aa) --(15:3cm)coordinate(bb);
\draw [dashed] (0,0) coordinate(oo) -- (75:1.5cm)coordinate(aa1) --(75:3cm)coordinate(bb1);
\draw[fill=yellow] (aa) arc (15:75:1.5cm) -- (bb1) arc (75:15:3cm) --(aa);
\draw[-latex] (0,0) -- (3.5,0) node[above]{$\vv{x}$};
\draw[-latex] (0,0) coordinate(oo) -- (0,3) node[right]{$\vv{y}$};

\draw [-latex] (2.5,0) arc(0:15:2.5cm);
\path (0,0) -- (60:.9cm)node[above right=0em]  {$\theta_2$} ;
\draw [-latex] (1,0) arc (0:75:1cm);
\path (0,0) -- (5:2.5cm)node[right]  {$\theta_1$} ;
\draw[dashed] (1.5,0) node[below]{$R_1$}arc (0:15:1.5cm);
\draw[dashed] (3,0) node[below](R2){$R_2$}arc (0:15:3cm);

\draw[fill=gray] (35:2cm) coordinate(aa) arc (35:43:2cm)coordinate(bb) --(43:2.5) arc (43:35:2.5) -- (35:2cm) ;
\draw[dashed] (0,0) -- (aa);
\draw[dashed] (0,0) --(bb);
\node (P) at (39:2.25){+};
\node[above right=0em of P]{$r\cdot\mathrm{d}\theta$};
\draw[dashed] (0,0) --(P.center)node[right]{$P$};
\node[above left=0em of P]{$\mathrm{d}r$};
\draw[latex-latex] (46:2cm) -- (46:2.5cm);
\draw[latex-latex] (35:2.7cm) arc (35:43:2.7cm);
\draw[dashed] (2.25,0) node[below]{$r$}arc (0:39:2.25cm);
\draw [-latex] (1.7,0) arc (0:38:1.7cm);
\path (0,0) -- (6:1.7cm)node[right]  {$\theta$} ;

\node[fit=(xx) (yy) (R2)](cadre){};
\node[below=0em of cadre]{$\mathrm{d} s=r\cdot \mathrm{d} \theta \cdot \mathrm{d} r$};
\end{tikzpicture}
}



\subfloat[coordonnées cylindriques ]{

 \begin{tikzpicture}[scale=2.6]

   \begin{scope}[canvas is zx plane at y=0]
     %\draw (0,0) circle (1cm);
     \draw (0,0)coordinate(O) -- (1,0) (0,0) -- (0,1);
      \coordinate (Z0) at (0:0.5);
     \draw[fill=green!30,opacity=0.3] (0,0) -- (10:1)coordinate(A1) arc (10:110:1) coordinate(A2)-- (0,0);
     \foreach \aa in {10,15,20,...,110}{
     \coordinate (A\aa) at (\aa:1); 
     }
   \end{scope}
   
      \begin{scope}[canvas is zx plane at y=0.9]
     \draw[fill=green!30,opacity=0.3] (0,0) -- (10:1)coordinate(B1) arc (10:110:1) coordinate(B2)-- (0,0);
     \foreach \aa in {10,15,20,...,110}{
     \coordinate (B\aa) at (\aa:1);
     }
     
   \end{scope}
   
    \begin{scope}[canvas is zx plane at y=0.4]
          \foreach \aa in {30,32,34,...,42}{
     \coordinate (C\aa) at (\aa:1);
     }
     \draw[dashed](0,0)-- (0:1.5);   
     \coordinate (Z4) at (0:0.5);     
     \draw[dashed](0,0) -- (C30) coordinate[pos=2] (ff) -- (ff);    
     \draw[dashed](0,0) -- (C42) coordinate[pos=2] (ff) -- (ff);
     \draw[-latex] (0:1.5) arc (0:30:1.5)node[pos=0.5,below]{$\theta$};
      \draw[latex-latex] (30:1.6) arc (30:40:1.6)node[pos=0.5,below]{$\mathrm{d}\,\theta$};
   \end{scope}
   
    \begin{scope}[canvas is zx plane at y=0.65]
          \foreach \aa in {30,32,34,...,42}{
     \coordinate (D\aa) at (\aa:1);
     }
     \draw[dashed](0,0)coordinate(Z6) -- (D30);    
     \draw[dashed](0,0) -- (D42);
     \coordinate (Z6) at (0:0.5);
   \end{scope}

 \draw[-latex] (0,0,0) -- (1.1,0,0) node[above](yy){$\vv{y_0}$};
  \draw[-latex] (0,0,0) -- (0,1.1,0) node[above](zz){$\vv{z_0}$};
    \draw[-latex] (0,0,0) -- (0,0,1.1) node[above](xx){$\vv{x_0}$};

\foreach \aa in {10,15,20,...,105}{
\pgfmathsetmacro{\bb}{\aa+5}
\fill[fill=black!30,opacity=0.3] (A\aa) -- (A\bb) -- (B\bb) -- (B\aa) -- cycle;   
}

\foreach \aa in {30,32,34,...,40}{
\pgfmathsetmacro{\bb}{\aa+2}
\fill[fill=blue,opacity=0.3] (C\aa) -- (C\bb) -- (D\bb) -- (D\aa) -- cycle;   
}

\draw[-latex] (Z0) -- (Z4) node[left,pos=0.5]{$z$};
\draw[latex-latex] (Z4) -- (Z6) node[left,pos=0.5]{$\mathrm{d}\,z$};

\node[fit=(xx) (yy) (zz)](cadre){};
\node[below=0.5em of cadre]{ $\mathrm{d}s=r\cdot \mathrm{d}\theta\cdot \mathrm{d} z $};
\end{tikzpicture}
}
\subfloat[coordonnées sphériques]{

\tdplotsetmaincoords{60}{110}

\pgfmathsetmacro{\rvec}{.8}
\pgfmathsetmacro{\thetavec}{30}
\pgfmathsetmacro{\phivec}{55}
\pgfmathsetmacro{\dphi}{12}
\pgfmathsetmacro{\dtheta}{12}
\pgfmathsetmacro{\drvec}{0.15}
\pgfmathsetmacro{\Rvec}{\rvec+\drvec}
\pgfmathsetmacro{\Thetavec}{\thetavec+\dtheta}
\pgfmathsetmacro{\Phivec}{\phivec+\dphi}

\begin{tikzpicture}[scale=4,tdplot_main_coords]


%-----------------------
\coordinate (O) at (0,0,0);


\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
\tdplotsetcoord{P3}{\rvec}{\Thetavec}{\phivec}

\tdplotsetcoord{Q}{\rvec}{\thetavec}{\Phivec}

\tdplotsetcoord{Q3}{\rvec}{\Thetavec}{\Phivec}

\tdplotsetthetaplanecoords{0}
\draw[red,fill=green!30,,tdplot_rotated_coords] (0,0) -- (\rvec,0,0) arc (0:90:\rvec) -- (0,0);

\tdplotsetthetaplanecoords{90}
\draw[red,fill=green!30,,tdplot_rotated_coords] (0,0) -- (\rvec,0,0) arc (0:90:\rvec) -- (0,0);
\draw (0,0) -- (30:\rvec) coordinate[pos=1.2](ff);
\draw[latex-] (30:\rvec) -- (ff)--++(0,0.1)node[above]{$R$};

\draw[] (\rvec,0,0) arc (0:90:\rvec);
\foreach \aa in {0,2,4,...,90}{
\coordinate (A\aa) at (\aa:\rvec);
}

 if you want to convince yourself that this works:
 \draw[blue,fill=green!30,opacity=0.5] plot[variable=\x,domain=90:0] 
 (z spherical cs: radius = \rvec, phi = 0, theta= \x)
 -- plot[variable=\x,domain=0:90] 
 (z spherical cs: radius = \rvec, phi = \x, theta= 0)
 -- plot[variable=\x,domain=0:90] 
 (z spherical cs: radius = \rvec, phi = 90, theta= \x) 
 -- plot[variable=\x,domain=90:0] 
 (z spherical cs: radius = \rvec, phi = \x, theta= 90);


%draw figure contents
%--------------------
%draw the main coordinate system axes
\draw[thick,->] (0,0,0) -- (0.9,0,0) node[above](xx){$\vv{x}$};
\draw[thick,->] (0,0,0) -- (0,0.9,0) node[above](yy){$\vv{y}$};
\draw[thick,->] (0,0,0) -- (0,0,0.9) node[right](zz){$\vv{z}$};

%draw a line from origin to point (P) 
\draw[,color=red] (O) -- (P)

;
\draw[,color=red] (O) -- (P3);
\draw[color=red] (O) -- (Q3);


\draw[dashed, color=red] (O) -- (Pxy);
\draw[dashed, color=red] (P) -- (Pxy);
%
\draw[dashed, color=red] (O) -- (P3xy);
\draw[dashed, color=red] (P3) -- (P3xy);

%draw a line from origin to point (Q) 
\draw[,color=red] (O) -- (Q);
\draw[,color=red] (O) -- (Q3);


\draw[dashed, color=red] (O) -- (Qxy);
\draw[dashed, color=red] (Q) -- (Qxy);
%
\draw[dashed, color=red] (O) -- (Q3xy);
\draw[dashed, color=red] (Q3) -- (Q3xy);

\pgfmathsetmacro{\Rproj}{\Rvec*sin(\Thetavec)}

\draw[latex-latex] (P3xy) -- (Q3xy)node[below]{$\mathrm{d}\theta$};


\tdplotdrawarc[-latex]{(O)}{0.3}{0}{\phivec}{anchor=north}{$\theta$}

\tdplotsetthetaplanecoords{\phivec}

\tdplotdrawarc[tdplot_rotated_coords,-latex]{(0,0,0)}{0.5}{0}{\thetavec}{anchor=south west}{$\varphi$}
\tdplotdrawarc[tdplot_rotated_coords,latex-latex]{(0,0,0)}{0.55}{\thetavec}{\Thetavec}{anchor=south west}{$\mathrm{d}\phi$}


\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);

\draw[dashed] (\rvec,0,0) arc (0:90:\rvec);

\tdplotsetthetaplanecoords{\Phivec}


\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
\begin{scope}[tdplot_main_coords]
\draw[blue,fill=blue!30 ] plot[variable=\x,domain=\thetavec:\Thetavec] 
(z spherical cs: radius = \rvec, phi = \Phivec, theta= \x)
-- plot[variable=\x,domain=\Phivec:\phivec] 
(z spherical cs: radius = \rvec, phi = \x, theta= \Thetavec)
-- plot[variable=\x,domain=\Thetavec:\thetavec] 
(z spherical cs: radius = \rvec, phi = \phivec, theta= \x) 
-- plot[variable=\x,domain=\phivec:\Phivec] 
(z spherical cs: radius = \rvec, phi = \x, theta= \thetavec);
%

\end{scope}
\node[fit=(xx) (yy) (zz)](cadre){};
\node[below=0em of cadre]{$\mathrm{d} s=R\cdot  \sin\varphi \cdot \mathrm{d} \theta \cdot R\cdot \mathrm{d} \varphi$};
\end{tikzpicture}
}

\caption{Élément de surface $\mathrm{d}s$}
\label{fig:elementdesurface}
\end{figure}




\begin{figure}[!htb]
\makeatletter
\define@key{x sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{x sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{x sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x
    \setkeys{x sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*cos(\mytheta)}{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}}

%along y axis
\define@key{y sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{y sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{y sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x
    \setkeys{y sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*cos(\mytheta)}{\myradius*sin(\mytheta)*sin(\myphi)}}


%along z axis
\define@key{z sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{z sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{z sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
    \setkeys{z sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}{\myradius*cos(\mytheta)}}

\makeatother

\tdplotsetmaincoords{60}{110}

\pgfmathsetmacro{\rvec}{.7}
\pgfmathsetmacro{\thetavec}{30}
\pgfmathsetmacro{\phivec}{50}
\pgfmathsetmacro{\dphi}{12}
\pgfmathsetmacro{\dtheta}{12}
\pgfmathsetmacro{\drvec}{0.2}
\pgfmathsetmacro{\Rvec}{\rvec+\drvec}
\pgfmathsetmacro{\Thetavec}{\thetavec+\dtheta}
\pgfmathsetmacro{\Phivec}{\phivec+\dphi}

\centering
\subfloat[coordonnées cartésiennes]{
\begin{tikzpicture}[scale=0.5]
\coordinate(O) at (0,0,0);
\coordinate(A1) at (4,4,4);
\draw[fill=red!80,opacity=0.5] ($(A1)+(0.4,0.4,0) $)coordinate(aa)  --($(A1)+(0.4,-0.4,0)$)coordinate(bb) --($(A1)+(-0.4,-0.4,0)$)coordinate(cc) --($(A1)+(-0.4,0.4,0)$)coordinate(dd)-- cycle;
\draw[fill=red!80,opacity=0.5] ($(A1)+(0.4,0.4,0.8) $)coordinate(aa1) --($(A1)+(0.4,-0.4,0.8)$)coordinate(bb1) --($(A1)+(-0.4,-0.4,0.8)$)coordinate(cc1)--($(A1)+(-0.4,0.4,0.8)$)coordinate(dd1)-- cycle;
\foreach \aa/\bb in {cc/dd,dd/aa,aa/bb,bb/cc}{
\draw[fill=red!80,opacity=0.5] (\aa) --(\aa1) --(\bb1) --(\bb) ;
}

\coordinate(A) at (6,5.8,4.8);
\draw[fill=green!50,opacity=0.5] ($(A)+(2,2,0) $)coordinate(aa)  --($(A)+(2,-2,0)$)coordinate(bb) --($(A)+(-2,-2,0)$)coordinate(cc) --($(A)+(-2,2,0)$)coordinate(dd)-- cycle;
\draw[fill=green!80,opacity=0.5] ($(A)+(2,2,4) $)coordinate(aa1) --($(A)+(2,-2,4)$)coordinate(bb1) --($(A)+(-2,-2,4)$)coordinate(cc1)--($(A)+(-2,2,4)$)coordinate(dd1)-- cycle;
\foreach \aa/\bb in {cc/dd,dd/aa,aa/bb,bb/cc}{
\draw[fill=green!50,opacity=0.5] (\aa) --(\aa1) --(\bb1) --(\bb) ;
}
%\draw[dashed]  (0,4,0)node[above left]{$y$}  --  (0,4,4)coordinate(aa) --(0,0,4);
%\draw[dashed]  (4,0,0) --(4,0,4) coordinate(bb)--(0,0,4)node[left]{$z$} ;
%\draw[dashed]  (4,0,0)node[above right]{$x$} --(4,4,0) coordinate(cc)--(0,4,0);
%\draw[dashed] (aa) --(A1);
%\draw[dashed] (bb) --(A1);
%\draw[dashed] (cc) --(A1);
\node[above =1em of A1]{$\mathrm{d}y$};
\node[left =1.8em of A1]{$\mathrm{d}z$};
\node[below right =0.5em of A1]{$\mathrm{d}x$};

\draw[-latex](0,0,0) -- (5,0,0) node[right](xx){$\vv{y_0}$};
\draw[-latex](0,0,0) -- (0,5,0) node[right](yy){$\vv{z_0}$};
\draw[-latex](0,0,0) -- (0,0,3) node[right](zz){$\vv{x_0}$};

\node[fit=(xx) (yy) (zz)](cadre){};
\node[below=0em of cadre]{ $\mathrm{d}v= \mathrm{d}x\cdot \mathrm{d} y \cdot\mathrm{d}z$};
\end{tikzpicture}}
\hspace{1em}
\subfloat[coordonnées cylindriques]{
 \begin{tikzpicture}[scale=2.6]

   \begin{scope}[canvas is zx plane at y=0]
     %\draw (0,0) circle (1cm);
     \draw (0,0)coordinate(O) -- (1,0) (0,0) -- (0,1);
      \coordinate (Z0) at (0:0.1);
     \draw[fill=green!30,opacity=0.3] (0,0) -- (10:1)coordinate(A1) arc (10:110:1) coordinate(A2)-- (0,0);
     \foreach \aa in {10,15,20,...,110}{
     \coordinate (A\aa) at (\aa:1);
     }
   \end{scope}
   
      \begin{scope}[canvas is zx plane at y=0.9]
     %\draw (0,0) circle (1cm);
     \draw[fill=green!30,opacity=0.3] (0,0) -- (10:1)coordinate(B1) arc (10:110:1) coordinate(B2)-- (0,0);
     \foreach \aa in {10,15,20,...,110}{
     \coordinate (B\aa) at (\aa:1);
     }
     
   \end{scope}
   
    \begin{scope}[canvas is zx plane at y=0.4]
     %\draw (0,0) circle (1cm);
     \draw[fill=red!30,opacity=0.3] (30:0.7) -- (30:0.5)coordinate(A1) arc (30:50:0.5) -- (50:0.7) arc (50:30:0.7) -- cycle;
          \foreach \aa in {30,32,34,...,50}{
     \coordinate (C\aa) at (\aa:0.7);
     \coordinate (E\aa) at (\aa:0.5);     
     }
     \draw[dashed](0,0)-- (0:1);   
     \coordinate (Z4) at (0:0.1);     
     \draw[dashed](0,0) -- (C30) coordinate[pos=2] (ff) -- (ff);    
     \draw[dashed](0,0) -- (C50) coordinate[pos=2] (ff) -- (ff);
     \draw[-latex] (0:0.8) arc (0:30:0.8)node[pos=0.5,below]{$\theta$};
      \draw[latex-latex] (30:1) arc (30:50:1)node[pos=0.5,below]{$\mathrm{d}\,\theta$};
   \end{scope}
   
    \begin{scope}[canvas is zx plane at y=0.6]
     %\draw (0,0) circle (1cm);
     \draw[fill=red!30,opacity=0.3] (30:0.7) -- (30:0.5)coordinate(A1) arc (30:50:0.5) -- (50:0.7) arc (50:30:0.7) -- cycle;
               \foreach \aa in {30,32,34,...,50}{
     \coordinate (D\aa) at (\aa:0.7);
     \coordinate (F\aa) at (\aa:0.5);
     }
     \draw[dashed](0,0)coordinate(Z6) -- (D30) coordinate[pos=2] (ff) -- (ff);    
     \draw[dashed](0,0) -- (D50) coordinate[pos=2] (ff) -- (ff);
     \coordinate (Z6) at (0:0.1);
   \end{scope}

 \draw[-latex] (0,0,0) -- (1.1,0,0) node[above](yy){$\vv{y_0}$};
  \draw[-latex] (0,0,0) -- (0,1.1,0) node[above](zz){$\vv{z_0}$};
    \draw[-latex] (0,0,0) -- (0,0,1.1) node[above](xx){$\vv{x_0}$};

\foreach \aa in {10,15,20,...,105}{
\pgfmathsetmacro{\bb}{\aa+5}
\fill[fill=green!30,opacity=0.3] (A\aa) -- (A\bb) -- (B\bb) -- (B\aa) -- cycle;   
}

\foreach \aa in {30,32,34,...,48}{
\pgfmathsetmacro{\bb}{\aa+2}
\fill[fill=red!30,opacity=0.3] (C\aa) -- (C\bb) -- (D\bb) -- (D\aa) -- cycle;   
\fill[fill=red!30,opacity=0.3] (E\aa) -- (E\bb) -- (F\bb) -- (F\aa) -- cycle;   
}
\draw[fill=red!30,opacity=0.3] (C30) -- (E30) -- (F30) -- (D30) -- cycle;

\draw[fill=red!30,opacity=0.3] (C50) -- (E50) -- (F50) -- (D50) -- cycle;

\draw[-latex] (Z0) -- (Z4) node[left,pos=0.5]{$z$};
\draw[latex-latex] (Z4) -- (Z6) node[left,pos=0.5]{$\mathrm{d}\,z$};
\draw [dashed] (D50) --++(0,0.15)coordinate(aa);
\draw [dashed] (F50) --++(0,0.15)coordinate(bb);
\draw[latex-latex] (aa) -- (bb) node[above,pos=0.5,sloped]{$\mathrm{d}\,r$};


\node[fit=(xx) (yy) (zz)](cadre){};
\node[below=0.5em of cadre]{ $\mathrm{d}v=r\cdot \mathrm{d}\theta\cdot \mathrm{d} r \cdot\mathrm{d}z$};
\end{tikzpicture}


}\hspace{1em}
\subfloat[coordonnées sphériques]{
\begin{tikzpicture}[scale=0.9]
%\clip[draw] (-1.7,-2) rectangle (3.5,3.5);
\begin{scope}[scale=4.2,tdplot_main_coords]


%-----------------------
\coordinate (O) at (0,0,0);


\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
\tdplotsetcoord{P1}{\Rvec}{\thetavec}{\phivec}
\tdplotsetcoord{P2}{\Rvec}{\Thetavec}{\phivec}
\tdplotsetcoord{P3}{\rvec}{\Thetavec}{\phivec}

\tdplotsetcoord{Q}{\rvec}{\thetavec}{\Phivec}
\tdplotsetcoord{Q1}{\Rvec}{\thetavec}{\Phivec}
\tdplotsetcoord{Q2}{\Rvec}{\Thetavec}{\Phivec}
\tdplotsetcoord{Q3}{\rvec}{\Thetavec}{\Phivec}

\draw[thick,fill=green!30] (P) -- (P1) -- (Q1) -- (Q)--cycle;
\draw[thick,fill=green!30] (P3) -- (P2) -- (Q2) -- (Q3)--cycle;
%draw figure contents
%--------------------
%draw the main coordinate system axes
\draw[thick,->] (0,0,0) -- (0.9,0,0) node[above](xx){$\vv{x_0}$};
\draw[thick,->] (0,0,0) -- (0,0.9,0) node[above](yy){$\vv{y_0}$};
\draw[thick,->] (0,0,0) -- (0,0,1) node[right](zz){$\vv{z_0}$};

%draw a line from origin to point (P) 
\draw[,color=red] (O) -- (P);
\draw[,color=red] (O) -- (P2);
\draw[color=red] (O) -- (P3);


\draw[dashed, color=red] (O) -- (Pxy);
\draw[dashed, color=red] (P) -- (Pxy);
%
\draw[dashed, color=red] (O) -- (P2xy);
\draw[dashed, color=red] (P2) -- (P2xy);

%draw a line from origin to point (Q) 
\draw[,color=red] (O) -- (Q);
\draw[,color=red] (O) -- (Q2);
\draw[color=red] (O) -- (Q3);

%\draw[,color=red] (P) -- (P1) --(P2) --(P3)--(P);
%draw projection on xy plane, and a connecting line
\draw[dashed, color=red] (O) -- (Qxy);
\draw[dashed, color=red] (Q) -- (Qxy);
%
\draw[dashed, color=red] (O) -- (Q2xy);
\draw[dashed, color=red] (Q2) -- (Q2xy);

\pgfmathsetmacro{\Rproj}{\Rvec*sin(\Thetavec)}

\draw[fill=gray!50] (Pxy) -- (Qxy) -- (Q2xy) -- (P2xy)--cycle;

\tdplotdrawarc[-latex]{(O)}{0.25}{0}{\phivec}{anchor=north}{$\theta$}
\tdplotdrawarc[latex-latex]{(O)}{0.65}{\phivec}{\Phivec}{anchor=north}{$\mathrm{d}\,\theta$}

\tdplotsetthetaplanecoords{\phivec}

\tdplotdrawarc[tdplot_rotated_coords,-latex]{(0,0,0)}{0.5}{0}{\thetavec}{anchor=south west}{$\varphi$}

\tdplotdrawarc[tdplot_rotated_coords,latex-latex]{(0,0,0)}{1.2}{\thetavec}{\Thetavec}{above,rotate=-55}{$\mathrm{d}\,\varphi$}

\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed,tdplot_rotated_coords] (\Rvec,0,0) arc (0:90:\Rvec);


\draw[dashed] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed] (\Rvec,0,0) arc (0:90:\Rvec);

\tdplotsetthetaplanecoords{\Phivec}


\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed,tdplot_rotated_coords] (\Rvec,0,0) arc (0:90:\Rvec);

\begin{scope}[tdplot_main_coords]
\draw[blue,fill=red!30,opacity=0.3] plot[variable=\x,domain=\thetavec:\Thetavec] 
(z spherical cs: radius = \rvec, phi = \Phivec, theta= \x)
-- plot[variable=\x,domain=\Phivec:\phivec] 
(z spherical cs: radius = \rvec, phi = \x, theta= \Thetavec)
-- plot[variable=\x,domain=\Thetavec:\thetavec] 
(z spherical cs: radius = \rvec, phi = \phivec, theta= \x) 
-- plot[variable=\x,domain=\phivec:\Phivec] 
(z spherical cs: radius = \rvec, phi = \x, theta= \thetavec);
%
\draw[blue,fill=red!30] plot[variable=\x,domain=\thetavec:\Thetavec] 
(z spherical cs: radius = \Rvec, phi = \Phivec, theta= \x)
-- plot[variable=\x,domain=\Phivec:\phivec] 
(z spherical cs: radius = \Rvec, phi = \x, theta= \Thetavec)
-- plot[variable=\x,domain=\Thetavec:\thetavec] 
(z spherical cs: radius = \Rvec, phi = \phivec, theta= \x) 
-- plot[variable=\x,domain=\phivec:\Phivec] 
(z spherical cs: radius = \Rvec, phi = \x, theta= \thetavec);

\end{scope}

\tdplotsetthetaplanecoords{\phivec}

%\tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}{\thetavec}{anchor=south west}{$\theta$}


\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed,tdplot_rotated_coords] (\Rvec,0,0) arc (0:90:\Rvec);
\draw[tdplot_rotated_coords,black,fill=blue!30,opacity=0.3] (P) -- (P1) arc (\thetavec:\Thetavec:\Rvec) -- (P3)  arc (\Thetavec:\thetavec:\rvec);

\draw[dashed] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed] (\Rvec,0,0) arc (0:90:\Rvec);

\draw[latex-latex] (60:\rvec) -- (60:\Rvec) node[right]{$\mathrm{d}\,r$};
\draw[latex-latex] (75:0) --node[sloped,above,pos=0.8]{$r$} (75:\rvec) ;

\tdplotsetthetaplanecoords{\Phivec}

\draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
\draw[dashed,tdplot_rotated_coords] (\Rvec,0,0) arc (0:90:\Rvec);
\draw[tdplot_rotated_coords,black,fill=blue!30,opacity=0.3] (Q) -- (Q1) arc (\thetavec:\Thetavec:\Rvec) -- (Q3)  arc (\Thetavec:\thetavec:\rvec);
\end{scope}

\node[fit=(xx) (yy) (zz)](cadre){};
\node[below=1em of cadre]{$\mathrm{d}v=r\cdot  \sin \varphi \cdot\mathrm{d}\theta\cdot  r \cdot\mathrm{d}\phi \cdot\mathrm{d}r$.};
\end{tikzpicture}


}

\caption{Élément de volume }
\label{fig:elementdevolume}
\end{figure}
\end{document}

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答案3

你可以尝试这个代码

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usepackage{esvect}
\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=2;h=4;myalgle=30;myphi = 50;}]
\draw[3d/hidden]
(0,0,0) -- (R,0,0)
 (0,0,0) -- (0,R,0)
 (0,0,0) -- (0,0,h);
\draw[3d/visible,-latex] (R,0,0) -- (R+ 2,0,0) node[below]{$x$};
\draw[3d/visible,-latex] (0,R,0) -- (0,R+1.5,0) node[below]{$y$};
\draw[3d/visible,-latex] (0,0,h) -- (0,0,h + 2) node[right]{$z$};
\pic{3d/frustum={R=R,r=R,h=h}};
\path ({R*cos(myalgle)},{R*sin(myalgle)},h-2) coordinate (A)
({R*cos(myalgle+ myphi)},{R*sin(myalgle+ myphi)},h-2) coordinate (B)
({R*cos(myalgle)},{R*sin(myalgle)},h-1) coordinate (C)
({R*cos(myalgle+ myphi)},{R*sin(myalgle+ myphi)},h-1) coordinate (D)
;
\draw[red, fill=pink, opacity=0.5] (A) arc[start angle=myalgle,end angle=myalgle +myphi ,radius=R]-- (D) arc[start angle=myalgle +myphi,end angle=myalgle,radius=R] -- cycle;

\pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D)")}
        \path (\mybarycenter) coordinate (G);
\path[overlay,3d coordinate={(N)=(G)-(A)x(G)-(B)},3d coordinate={(H)=(G)+ (N)}];
\pgfmathsetmacro{\absn}{sqrt(TD("(H)o(H)"))};
\path[overlay,3d coordinate={(myn)=(H)/\absn}];
\draw[-latex,red] (G) -- (myn) node[above]{$\vv{E}$};
\draw[-latex,green] (0,0,0) -- (N);
\end{tikzpicture}
\end{document}

在此处输入图片描述

或者

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usepackage{esvect}
\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=2;h=4;myalgle=0;myphi = 90;}]
\draw[3d/hidden]
(0,0,0) -- (R,0,0)
 (0,0,0) -- (0,R,0)
 (0,0,0) -- (0,0,h);
\draw[3d/visible,-latex] (R,0,0) -- (R+ 2,0,0) node[below]{$x$};
\draw[3d/visible,-latex] (0,R,0) -- (0,R+1.5,0) node[below]{$y$};
\draw[3d/visible,-latex] (0,0,h) -- (0,0,h + 2) node[right]{$z$};
\pic{3d/frustum={R=R,r=R,h=h}};
\path ({R*cos(myalgle)},{R*sin(myalgle)},h) coordinate (A)
({R*cos(myalgle+ myphi)},{R*sin(myalgle+ myphi)},h) coordinate (B)
({R*cos(myalgle)},{R*sin(myalgle)},0) coordinate (C)
({R*cos(myalgle+ myphi)},{R*sin(myalgle+ myphi)},0) coordinate (D)
;
\draw[red, fill=pink, opacity=0.5] (A) arc[start angle=myalgle,end angle=myalgle +myphi ,radius=R]-- (D) arc[start angle=myalgle +myphi,end angle=myalgle,radius=R] -- cycle;

\pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D)")}
        \path (\mybarycenter) coordinate (G);
\path[overlay,3d coordinate={(N)=(G)-(A)x(B)-(G)},3d coordinate={(H)=(G)+ (N)}];
\pgfmathsetmacro{\absn}{sqrt(TD("(H)o(H)"))};
\path[overlay,3d coordinate={(myn)=(H)/\absn}];
\draw[-latex,red] (G) -- (myn) node[above]{$\vv{E}$};
%\draw[-latex,green] (0,0,0) -- (N);
\end{tikzpicture}
\end{document}

在此处输入图片描述

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