如何在三维笛卡尔坐标系中绘制中心圆盘表面

Question

在 3D 笛卡尔坐标系中，以原点为中心的圆盘表面的最佳绘制方法是什么？该表示还应包含一个点磷位于圆盘中心上方是轴。此外，你能画一个无穷小区域吗dA=rdrdθ使用极坐标？请参阅附图以了解详情：

Answer 1

我不会使用任何 3D 工具pgfplots，但只需使用普通的 Ti 绘制即可钾为了简单起见，Z 使用极坐标：

\documentclass[border=10pt]{standalone}
\usepackage{tikz}

\tikzset{
    point/.style={
        fill,
        circle,
        inner sep=1pt
    }
}

\newcommand*\diff{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{tikzpicture}[
    x={(1cm,0cm)}, 
    y={(0cm,0.5cm)},
    font=\scriptsize,
    >=stealth, 
    pin distance=0.25cm,
    pin position=240,
    every pin edge/.style={
        very thin,
        bend right
    },
    every pin/.append style={
        align=center,
        inner sep=2pt
    }
]

    \draw[->] (0:0) -- (90:4.5) node[right] {$z$};
    \draw[->] (0:0) -- (240:4.5) node[below right] {$y$};
    \draw[->] (0:0) -- (0:4.5) node[below] {$x$};

    \node[point, label={right:$P$}] at (90:3.5) {}; 

    \pgfmathsetmacro{\rmeta}{3};

    \draw (0:0) ellipse[radius=\rmeta];
    \draw[->] (0:0) -- (30:\rmeta) node[midway, above] {$R$};

    \pgfmathsetmacro{\alpha}{-35};
    \pgfmathsetmacro{\beta}{-65};
    \pgfmathsetmacro{\rinner}{1};
    \pgfmathsetmacro{\router}{2};

    \draw (0:0) -- (\alpha:\rinner);
    \draw (0:0) -- (\beta:\rinner);

    \draw 
        (\beta:0.5) 
        arc[start angle=\beta, end angle=\alpha, radius=0.5];
    \coordinate[pin={$\varphi$}] 
        (a) at ({(\alpha+\beta)/2}:{0.33});

    \draw[thick, fill=red!50] 
        (\beta:\rinner) 
        arc[start angle=\beta, end angle=\alpha, radius=\rinner]
        -- (\alpha:\router) 
        arc[start angle=\alpha, end angle=\beta, radius=\router]
        -- cycle;
    \coordinate[pin={$\diff A =$ \\ $r \cdot \diff y \cdot \diff\varphi$}] 
        (c) at ({(\alpha+\beta)/2}:{(\rinner+\router)/2});

    \draw[<->, shift={(0.15,0.15)}] 
        (\alpha:\rinner) -- ([]\alpha:\router)
        node[pos=0.75, above] {$\diff r$};

    \draw[<->] 
        ([shift={(\alpha:0.15)}]\alpha:\router) 
        arc[start angle=\alpha, end angle=\beta, radius={\router+0.15}]
        node[pos=0.25, below] {$r \cdot \diff y$};

\end{tikzpicture}
\end{document}

Answer 2

从这个开始：

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
    title={Disc with Sector and Point P},
    axis lines = center,
    xlabel = {$x$},
    ylabel = {$y$},
    zlabel = {$z$},
    ticks=none,
    xmin=-1.5, xmax=1.5,
    ymin=-1.5, ymax=1.5,
    zmin=0, zmax=2,
    view={120}{25}
]

% Draw the blue outline of the disc
\addplot3[
    samples=50,
    domain=0:360,
    color=blue,
    variable=\t,
] 
({cos(t)}, {sin(t)}, {0});

% Draw a sector in the disc
\addplot3[
    surf,
    domain=35:55,    % Adjust the angle for the desired sector size
    y domain=0:0.8, % Slightly less than the disc radius
    samples=30,
    opacity=0.5,    % Semi-transparent for visibility
] 
({y*cos(x)}, {y*sin(x)}, {0});

% Draw the point P and label it
\addplot3[mark=*, mark options={color=red}] coordinates {(0,0,1.5)};
\node at (axis cs:0,0,1.7) {$P$};

\end{axis}
\end{tikzpicture}

\end{document}