3D 球面坐标在 varphi 中添加新圆弧角并更改 theta 角的位置

Question

我从 tikz.net 获得了这个 MWE，但我想编辑角度：

1. 在 x 轴和 z 轴之间添加新角度 (\varphi)
2. 将当前 y 轴和 z 轴之间的角度 (\theta) 更改为 y 轴和向量 r 之间的角度，而不是 z 轴和向量 r 之间的角度

这就是我想要实现的目标：

这是 Latex 代码：

\documentclass[border=3pt]{standalone}

%Drawing
\usepackage{tikz}

%3D
\usepackage{tikz-3dplot}

%Tikz Library
\usetikzlibrary{angles, quotes, intersections}

%Styles
\tikzset{axis/.style={thick,-latex}}
\tikzset{vec/.style={thick,blue}}
\tikzset{univec/.style={thick,red,-latex}}

%Notation
\usepackage{physics}
\usepackage{bm}

\begin{document}
    
    \tdplotsetmaincoords{70}{110}
    %
    \pgfmathsetmacro{\thetavec}{48.17}
    \pgfmathsetmacro{\phivec}{63.5}
    %
    
    \begin{tikzpicture}[tdplot_main_coords]
        %Axis
        \draw[axis] (0,0,0) -- (6.5,0,0) node [pos=1.1] {$x$};
        \draw[axis] (0,0,0) -- (0,6,0) node [pos=1.05] {$y$};
        \draw[axis] (0,0,0) -- (0,0,5.5)  node [pos=1.05] {$z$};   
        
        %Vectors
        \tdplotsetcoord{P}{6}{\thetavec}{\phivec}
        \draw[vec] (0,0,0) -- (P) node [midway, above] {$r$};
        \draw[thick] (0,0,0) -- (2,4,0);
        \draw[dashed] (0,0,0) -- (2,0,4);
        \draw[dashed] (2,0,4) -- (2,0,0);
        \draw[dashed] (2,0,4) -- (P);
        
        %Help Lines
        \draw[dashed] (2,4,4) -- (2,4,0);
        \draw[dashed] (2,0,0) -- (2,4,0) node [pos=-0.1] {$$};
        \draw[dashed] (0,4,0) -- (2,4,0) node [pos=-0.3] {$$};
        \draw[dashed] (0,0,4) -- (2,4,4) node [pos=-0.1] {$$};
    
        %Point
        \node[fill=black, circle, inner sep=0.8pt] at (2,4,4) {};
        
        %Angles
        \tdplotdrawarc{(0,0,0)}{0.7}{0}{\phivec}{below}{$\phi$}
        
        \tdplotsetthetaplanecoords{\phivec}
        \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}{\thetavec}{}{}
        \node at (0,0.25,0.67) {$\theta$};
        
    \end{tikzpicture}
    
\end{document}

Answer 1

极坐标 - 圆柱坐标 - 球坐标

这是我很久以前画的图。希望对你有帮助！

我只使用普通的 TikZ（参见下页）。

\documentclass[tikz,border=5mm]{standalone}
\usepackage[utf8]{vietnam}
\usepackage{amssymb,amsmath,amsthm}
\usetikzlibrary{calc,angles,quotes}
\pagecolor{yellow!15}
\begin{document}
    \def\r{{\color{cyan}r}}
    \def\cphi{{\color{blue}\varphi}}
    \def\ctheta{{\color{red}\theta}}
    \begin{tikzpicture}
        \path
        (0,0) coordinate (O) node[below left]{O}
        (3.5,0) coordinate (X) node[below]{$x$}
        (0,2) coordinate (Y) node[left]{$y$}
        ($(X)+(Y)$) coordinate (M) node[above right]{$M$};
        \pic[blue,-stealth,draw,"$\varphi$",angle radius=8mm, angle eccentricity=1.3]{angle=X--O--M};
        \draw[dashed] (X)--(M) (Y)--(M);
        \draw[cyan,thick] (O)--(M) node[midway,above]{$r$};
        \begin{scope}[shorten >=-5mm,shorten <=-10mm,->]
            \draw (O)--(X);
            \draw (O)--(Y);
        \end{scope}
        \foreach \p in {X,Y,O,M}
        \draw[fill=white] (\p) circle(1pt);
        \path (current bounding box.west) +(-2,1) node[align=left,font=\sffamily,fill=gray!20,inner sep=2mm,rounded corners]{
            Polar Coordinates\\
            Hệ tọa độ cực $(\r,\cphi)$\\[2mm]
            $x=\r \cos\cphi$\\
            $y=\r \sin\cphi$\\[2mm]
            $0\leq \r$\\
            $0\leq\cphi< 2\pi$
        };
    \end{tikzpicture}
    \begin{tikzpicture}
        \path
        (0,0) coordinate (O) +(150:.25) node{O}
        (-135:1.5) coordinate (X) node[left]{$x$}
        (0:3.5) coordinate (Y) node[above]{$y$}
        (90:3.5) coordinate (Z) node[left]{$z$}
        ($(X)+(Y)$) coordinate (Mxy)
        ($(Mxy)+(Z)$) coordinate (M) node[above right]{$M$};
        \pic[blue,-stealth,draw,"$\varphi$",angle radius=5mm]{angle=X--O--Mxy};
        \draw[dashed] (O)--(M)
        (X)--(Mxy) (Y)--(Mxy) (Mxy)--(M) (Z)--(M);
        \draw[cyan,thick] (O)--(Mxy) node[pos=.6,above]{$r$};
        \begin{scope}[shorten >=-5mm,->]
            \draw (O)--(X);
            \draw (O)--(Y);
            \draw (O)--(Z);
        \end{scope}
        \foreach \p in {X,Y,Z,O,M,Mxy}
        \draw[fill=white] (\p) circle(1pt);
        \path (current bounding box.west) +(-1.5,1) node[align=left,font=\sffamily,fill=gray!20,inner sep=2mm,rounded corners]{
            Cylindrical Coordinates\\
            Hệ tọa độ trụ $(\r,\cphi,z)$\\[2mm]
            $x=\r \cos\cphi$\\
            $y=\r \sin\cphi$\\
            $z=z$\\[2mm]
            $0\leq \r$\\
            $0\leq\cphi< 2\pi$\\
            $z\in\mathbb{R}$
        };
    \end{tikzpicture}
    \begin{tikzpicture}
        \path
        (0,0) coordinate (O) +(150:.25) node{O}
        (-135:1.5) coordinate (X) node[left]{$x$}
        (0:3.5) coordinate (Y) node[above]{$y$}
        (90:3.5) coordinate (Z) node[left]{$z$}
        ($(X)+(Y)$) coordinate (Mxy)
        ($(Mxy)+(Z)$) coordinate (M) node[above right]{$M$};
        \pic[blue,-stealth,draw,"$\varphi$",angle radius=5mm]{angle=X--O--Mxy};
        \pic[red,stealth-,draw,"$\theta$",angle radius=8mm]{angle=M--O--Z};
        \draw[dashed] (O)--(Mxy)
        (X)--(Mxy) (Y)--(Mxy) (Mxy)--(M) (Z)--(M);
        \draw[cyan,thick] (O)--(M) node[midway,above]{$r$};
        \begin{scope}[shorten >=-5mm,->]
            \draw (O)--(X);
            \draw (O)--(Y);
            \draw (O)--(Z);
        \end{scope}
        \foreach \p in {X,Y,Z,O,M,Mxy}
        \draw[fill=white] (\p) circle(1pt);
        \path (current bounding box.west) +(-1.5,1) node[align=left,font=\sffamily,fill=gray!20,inner sep=2mm,rounded corners]{
            Spherical Coordinates\\
            Hệ tọa độ cầu $(\r,\cphi,\ctheta)$\\[2mm]
            $x=\r \cos\cphi\;\sin\ctheta$\\
            $y=\r \sin\cphi\;\sin\ctheta$\\
            $z=\r \cos\ctheta$\\[2mm]
            $0\leq \r$\\
            $0\leq\cphi< 2\pi$\\
            $0\leq\ctheta\leq\pi$
        };
    \end{tikzpicture}
\end{document}