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如何制作径向梯度减小的二维球体

tag-icon • tag-icon tikz-pgf tikz-3dplot
如何制作径向梯度减小的二维球体

我正在使用这个代码：

\documentclass[a4paper]{article}
\usepackage{tikz} 
\usepackage{tikz-3dplot} 

\begin{document}
  \tdplotsetmaincoords{45}{135}
  \pgfmathsetmacro{\rvec}{.8}
  \pgfmathsetmacro{\thetavec}{45}
  \pgfmathsetmacro{\phivec}{75}

  \begin{tikzpicture}[scale=9,tdplot_main_coords]
    \shade[tdplot_screen_coords,ball color = gray!60] (0,0) circle (\rvec);
    \coordinate (O) at (0,0,0);
    \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}

    \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
    \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
    \draw[thick,->] (0,0,-1) -- (0,0,1) node[anchor=south]{$z$};
    \draw[-stealth,color=black] (O) -- (P) node[midway,above] {$r$};
    \draw[dashed, color=red] (O) -- (Pxy);
    \draw[dashed, color=red] (P) -- (Pxy);
    \tdplotdrawarc{(O)}{0.2}{0}{\phivec}{anchor=north}{$\phi$}

    \tdplotsetthetaplanecoords{\phivec}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{\thetavec}{90}{anchor=south west}{$\theta$}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{\rvec}{-180}{180}{anchor=south west}{}
  \end{tikzpicture} 
\end{document}

这将创建：

在此处输入图片描述

如何应用递减的径向渐变？

预期结果将是类似于（轴等保持可见）：

在此处输入图片描述

答案1

如果您只想要径向衰落，那么第 23.4.2 节之前的示例可能是可行的方法。

\documentclass[a4paper]{article}
\usepackage{tikz} 
\usepackage{tikz-3dplot} 
\usetikzlibrary{fadings}
\tikzfading[name=fade out,
inner color=transparent!0,
outer color=transparent!100]

\begin{document}
  \tdplotsetmaincoords{45}{135}
  \pgfmathsetmacro{\rvec}{.8}
  \pgfmathsetmacro{\thetavec}{45}
  \pgfmathsetmacro{\phivec}{75}

  \begin{tikzpicture}[scale=9,tdplot_main_coords]
    \fill[tdplot_screen_coords,gray!40!black,%ball color = gray,
    path fading=fade out] (0,0) circle (\rvec);
    \coordinate (O) at (0,0,0);
    \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}

    \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
    \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
    \draw[thick,->] (0,0,-1) -- (0,0,1) node[anchor=south]{$z$};
    \draw[-stealth,color=black] (O) -- (P) node[midway,above] {$r$};
    \draw[dashed, color=red] (O) -- (Pxy);
    \draw[dashed, color=red] (P) -- (Pxy);
    \tdplotdrawarc{(O)}{0.2}{0}{\phivec}{anchor=north}{$\phi$}

    \tdplotsetthetaplanecoords{\phivec}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{\thetavec}{90}{anchor=south west}{$\theta$}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{\rvec}{-180}{180}{anchor=south west}{}
  \end{tikzpicture} 
\end{document}

在此处输入图片描述

另一个选择是稍微修改shadings库中的模糊圆圈。（我只是从库中复制并稍微修改了模糊圆圈的淡入淡出，以便您可以立即访问不同距离的透明度级别。我并不是说我的选择特别好，但最终您需要自己决定最适合您的选择。数字 23 实际上并不代表百分比，但如果您打篮球，您可能会理解我为什么选择它。;-)

\documentclass[a4paper]{article}
\usepackage{tikz} 
\usepackage{tikz-3dplot} 
\usetikzlibrary{fadings}
\makeatletter
\pgfdeclareradialshading{tikz@lib@fade@circle@23}{\pgfpointorigin}{
  color(0pt)=(pgftransparent!0); color(20bp)=(pgftransparent!50);
  color(25bp)=(pgftransparent!92); color(50bp)=(pgftransparent!100)}
\pgfdeclarefading{circle with fuzzy edge 23 percent}{\pgfuseshading{tikz@lib@fade@circle@23}}
\makeatother
\tikzfading[name=fade out,
inner color=transparent!0,
outer color=transparent!100]

\begin{document}
  \tdplotsetmaincoords{45}{135}
  \pgfmathsetmacro{\rvec}{.8}
  \pgfmathsetmacro{\thetavec}{45}
  \pgfmathsetmacro{\phivec}{75}

  \begin{tikzpicture}[scale=9,tdplot_main_coords]
    \shade[tdplot_screen_coords,ball color=gray!60,
    path fading={circle with fuzzy edge 23 percent}] (0,0) circle (\rvec);
    \coordinate (O) at (0,0,0);
    \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}

    \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
    \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
    \draw[thick,->] (0,0,-1) -- (0,0,1) node[anchor=south]{$z$};
    \draw[-stealth,color=black] (O) -- (P) node[midway,above] {$r$};
    \draw[dashed, color=red] (O) -- (Pxy);
    \draw[dashed, color=red] (P) -- (Pxy);
    \tdplotdrawarc{(O)}{0.2}{0}{\phivec}{anchor=north}{$\phi$}

    \tdplotsetthetaplanecoords{\phivec}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{\thetavec}{90}{anchor=south west}{$\theta$}
    \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{\rvec}{-180}{180}{anchor=south west}{}
  \end{tikzpicture} 
\end{document}

在此处输入图片描述

答案2

在此处输入图片描述

将 \ 阴影线替换为

`\node[circle,shading=radial,外部颜色=gray!30,内部颜色=black!80,最小宽度=14.5cm]{};

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