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布洛赫球体顶部的动画矢量

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布洛赫球体顶部的动画矢量

我有一个矢量a，它只能在x-y平面内移动，其大小为球体的半径。有没有办法让它变成动画a。动画是指它在x-y平面内旋转，角度也随之变化。

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \draw (0,0) node[circle,fill,inner sep=1] (orig) {} -- (\r/5,-\r/3) node[circle,fill,inner sep=0.7,label=above:$\vec{a}$] (a) {};

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--phi};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}
\end{document}

有可能吗TikZ？

答案1

这很容易这个答案。

\documentclass{article}

\usepackage{animate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{animateinline}[autoplay,loop]{2}
\multiframe{21}{i=0+1}{\pgfmathsetmacro{\myangle}{-4*\i}

\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \coordinate[label=above:$\vec{a}$] (a) at (\myangle:{\r} and {\r/3});
    \coordinate (orig) at (0,0);
    \draw (orig) circle(0.1);
    \draw[-latex] (orig) -- (a);

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--a};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}}
\end{animateinline}
\end{document}

在此处输入图片描述

如果要在整个平面上旋转它，请使用

\documentclass{article}

\usepackage{animate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother

\usepackage{tikz}
\usetikzlibrary{angles,quotes}

\begin{document}
\begin{animateinline}[autoplay,loop]{2}
\multiframe{91}{i=0+1}{\pgfmathsetmacro{\myangle}{-4*\i}

\begin{tikzpicture}

    % Define radius
    \def\r{3}

    % Bloch vector
    \coordinate[label={\myangle+90}:$\vec{a}$] (a) at (\myangle:{\r} and {\r/3});
    \coordinate (orig) at (0,0);
    \draw (orig) circle(0.1);
    \draw[-latex] (orig) -- (a);

    % Sphere
    \draw (orig) circle (\r);
    \draw[dashed] (orig) ellipse (\r{} and \r/3);

    % Axes
    \draw[->] (orig) -- ++(-\r/5,-\r/3) node[below] (x1) {$x$};
    \draw[->] (orig) -- ++(\r,0) node[right] (x2) {$y$};
    \draw[->] (orig) -- ++(0,\r) node[above] (x3) {$z$};

    %Angles
    \pic [draw=gray,text=gray,->,"$\phi$"] {angle = x1--orig--a};
    \pic [draw=gray,text=gray,<-,"$\theta$"] {angle = a--orig--x3};

\end{tikzpicture}}
\end{animateinline}
\end{document}

在此处输入图片描述

请注意，我的代码用于导出动画。如果您不想导出它，而只是将其合并到您的 pdf 文档中，请注释掉该块

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[active,tightpage]{preview}
\makeatletter
\def\@anim@@newframe{\@ifstar\@anim@newframe\@anim@newframe}
\def\@anim@newframe{\end{preview}\begin{preview}}
\renewenvironment{animateinline}[2][]{%
  \let\newframe\@anim@@newframe%
  \let\multiframe\@anim@multiframe%
  \begin{preview}}{%
  \end{preview}}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

动画将显示在选定的查看器上，例如 acroread。

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