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如何绘制具有切向单位向量和标签的螺旋？

tag-icon • tag-icon tikz-pgf tikz-styles
如何绘制具有切向单位向量和标签的螺旋？

请问，如何使用 TiKZ 绘制这些图表？ 在此处输入图片描述

r = r_{0} e^{bt}, \theta= bt

在此处输入图片描述 x= R cos wt，y=R sin wt，z=hwt

答案1

直接来自手册。

\documentclass{article}

\usepackage{tikz}
\begin{document}
\begin{tikzpicture}

 \draw[domain=0:720,smooth,variable=\t]
plot ({1.5*sin(\t)},0.8*\t/360,{1.5*cos(\t)});
\draw[->] (0,0,0) --( 2,0,0) node[above]{y};
\draw[->] (0,0,0) --( 0,2,0) node[right]{z};
\draw[->] (0,0,0) --( 0,0,2,) node[above]{x};
\end{tikzpicture}
\hspace{3em}
\begin{tikzpicture}

 \draw[domain=0:20,smooth,variable=\t,samples=200]
plot ({\t r:3*exp(-0.1*\t)});
\draw[->] (0,0,0) --( 4,0) node[above]{x};
\draw[->] (0,0,0) --( 0,4) node[right]{y};

\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

pstricks这是第一个图形（对数螺旋）的解决方案：

\documentclass[a4paper, pdf, svgnames]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[f]{esvect}
\pagestyle{empty}
\usepackage{pstricks-add}
\def\localbasis{\psline{<->}(1,0)(0,0)(0,1)}

\begin{document}

\small
\psset{plotpoints=500, algebraic, arrowinset=0.2, labelsep=3pt}
\begin{pspicture}
\psaxes[labels=none, ticks=none]{->}(0,0)(-4.5,-3)(6,5)
\radians
\pnodes(0,0){O}( 4.524; 0.5){M}
\uput{6pt}[u](M){\,\,M}
\rput(O){\localbasis}\uput{3pt}[dr](O){$ O $}\uput[d](1,0){{$ \vv*{e}{\!\!x }$}}\uput{2pt}[dl](0,0.9){{$ \vv*{e}{\!\!y} $}}
\psplot[polarplot, arrows=*-, linecolor=VioletRed, linewidth=1.2pt, dotsize=2.5pt]{0}{25}{5*EXP(-x/5)}
\uput[d](5,0){$ \mathrm M(t = 0) $}
\rput{0.5}(M){\localbasis}
\pcline{-o}(O)(M)\naput {$ r $}
\psarc[linewidth 0.5pt]{->}{2.2}{0}{0.5}\uput[r](2.2; 0.3){ $ θ $}
\pnode(5.7; 0.5){I}\rput[I](I){$\vv*{e}{\!\!r}$}
\psRelNodeVar(M )( I)( 1;1.57){J}\rput[B](J){$\vv*{e}{\!\!θ}$}
\end{pspicture}

\end{document}

在此处输入图片描述

helix然后是带有包的代码pst-3dplot：

\documentclass[a4paper, pdf, x11names]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{MinionPro}
\usepackage[f]{esvect}
\pagestyle{empty}
\usepackage{pstricks-add, pst-3dplot}
\def\localbasis{\psline{<->}(1,0)(0,0)(0,1)}
\def\\M{6*\pstPI1}
\begin{document}

\small
\psset{xPlotpoints = 500, plotstyle=curve, linecolor = DarkSeaGreen3, algebraic, arrowinset=0.2, labelsep=3pt}
\begin{pspicture}(-4,-2.5)(4,5.5)
\pstThreeDCoor[zMax=5.5, yMax=5, xMax=5, linewidth=0.6pt, linecolor=Coral1]
\psset{linewidth=1.5pt}
\parametricplotThreeD(0, 20){% radiant % 18.86
2.5 * cos(t) | 2.5 * sin(t) | t/5}
\psset{border=1.5pt}
\parametricplotThreeD(0.1, 4){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
\parametricplotThreeD(5.240, 8.38){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
\parametricplotThreeD(11.52, 14.66){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
\parametricplotThreeD(17.80, 20.5){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
\psset{linewidth=0.6pt, linecolor=Coral1}
\pstThreeDLine(0,0,2)(0,0,2.4)
\pstThreeDLine(0,0,3.3)(0,0,5.0)
\pstThreeDLine[linecolor=black, border = 0pt]{-> }(0,0,0)(0, 2.5, 2.79)
\uput[u](1.7,1.6){ $ M $}\uput[-120](0,0){$ O $}
\pstThreeDDot[linecolor = DarkSeaGreen3](0, 2.5, 2.83)
\pstThreeDDot(0,0,0)
\end{pspicture}

\end{document}

在此处输入图片描述

答案3

完全使用 TikZ 制作的解决方案。我在两张图片中都使用了样式thick和>=stealth'（来自arrows库）来使它们看起来更漂亮。这当然是完全可选的。

\documentclass[tikz]{standalone}
\usepackage{tikz,bm}
\usetikzlibrary{angles,arrows,calc,quotes}
\begin{document}
\begin{tikzpicture}[
  thick,>=stealth',
  declare function = {
    logx(\a,\b,\r) = \a*exp(-\b*\r)*cos(deg(\r));
    logy(\a,\b,\r) = \a*exp(-\b*\r)*sin(deg(\r));
  },
  point/.style={draw,thick,circle,inner sep=1pt,label={#1}},
  plot/.style={blue,smooth,samples=100}
  ]
  % Spiral parameters
  \def\a{5}
  \def\b{.2}
  % Axes
  \draw[->] (-4.5,0) -- (6,0) coordinate[label={below:$x$}] (A);
  \draw[->] (0,-3) -- (0,5) node[left] {$y$};
  % Spiral
  \draw[plot] plot[domain=0:25] ({logx(\a,\b,\x)},{logy(\a,\b,\x)});
  % Points M, O and M(t=0)
  \coordinate[label={below right:$O$}] (B) at (0,0);
  \node[point={above:$M$}] (C) at ({logx(\a,\b,.7)},{logy(\a,\b,.7)}) {};
  \node[below] at ({logx(\a,\b,0)},{logy(\a,\b,0)}) {$M(t=0)$};
  % Angle
  \draw pic[->,draw,"$\varphi$",angle radius=1.5cm] {angle};
  % Unit vectors
  \draw[->] (B) -- ($(B)!1.3!(C)$)       node[below right] {$\bm{e}_r$};
  \draw[->] (C) -- ($(C)!-1.5cm!90:(B)$) node[above right] {$\bm{e}_\theta$};
  \draw[->] (B) -- +(1,0)                node[below]       {$\bm{e}_x$};
  \draw[->] (B) -- +(0,1)                node[left]        {$\bm{e}_y$};
\end{tikzpicture}

\begin{tikzpicture}[
  x={(-.707cm,-.353cm)},y={(1cm,0cm)},z={(0cm,1cm)},
  thick,>=stealth',
  plot/.style={blue,smooth,samples=100}
  ]
  % Origin and axes
  \coordinate[label={above left:$O$}] (O) at (0,0,0);
  \draw[->] (O) -- (2,0,0) node[above left] {$x$};
  \draw[->] (O) -- (0,2,0) node[above] {$y$};
  \draw[->] (O) -- (0,0,4) node[right] {$z$};
  % Plot
  \draw[plot] plot[domain=0:16] ({cos(deg(\x))},{sin(deg(\x))},{.25*\x});
  % Arrow to M
  \draw[->] (O) -- ({cos(deg(8))},{sin(deg(8))},2) node[right] {$M$};
\end{tikzpicture}
\end{document}

在此处输入图片描述

在此处输入图片描述

答案4

我使用 pgfplots 绘制了你的函数。

在此处输入图片描述

% pdflatex
\documentclass[margin=2mm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
\begin{tikzpicture}
       \pgfmathdeclarefunction{F}{3}{\pgfmathparse{#1* exp(#2*#3)}}
\begin{axis}
        [
        smooth, grid=both,minor tick num=1,
        xlabel=$x$,ylabel=$y$,
        tick align=inside,
        samples=1000,
        samples y=0,
        ]

        \addplot [solid, thick, data cs=polarrad, domain=0:10*pi] {F(5,-0.1,x)};
\end{axis}
\end{tikzpicture}
~
\begin{tikzpicture}
       \pgfmathdeclarefunction{F}{3}{\pgfmathparse{#1* exp(#2*#3)}}
\begin{axis}
        [smooth, grid=both,minor tick num=1,
        xlabel=$x$,ylabel=$y$,zlabel=$z$,
        samples=1000,
        samples y=0,
        ]

        \addplot3+
        [solid, thick, black,
        mark=none,
        thick,
        domain=0:10*pi,
        ]
        ({F(5,-0.1,x)*cos(deg(x))},{F(5,-0.1,x)*sin(deg(x))},{F(5,-0.1,x)});
\end{axis}
\end{tikzpicture}
\end{document}

以下问题也可能有助于解决您的问题； 绘制螺旋锥体 Tikz

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