使用 pgfplots 绘制样条线

Question

是否可以简化代码，也就是说不要使用三次命令 \addplot[] ？

 \documentclass[tikz]{standalone}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{pgfplots}
 \usepgfplotslibrary{patchplots}
 \pgfplotsset{compat=newest}

 \begin{document}

 \begin{tikzpicture}

 \begin{axis}[
 restrict x to domain=-5:9, xmax=9, xmin=-5,
 restrict y to domain=-3:4, ymax=4, ymin=-3,
 x=1cm,
 y=1cm,
 axis x line = middle,
 axis y line = middle,
 axis line style =ultra thick,
 major tick style=black,
 grid=both,
 major grid style=lightgray,
 minor grid style=lightgray,
 minor tick num=1,
 xtick={-5,...,8},
 ytick={-3,...,3},
 samples=1000,
 >=stealth,
 ]

\addplot[
patch,
red,
patch type=quadratic spline,
thick,
]
coordinates{
(-4,0) (0,1)(-2,-3) (-0.6,0) 
};

\addplot[
patch,
blue,
patch type=quadratic spline,
thick,
]
coordinates{
(0,1) (2,1)(1,2)(1.4,1.8)
};

\addplot[
patch,
green,
patch type=cubic spline,
thick,
]
coordinates{
(2,1) (7,0)(3,0.4)(5,0.1)
};

\node[fill=black,circle,scale=0.4] at (-4,0){};
\node[fill=black,circle,scale=0.4] at (7,0){};

\node[below left] at (axis cs:0,0) {$0$};
\node[below] at (axis cs:9.8,-0.1) {$x$};
\node[left] at (axis cs:-0.1,3.8) {$y$};

\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

据我所知，您希望生成一个“接近”屏幕截图的图，而无需 100% 的准确度。这听起来很像“使其平滑并确保它在某些关键点进行插值”。

虽然这可以使用手动计算的样条线来完成，但它很麻烦，因为您需要摆弄交叉点处的角度。

还有一个自动解决方案，它由两个步骤组成：首先生成图（在整个域上，这意味着您可以使用 tikz 的smoother），其次计算交叉点段并以所需的颜色绘制它们。整个方法的工作原理如下：

\documentclass{standalone}
 \usepackage{pgfplots}
 \usepgfplotslibrary{fillbetween}
 \pgfplotsset{compat=1.12}

 \begin{document}

 \begin{tikzpicture}

 \begin{axis}[
 xmax=9, xmin=-5,
 ymax=4, ymin=-3,
 x=1cm,
 y=1cm,
 axis x line = middle,
 axis y line = middle,
 axis line style =ultra thick,
 major tick style=black,
 grid=both,
 major grid style=lightgray,
 minor grid style=lightgray,
 minor tick num=1,
 xtick={-5,...,8},
 ytick={-3,...,3},
 >=stealth,
 clip=false,% <--- otherwise $x$ will be clipped
 ]

\addplot[smooth,
    draw=none,% <- this plot is INVISIBLE
    tension=0.6,
    name path=plot]
coordinates{
(-4,0) (-2,-3) %(-0.6,0) 
(0,1) (1,2) %(1.4,1.8) 
(2,1)(3,0.4)
(5,0.1) (7,0)
};

\path[name path=cut line] (-4,1) -- (10,1);

\draw[red,ultra thick,
   intersection segments={of=plot and cut line,sequence=L1}];

\draw[blue,ultra thick,
    intersection segments={of=plot and cut line,sequence=L2}];

\draw[green,ultra thick,
    intersection segments={of=plot and cut line,sequence=L3}];

\node[fill=black,circle,scale=0.4] at (-4,0){};
\node[fill=black,circle,scale=0.4] at (7,0){};

\node[below left] at (0,0) {$0$};
\node[below] at (9.8,-0.1) {$x$};
\node[left] at (-0.1,3.8) {$y$};

\end{axis}
\end{tikzpicture}
\end{document}

您会看到我将插值点组合成一个\addplot。该图使用 tikz 的图处理程序，可实现平滑过渡并使用某些参数smooth控制自由度。具有，即仅记住，tension\addplotdraw=none, name path=plot不是画。

然后我们有\path[name path=cut line] (-4,1) -- (10,1);定义和名称cut line。

最后，有三条\draw指令定义特定 的颜色intersection segments。该指令属于fillbetween附带的库pgfplots。该参数of=plot and cut line计算这两个图的交点，并sequence允许选择结果中的单个项：“L”是 中左参数的第项of=left and right，“R”是 中右参数的第项（此处未使用）。

Answer 2

出于完整性考虑，以下是您可以使用 执行的操作to[in=<angle>, out=<angle>, looseness=<value>]。主要缺点是您必须猜测并改进值，因此您可能需要进行几次迭代，直到结果令人满意。

代码

\documentclass[tikz]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}

\begin{tikzpicture}

\begin{axis}
[   xmin=-4.5,
    xmax=7.5,
    ymin=-3.5,
    ymax=2.5, 
    x=1cm,
    y=1cm,
    domain=-4:7,
    axis x line = middle,
    axis y line = middle,
    axis line style =ultra thick,
    major tick style=black,
    grid=both,
    major grid style=lightgray,
    minor grid style=lightgray,
    minor tick num=1,
    xtick={-4,...,7},
    ytick={-3,...,2},
    samples=100,
    >=stealth,
]

    \draw[thick, red]
        (-4,0)  to[out=-80, in=180, looseness=0.6]
    (-2,-3) to[out=0, in=250, looseness=0.4]
    (-0.5,0) to[out=70, in=240, looseness=0.8]
    (0,1) to[out=60, in=180, looseness=0.7]
    (1,2) to[out=0, in=120, looseness=0.8]
    (2,1) to[out=300, in=180, looseness=0.5]
    (7,0);

    \node[fill=black,circle,scale=0.4] at (-4,0){};
    \node[fill=black,circle,scale=0.4] at (7,0){};

    \node[below left] at (0,0) {$0$};
    \node[above left] at (7.5,0) {$x$};
    \node[below right] at (0,2.5) {$y$};
\end{axis}
\end{tikzpicture}

\end{document}

输出

Answer 3

使用 TikZ 的解决方案..controls：

 \documentclass[tikz]{standalone}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{pgfplots}
 \usepgfplotslibrary{patchplots}
 \pgfplotsset{compat=newest}

 \begin{document}

 \begin{tikzpicture}

 \draw[step=1.0,lightgray,thin] (-6,-4) grid (9,4);

 \draw[ultra thick,->,>=stealth](-6,0)--(9,0);
 \draw[ultra thick,->,>=stealth](0,-4)--(0,4);


 \draw [thick,red](-4,0)..controls(-2,-4)..(-0.5,0)..controls(0,1)..(0,1)..controls(1,2.31)..(2,1)..controls(3.1,0.2)..(7,0);

 \draw [thick](1,0.1)--(1,-0.1);
 \draw [thick](-0.1,1)--(0.1,1);

 \node[below] at (1,0) {$1$};
 \node[left] at (0,1) {$1$};
 \node[below left] at (0,0) {$0$};

 \node[below] at (8.8,-0.1) {$x$};
 \node[left] at (-0.1,3.8) {$y$};

 \node[fill=black,circle,scale=0.4] at (-4,0){};
 \node[fill=black,circle,scale=0.4] at (7,0){};


 \end{tikzpicture}

 \end{document}