☰

在一条线上绘制函数的符号

tag-icon • tag-icon tikz-pgf macros
在一条线上绘制函数的符号

我需要一个函数，给定起点和终点、一些可以包含和排除的点以及起始符号，它将绘制一条线、一个圆圈代替这些点（如果包含则填充黑色，如果排除则填充白色）和 + 或 - 符号。基本上我需要类似

除了+前后有符号外0，3还可以选择这些点是否包含在函数的定义域内。

我现在拥有的是

\documentclass[a4paper]{article}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{
  arrows,
  decorations,
  calc,
  intersections,
  matrix,
  decorations.pathmorphing,
  spy,
}

\newcommand\signplot[4]{ % start end points signStart
  % Draws a line between #1 and #2
  \draw[shorten <= -1cm, shorten >= -1cm] (#1) -- (#2);

  % Checking whether the first sign is positive or not
  \ifnum1=#4\relax % It starts positive
    % Cycle between the list of points given at which the sign changes
    \foreach \x in #3{
      % Drawing circles with the text
      \coordinate (A) at (#1);
      \coordinate (B) at (\x,0);
      \filldraw[fill=black,draw=black] (A-|B) circle(2pt)
        node[below]{\x};
      % Going through 0->\x (where \x = current coordinate) with a step of 0.3
      \foreach \c in {0,0.3,0.6,...,\x}{
        \coordinate (A1) at ($(A)+(-1cm,0)$);
        % Drawing the + sign above the line
        \coordinate (C) at ($(A1-|B)+(0,0.2)$);
        \coordinate (D) at (\c,0);
        \node at (C-|D) {+};
      }
    }
  \else % Same as above
    \foreach \x in #3{
      \coordinate (A) at (#1);
      \coordinate (B) at (\x,0);
      \filldraw[fill=black,draw=black] (A-|B) circle(2pt)
        node[below]{\x};
      \foreach \c in {0.3,0.6,...,\x}{
        % Just drawing the - sign below
        \coordinate (C) at ($(A-|B)+(0,-0.2)$);
        \coordinate (D) at (\c,0);
        \node at (C-|D) {-};
      }
    }
  \fi
}

\begin{document}
    \begin{tikzpicture}
        \coordinate (O) at (0,0);
        \coordinate (A) at (5,0);
        \signplot{O}{A}{{0,3}}{0}
    \end{tikzpicture}
\end{document}

正如你所见，我没有处理超过 2 个点的情况，因为这种情况会发生

而实际上，标志应该+在线上方。

因此，如果碰巧有一种自动“反转”符号及其位置的方法，每次给出一个新点时，我该怎么做？另外，正如您所见，我没有处理不在域内的点并将它们全部绘制为黑色。顺便提一下，给定函数，是否有一种自动获取函数符号的方法？为此再添加一个命令可能会很有用。

抱歉，如果我的解释不是最好的，但我找不到合适的词。最后它应该是这样的

感谢您在创建此命令时提供的帮助。我对命令创建和条件语句还不太熟悉，所以请解释一下，这样我就可以自己做其他事情了。谢谢阅读。

编辑： 经过一番研究和 @marmot 的帮助，我最终创建了一个可以满足我需求的函数。它在这里

\newcommand{\mysign}[1]{
  \pgfmathtruncatemacro\tmpsign{sign(#1)}
    \ifnum\tmpsign<0
      -
    \else
      \ifnum\tmpsign>0
      +
      \else
      \relax
    \fi
  \fi
}

\newcommand{\drawSign}[6][]{% f(x) xmin xmax delta exclpoints
  \begin{scope}[#1,declare function={Test(\x) = #2;}]
    \draw [->, thick] (#3,0) -- (#4,0)node[right] {$x$};
    \pgfmathsetmacro{\NextI}{#3+#5}
    \foreach \i in {#3,\NextI,...,#4}{
      \node at (\i,{0.35*sign(max(min(Test(\i),1),-1))}) {$\mysign{Test(\i)}$};
      \pgfmathtruncatemacro\signum{sign(Test(\i))}
      \ifnum\signum=0
        \filldraw[black] (\i,0) circle(2pt);
        %\node[circle,fill,maximum size=2pt] at (\i,0){};
        \node[below] at (\i,-0.2){$\i$};
      \fi
    }
  \ifx&#6&%
  \else  
    % Excluded points
    \foreach \x in #6{
      \filldraw[fill=white,draw=black] (\x,0) circle(2pt);
      \node[below] at (\x,-0.2) {$\x$};
    }
  \fi
  \end{scope}
}

现在函数的图\drawSign{(\x^2-5*\x+4)/(\x-5+0.001)}{-2}{7}{0.25}{5}是

这就是期望的结果。

如果有一种自动知道函数零点的方法，那真是太好了！谢谢阅读。

答案1

在此处输入图片描述

\documentclass{article}
\usepackage{pgfplots}
\usepackage{amsmath}
\newcommand{\mysign}[1]{\pgfmathtruncatemacro\tmpsign{sign(#1)}
\ifnum\tmpsign<0
-
\else\ifnum\tmpsign>0
+
\else
\relax
\fi
\fi
}




\begin{document}
The basic idea is to define a function that changes its signs at some locations.
Call the locations $x_1,\dots x_n$, then a convenient choice of the function is
\[ T(x)~=~\pm\prod\limits_{i=1}^n(x_i-x_n)\]
and this function is called \texttt{Test} in the snippet below. In addition, one
may want to introduce a function
\[ \backslash\texttt{mysign}(x)~=~\left\{\begin{array}{ll}
+ &\text{if}~x>0\;,\\
- &\text{if}~x<0\;,\\
\backslash\texttt{empty} & \text{if}~x=0\;.
\end{array}\right.\] 
Then one can simply plot the combination of these functions.\\[1cm]
\begin{tikzpicture}[scale=1.5,
declare function={Test(\i) = \i*(3-\i)*(\i-4);}]
\draw [->, thick] (-2,0) -- (7.5,0)node[right] {$x$};
\foreach \i in {-2,-1.75,...,7}
{
\node at (\i,{0.35*sign(Test(\i))}) {$\mysign{Test(\i)}$};
\pgfmathtruncatemacro\signum{sign(Test(\i))}
\ifnum\signum=0
\node[circle,fill,minimum size=2pt] at (\i,0){};
\node[below] at (\i,-0.2){$\i$};
\fi
}
\end{tikzpicture}

One may also write a function for that, 
$\backslash\texttt{DrawSign}\{f(\backslash x)\}\{x_\mathrm{min}\}
\{x_\mathrm{max}\}\{\Delta x\}$, see below.\\[1cm]
\newcommand{\DrawSign}[5][]{\begin{scope}[#1,declare function={Test(\x) = #2;}]
\draw [->, thick] (#3,0) -- (#4,0)node[right] {$x$};
\pgfmathsetmacro{\NextI}{#3+#5}
\foreach \i in {#3,\NextI,...,#4}
{
\node at (\i,{0.35*sign(Test(\i))}) {$\mysign{Test(\i)}$};
\pgfmathtruncatemacro\signum{sign(Test(\i))}
\ifnum\signum=0
\node[circle,fill,minimum size=2pt] at (\i,0){};
\node[below] at (\i,-0.2){$\i$};
\fi
}
\end{scope}
}
\begin{tikzpicture}
\DrawSign[scale=1.5]{(\x-1)*(\x+3)}{-5}{3}{0.25}
\end{tikzpicture}
\end{document}

基于这个帖子。

相关内容