使用 tikz 时斜率场不对称

Question

使用此代码尝试绘制 xy' - y = 0（即 y = cx）的斜率场，两侧明显缺乏对称性。

\documentclass{article}

\usepackage{amsmath}            
\usepackage{amsfonts}           
\usepackage{amssymb}        
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[declare function={f(\x,\y)=\y/\x;}]
    \def\xmax{3} \def\xmin{-3}
    \def\ymax{3} \def\ymin{-3}
    \def\nx{15}
    \def\ny{15}

    \pgfmathsetmacro{\hx}{(\xmax-\xmin)/\nx}
    \pgfmathsetmacro{\hy}{(\ymax-\ymin)/\ny}
    \foreach \i in {0,...,\nx}
    \foreach \j in {0,...,\ny}{
    \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx},{\ymin+\j*\hy})}
    \draw[blue,shift={({\xmin+\i*0.4},{\ymin+\j*0.4})}] 
    (0,0)--($(0,0)!2mm!(.1,.1*\yprime)$);
    }

    \draw[->] (\xmin-.5,0)--(\xmax+.5,0) node[below right] {$x$};
    \draw[->] (0,\ymin-.5)--(0,\ymax+.5) node[above left] {$y$};
    \draw (current bounding box.north) node[above]
    {Slope field of \quad $y'=x+y$.};
    \end{tikzpicture}

\end{document}

取自这里

我能够使用这画出我想要的，但我不喜欢输出。另外，我真的想知道为什么我发布的代码不对称。我甚至用 python 输入了它来尝试弄清楚：

xmax = 3
xmin = -3
ymax = 3
ymin = -3
nx = 15
ny = 15
hx = (xmax - xmin)/nx
hy = (ymax - ymin)/ny
for i in range(0, nx+1):
    for j in range(0, ny+1):
        yprime = (xmin+(i*hx))/(ymin+(j*hy))

        if -1 == yprime or yprime == 1:
            print((xmin+(i*hx)))
            print((ymin+(j*hy)))

            print("xmin", xmin,"i", i,"hx", hx,"ymin", ymin,"j", j,"hy", hy)
            print ("yprime ", yprime)

它没有帮助，但也许对其他人有用。

Answer 1

它不对称，因为线的末端不在

\draw[blue,shift={({\xmin+\i*0.4},{\ymin+\j*0.4})}] 
(0,0)--($(0,0)!2mm!(.1,.1*\yprime)$);

使它们对称很简单，只需将其替换为

     \draw[blue,shift={({\xmin+\i*0.4},{\ymin+\j*0.4})}] 
    ($(0,0)!1mm!(-.1,-.1*\yprime)$)--($(0,0)!1mm!(.1,.1*\yprime)$);

完整 MWE：

\documentclass{article}

\usepackage{amsmath}            
\usepackage{amsfonts}           
\usepackage{amssymb}        
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[declare function={f(\x,\y)=\y/\x;}]
    \def\xmax{3} \def\xmin{-3}
    \def\ymax{3} \def\ymin{-3}
    \def\nx{15}
    \def\ny{15}

    \pgfmathsetmacro{\hx}{(\xmax-\xmin)/\nx}
    \pgfmathsetmacro{\hy}{(\ymax-\ymin)/\ny}
    \foreach \i in {0,...,\nx}
    \foreach \j in {0,...,\ny}{
    \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx},{\ymin+\j*\hy})}
    \draw[blue,shift={({\xmin+\i*0.4},{\ymin+\j*0.4})}] 
    ($(0,0)!1mm!(-.1,-.1*\yprime)$)--($(0,0)!1mm!(.1,.1*\yprime)$);
    }

    \draw[->] (\xmin-.5,0)--(\xmax+.5,0) node[below right] {$x$};
    \draw[->] (0,\ymin-.5)--(0,\ymax+.5) node[above left] {$y$};
    \draw (current bounding box.north) node[above]
    {Slope field of \quad $y'=x+y$.};
    \end{tikzpicture}

\end{document}

附录：至于您的评论：您需要避免奇点。为了简化这一点，我稍微重写了代码，以便从输入参数计算步长。为了避免 处的奇点x=-1，我将 设置\nx为16（并且 也设置为 以\ny保持对称性）。

\documentclass{article}

\usepackage{amsmath}            
\usepackage{amsfonts}           
\usepackage{amssymb}        
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}[declare function={f(\x,\y)=-2*\y/(\x+1);}]
    \def\xmax{3} \def\xmin{-3}
    \def\ymax{3} \def\ymin{-3}
    \def\nx{16}
    \def\ny{16}

    \pgfmathsetmacro{\hx}{(\xmax-\xmin)/\nx}
    \pgfmathsetmacro{\hy}{(\ymax-\ymin)/\ny}
    \foreach \i in {0,...,\nx}
    \foreach \j in {0,...,\ny}{
    \pgfmathsetmacro{\yprime}{f({\xmin+\i*\hx},{\ymin+\j*\hy})}
    \draw[blue,shift={({\xmin+\i*(\xmax-\xmin)/\nx},{\ymin+\j*(\ymax-\ymin)/\ny})}] 
    ($(0,0)!1mm!(-.1,-.1*\yprime)$)--($(0,0)!1mm!(.1,.1*\yprime)$);
    }

    \draw[->] (\xmin-.5,0)--(\xmax+.5,0) node[below right] {$x$};
    \draw[->] (0,\ymin-.5)--(0,\ymax+.5) node[above left] {$y$};
    \draw (current bounding box.north) node[above]
    {Slope field of \quad $y'=-2y/(x+1)$.};
    \end{tikzpicture}

\end{document}