如何绘制 n 条水平 y 轴平行线与 m 条垂直 x 轴平行线相交

Question

使用 \foreach 命令添加节点圆

\begin{tikzpicture}[scale=0.5]
  \draw[->] (-10, 0) -- (10, 0) node[right] {$x$};
  \draw[->] (0, -10) -- (0, 10) node[above] {$y$};
 {
  \foreach \n in {8,7,...,-8}
  \draw[name path global=a,domain=-8:8,smooth, variable=\y, blue] plot ({\y}, {\n});
 { \foreach \n in {8,7,...,-8}
  \draw[name path global=b,rotate=90,domain=-8:8,smooth, variable=\y, green] plot ({\y}, {\n});

  \draw[name intersections={of={a} and {b}}](intersection-1) circle (1pt);
  }
}
\end{tikzpicture}

Answer 1

我不确定你需要什么。如果它类似于你的图片，但带有 x、y 轴，你可以执行以下操作：

\documentclass[tikz, border=2mm]{standalone}

\begin{document}
\begin{tikzpicture}[scale=0.5]
  \draw[blue,very thin] (-8.5,-8.5) grid (8.5,8.5);
  \draw[thick,->] (-10, 0) -- (10, 0) node[right] {$x$};
  \draw[thick,->] (0, -10) -- (0, 10) node[above] {$y$}; 
  \foreach \x in {-8,...,8} \foreach \y in {-8,...,8}
    \draw[blue,very thin,fill=white] (\x,\y) circle (1pt);
\end{tikzpicture}
\end{document}

Answer 2

如果您不需要网格的两种颜色（如@Juan的回答中所述），我将使用网格。以下是变体。

\documentclass[tikz]{standalone}
\usetikzlibrary{intersections}

\begin{document}
    \begin{tikzpicture}[scale=0.5]
    \pgfmathsetmacro\xmin{-8}
    \pgfmathsetmacro\xmax{8}
    \pgfmathsetmacro\ymin{-8}
    \pgfmathsetmacro\ymax{8}
    \pgfdeclarelayer{foreground layer}
    \pgfsetlayers{main,foreground layer}
    \begin{scope}
    \draw[->] (\xmin-2, 0) -- (\xmax+2, 0) node[right] {$x$};
    \draw[->] (0, \ymin-2) -- (0, \ymax+2) node[above] {$y$};
    
    \foreach \x in {\xmin,...,\xmax}{
        \draw [blue] (\x, \ymin) -- (\x, \ymax);
    }
    \foreach \y in {\ymin,...,\ymax}{
        \draw [green] (\xmin, \y) -- (\xmax, \y);
    }
    \foreach \x in {\xmin,...,\xmax}{
        \foreach \y in {\ymin,...,\ymax}{
            \fill[red] (\x,\y) circle [radius=2pt];
    }}
    \end{scope}
    
    \begin{scope}[xshift=22cm]
    \draw[->] (\xmin-2, 0) -- (\xmax+2, 0) node[right] {$x$};
    \draw[->] (0, \ymin-2) -- (0, \ymax+2) node[above] {$y$};
    \draw[step=1cm,blue,very thin] (\xmin, \ymin) grid (\xmax, \ymax);
    \foreach \x in {\xmin,...,\xmax}{
        \foreach \y in {\ymin,...,\ymax}{
            \fill[red] (\x,\y) circle [radius=2pt];
    }}
    \end{scope}
    
    \begin{scope}[xshift=44cm]
    
    \draw[->] (\xmin-2, 0) -- (\xmax+2, 0) node[right] {$x$};
    \draw[->] (0, \ymin-2) -- (0, \ymax+2) node[above] {$y$};
    
    \foreach \x in {\xmin,...,\xmax}{
        \draw[name path=a, blue] (\x, \ymin) -- (\x, \ymax);
        \foreach \y in {\ymin,...,\ymax}{
            \draw[name path=b, green] (\xmin,\y) -- (\xmax,\y);
            \begin{pgfonlayer}{foreground layer}
            \fill[name intersections={of=a and b}, red](intersection-1) circle (2pt);
            \end{pgfonlayer}
        }
    }
    \end{scope}
    \end{tikzpicture}
\end{document}