在条件中乘以数字

Question

我需要填写高于该线的圆圈。

\begin{tikzpicture}
    \foreach \a in {0,...,5}{
        \draw (0,\a)--(13,\a);
    }
    \foreach \a in {0,...,13}{
        \draw (\a,0)--(\a,5);
    }

    \foreach \a in {0,...,5}{
        \foreach \b in {0,...,13}{
            \ifnum \a > \b 
            % \ifnum 13*\a > 5*\b  
            \draw[fill=black] (\b,\a) circle (0.1); \else 
            \draw[] (\b,\a) circle (0.1); \fi
      }
    }

    \draw[dashed] (0,0)--(13,5);
\end{tikzpicture}

最终结果如下：

Tikz 中的条件不太简单，您不能将数字定义为仅仅是数字，并且操作需要特别小心。

例如Tikz/Pgf if 语句

Answer 1

TikZ/pgf还支持计算，例如通过\pgfmathsetmacro：

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \draw[line cap=rect]
        \foreach \a in {0,...,5}{
            (0,\a)--(13,\a)
        }
        \foreach \a in {0,...,13}{
            (\a,0)--(\a,5)
        }
    ;

    \foreach \a in {0,...,5}{
        \draw (0,\a)--(13,\a);
    }
    \foreach \a in {0,...,13}{
        \draw (\a,0)--(\a,5);
    }

    \foreach \a in {0,...,5}{
        \foreach \b in {0,...,13}{
            \pgfmathsetmacro\q{5*\b/13}
            \ifdim\q pt<\a pt
                \draw[fill=black] (\b,\a) circle (0.1);
            \else
                \draw[] (\b,\a) circle (0.1);
            \fi
        }
    }

    \draw[dashed] (0,0)--(13,5);
\end{tikzpicture}
\end{document}

通过 e-TeX 进行计算的变体，无需除法，以避免舍入问题。

\foreach \a in {0,...,5}{
    \foreach \b in {0,...,13}{
        \ifnum\numexpr 5 * \b\relax < \numexpr \a * 13\relax
            \draw[fill=black] (\b,\a) circle (0.1);
        \else
            \draw[] (\b,\a) circle (0.1);
        \fi
    }
}

该选项line cap=rect改进了外部水平线和垂直线在角落处的相交方式。

Answer 2

使用\pgfmathparse：

\documentclass[tikz,border=4mm]{standalone}


\begin{document}
\begin{tikzpicture}
    \foreach \a in {0,...,5}{
        \draw (0,\a)--(13,\a);
    }
    \foreach \a in {0,...,13}{
        \draw (\a,0)--(\a,5);
    }

    \foreach \a in {0,...,5}{
        \foreach \b in {0,...,13}{
            \pgfmathparse{13/5*\a}
            \ifdim \pgfmathresult pt > \b pt
            % \ifnum 13*\a > 5*\b  
            \draw[fill=black] (\b,\a) circle (0.1); \else 
            \draw[] (\b,\a) circle (0.1); \fi
      }
    }

    \draw[dashed] (0,0)--(13,5);
\end{tikzpicture}
\end{document}