平行四边形规则和头尾规则

Question

这是我当前的 MWE：

\documentclass{article}

\usepackage{tikz}

\usetikzlibrary{calc}

\tikzset{>=stealth}
\colorlet{veccol}{green!45!black}
\tikzstyle{vector}=[->,very thick,veccol]

\begin{document}
  \begin{figure}
    \centering
    \begin{tikzpicture}
      \draw[<->] (0,0)--(5.5,0) node[right]{$x$};
      \draw[<->] (0,0)--(0,5.5) node[above]{$y$};

      \coordinate (O) at (0,0);
      \coordinate (A) at (125:5);
      \coordinate (B) at (0:4);
      \coordinate (A+B) at ($(A)+(B)$);

      \draw[vector,blue] (0,0)--(A) node[midway,left] {$\vec{x}$};
      \draw[vector,red] (0,0)--(B) node[midway,above] {$\vec{y}$};

      \draw[vector,thin,dashed] (A)--(A+B);
      \draw[vector,thin,dashed] (B)--(A+B);

      \draw[vector,purple] (O)--(A+B) node[above,rotate=-60] {$\vec{x}+\vec{y}$};
      \draw[rotate=180] (O)--(A+B);
    \end{tikzpicture}
  \end{figure}
\end{document}

生成此 pdf：

问题就在这里。我总是把这段代码写出来。我有 10 多个地方都有它。有没有办法我可以创建一个类似函数的东西，使用极坐标给它输入两个（或更多）向量，然后像这样绘制它？

另外，我如何使用头尾规则而不是平行四边形规则绘制相同的向量？是否也可以创建某种可重复使用的函数（如上面的问题），但将其用于头尾规则而不是平行四边形规则？

Answer 1

对于平行四边形部分：

\documentclass{article}

\usepackage{tikz}

\usetikzlibrary{calc}

\newcommand{\parallelogramRule}[2]{%
    \begin{tikzpicture}[inner sep=1pt,>=stealth]
        \draw[<->] (0,0)--(5.5,0) node[right]{$x$};
        \draw[<->] (0,0)--(0,5.5) node[above]{$y$};
        
        \tikzstyle{vector label} = [midway,fill=white,sloped]
        \tikzstyle{vector}=[->,very thick]
        \tikzstyle{construction} = [->,thin,dashed,draw=green!45!black]
        
        \coordinate (O) at (0,0);
        \coordinate (A) at (#1);
        \coordinate (B) at (#2);
        \coordinate (A+B) at ($(A)+(B)$);
        
        \draw[vector,blue] (O)--(A) node[vector label] {$\vec{x}$};
        \draw[vector,red] (O)--(B) node[vector label] {$\vec{y}$};
        
        \draw[construction] (A)--(A+B);
        \draw[construction] (B)--(A+B);
        
        \draw[vector,purple] (O)--(A+B) node[vector label] {$\vec{x}+\vec{y}$};
    \end{tikzpicture}
}

\begin{document}
    \begin{figure}
        \centering
        \parallelogramRule{30:5}{0:4}%
        \parallelogramRule{130:2}{90:2}%
        \parallelogramRule{130:4}{-10:2}
    \end{figure}
\end{document}

实现头尾规则很简单，只需用减法代替加法，并改变结果向量的标签。

编辑

用于添加多个向量

\documentclass{article}

\usepackage{listofitems}
\usepackage{tikz}
\usetikzlibrary{calc}

\newcommand{\multipleVecAdd}[1]{%
    \begin{tikzpicture}[inner sep=0pt]
        \tikzstyle{vector}=[->,very thick,blue]
        \tikzstyle{vector label} = [midway,fill=white,sloped]
        \tikzstyle{resultant}=[->,very thick,red]
        
        \coordinate (O) at (0,0);
        \draw [->] (O) -- (4,0) node [right] {$x$};
        \draw [->] (O) -- (0,4) node [right] {$y$};
        
        \setsepchar{;}
        \readlist*{\veclist}{#1}
        \coordinate (resultant) at (O);
        \foreach \i in {1,2,...,\veclistlen}{%
            \coordinate (vec\i) at (\veclist[\i]);
            \draw [vector] (O) -- (vec\i) node [vector label] {$\vec{v}_\i$};
            \coordinate (resultant) at ($(resultant)+(vec\i)$);
        }
        \draw [resultant] (O) -- (resultant) node [vector label] {resultant};
    \end{tikzpicture}
}

\begin{document}
    \begin{figure}
        \centering
        \multipleVecAdd{1,1;-2,3;4,1;4,-2;-1,-4}
    \end{figure}
\end{document}

编辑2

按照 Qrrbrbirlbel 和 SebGlav 的建议，直接使用tikzset和\pgffor。

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc}

\newcommand{\multipleVecAdd}[1]{%
    \begin{tikzpicture}[inner sep=0pt]
        \tikzset{%
            vector/.style={->,very thick,blue},
            vector label/.style={midway,fill=white,sloped},
            resultant/.style={->,very thick,red}
        }
        
        \coordinate (O) at (0,0);
        \draw [->] (O) -- (4,0) node [right] {$x$};
        \draw [->] (O) -- (0,4) node [above] {$y$};
        
        \coordinate (resultant) at (O);
        \foreach \vecPos [count=\vecId] in {#1}{%
            \draw [vector] (O) -- \vecPos node [vector label] {$\vec{v}_\vecId$};
            \draw (resultant) +\vecPos coordinate (resultant);
        }
        \draw [resultant] (O) -- (resultant) node [vector label] {resultant};
    \end{tikzpicture}
}

\begin{document}
    \begin{figure}
        \centering
        \multipleVecAdd{(1,1),(-2,3),(4,1),(4,-2),(-1,-4)}
    \end{figure}
\end{document}