更新新坐标系

Question

我想使用 tikz LaTeX 在三角形网格中绘制一条特定路径，如下图所示。我该怎么做？

Answer 1

为了构建箭头，我创建了一个新的坐标系，其中 x 轴为水平，y 轴为 60° 角的一侧。它被称为triangular，其别名为tri。

更新新坐标系

\documentclass[tikz,border=5mm]{standalone}
\makeatletter
\define@key{triangularkeys}{x}{\def\myx{#1}}
\define@key{triangularkeys}{y}{\def\myy{#1}}
\tikzdeclarecoordinatesystem{triangular}%
{%
\setkeys{triangularkeys}{#1}%
\pgfpointadd{\pgfpointpolarxy{60}{\myx}}{\pgfpointpolarxy{120}{\myy}}
}
\makeatother
\tikzaliascoordinatesystem{tri}{triangular}

\usetikzlibrary{arrows.meta}
\begin{document}

\begin{tikzpicture}[x=0.75cm, y=0.75cm,>=Latex]

% the grid
\foreach \j in {0,...,1} {
  \foreach \i in {0,...,5} {
    \draw[gray](0:\i)++(60:\j)++(120:\j)--++(60:2)--++(-1,0)--++(-60:2);
    
    \draw[gray](0:\i)++(90:{(1+2*\j)*sin(60)})--++(1,0);
}}
\draw(current bounding box.north west)rectangle(current bounding box.south east);


% the arrows
\draw [thick,red,->](tri cs:x=1,y=0)--node[below]{x}++(tri cs:x=1,y=0);
\draw [thick,blue,->](tri cs:x=1,y=0)--node[below]{y}++(tri cs:x=0,y=1);

\draw [thick,violet,->] (1,0)++(tri cs:x=1,y=0)--++(tri cs:x=1,y=0);
\draw [thick,violet,->] (tri cs:x=2,y=0)++(1,0)--++(tri cs:x=0,y=-1);
\draw [thick,violet,->] (2,0)++(tri cs:x=1,y=0)--++(tri cs:x=1,y=0);
\draw [thick,violet,->] (2,0)++(tri cs:x=2,y=0)--++(tri cs:x=0,y=-1);
\end{tikzpicture}

\end{document}

\documentclass[tikz,border=5mm]{standalone}
\makeatletter
\define@key{triangularkeys}{x}{\def\myx{#1}}
\define@key{triangularkeys}{y}{\def\myy{#1}}
\tikzdeclarecoordinatesystem{triangular}%
{%
\setkeys{triangularkeys}{#1}%
\pgfpointadd{\pgfpointxy{\myx}{0}}{\pgfpointpolarxy{60}{\myy}}
}
\makeatother
\tikzaliascoordinatesystem{tri}{triangular}

\usetikzlibrary{arrows.meta}
\begin{document}

\begin{tikzpicture}[x=0.75cm, y=0.75cm,>=Latex]

% the grid
\foreach \j in {0,...,1} {
  \foreach \i in {0,...,5} {
    \draw[gray](0:\i)++(60:\j)++(120:\j)--++(60:2)--++(-1,0)--++(-60:2);
    
    \draw[gray](0:\i)++(90:{(1+2*\j)*sin(60)})--++(1,0);
}}
\draw(current bounding box.north west)rectangle(current bounding box.south east);


% the arrows
\draw [thick,blue,->](tri cs:x=0,y=0)--node[below]{x}(tri cs:x=3,y=0);
\draw [thick,blue,->](tri cs:x=0,y=0)--node[left]{y}(tri cs:x=0,y=3);

\draw [thick,violet,->] (tri cs:x=1,y=1)--(tri cs:x=1,y=2);
\draw [thick,violet,->] (tri cs:x=1,y=2)--(tri cs:x=2,y=1);
\draw [thick,violet,->] (tri cs:x=2,y=1)--(tri cs:x=2,y=2);
\draw [thick,violet,->] (tri cs:x=2,y=2)--(tri cs:x=3,y=1);
\end{tikzpicture}

\end{document}

Answer 2

这是一种通过在循环中定义三角形来实现所需效果的方法。只需修改尺寸并在循环中添加步骤即可增加绘图的大小。

\documentclass{standalone}

\usepackage{tikz}
    \usetikzlibrary{arrows.meta}

\begin{document}
    
    \begin{tikzpicture}
    
        \draw[thick] (-2.5, -{sqrt(3)/2}) rectangle (2.5, {sqrt(3)});
        
        \path[clip] (-2.5, -{sqrt(3)/2}) rectangle (2.5, {sqrt(3)});
        
        \foreach \x in {-1,0,1}{
            \foreach \y in {-3.5,-2.5,...,2.5}{
                \draw ({\y - 0.5*Mod(\x+1,2)},{\x*sqrt(3)/2}) -- ++ (60:1) -- ++ (-60:1) -- cycle;
            }
        }

        \coordinate (next) at (-2, 0);
    
        \foreach \x in {1,2,...,4}{
            \draw[-Latex,blue] (next) -- ++ (60:1) coordinate (next);
            \draw[-Latex,blue] (next) -- ++ (-60:1) coordinate (next);
        }
    
    \end{tikzpicture}
    
\end{document}

得出的结果是：