将分段区域合并为一个区域

Question

我正在寻找一种方法将分段区域连接成一个彼此重叠的区域，如下所示：

对于左图中的灰色区域，我根据这个问题的答案生成了一个五边形：在 TikZ 中创建随机图案。但我怎样才能像右图那样将这些区域连接成一个区域，同时仍然保持距离呢？这是来自 BLICHFELD 定理https://cims.nyu.edu/~regev/teaching/lattices_fall_2004/ln/introduction.pdf

\begin{tikzpicture}[scale=0.45]
        \coordinate (Origin)   at (0,0);
        \coordinate (XAxisMin) at (-3,0);
        \coordinate (XAxisMax) at (10,0);
        \coordinate (YAxisMin) at (0,-2);
        \coordinate (YAxisMax) at (0,10);
        
        \draw [thin, black,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
        \draw [thin, black,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis
        
        \clip (0, 0) rectangle (8cm,4cm);
        \coordinate (Bone) at (0,2);
        \coordinate (Btwo) at (4,2);
        %\coordinate (Bthree) at (2, 4);
        \draw[style=help lines,dashed] (-14,-14) grid[step=2cm] (14,14);
        
       \foreach \x in {-7,-6,...,7}{% Two indices running over each
            \foreach \y in {-7,-6,...,7}{% node on the grid we have drawn 
                \node[draw,circle,inner sep=2pt,fill] at (4*\x, 4*\x + 2*\y) {};
                    % Places a dot at those points
            }
        }
            
        %\draw [ultra thick,-latex,red] (Origin)
        %    -- (Bthree) node [above, right] {$b_3$};
        \fill[fill=gray, fill opacity=0.3, draw=black] (4,2) ellipse (3cm and 1.75cm);
        
    \end{tikzpicture}

Answer 1

这可能需要一些改进，但您也许可以使用该spy库：

\documentclass[border=1mm, tikz]{standalone}
\usetikzlibrary{spy}

\begin{document}

\begin{tikzpicture}[scale=0.45, spy using overlays={black!0, height={0.45*2cm}, width={0.45*4cm}, anchor=south west}]
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (-3,0);
    \coordinate (XAxisMax) at (10,0);
    \coordinate (YAxisMin) at (0,-2);
    \coordinate (YAxisMax) at (0,10);
    
    \draw [thin, black,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [thin, black,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis
    
    \begin{scope}
    \clip (0, 0) rectangle (8cm,4cm);
    \coordinate (Bone) at (0,2);
    \coordinate (Btwo) at (4,2);
    %\coordinate (Bthree) at (2, 4);
    \draw[style=help lines,dashed] (-14,-14) grid[step=2cm] (14,14);
    
    \foreach \x in {-7,-6,...,7}{% Two indices running over each
        \foreach \y in {-7,-6,...,7}{% node on the grid we have drawn 
            \node[draw,circle,inner sep=2pt,fill] at (4*\x, 4*\x + 2*\y) {};
                % Places a dot at those points
        }
    }
        
    %\draw [ultra thick,-latex,red] (Origin)
    %    -- (Bthree) node [above, right] {$b_3$};
    \fill[fill=gray, fill opacity=0.3, draw=black] (4,2) ellipse (3cm and 1.75cm);
    \end{scope}
    
    \spy on (0,0) in node at (2,6);
    \spy on ({.45*4},0) in node at (2,6);
    \spy on (0,{.45*2}) in node at (2,6);
    \spy on ({.45*4},{.45*2}) in node at (2,6);
\end{tikzpicture}
\end{document}

---

要使间谍图像更大，可以使用选项magnification。但请注意，由于您不是使用常规圆形或正方形进行间谍操作，因此需要明确说明间谍图像的高度和宽度：

\documentclass[border=1mm, tikz]{standalone}
\usetikzlibrary{spy}

\begin{document}

\begin{tikzpicture}[scale=0.45, spy using overlays={black!0, height={2*0.45*4cm}, width={2*0.45*8cm}, anchor=south west, magnification=2}]
    \coordinate (Origin)   at (0,0);
    \coordinate (XAxisMin) at (-3,0);
    \coordinate (XAxisMax) at (10,0);
    \coordinate (YAxisMin) at (0,-2);
    \coordinate (YAxisMax) at (0,10);
    
    \draw [thin, black,-latex] (XAxisMin) -- (XAxisMax);% Draw x axis
    \draw [thin, black,-latex] (YAxisMin) -- (YAxisMax);% Draw y axis
    
    \begin{scope}
    \clip (0, 0) rectangle (8cm,4cm);
    \coordinate (Bone) at (0,2);
    \coordinate (Btwo) at (4,2);
    %\coordinate (Bthree) at (2, 4);
    \draw[style=help lines,dashed] (-14,-14) grid[step=2cm] (14,14);
    
    \foreach \x in {-7,-6,...,7}{% Two indices running over each
        \foreach \y in {-7,-6,...,7}{% node on the grid we have drawn 
            \node[draw,circle,inner sep=2pt,fill] at (4*\x, 4*\x + 2*\y) {};
                % Places a dot at those points
        }
    }
        
    %\draw [ultra thick,-latex,red] (Origin)
    %    -- (Bthree) node [above, right] {$b_3$};
    \fill[fill=gray, fill opacity=0.3, draw=black] (4,2) ellipse (3cm and 1.75cm);
    \end{scope}
    
    \spy on (0,0) in node at (2,6);
    \spy on ({.45*4},0) in node at (2,6);
    \spy on (0,{.45*2}) in node at (2,6);
    \spy on ({.45*4},{.45*2}) in node at (2,6);
\end{tikzpicture}
\end{document}