vault backup: 2025-11-04 16:43:34

2025-11-04 16:43:34 -05:00
parent 29b0794b01
commit eddfbb3b7c
36 changed files with 8811 additions and 86 deletions
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+---
+id:
+aliases: []
+tags: []
+title: Convex Hull
+---
+# Convex Hull
+
+[Convex Hull](https://en.wikipedia.org/wiki/Convex_hull)
+
+```tikz
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.16}
+
+\begin{document}
+\begin{tikzpicture}
+  \begin{axis}[
+    axis equal,
+    xmin=0, xmax=3.5,
+    ymin=0, ymax=3.4,
+    grid=both,
+    xlabel={$x$}, ylabel={$y$},
+    tick style={black!60},
+    title={Convex Hull of a Point Set}
+  ]
+    % Point cloud
+    \addplot[
+      only marks,
+      mark=*,
+      mark size=1.8pt
+    ] coordinates {
+      (0.5,0.5)
+      (1.0,2.0)
+      (2.0,1.0)
+      (2.5,2.2)
+      (3.0,0.5)
+      (1.8,3.0)
+      (0.2,2.5)
+      (3.2,1.5)
+    };
+
+    % Convex hull (listed in counterclockwise order)
+    \addplot[
+      thick,
+      fill opacity=0.15,
+      fill=blue
+    ] coordinates {
+      (0.5,0.5)
+      (3.0,0.5)
+      (3.2,1.5)
+      (1.8,3.0)
+      (0.2,2.5)
+    } -- cycle;
+
+    % (Optional) label hull vertices
+    \addplot[only marks, mark=*, mark size=2.2pt] coordinates {
+      (0.5,0.5)
+      (3.0,0.5)
+      (3.2,1.5)
+      (1.8,3.0)
+      (0.2,2.5)
+    };
+    \node[anchor=north west] at (axis cs:0.5,0.5) {$H_1$};
+    \node[anchor=north east] at (axis cs:3.0,0.5) {$H_2$};
+    \node[anchor=west]       at (axis cs:3.2,1.5) {$H_3$};
+    \node[anchor=south]      at (axis cs:1.8,3.0) {$H_4$};
+    \node[anchor=east]       at (axis cs:0.2,2.5) {$H_5$};
+  \end{axis}
+\end{tikzpicture}
+\end{document}
+
+```