https://github.com/tomtkg/largest-small-polygon

Generate largest small n-polygons.
https://github.com/tomtkg/largest-small-polygon

biggest-little-polygon grahams-biggest-little-hexagon largest-small-polygon lsp matlab numerical-methods optimization polygons solve

Last synced: 4 months ago
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Generate largest small n-polygons.

• Host: GitHub
• URL: https://github.com/tomtkg/largest-small-polygon
• Owner: tomtkg
• License: mit
• Created: 2025-01-20T05:11:16.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2025-02-12T11:32:13.000Z (8 months ago)
• Last Synced: 2025-04-09T05:44:17.041Z (6 months ago)
• Topics: biggest-little-polygon, grahams-biggest-little-hexagon, largest-small-polygon, lsp, matlab, numerical-methods, optimization, polygons, solve
• Language: MATLAB
• Homepage:
• Size: 1.41 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

          
# Largest Small Polygon (LSP)

![](https://img.shields.io/github/languages/top/tomtkg/Largest-Small-Polygon)

![](https://img.shields.io/github/languages/code-size/tomtkg/Largest-Small-Polygon)

![](https://img.shields.io/github/last-commit/tomtkg/Largest-Small-Polygon)

Generate largest small $n$-polygons.

Largest Small Polygon (LSP) or largest small $n$-polygons or the biggest little polygon is the $n$-sided polygon that has diameter one (that is, every two of its points are within unit distance of each other) and that has the largest area among all diameter-one-$n$-gons. (from [wikipedia](https://en.wikipedia.org/wiki/Biggest_little_polygon))

# How to use

`main.m` is the main file. You can execute `main.m` in one of the following ways:

### Run from the Command Line

Execute the script using MATLAB's batch mode:

```

matlab -batch main

```

### Run in MATLAB

Open and run `main.m` directly in MATLAB, or use the following example in the MATLAB command window:

```MATLAB:

X = LSP(6); % Graham's Biggest Little Hexagon

plot([X(:,1); X(1,1)], [X(:,2);  X(1,2)], 'r-o');

```

This code will plot [Graham's Biggest Little Hexagon](https://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html) in red with circular markers.

### Requirements

To execute this script, the [Optimization Toolbox](https://www.mathworks.com/help/optim) is required.  

# Gallery

|![](image/LSP(3)-1.png)|![](image/LSP(4)-1.png)|![](image/LSP(5)-1.png)|

|:-:|:-:|:-:|

|LSP(3) $A=0.43301270$|LSP(4) $A=0.50000000$|LSP(5) $A=0.65716389$|

|![](image/LSP(6)-1.png)|![](image/LSP(7)-1.png)|![](image/LSP(8)-1.png)|

|LSP(6) $A=0.67498144$|LSP(7) $A=0.71974093$|LSP(8) $A=0.72686848$|

|![](image/LSP(3)-2.png)|![](image/LSP(4)-2.png)|![](image/LSP(5)-2.png)|

|LSP(3) with distance|LSP(4) with distance|LSP(5) with distance|

|![](image/LSP(6)-2.png)|![](image/LSP(7)-2.png)|![](image/LSP(8)-2.png)|

|LSP(6) with distance|LSP(7) with distance|LSP(8) with distance|

# Related articles

* [2点間の距離が1以下で面積が最大となる多角形 LSP](https://qiita.com/tomtkg/items/55ccaa24c04c22d5baa9)

* [Largest Small n-Polygons 生成プログラムの紹介](https://qiita.com/tomtkg/items/e316ba5766e3e6ca8125)