A Collection of Code Snippets in as Many Programming Languages as Possible

This project is maintained by TheRenegadeCoder

Welcome to the Convex Hull in Mathematica page! Here, you'll find the source code for this program as well as a description of how the program works.

```
(* Code *)
(* Convex hull option convexHull1 is based on the built-in ConvexHullMesh: *)
convexHull1 = Function[{ps},
Module[{mesh = ConvexHullMesh[ps]},
Round /@ Part[
MeshCoordinates[mesh],
First[First[MeshCells[mesh, 2]]]]]];
(* If that is considered cheating, then option convexHull2 implements it directly using Jarvis' algorithm: *)
convexHull2 = Function[{inputList},
Module[{orientation, l = inputList, i, j},
(* compute the direction in which three vertices are oriented *)
orientation = Function[{a, b, c}, Det[{a - b, c - b}]];
(* keep sorting the convex hull vertices to the beginning of the list;
'i' is the index of the last vertex in the convex hull;
'j' is the index of the next vertex selected to be permuted to the front *)
For[
(* initially *)
i = 0; (* no vertices selected into the convex hull *)
j = First[OrderingBy[l, First, 1]], (* find the first vertex by minimum x-coordinate *)
(* continue as long as the next selected vertex is not already in the convex hull *)
j > i,
(* iteration done in the body *),
(* permute the next selected vertex to the front of the list *)
i++;
l = Permute[l, If[i != j, Cycles[{{i, j}}], {}]];
(* find the next vertex that is clockwise to all other vertices *)
j = Mod[i + 1, Length[l], 1];
Do[ (* for all vertices *)
(* if 'k' is such that 'i', 'j', 'k' are counterclockwise, let 'k' become the new 'j' *)
If[orientation @@ l[[{i, j, k}]] > 0, j = k],
{k, Length[l]}];
];
(* return only the front part of the list containing the convex hull *)
Take[l, i]]];
(* The outer function provides the 'user interface' (e.g., the string parsing): *)
convexHullMain = Function[{lx, ly},
Module[{e = "Usage: please provide at least 3 x and y coordinates as separate lists (e.g. \"100, 440, 210\")"},
Catch[
convexHull2[
Transpose[
If[MatrixQ[#] \[And] Length[First[#]] >= 3,
#, Throw[e]] &[
Map[
(* convert string to integer, or throw *)
s \[Function] If[StringMatchQ[s, DigitCharacter ..],
FromDigits[s],
Throw[e]],
(* construct two arguments to convexHull: list of x coordinates, list of y coordinates *)
{StringSplit[lx, ", "], StringSplit[ly, ", "]},
{-1} (* at each leaf *)]]]]]]];
(* Valid Tests *)
Print /@ Apply[convexHullMain] /@ {
{"100, 180, 240", "220, 120, 20"},
{"100, 140, 320, 480, 280", "240, 60, 40, 200, 300"},
{"260, 280, 300, 320, 600, 360, 20, 240",
"160, 100, 180, 140, 160, 320, 200, 0"}
};
(* Invalid Tests *)
convexHullMain["100, 180", "240, 60, 40, 200, 300"]
convexHullMain["100, 180, 240", "240, 60, 40, 200, 300"]
convexHullMain["100, 180, 240", ""]
convexHullMain["100, 1A0, 240", "220, 120, 20"]
```

Convex Hull in Mathematica was written by:

- Ben Hekster

If you see anything you'd like to change or update, please consider contributing.

No 'How to Implement the Solution' section available. Please consider contributing.

No 'How to Run the Solution' section available. Please consider contributing.