/// <summary>
/// Implementation of Convex Hull using the Monotone Chain Convex Hull Algorithm.
/// The algorithm was chosen for implementation due to its simplicity. Chan's
/// Convex Hull algorithm is a tad more efficient when the output point set
/// is smaller than the input set.
///
/// based on http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
/// </summary>
/// <param name="input"></param>
/// <returns>
/// The convex hull of the points in counterclockwise order (starting from the
/// rightmost point)
/// </returns>
public static Point2D[] ConvexHull(Point2D[] input)
{
// sort input by x, then y
Array.Sort(
input,
new LambdaComparer<Point2D>(
(a, b) => {
if (a.X < b.X)
return -1;
if (a.X > b.X)
return 1;
return a.Y.CompareTo(b.Y);
}
)
);
// Initialize upper and lower hull lists
var h = new Point2D[2 * input.Length];
int k = 0;
// build lower hull
for (int i = 0; i < input.Length; i++)
{
while (k >= 2 && Cross(h[k - 2], h[k - 1], input[i]) <= 0)
k--;
h[k++] = input[i];
}
// build upper hull
for (int i = input.Length - 2, t = k + 1; i >= 0; i--)
{
while (k >= t && Cross(h[k - 2], h[k - 1], input[i]) <= 0)
k--;
h[k++] = input[i];
}
return h.TakeWhile(x => x != null).ToArray();
}
