public static Polygon2 Convexhull(IEnumerable <Vector2> vertices)
{
var pts = vertices.ToArray();
if (!pts.Any())
{
return(new Polygon2());
}
// Sort points lexicographically by increasing (x, y)
int n = pts.Length;
Polysort.Quicksort(pts);
var left = pts[0];
var right = pts[n - 1];
// Partition into lower hull and upper hull
var lower = new CircularDoublyLinkedList <Vector2>(left);
var upper = new CircularDoublyLinkedList <Vector2>(left);
for (int i = 0; i < n; i++)
{
double det = Vector2.Area2(left, right, pts[i]);
if (det > 0)
{
upper = upper.Append(new CircularDoublyLinkedList <Vector2>(pts[i]));
}
else if (det < 0)
{
lower = lower.Prepend(new CircularDoublyLinkedList <Vector2>(pts[i]));
}
}
lower = lower.Prepend(new CircularDoublyLinkedList <Vector2>(right));
upper = upper.Append(new CircularDoublyLinkedList <Vector2>(right)).Next;
// Eliminate points not on the hull
Eliminate(lower);
Eliminate(upper);
// Eliminate duplicate endpoints
if (lower.Prev.Value.Equals(upper.Value))
{
lower.Prev.Delete();
}
if (upper.Prev.Value.Equals(lower.Value))
{
upper.Prev.Delete();
}
// Join the lower and upper hull
var res = new Vector2[lower.Size() + upper.Size()];
lower.CopyInto(res, 0);
upper.CopyInto(res, lower.Size());
return(new Polygon2(res));
}
