// Graham's scan
private static void eliminate(CDLL start)
{
CDLL v = start, w = start.Prev;
bool fwd = false;
while (v.Next != start || !fwd)
{
if (v.Next == w)
fwd = true;
if (Utility.Area(v.val, v.Next.val, v.Next.Next.val) < 0) // right turn
v = v.Next;
else
{ // left turn or straight
v.Next.Delete();
v = v.Prev;
}
}
}
public static Point[] convexhull(Point[] pts)
{
// Sort points lexicographically by increasing (x, y)
int N = pts.Length;
Polysort.Quicksort(pts);
Point left = pts[0], right = pts[N - 1];
// Partition into lower hull and upper hull
CDLL lower = new CDLL(left), upper = new CDLL(left);
for (int i = 0; i < N; i++)
{
double det = Utility.Area(left, right, pts[i]);
if (det > 0)
upper = upper.Append(new CDLL(pts[i]));
else if (det < 0)
lower = lower.Prepend(new CDLL(pts[i]));
}
lower = lower.Prepend(new CDLL(right));
upper = upper.Append(new CDLL(right)).Next;
// Eliminate points not on the hull
eliminate(lower);
eliminate(upper);
// Eliminate duplicate endpoints
if (lower.Prev.val.Equals(upper.val))
lower.Prev.Delete();
if (upper.Prev.val.Equals(lower.val))
upper.Prev.Delete();
// Join the lower and upper hull
Point[] res = new Point[lower.Size() + upper.Size()];
lower.CopyInto(res, 0);
upper.CopyInto(res, lower.Size());
return res;
}
public CDLL Prepend(CDLL elt)
{
elt.next = this; elt.prev = prev; prev.next = elt; prev = elt;
return elt;
}
// Delete: adjust the remaining elements, make this one point nowhere
public void Delete()
{
next.prev = prev; prev.next = next;
next = prev = null;
}
public CDLL Append(CDLL elt)
{
elt.prev = this; elt.next = next; next.prev = elt; next = elt;
return elt;
}
private CDLL prev, next; // not null, except in deleted elements
#endregion Fields
#region Constructors
// A new CDLL node is a one-element circular list
public CDLL(Point val)
{
this.val = val; next = prev = this;
}