/*
* Returns the smallest circle that encloses all the given points. Runs in expected O(n) time, randomized.
* Note: If 0 points are given, a circle of radius -1 is returned. If 1 point is given, a circle of radius 0 is returned.
*/
// Initially: No boundary points known
public static Circle GetMinimumCoverCircle(List <Dot> dots)
{
List <Point> points = new List <Point>();
foreach (Dot d in dots)
{
points.Add(new Point(d.Position.X, d.Position.Y));
}
// Clone list to preserve the caller's data, do Durstenfeld shuffle
List <Point> shuffled = new List <Point>(points);
Random rand = new Random();
for (int i = shuffled.Count - 1; i > 0; i--)
{
int j = rand.Next(i + 1);
Point temp = shuffled[i];
shuffled[i] = shuffled[j];
shuffled[j] = temp;
}
// Progressively add points to circle or recompute circle
Circle c = new Circle(new Point(0, 0), -1);
for (int i = 0; i < shuffled.Count; i++)
{
Point p = shuffled[i];
if (c.r < 0 || !c.Contains(p))
{
c = MakeCircleOnePoint(shuffled.GetRange(0, i + 1), p);
}
}
return(c);
}
// Two boundary points known
private static Circle MakeCircleTwoPoints(List <Point> points, Point p, Point q)
{
Circle circ = MakeDiameter(p, q);
Circle left = new Circle(new Point(0, 0), -1);
Circle right = new Circle(new Point(0, 0), -1);
// For each point not in the two-point circle
Point pq = q.Subtract(p);
foreach (Point r in points)
{
if (circ.Contains(r))
{
continue;
}
// Form a circumcircle and classify it on left or right side
double cross = pq.Cross(r.Subtract(p));
Circle c = MakeCircumcircle(p, q, r);
if (c.r < 0)
{
continue;
}
else if (cross > 0 && (left.r < 0 || pq.Cross(c.c.Subtract(p)) > pq.Cross(left.c.Subtract(p))))
{
left = c;
}
else if (cross < 0 && (right.r < 0 || pq.Cross(c.c.Subtract(p)) < pq.Cross(right.c.Subtract(p))))
{
right = c;
}
}
// Select which circle to return
if (left.r < 0 && right.r < 0)
{
return(circ);
}
else if (left.r < 0)
{
return(right);
}
else if (right.r < 0)
{
return(left);
}
else
{
return(left.r <= right.r ? left : right);
}
}
// One boundary point known
private static Circle MakeCircleOnePoint(List <Point> points, Point p)
{
Circle c = new Circle(p, 0);
for (int i = 0; i < points.Count; i++)
{
Point q = points[i];
if (!c.Contains(q))
{
if (c.r == 0)
{
c = MakeDiameter(p, q);
}
else
{
c = MakeCircleTwoPoints(points.GetRange(0, i + 1), p, q);
}
}
}
return(c);
}