/// <summary>
/// Finds the ConvexHull of a series of points. See
/// http://www.cs.princeton.edu/courses/archive/spr10/cos226/demo/ah/GrahamScan.html
/// for further information.
/// </summary>
/// <param name="points">The points to compute the ConvexHull for</param>
/// <returns>a collection of points that represents the polygon
/// of the ConvexHull</returns>
public static ICollection <Point> CalculateConvexHull(ICollection <Point> points)
{
if (points.Count <= 3)
{
return(points);
}
List <ConvexHullPoint> chPoints = new List <ConvexHullPoint>();
// Get the current anchor point
anchor = new ConvexHullPoint(DetermineAnchorPoint(points), 0, null);
// Loop over the points
foreach (Point currentPoint in points)
{
// Ensure that this point is not the anchor
if (currentPoint != anchor.Point)
{
// Create a new ConvexHUllPoint and save it for later use
ConvexHullPoint newConvexHullPoint = new ConvexHullPoint(currentPoint, CalculateCartesianAngle(currentPoint.X - anchor.Point.X, currentPoint.Y - anchor.Point.Y), anchor);
chPoints.Add(newConvexHullPoint);
}
}
// Sort the points
chPoints.Sort();
// Actually calculate and return the ConvexHull
return(GrahamScan(chPoints));
}
/// <summary>
/// Finds the ConvexHull of a series of points. See
/// http://www.cs.princeton.edu/courses/archive/spr10/cos226/demo/ah/GrahamScan.html
/// for further information.
/// </summary>
/// <param name="points">The points to compute the ConvexHull for</param>
/// <returns>a collection of points that represents the polygon
/// of the ConvexHull</returns>
private static ICollection <Point> GrahamScan(List <ConvexHullPoint> chPoints)
{
Stack <ConvexHullPoint> chPointStack = new Stack <ConvexHullPoint>();
IEnumerator <ConvexHullPoint> enumerator = chPoints.GetEnumerator();
chPointStack.Push(anchor);
chPointStack.Push(chPoints[0]);
// Advance the enumerator to account for the two points
// that we already got
enumerator.MoveNext();
enumerator.MoveNext();
int i = 1;
// Loop over all the points that were provided
while (i < chPoints.Count)
{
// Ensure that stack contains points
if (chPointStack.Count > 1)
{
ConvexHullPoint firstCHPoint = chPointStack.Pop();
ConvexHullPoint secondCHPoint = chPointStack.Pop();
chPointStack.Push(secondCHPoint);
chPointStack.Push(firstCHPoint);
if (Orientation(secondCHPoint, firstCHPoint, enumerator.Current) == COUNTER_CLOCKWISE)
{
chPointStack.Push(enumerator.Current);
enumerator.MoveNext();
i++;
}
else
{
chPointStack.Pop();
}
}
else // No points in stack
{
chPointStack.Push(enumerator.Current);
enumerator.MoveNext();
i++;
}
}
return(GetSortedPoints(chPointStack));
}
/// <summary>
/// Determines the orientation of the provided points
/// </summary>
/// <param name="chPoint1">The first ConvexHullPoint</param>
/// <param name="chPoint2">The second ConvexHullPoint</param>
/// <param name="chPoint3">The third ConvexHullPoint</param>
/// <returns>a value indicating how the provided points are oriented</returns>
private static int Orientation(ConvexHullPoint chPoint1, ConvexHullPoint chPoint2, ConvexHullPoint chPoint3)
{
return(Orientation(chPoint1.Point.X, chPoint1.Point.Y, chPoint2.Point.X, chPoint2.Point.Y, chPoint3.Point.X, chPoint3.Point.Y));
}