/// <summary>
/// Implements gift wrapping algorithm.
/// </summary>
/// <param name="points">Set of points.</param>
/// <returns>Polygon representing convex hull.</returns>
public static Polygon ConvexHull(IList<Vector> points)
{
Debug.Assert(points != null);
Debug.Assert(points.Count >= 3);
// Leave only distinct points
points = new List<Vector>(points.Distinct());
// Find first point
Vector hullStart = points[0];
for (int i = 1; i < points.Count; ++i)
{
Vector point = points[i];
if (point.X < hullStart.X || (point.X == hullStart.X && point.Y < hullStart.Y))
hullStart = point;
}
Vector currentHullPoint = hullStart;
Polygon result = new Polygon();
bool[] usedPoints = new bool[points.Count];
do
{
result.vertices.Add(currentHullPoint);
int nextHullPointIndex = 0;
for (int i = 1; i < points.Count; ++i)
{
if (usedPoints[nextHullPointIndex] ||
points[nextHullPointIndex] == currentHullPoint ||
Vector.CrossProduct(points[i] - currentHullPoint, points[nextHullPointIndex] - currentHullPoint) < 0)
{
nextHullPointIndex = i;
}
}
currentHullPoint = points[nextHullPointIndex];
usedPoints[nextHullPointIndex] = true;
} while (currentHullPoint != hullStart);
return result;
}
public static Polygon FromPoints(IEnumerable<Vector> vertices)
{
Polygon result = new Polygon();
result.vertices.AddRange(vertices);
return result;
}
public static Polygon FromPoints(params Vector[] vertices)
{
Polygon result = new Polygon();
result.vertices.AddRange(vertices);
return result;
}
private static void MinMaxDistanceForEdge(
Vector point,
Polygon convexHull,
VertexConstraints constraints1,
VertexConstraints constraints2,
out double minDistanceSqr,
out double maxDistanceSqr)
{
if (convexHull.IsPointInside(point))
minDistanceSqr = 0;
else
{
minDistanceSqr = Double.PositiveInfinity;
for (int i = 0; i < convexHull.Vertices.Count; ++i)
{
double distanceSqr = point.DistanceToSegmentSquared(
convexHull.Vertices[i],
convexHull.Vertices[(i + 1) % convexHull.Vertices.Count]);
minDistanceSqr = Math.Min(minDistanceSqr, distanceSqr);
}
}
maxDistanceSqr = 0;
foreach (Vector vertex1 in constraints1.Corners)
{
foreach (Vector vertex2 in constraints2.Corners)
{
double distanceSqr = point.DistanceToSegmentSquared(vertex1, vertex2);
maxDistanceSqr = Math.Max(maxDistanceSqr, distanceSqr);
}
}
}
