Alpha Shape Code / Convex Hull
public class Edge
{
public PointF A { get; set; }
public PointF B { get; set; }
}
public class AlphaShape
{
public List<Edge> BorderEdges { get; private set; }
public AlphaShape(List<PointF> points, float alpha)
{
// 0. error checking, init
if (points == null || points.Count < 2) { throw new ArgumentException("AlphaShape needs at least 2 points"); }
BorderEdges = new List<Edge>();
var alpha_2 = alpha * alpha;
// 1. run through all pairs of points
for (int i = 0; i < points.Count - 1; i++)
{
for (int j = i + 1; j < points.Count; j++)
{
if (points[i] == points[j]) { throw new ArgumentException("AlphaShape needs pairwise distinct points"); } // alternatively, continue
var dist = Dist(points[i], points[j]);
if (dist > 2 * alpha) { continue; } // circle fits between points ==> p_i, p_j can't be alpha-exposed
float x1 = points[i].X, x2 = points[j].X, y1 = points[i].Y, y2 = points[j].Y; // for clarity & brevity
var mid = new PointF((x1 + x2) / 2, (y1 + y2) / 2);
// find two circles that contain p_i and p_j; note that center1 == center2 if dist == 2*alpha
var center1 = new PointF(
mid.X + (float)Math.Sqrt(alpha_2 - (dist / 2) * (dist / 2)) * (y1 - y2) / dist,
mid.Y + (float)Math.Sqrt(alpha_2 - (dist / 2) * (dist / 2)) * (x2 - x1) / dist
);
var center2 = new PointF(
mid.X - (float)Math.Sqrt(alpha_2 - (dist / 2) * (dist / 2)) * (y1 - y2) / dist,
mid.Y - (float)Math.Sqrt(alpha_2 - (dist / 2) * (dist / 2)) * (x2 - x1) / dist
);
// check if one of the circles is alpha-exposed, i.e. no other point lies in it
bool c1_empty = true, c2_empty = true;
for (int k = 0; k < points.Count && (c1_empty || c2_empty); k++)
{
if (points[k] == points[i] || points[k] == points[j]) { continue; }
if ((center1.X - points[k].X) * (center1.X - points[k].X) + (center1.Y - points[k].Y) * (center1.Y - points[k].Y) < alpha_2)
{
c1_empty = false;
}
if ((center2.X - points[k].X) * (center2.X - points[k].X) + (center2.Y - points[k].Y) * (center2.Y - points[k].Y) < alpha_2)
{
c2_empty = false;
}
}
if (c1_empty || c2_empty)
{
// yup!
BorderEdges.Add(new Edge() { A = points[i], B = points[j] });
}
}
}
}
// Euclidian distance between A and B
public static float Dist(PointF A, PointF B)
{
return (float)Math.Sqrt((A.X - B.X) * (A.X - B.X) + (A.Y - B.Y) * (A.Y - B.Y));
}
}