/// <summary>
/// Compute the convex hull given a set of points on a 2D plane.
/// </summary>
/// <param name="input">A set of points on a 2D plane.</param>
/// <returns>The convex hull.</returns>
public List <Vector2> Compute(List <Vector2> input)
{
// Three or less points is already the convex hull.
if (input.Count <= 3)
{
return(new List <Vector2>(input));
}
// Swap the lowest y to input[0].
SwapLowestY(input);
// Calculate angle and distance for each vector based on the lowest point.
// The idea is to update the vector in the dictionary if it has a lesser distance
// to the starting point than the new vector.
Dictionary <double, VectorAttributes> dict = new Dictionary <double, VectorAttributes>();
foreach (Vector2 v in input)
{
// Create the vector angle and distance attributes.
VectorAttributes vectorAttr = new VectorAttributes
{
Vector = v,
Angle = VectorUtils.FindAngle(lowest, v),
DistanceSquared = VectorUtils.DistanceSquared(lowest, v)
};
// Add the vector to the dictionary.
if (dict.ContainsKey(vectorAttr.Angle))
{
// If the distance is greater, update the value in the dictionary.
if (dict[vectorAttr.Angle].DistanceSquared < vectorAttr.DistanceSquared)
{
dict[vectorAttr.Angle] = vectorAttr;
}
}
else
{
// A vector for this angle doesn't exist, so add one.
dict.Add(vectorAttr.Angle, vectorAttr);
}
}
// Create a list of the vectors.
VectorAttributes lowestVectorAttr = new VectorAttributes
{
Vector = input[0],
Angle = VectorUtils.FindAngle(lowest, input[0]),
DistanceSquared = VectorUtils.DistanceSquared(lowest, input[0])
};
List <VectorAttributes> vectorAttributeList = new List <VectorAttributes>();
vectorAttributeList.Add(lowestVectorAttr);
vectorAttributeList.AddRange(dict.Values.ToList());
// Sort remaining vectors based on angle with lowest point.
vectorAttributeList = vectorAttributeList.OrderBy(v => v.Angle).ToList();
// The guts of the Graham Scan algorithm.
List <Vector2> output = new List <Vector2>();
output.Add(vectorAttributeList[0].Vector);
output.Add(vectorAttributeList[1].Vector);
output.Add(vectorAttributeList[2].Vector);
for (int i = 3; i < vectorAttributeList.Count; ++i)
{
while (VectorUtils.Orientation(output[output.Count - 2], output[output.Count - 1], vectorAttributeList[i].Vector) < 0)
{
// Remove vectors that make a clockwise turn.
output.RemoveAt(output.Count - 1);
}
output.Add(vectorAttributeList[i].Vector);
}
return(output);
}