/// <summary>
/// Gets the repulsion force.
/// </summary>
/// <param name="of">The node under observation.</param>
/// <param name="from">The other node.</param>
/// <param name="repulsionForce">The repulsion force.</param>
/// <returns>The force vector.</returns>
private static Vector GetRepulsionForce(Location of, Location @from, double repulsionForce = VertexRepulsionForceStrength)
{
// get the proximity and the direction
double currentDistance;
var direction = (of - @from).Normalized(out currentDistance);
// strength decrease is proportional to the squared distance;
// this imitates Coulomb's Law of the repulsion of charged particles (F = k*Q1*Q2/r^2)
// where we assume the charge to be equal for all particles.
var strength = repulsionForce / (currentDistance * currentDistance);
// return the force vector
return direction*strength;
}
/// <summary>
/// Gets the attraction force.
/// </summary>
/// <param name="graph">The graph.</param>
/// <param name="of">The node under observation.</param>
/// <param name="locationOf">The location of.</param>
/// <param name="from">The other node.</param>
/// <param name="locationFrom">The location from.</param>
/// <param name="attractionStrength">The attraction strength.</param>
/// <returns>The force vector.</returns>
private static Vector GetAttractionForce([NotNull] Graph graph, [NotNull] Vertex of, Location locationOf, [NotNull] Vertex from, Location locationFrom, double attractionStrength = VertexAttractionForceStrength)
{
// if vertices are unconnected, there is no force that
// pulls them together.
Edge edge;
if (!graph.TryGetEdge(of, from, out edge)) return Vector.Zero;
// the actual distance between the two vertices is given by the edge weight
var expectedDistance = edge.Weight;
// fetch the force direction and the actual distance
double currentDistance;
var direction = (locationOf - locationFrom).Normalized(out currentDistance);
// determine the spring strength by Hooke's law:
// If the expected distance is larger than the current distance, the spring is
// too short and should thus expand; hence the attraction force is zero.
// If the expected distance is smaller than the current distance, the spring needs
// to contract, hence the strength is positive.
var strength = attractionStrength * Math.Max(currentDistance - expectedDistance, 0);
// In order to contract, we reverse the force direction
return direction*(-strength);
}
/// <summary>
/// Calculates the total attraction force.
/// </summary>
/// <param name="graph">The graph.</param>
/// <param name="vertex">The vertex.</param>
/// <param name="vertexLocation"></param>
/// <param name="currentLocations">The current locations.</param>
/// <returns>Vector.</returns>
private static Vector CalculateTotalAttraction([NotNull] Graph graph, Vertex vertex, Location vertexLocation, [NotNull] IReadOnlyDictionary<Vertex, Location> currentLocations)
{
var forces =
from edges in graph[vertex].AsParallel()
let other = edges.Other(vertex)
let otherLocation = currentLocations[other]
select GetAttractionForce(graph, vertex, vertexLocation, other, otherLocation);
var force = forces.Aggregate(Vector.Zero, (current, sumOfForces) => sumOfForces + current);
return force;
}
/// <summary>
/// Calculates the total repulsion force.
/// </summary>
/// <param name="graph">The graph.</param>
/// <param name="vertex">The vertex.</param>
/// <param name="vertexLocation"></param>
/// <param name="currentLocations">The current locations.</param>
/// <returns>Vector.</returns>
private static Vector CalculateTotalRepulsion([NotNull] Graph graph, Vertex vertex, Location vertexLocation, [NotNull] IReadOnlyDictionary<Vertex, Location> currentLocations)
{
var forces =
from other in graph.Vertices.AsParallel()
where !other.Equals(vertex)
let otherLocation = currentLocations[other]
select GetRepulsionForce(vertexLocation, otherLocation);
var force = forces.Aggregate(Vector.Zero, (current, sumOfForces) => sumOfForces + current);
return force;
}
/// <summary>
/// Determines whether the specified <see cref="Location" /> is equal to this instance.
/// </summary>
/// <param name="other">The object to compare with the current instance.</param>
/// <returns><c>true</c> if the specified <see cref="Location" /> is equal to this instance; otherwise, <c>false</c>.</returns>
public bool Equals(Location other)
{
return X.Equals(other.X) && Y.Equals(other.Y);
}
