source: trunk/sources/HeuristicLab.ExtLibs/HeuristicLab.Netron/3.0.2672.12446/Netron.Diagramming.Core-3.0.2672.12446/Layout/Force/NBodyForce.cs @ 4068

using System;
using System.Collections.Generic;
using System.Diagnostics;
namespace Netron.Diagramming.Core.Layout.Force {
  /// <summary>
  /// <para>
  /// Force function which computes an n-body force such as gravity,
  /// anti-gravity, or the results of electric charges. This function implements
  /// the the Barnes-Hut algorithm for efficient n-body force simulations,
  /// using a quad-tree with aggregated mass values to compute the n-body
  /// force in O(N log N) time, where N is the number of ForceItems.</para>
  /// 
  /// <para>The algorithm used is that of J. Barnes and P. Hut, in their research
  /// paper <i>A Hierarchical  O(n log n) force calculation algorithm</i>, Nature, 
  ///  v.324, December 1986. For more details on the algorithm, see one of
  ///  the following links --
  /// <list type="bullet">
  /// 
  ///   <item><a href="http://www.cs.berkeley.edu/~demmel/cs267/lecture26/lecture26.html">James Demmel's UC Berkeley lecture notes</a></item>
  ///   <item><a href="http://www.physics.gmu.edu/~large/lr_forces/desc/bh/bhdesc.html">Description of the Barnes-Hut algorithm</a></item>
  ///   <item><a href="http://www.ifa.hawaii.edu/~barnes/treecode/treeguide.html">Joshua Barnes' recent implementation</a></item>
  /// </list></para>
  /// </summary>
  public class NBodyForce : AbstractForce {

    /* 
      The indexing scheme for quadtree child nodes goes row by row.
        0 | 1    0 -> top left,    1 -> top right
       -------
        2 | 3    2 -> bottom left, 3 -> bottom right
     */

    #region Fields
    private static String[] pnames = new String[] { "GravitationalConstant", 
            "Distance", "BarnesHutTheta"  };

    public static float DEFAULT_GRAV_CONSTANT = -1.0f;
    public static float DEFAULT_MIN_GRAV_CONSTANT = -10f;
    public static float DEFAULT_MAX_GRAV_CONSTANT = 10f;

    public static float DEFAULT_DISTANCE = -1f;
    public static float DEFAULT_MIN_DISTANCE = -1f;
    public static float DEFAULT_MAX_DISTANCE = 500f;

    public static float DEFAULT_THETA = 0.9f;
    public static float DEFAULT_MIN_THETA = 0.0f;
    public static float DEFAULT_MAX_THETA = 1.0f;

    public static int GRAVITATIONAL_CONST = 0;
    public static int MIN_DISTANCE = 1;
    public static int BARNES_HUT_THETA = 2;

    private float xMin, xMax, yMin, yMax;
    private QuadTreeNodeFactory factory = new QuadTreeNodeFactory();
    private QuadTreeNode root;

    private Random rand = new Random(12345678); // deterministic randomness

    #endregion

    #region Properties

    /**
         * Gets whether this is a force item.
         */
    public override bool IsItemForce {
      get {
        return true;
      }
    }

    /// <summary>
    /// Gets the parameter names.
    /// </summary>
    /// <value></value>
    /// <returns></returns>
    protected override String[] ParameterNames {
      get {
        return pnames;
      }
    }
    #endregion

    #region Constructor



    /// <summary>
    /// Create a new NBodyForce with default parameters.
    /// </summary>
    public NBodyForce()
      : this(DEFAULT_GRAV_CONSTANT, DEFAULT_DISTANCE, DEFAULT_THETA) {

    }
    #endregion

    #region Methods
    /// <summary>
    /// Create a new NBodyForce.
    /// </summary>
    /// <param name="gravConstant">the gravitational constant to use. Nodes will attract each other if this value is positive, and will repel each other if it is negative.</param>
    /// <param name="minDistance">the distance within which two particles will  interact. If -1, the value is treated as infinite.</param>
    /// <param name="theta">the Barnes-Hut parameter theta, which controls when an aggregated mass is used rather than drilling down to individual  item mass values.</param>
    public NBodyForce(float gravConstant, float minDistance, float theta) {
      parms = new float[] { gravConstant, minDistance, theta };
      minValues = new float[] { DEFAULT_MIN_GRAV_CONSTANT,
            DEFAULT_MIN_DISTANCE, DEFAULT_MIN_THETA };
      maxValues = new float[] { DEFAULT_MAX_GRAV_CONSTANT,
            DEFAULT_MAX_DISTANCE, DEFAULT_MAX_THETA };
      root = factory.GetQuadTreeNode();
    }




    /// <summary>
    /// Set the bounds of the region for which to compute the n-body simulation
    /// </summary>
    /// <param name="xMin">the minimum x-coordinate</param>
    /// <param name="yMin">the minimum y-coordinate/param>
    /// <param name="xMax"> the maximum x-coordinate</param>
    /// <param name="yMax">the maximum y-coordinate</param>
    private void setBounds(float xMin, float yMin, float xMax, float yMax) {
      this.xMin = xMin;
      this.yMin = yMin;
      this.xMax = xMax;
      this.yMax = yMax;
    }


    /// <summary>
    ///Clears the quadtree of all entries.
    /// </summary>
    public void clear() {
      ClearHelper(root);
      root = factory.GetQuadTreeNode();
    }

    /// <summary>
    /// Clearing aid
    /// </summary>
    /// <param name="n">The n.</param>
    private void ClearHelper(QuadTreeNode n) {
      for (int i = 0; i < n.children.Length; i++) {
        if (n.children[i] != null)
          ClearHelper(n.children[i]);
      }
      factory.Reclaim(n);
    }

    /// <summary>
    /// Initialize the simulation with the provided enclosing simulation. After
    /// this call has been made, the simulation can be queried for the
    /// n-body force acting on a given item.
    /// </summary>
    /// <param name="fsim">the encompassing ForceSimulator</param>        
    public override void Init(ForceSimulator fsim) {
      clear(); // clear internal state

      // compute and squarify bounds of quadtree
      float x1 = float.MaxValue, y1 = float.MaxValue;
      float x2 = float.MinValue, y2 = float.MinValue;
      foreach (ForceItem item in fsim.Items) {
        float x = item.Location[0];
        float y = item.Location[1];
        if (x < x1) x1 = x;
        if (y < y1) y1 = y;
        if (x > x2) x2 = x;
        if (y > y2) y2 = y;
      }
      float dx = x2 - x1, dy = y2 - y1;
      if (dx > dy) { y2 = y1 + dx; } else { x2 = x1 + dy; }
      setBounds(x1, y1, x2, y2);

      // Insert items into quadtree
      foreach (ForceItem item in fsim.Items) {
        Insert(item);
      }

      // calculate magnitudes and centers of mass
      CalculateMass(root);
    }

    /// <summary>
    /// Inserts an item into the quadtree.
    /// </summary>
    /// <param name="item"> the ForceItem to add.</param>
    public void Insert(ForceItem item) {
      // Insert item into the quadtrees
      try {
        Insert(item, root, xMin, yMin, xMax, yMax);
      }
      catch (StackOverflowException e) {
        // TODO: safe to remove?
        Trace.WriteLine(e.Message);
      }
    }

    /// <summary>
    /// Inserts the specified force.
    /// </summary>
    /// <param name="p">The p.</param>
    /// <param name="n">The n.</param>
    /// <param name="x1">The x1.</param>
    /// <param name="y1">The y1.</param>
    /// <param name="x2">The x2.</param>
    /// <param name="y2">The y2.</param>
    private void Insert(ForceItem p, QuadTreeNode n, float x1, float y1, float x2, float y2) {
      // try to Insert particle p at node n in the quadtree
      // by construction, each leaf will contain either 1 or 0 particles
      if (n.hasChildren) {
        // n contains more than 1 particle
        InsertHelper(p, n, x1, y1, x2, y2);
      } else if (n.value != null) {
        // n contains 1 particle
        if (IsSameLocation(n.value, p)) {
          InsertHelper(p, n, x1, y1, x2, y2);
        } else {
          ForceItem v = n.value; n.value = null;
          InsertHelper(v, n, x1, y1, x2, y2);
          InsertHelper(p, n, x1, y1, x2, y2);
        }
      } else {
        // n is empty, so is a leaf
        n.value = p;
      }
    }

    /// <summary>
    /// Determines whether the two force are at the same location.
    /// </summary>
    /// <param name="f1">The f1.</param>
    /// <param name="f2">The f2.</param>
    /// <returns>
    ///   <c>true</c> if [is same location] [the specified f1]; otherwise, <c>false</c>.
    /// </returns>
    private static bool IsSameLocation(ForceItem f1, ForceItem f2) {
      float dx = Math.Abs(f1.Location[0] - f2.Location[0]);
      float dy = Math.Abs(f1.Location[1] - f2.Location[1]);
      return (dx < 0.01 && dy < 0.01);
    }

    /// <summary>
    /// Inserts helper method.
    /// </summary>
    /// <param name="p">The p.</param>
    /// <param name="n">The n.</param>
    /// <param name="x1">The x1.</param>
    /// <param name="y1">The y1.</param>
    /// <param name="x2">The x2.</param>
    /// <param name="y2">The y2.</param>
    private void InsertHelper(ForceItem p, QuadTreeNode n, float x1, float y1, float x2, float y2) {
      float x = p.Location[0], y = p.Location[1];
      float splitx = (x1 + x2) / 2;
      float splity = (y1 + y2) / 2;
      int i = (x >= splitx ? 1 : 0) + (y >= splity ? 2 : 0);
      // create new child node, if necessary
      if (n.children[i] == null) {
        n.children[i] = factory.GetQuadTreeNode();
        n.hasChildren = true;
      }
      // update bounds
      if (i == 1 || i == 3) x1 = splitx; else x2 = splitx;
      if (i > 1) y1 = splity; else y2 = splity;
      // recurse 
      Insert(p, n.children[i], x1, y1, x2, y2);
    }

    /// <summary>
    /// Calculates the mass.
    /// </summary>
    /// <param name="n">The n.</param>
    private void CalculateMass(QuadTreeNode n) {
      float xcom = 0, ycom = 0;
      n.mass = 0;
      if (n.hasChildren) {
        for (int i = 0; i < n.children.Length; i++) {
          if (n.children[i] != null) {
            CalculateMass(n.children[i]);
            n.mass += n.children[i].mass;
            xcom += n.children[i].mass * n.children[i].com[0];
            ycom += n.children[i].mass * n.children[i].com[1];
          }
        }
      }
      if (n.value != null) {
        n.mass += n.value.Mass;
        xcom += n.value.Mass * n.value.Location[0];
        ycom += n.value.Mass * n.value.Location[1];
      }
      n.com[0] = xcom / n.mass;
      n.com[1] = ycom / n.mass;
    }

    /**
     * Calculates the force vector acting on the given item.
     * @param item the ForceItem for which to compute the force
     */
    public override void GetForce(ForceItem item) {
      try {
        ForceHelper(item, root, xMin, yMin, xMax, yMax);
      }
      catch (StackOverflowException e) {
        // TODO: safe to remove?
        Trace.WriteLine(e.Message);
      }
    }

    /// <summary>
    /// Utility method.
    /// </summary>
    /// <param name="item">The item.</param>
    /// <param name="n">The n.</param>
    /// <param name="x1">The x1.</param>
    /// <param name="y1">The y1.</param>
    /// <param name="x2">The x2.</param>
    /// <param name="y2">The y2.</param>
    private void ForceHelper(ForceItem item, QuadTreeNode n, float x1, float y1, float x2, float y2) {
      float dx = n.com[0] - item.Location[0];
      float dy = n.com[1] - item.Location[1];
      float r = (float)Math.Sqrt(dx * dx + dy * dy);
      bool same = false;
      if (r == 0.0f) {
        // if items are in the exact same place, add some noise
        dx = Convert.ToSingle((rand.NextDouble() - 0.5D) / 50.0D);
        dy = Convert.ToSingle((rand.NextDouble() - 0.5D) / 50.0D);
        r = (float)Math.Sqrt(dx * dx + dy * dy);
        same = true;
      }
      bool minDist = parms[MIN_DISTANCE] > 0f && r > parms[MIN_DISTANCE];

      // the Barnes-Hut approximation criteria is if the ratio of the
      // size of the quadtree box to the distance between the point and
      // the box's center of mass is beneath some threshold theta.
      if ((!n.hasChildren && n.value != item) ||
           (!same && (x2 - x1) / r < parms[BARNES_HUT_THETA])) {
        if (minDist) return;
        // either only 1 particle or we meet criteria
        // for Barnes-Hut approximation, so calc force
        float v = parms[GRAVITATIONAL_CONST] * item.Mass * n.mass
                    / (r * r * r);
        item.Force[0] += v * dx;
        item.Force[1] += v * dy;
      } else if (n.hasChildren) {
        // recurse for more accurate calculation
        float splitx = (x1 + x2) / 2;
        float splity = (y1 + y2) / 2;
        for (int i = 0; i < n.children.Length; i++) {
          if (n.children != null && n.children[i] != null) {
            ForceHelper(item, n.children[i],
                (i == 1 || i == 3 ? splitx : x1), (i > 1 ? splity : y1),
                (i == 1 || i == 3 ? x2 : splitx), (i > 1 ? y2 : splity));
          }
        }
        if (minDist) return;
        if (n.value != null && n.value != item) {
          float v = parms[GRAVITATIONAL_CONST] * item.Mass * n.value.Mass
                      / (r * r * r);
          item.Force[0] += v * dx;
          item.Force[1] += v * dy;
        }
      }
    }
    #endregion

    #region Classes
    /// <summary>
    /// Represents a node in the quadtree.
    /// </summary>
    public sealed class QuadTreeNode {
      public QuadTreeNode() {
        com = new float[] { 0.0f, 0.0f };
        children = new QuadTreeNode[4];
      } //
      public bool hasChildren = false;
      public float mass; // total mass held by this node
      public float[] com; // center of mass of this node 
      public ForceItem value; // ForceItem in this node, null if node has children
      public QuadTreeNode[] children; // children nodes
    }




    ///<summary>
    ///Helper class to minimize number of object creations across multiple uses of the quadtree.
    ///</summary>
    public sealed class QuadTreeNodeFactory {
      #region Fields
      private int maxNodes = 50000;
      private List<QuadTreeNode> nodes = new List<QuadTreeNode>();
      #endregion

      /// <summary>
      /// Gets the quadtree node.
      /// </summary>
      /// <returns></returns>
      public QuadTreeNode GetQuadTreeNode() {
        if (nodes.Count > 0) {
          QuadTreeNode node = this.nodes[nodes.Count - 1];
          nodes.Remove(node);
          return node;
        } else {
          return new QuadTreeNode();
        }
      }
      /// <summary>
      /// Reclaims the specified node.
      /// </summary>
      /// <param name="n">The n.</param>
      public void Reclaim(QuadTreeNode n) {
        n.mass = 0;
        n.com[0] = 0.0f; n.com[1] = 0.0f;
        n.value = null;
        n.hasChildren = false;
        for (int i = 0; i < n.children.Length; i++) {
          n.children[i] = null;
        }
        //n.children = null;
        if (nodes.Count < maxNodes)
          nodes.Add(n);
      }
    }
    #endregion

  }

}