Nuclex.Support/Source/SpatialPartitioning/RTree2.cs

#region CPL License
/*
Nuclex Framework
Copyright (C) 2002-2007 Nuclex Development Labs

This library is free software; you can redistribute it and/or
modify it under the terms of the IBM Common Public License as
published by the IBM Corporation; either version 1.0 of the
License, or (at your option) any later version.

This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
IBM Common Public License for more details.

You should have received a copy of the IBM Common Public
License along with this library
*/
#endregion

using System;
using System.Collections.Generic;

using Microsoft.Xna.Framework;

namespace Nuclex.Support.SpatialPartitioning {

  /// <summary>R-Tree for two-dimensional data</summary>
  /// <remarks>
  ///   R-Trees essentially fullfill the same role that is traditionally
  ///   assigned to quadtrees in games. But unlike a quadtree, an R-Tree does not
  ///   require knowledge of the total area that is to be covered by the objects
  ///   that will populate the tree.
  /// </remarks>
  public partial class RTree2<ItemType> : SpatialIndex2 {

    /// <summary>Variants of R-Tree behaviors this implementation can assume</summary>
    public enum Variants {

      /// <summary>
      ///   Insertions and deletions take linear time at the cost of degrading the
      ///   tree's overall performance.
      /// </summary>
      /// <remarks>
      ///   Finds the two bounding boxes with the greatest normalized separation
      ///   along both axes, and split along this axis. The remaining bounding boxes
      ///   in the node are assigned to the nodes whose covering bounding box is
      ///   increased the least by the addition [Gutt84]. This method takes linear time.
      /// </remarks>
      Linear,

      /// <summary>
      ///   Insertions and deletions take quadratic time while keeping the tree's
      ///   overall performance at a reasonable level.
      /// </summary>
      /// <remarks>
      ///   Examines all the children of the overflowing node and find the pair of
      ///   bounding boxes that would waste the most area were they to be inserted
      ///   in the same node. This is determined by subtracting the sum of the areas
      ///   of the two bounding boxes from the area of the covering bounding box.
      ///   These two bounding boxes are placed in separate nodes, say j and k.
      ///   The set of remaining bounding boxes are examined and the bounding box i
      ///   whose addition maximizes the difference in coverage between the bounding
      ///   boxes associated with j and k is added to the node whose coverage
      ///   is minimized by the addition. This process is reapplied to the
      ///   remaining bounding boxes [Gutt84]. This method takes quadratic time.
      /// </remarks>
      Quadratic,

      /// <summary>
      ///   Insertions and deletions vary in performance but the tree's overall
      ///   performance is kept high.
      /// </summary>
      /// <remarks>
      ///   The R*-tree [Beck90c] is a name given to a variant of the R-tree which
      ///   makes use of the most complex of the node splitting algorithms. The
      ///   algorithm differs from the other algorithms as it attempts to reduce
      ///   both overlap and coverage. In particular, the primary focus is on
      ///   reducing overlap with ties broken by favoring the splits that reduce
      ///   the coverage by using the splits that minimize the perimeter of the
      ///   bounding boxes of the resulting nodes. In addition, when a node 'a'
      ///   overflows, instead of immediately splitting 'a', an attempt is made
      ///   first to see if some of the objects in 'a' could possibly be more suited
      ///   to being in another node. This is achieved by reinserting a fraction
      ///   (30% has been found to yield good performance [Beck90c]) of these
      ///   objects in the tree (termed 'forced reinsertion'). The node is only split
      ///   if it has been found to overflow after reinsertion has taken place.
      ///   This method is quite complex.
      /// </remarks>
      RStar

    }

  }

} // namespace Nuclex.Geometry.SpatialPartitioning