Nuclex.Support/Source/Packing/ArevaloRectanglePacker.cs

#region CPL License
/*
Nuclex Framework
Copyright (C) 2002-2008 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.Packing {

  /// <summary>Rectangle packer using an algorithm by Javier Arevalo</summary>
  /// <remarks>
  ///   <para>
  ///     Original code by Javier Arevalo (jare at iguanademos dot com). Rewritten
  ///     to C# / .NET by Markus Ewald (cygon at nuclex dot org).
  ///   </para>
  ///   <para>
  ///     You have a bunch of rectangular pieces. You need to arrange them in a 
  ///     rectangular surface so that they don't overlap, keeping the total area of the 
  ///     rectangle as small as possible. This is fairly common when arranging characters 
  ///     in a bitmapped font, lightmaps for a 3D engine, and I guess other situations as 
  ///     well.
  ///   </para>
  ///   <para>
  ///     The idea of this algorithm is that, as we add rectangles, we can pre-select 
  ///     "interesting" places where we can try to add the next rectangles. For optimal 
  ///     results, the rectangles should be added in order. I initially tried using area 
  ///     as a sorting criteria, but it didn't work well with very tall or very flat 
  ///     rectangles. I then tried using the longest dimension as a selector, and it 
  ///     worked much better. So much for intuition...
  ///   </para>
  ///   <para>
  ///     These "interesting" places are just to the right and just below the currently 
  ///     added rectangle. The first rectangle, obviously, goes at the top left, the next 
  ///     one would go either to the right or below this one, and so on. It is a weird way 
  ///     to do it, but it seems to work very nicely.
  ///   </para>
  ///   <para>
  ///     The way we search here is fairly brute-force, the fact being that for most off-
  ///     line purposes the performance seems more than adequate. I have generated a 
  ///     japanese font with around 8500 characters and all the time was spent generating 
  ///     the bitmaps.
  ///   </para>
  ///   <para>
  ///     Also, for all we care, we could grow the parent rectangle in a different way 
  ///     than power of two. It just happens that power of 2 is very convenient for 
  ///     graphics hardware textures.
  ///   </para>
  ///   <para>
  ///     I'd be interested in hearing of other approaches to this problem. Make sure
  ///     to post them on http://www.flipcode.com
  ///   </para>
  /// </remarks>
  public class ArevaloRectanglePacker : RectanglePacker {

    #region class AnchorRankComparer

    /// <summary>Compares the 'rank' of anchoring points</summary>
    /// <remarks>
    ///   Anchoring points are potential locations for the placement of new rectangles.
    ///   Each time a rectangle is inserted, an anchor point is generated on its upper
    ///   right end and another one at its lower left end. The anchor points are kept
    ///   in a list that is ordered by their closeness to the upper left corner of the
    ///   packing area (their 'rank') so the packer favors positions that are closer to
    ///   the upper left for new rectangles.
    /// </remarks>
    private class AnchorRankComparer : IComparer<Point> {

      /// <summary>Provides a default instance for the anchor rank comparer</summary>
      public static AnchorRankComparer Default = new AnchorRankComparer();

      /// <summary>Compares the rank of two anchors against each other</summary>
      /// <param name="left">Left anchor point that will be compared</param>
      /// <param name="right">Right anchor point that will be compared</param>
      /// <returns>The relation of the two anchor point's ranks to each other</returns>
      public int Compare(Point left, Point right) {
        //return Math.Min(left.X, left.Y) - Math.Min(right.X, right.Y);
        return (left.X + left.Y) - (right.X + right.Y);
      }

    }

    #endregion

    /// <summary>Initializes a new rectangle packer</summary>
    /// <param name="packingAreaWidth">Maximum width of the packing area</param>
    /// <param name="packingAreaHeight">Maximum height of the packing area</param>
    public ArevaloRectanglePacker(int packingAreaWidth, int packingAreaHeight)
      : base(packingAreaWidth, packingAreaHeight) {

      this.packedRectangles = new List<Rectangle>();
      this.anchors = new List<Point>();
      this.anchors.Add(new Point(0, 0));

      this.actualPackingAreaWidth = 1;
      this.actualPackingAreaHeight = 1;
    }

    /// <summary>Tries to allocate space for a rectangle in the packing area</summary>
    /// <param name="rectangleWidth">Width of the rectangle to allocate</param>
    /// <param name="rectangleHeight">Height of the rectangle to allocate</param>
    /// <param name="placement">Output parameter receiving the rectangle's placement</param>
    /// <returns>True if space for the rectangle could be allocated</returns>
    public override bool TryPack(
      int rectangleWidth, int rectangleHeight, out Point placement
    ) {

      // Try to find an anchor where the rectangle fits in, enlarging the packing
      // area and repeating the search recursively until it fits or the
      // maximum allowed size is exceeded.
      int anchorIndex = selectAnchorRecursive(
        rectangleWidth, rectangleHeight,
        this.actualPackingAreaWidth, this.actualPackingAreaHeight
      );

      // No anchor could be found at which the rectangle did fit in
      if(anchorIndex == -1) {
        placement = Point.Zero;
        return false;
      }

      placement = this.anchors[anchorIndex];

      // Move the rectangle either to the left or to the top until it collides with
      // a neightbouring rectangle. This is done to combat the effect of lining up
      // rectangles with gaps to the left or top of them because the anchor that
      // would allow placement there has been blocked by another rectangle
      optimizePlacement(ref placement, rectangleWidth, rectangleHeight);

      // Remove the used anchor and add new anchors at the upper right and lower left
      // positions of the new rectangle
      {
        // The anchor is only removed if the placement optimization didn't
        // move the rectangle so far that the anchor isn't blocked anymore
        bool blocksAnchor =
          ((placement.X + rectangleWidth) > this.anchors[anchorIndex].X) &&
          ((placement.Y + rectangleHeight) > this.anchors[anchorIndex].Y);

        if(blocksAnchor)
          this.anchors.RemoveAt(anchorIndex);

        // Add new anchors at the upper right and lower left coordinates of the rectangle
        this.anchors.Add(new Point(placement.X + rectangleWidth, placement.Y));
        this.anchors.Add(new Point(placement.X, placement.Y + rectangleHeight));
      }

      // Finally, we can add the rectangle to our packed rectangles list
      this.packedRectangles.Add(
        new Rectangle(placement.X, placement.Y, rectangleWidth, rectangleHeight)
      );

      return true;

    }

    /// <summary>
    ///   Optimizes the rectangle's placement by moving it either left or up to fill
    ///   any gaps resulting from rectangles blocking the anchors of the most optimal
    ///   placements.
    /// </summary>
    /// <param name="placement">Placement to be optimized</param>
    /// <param name="rectangleWidth">Width of the rectangle to be optimized</param>
    /// <param name="rectangleHeight">Height of the rectangle to be optimized</param>
    private void optimizePlacement(
      ref Point placement, int rectangleWidth, int rectangleHeight
    ) {
      Rectangle rectangle = new Rectangle(
        placement.X, placement.Y, rectangleWidth, rectangleHeight
      );

      // Try to move the rectangle to the left as far as possible
      int leftMost = placement.X;
      while(isFree(ref rectangle, PackingAreaWidth, PackingAreaHeight)) {
        leftMost = rectangle.X;
        --rectangle.X;
      }

      // Reset rectangle to original position
      rectangle.X = placement.X;

      // Try to move the rectangle upwards as far as possible
      int topMost = placement.Y;
      while(isFree(ref rectangle, PackingAreaWidth, PackingAreaHeight)) {
        topMost = rectangle.Y;
        --rectangle.Y;
      }

      // Use the dimension in which the rectangle could be moved farther
      if((leftMost - placement.X) > (topMost - placement.Y))
        placement.X = leftMost;
      else
        placement.Y = topMost;
    }

    /// <summary>
    ///   Searches for a free anchor and recursively enlarges the packing area
    ///   if none can be found.
    /// </summary>
    /// <param name="rectangleWidth">Width of the rectangle to be placed</param>
    /// <param name="rectangleHeight">Height of the rectangle to be placed</param>
    /// <param name="testedPackingAreaWidth">Width of the tested packing area</param>
    /// <param name="testedPackingAreaHeight">Height of the tested packing area</param>
    /// <returns>
    ///   Index of the anchor the rectangle is to be placed at or -1 if the rectangle
    ///   does not fit in the packing area anymore.
    /// </returns>
    private int selectAnchorRecursive(
      int rectangleWidth, int rectangleHeight,
      int testedPackingAreaWidth, int testedPackingAreaHeight
    ) {

      // Try to locate an anchor point where the rectangle fits in
      int freeAnchorIndex = findFirstFreeAnchor(
        rectangleWidth, rectangleHeight, testedPackingAreaWidth, testedPackingAreaHeight
      );

      // If a the rectangle fits without resizing packing area (any further in case
      // of a recursive call), take over the new packing area size and return the
      // anchor at which the rectangle can be placed.
      if(freeAnchorIndex != -1) {
        this.actualPackingAreaWidth = testedPackingAreaWidth;
        this.actualPackingAreaHeight = testedPackingAreaHeight;

        return freeAnchorIndex;
      }

      //
      // If we reach this point, the rectangle did not fit in the current packing
      // area and our only choice is to try and enlarge the packing area.
      //

      // For readability, determine whether the packing area can be enlarged
      // any further in its width and in its height
      bool canEnlargeWidth = (testedPackingAreaWidth < PackingAreaWidth);
      bool canEnlargeHeight = (testedPackingAreaHeight < PackingAreaHeight);

      // Try to enlarge the smaller of the two dimensions first (unless the smaller
      // dimension is already at its maximum size)
      if(
        canEnlargeHeight && (
          (testedPackingAreaHeight < testedPackingAreaWidth) || !canEnlargeWidth
        )
      ) {

        // Try to double the height of the packing area
        return selectAnchorRecursive(
          rectangleWidth, rectangleHeight,
          testedPackingAreaWidth, Math.Min(testedPackingAreaHeight * 2, PackingAreaHeight)
        );

      } else if(canEnlargeWidth) {

        // Try to double the width of the packing area
        return selectAnchorRecursive(
          rectangleWidth, rectangleHeight,
          Math.Min(testedPackingAreaWidth * 2, PackingAreaWidth), testedPackingAreaHeight
        );

      } else {

        // Both dimensions are at the maximum sizes and the rectangle still
        // didn't fit. We give up!
        return -1;

      }

    }

    /// <summary>Locates the first free anchor at which the rectangle fits</summary>
    /// <param name="rectangleWidth">Width of the rectangle to be placed</param>
    /// <param name="rectangleHeight">Height of the rectangle to be placed</param>
    /// <param name="testedPackingAreaWidth">Total width of the packing area</param>
    /// <param name="testedPackingAreaHeight">Total height of the packing area</param>
    /// <returns>The index of the first free anchor or -1 if none is found</returns>
    private int findFirstFreeAnchor(
      int rectangleWidth, int rectangleHeight,
      int testedPackingAreaWidth, int testedPackingAreaHeight
    ) {
      Rectangle potentialLocation = new Rectangle(
        0, 0, rectangleWidth, rectangleHeight
      );

      // Walk over all anchors (which are ordered by their distance to the
      // upper left corner of the packing area) until one is discovered that
      // can house the new rectangle.
      for(int index = 0; index < this.anchors.Count; ++index) {
        potentialLocation.X = this.anchors[index].X;
        potentialLocation.Y = this.anchors[index].Y;

        // See if the rectangle would fit in at this anchor point
        if(isFree(ref potentialLocation, testedPackingAreaWidth, testedPackingAreaHeight))
          return index;
      }

      // No anchor points were found where the rectangle would fit in
      return -1;
    }

    /// <summary>
    ///   Determines whether the rectangle can be placed in the packing area
    ///   at its current location.
    /// </summary>
    /// <param name="rectangle">Rectangle whose position to check</param>
    /// <param name="testedPackingAreaWidth">Total width of the packing area</param>
    /// <param name="testedPackingAreaHeight">Total height of the packing area</param>
    /// <returns>True if the rectangle can be placed at its current position</returns>
    private bool isFree(
      ref Rectangle rectangle, int testedPackingAreaWidth, int testedPackingAreaHeight
    ) {

      // If the rectangle is partially or completely outside of the packing
      // area, it can't be placed at its current location
      bool leavesPackingArea =
        (rectangle.X < 0) ||
        (rectangle.Y < 0) ||
        (rectangle.Right >= testedPackingAreaWidth) ||
        (rectangle.Bottom >= testedPackingAreaHeight);

      if(leavesPackingArea)
        return false;

      // Brute-force search whether the rectangle touches any of the other
      // rectangles already in the packing area
      for(int index = 0; index < this.packedRectangles.Count; ++index) {

        if(this.packedRectangles[index].Intersects(rectangle))
          return false;

      }

      // Success! The rectangle is inside the packing area and doesn't overlap
      // with any other rectangles that have already been packed.
      return true;

    }

    /// <summary>Inserts a new anchor point into the anchor list</summary>
    /// <param name="anchor">Anchor point that will be inserted</param>
    /// <remarks>
    ///   This method tries to keep the anchor list ordered by ranking the anchors
    ///   depending on the distance from the top left corner in the packing area.
    /// </remarks>
    private void insertAnchor(ref Point anchor) {

      // Find out where to insert the new anchor based on its rank (which is
      // calculated based on the anchor's distance to the top left corner of
      // the packing area).
      //
      // From MSDN on BinarySearch():
      //   "If the List does not contain the specified value, the method returns
      //    a negative integer. You can apply the bitwise complement operation (~) to
      //    this negative integer to get the index of the first element that is
      //    larger than the search value."
      int insertIndex = this.anchors.BinarySearch(anchor, AnchorRankComparer.Default);
      if(insertIndex < 0)
        insertIndex = ~insertIndex;

      // Insert the anchor at the index matching its rank
      this.anchors.Insert(insertIndex, anchor);

    }

    /// <summary>Current width of the packing area</summary>
    private int actualPackingAreaWidth;
    /// <summary>Current height of the packing area</summary>
    private int actualPackingAreaHeight;
    /// <summary>Rectangles contained in the packing area</summary>
    private List<Rectangle> packedRectangles;
    /// <summary>Anchoring points where new rectangles can potentially be placed</summary>
    private List<Point> anchors;

  }

} // namespace Nuclex.Support.Packing