/**
   * Gets all neighbors of a location that satisfy abs(x-X) + abs(y-Y) + abs(z-Z) <= dist. This
   * region forms an <a href="http://images.google.com/images?q=octahedron">octohedron</a> 2*dist+1
   * cells from point to opposite point inclusive, centered at (X,Y,Y). If dist==1 this is
   * equivalent to the six neighbors above, below, left, and right, front, and behind (X,Y,Z)), plus
   * (X,Y,Z) itself. Places each x, y, and z value of these locations in the provided IntBags xPos,
   * yPos, and zPos, clearing the bags first. Then places into the result IntBag the elements at
   * each of those <x,y,z> locations clearning it first. Returns the result IntBag (constructing one
   * if null had been passed in). null may be passed in for the various bags, though it is more
   * efficient to pass in a 'scratch bag' for each one.
   */
  public final void getNeighborsHamiltonianDistance(
      final int x,
      final int y,
      final int z,
      final int dist,
      final boolean toroidal,
      IntBag result,
      IntBag xPos,
      IntBag yPos,
      IntBag zPos) {
    if (xPos == null) xPos = new IntBag();
    if (yPos == null) yPos = new IntBag();
    if (zPos == null) zPos = new IntBag();

    getNeighborsHamiltonianDistance(x, y, z, dist, toroidal, xPos, yPos, zPos);

    if (result != null) {
      result.clear();
      result.resize(xPos.size());
    } else result = new IntBag(xPos.size());

    for (int i = 0; i < xPos.numObjs; i++)
      result.add(field[xPos.objs[i]][yPos.objs[i]][zPos.objs[i]]);
  }
  public void getNeighborsHamiltonianDistance(
      final int x,
      final int y,
      final int z,
      final int dist,
      final boolean toroidal,
      IntBag xPos,
      IntBag yPos,
      IntBag zPos) {
    // won't work for negative distances
    if (dist < 0) {
      throw new RuntimeException(
          "Runtime exception in method getNeighborsHamiltonianDistance: Distance must be positive");
    }

    if (xPos == null || yPos == null || zPos == null) {
      throw new RuntimeException(
          "Runtime exception in method getNeighborsHamiltonianDistance: xPos and yPos should not be null");
    }

    xPos.clear();
    yPos.clear();
    zPos.clear();

    // local variables are faster
    final int height = this.height;
    final int width = this.width;
    final int length = this.length;

    // for toroidal environments the code will be different because of wrapping arround
    if (toroidal) {
      // compute xmin and xmax for the neighborhood
      final int xmax = x + dist;
      final int xmin = x - dist;
      for (int x0 = xmin; x0 <= xmax; x0++) {
        final int x_0 = stx(x0, width);
        // compute ymin and ymax for the neighborhood; they depend on the curreny x0 value
        final int ymax = y + (dist - ((x0 - x >= 0) ? x0 - x : x - x0));
        final int ymin = y - (dist - ((x0 - x >= 0) ? x0 - x : x - x0));
        for (int y0 = ymin; y0 <= ymax; y0++) {
          final int y_0 = sty(y0, height);
          final int zmax =
              z + (dist - ((x0 - x >= 0) ? x0 - x : x - x0) - ((y0 - y >= 0) ? y0 - y : y - y0));
          final int zmin =
              z - (dist - ((x0 - x >= 0) ? x0 - x : x - x0) - ((y0 - y >= 0) ? y0 - y : y - y0));
          for (int z0 = zmin; z0 <= zmax; z0++) {
            final int z_0 = stz(z0, length);
            if (x_0 != x || y_0 != y || z_0 != z) {
              xPos.add(x_0);
              yPos.add(y_0);
              zPos.add(z_0);
            }
          }
        }
      }
    } else // not toroidal
    {
      // compute xmin and xmax for the neighborhood such that they are within boundaries
      final int xmax = ((x + dist <= width - 1) ? x + dist : width - 1);
      final int xmin = ((x - dist >= 0) ? x - dist : 0);
      for (int x0 = xmin; x0 <= xmax; x0++) {
        final int x_0 = x0;
        // compute ymin and ymax for the neighborhood such that they are within boundaries
        // they depend on the curreny x0 value
        final int ymax =
            ((y + (dist - ((x0 - x >= 0) ? x0 - x : x - x0)) <= height - 1)
                ? y + (dist - ((x0 - x >= 0) ? x0 - x : x - x0))
                : height - 1);
        final int ymin =
            ((y - (dist - ((x0 - x >= 0) ? x0 - x : x - x0)) >= 0)
                ? y - (dist - ((x0 - x >= 0) ? x0 - x : x - x0))
                : 0);
        for (int y0 = ymin; y0 <= ymax; y0++) {
          final int y_0 = y0;
          final int zmin =
              ((z - (dist - ((x0 - x >= 0) ? x0 - x : x - x0) - ((y0 - y >= 0) ? y0 - y : y - y0))
                      >= 0)
                  ? z
                      - (dist
                          - ((x0 - x >= 0) ? x0 - x : x - x0)
                          - ((y0 - y >= 0) ? y0 - y : y - y0))
                  : 0);
          final int zmax =
              ((z + (dist - ((x0 - x >= 0) ? x0 - x : x - x0) - ((y0 - y >= 0) ? y0 - y : y - y0))
                      <= length - 1)
                  ? z
                      + (dist
                          - ((x0 - x >= 0) ? x0 - x : x - x0)
                          - ((y0 - y >= 0) ? y0 - y : y - y0))
                  : length - 1);
          for (int z0 = zmin; z0 <= zmax; z0++) {
            final int z_0 = z0;
            if (x_0 != x || y_0 != y || z_0 != z) {
              xPos.add(x_0);
              yPos.add(y_0);
              zPos.add(z_0);
            }
          }
        }
      }
    }
  }