/// <summary>
/// Area of covered rectangle for two sepcified rectangles
/// </summary>
public static long JoinArea(Rectangle a, Rectangle b)
{
int _left = (a._left < b._left) ? a._left : b._left;
int _right = (a._right > b._right) ? a._right : b._right;
int _top = (a._top < b._top) ? a._top : b._top;
int _bottom = (a._bottom > b._bottom) ? a._bottom : b._bottom;
return (long)(_bottom-_top)*(_right-_left);
}
internal RtreePage(Storage storage, object obj, Rectangle r)
{
branch = storage.CreateLink(card);
branch.Length = card;
b = new Rectangle[card];
setBranch(0, new Rectangle(r), obj);
n = 1;
for (int i = 1; i < card; i++)
{
b[i] = new Rectangle();
}
}
internal RtreePage(Storage storage, RtreePage root, RtreePage p)
{
branch = storage.CreateLink(card);
branch.Length = card;
b = new Rectangle[card];
n = 2;
setBranch(0, root.cover(), root);
setBranch(1, p.cover(), p);
for (int i = 2; i < card; i++)
{
b[i] = new Rectangle();
}
}
internal RtreePage insert(Storage storage, Rectangle r, object obj, int level)
{
Modify();
if (--level != 0)
{
// not leaf page
int i, mini = 0;
long minIncr = long.MaxValue;
long minArea = long.MaxValue;
for (i = 0; i < n; i++)
{
long area = b[i].Area();
long incr = Rectangle.JoinArea(b[i], r) - area;
if (incr < minIncr)
{
minIncr = incr;
minArea = area;
mini = i;
}
else if (incr == minIncr && area < minArea)
{
minArea = area;
mini = i;
}
}
RtreePage p = (RtreePage)branch[mini];
RtreePage q = p.insert(storage, r, obj, level);
if (q == null)
{
// child was not split
b[mini].Join(r);
return null;
}
else
{
// child was split
setBranch(mini, p.cover(), p);
return addBranch(storage, q.cover(), q);
}
}
else
{
return addBranch(storage, new Rectangle(r), obj);
}
}
/// <summary>
/// Checks if this rectangle contains the specified rectangle
/// </summary>
public bool Contains(Rectangle r)
{
return _left <= r._left && _top <= r._top && _right >= r._right && _bottom >= r._bottom;
}
/// <summary>
/// Checks if this rectangle intersects with specified rectangle
/// </summary>
public bool Intersects(Rectangle r)
{
return _left <= r._right && _top <= r._bottom && _right >= r._left && _bottom >= r._top;
}
/// <summary>
/// Non destructive join of two rectangles.
/// </summary>
/// <param name="a">first joined rectangle
/// </param>
/// <param name="b">second joined rectangle
/// </param>
/// <returns>rectangle containing cover of these two rectangles
/// </returns>
public static Rectangle Join(Rectangle a, Rectangle b)
{
Rectangle r = new Rectangle(a);
r.Join(b);
return r;
}
/// <summary>
/// Join two rectangles. This rectangle is updates to contain cover of this and specified rectangle.
/// </summary>
/// <param name="r">rectangle to be joined with this rectangle
/// </param>
public void Join(Rectangle r)
{
if (_left > r._left)
{
_left = r._left;
}
if (_right < r._right)
{
_right = r._right;
}
if (_top > r._top)
{
_top = r._top;
}
if (_bottom < r._bottom)
{
_bottom = r._bottom;
}
}
/// <summary>
/// Create copy of the rectangle
/// </summary>
public Rectangle(Rectangle r)
{
this._top = r._top;
this._left = r._left;
this._bottom = r._bottom;
this._right = r._right;
}
internal int remove(Rectangle r, object obj, int level, ArrayList reinsertList)
{
if (--level != 0)
{
for (int i = 0; i < n; i++)
{
if (r.Intersects(b[i]))
{
RtreePage pg = (RtreePage)branch[i];
int reinsertLevel = pg.remove(r, obj, level, reinsertList);
if (reinsertLevel >= 0)
{
if (pg.n >= minFill)
{
setBranch(i, pg.cover(), pg);
Modify();
}
else
{
// not enough entries in child
reinsertList.Add(pg);
reinsertLevel = level - 1;
removeBranch(i);
}
return reinsertLevel;
}
}
}
}
else
{
for (int i = 0; i < n; i++)
{
if (branch.ContainsElement(i, obj))
{
removeBranch(i);
return 0;
}
}
}
return -1;
}
internal Rectangle cover()
{
Rectangle r = new Rectangle(b[0]);
for (int i = 1; i < n; i++)
{
r.Join(b[i]);
}
return r;
}
RtreePage splitPage(Storage storage, Rectangle r, object obj)
{
int i, j, seed0 = 0, seed1 = 0;
long[] rectArea = new long[card+1];
long waste;
long worstWaste = long.MinValue;
//
// As the seeds for the two groups, find two rectangles which waste
// the most area if covered by a single rectangle.
//
rectArea[0] = r.Area();
for (i = 0; i < card; i++)
{
rectArea[i+1] = b[i].Area();
}
Rectangle bp = r;
for (i = 0; i < card; i++)
{
for (j = i+1; j <= card; j++)
{
waste = Rectangle.JoinArea(bp, b[j-1]) - rectArea[i] - rectArea[j];
if (waste > worstWaste)
{
worstWaste = waste;
seed0 = i;
seed1 = j;
}
}
bp = b[i];
}
byte[] taken = new byte[card];
Rectangle group0, group1;
long groupArea0, groupArea1;
int groupCard0, groupCard1;
RtreePage pg;
taken[seed1-1] = 2;
group1 = new Rectangle(b[seed1-1]);
if (seed0 == 0)
{
group0 = new Rectangle(r);
pg = new RtreePage(storage, obj, r);
}
else
{
group0 = new Rectangle(b[seed0-1]);
pg = new RtreePage(storage, branch.GetRaw(seed0-1), group0);
setBranch(seed0-1, r, obj);
}
groupCard0 = groupCard1 = 1;
groupArea0 = rectArea[seed0];
groupArea1 = rectArea[seed1];
//
// Split remaining rectangles between two groups.
// The one chosen is the one with the greatest difference in area
// expansion depending on which group - the rect most strongly
// attracted to one group and repelled from the other.
//
while (groupCard0 + groupCard1 < card + 1
&& groupCard0 < card + 1 - minFill
&& groupCard1 < card + 1 - minFill)
{
int betterGroup = -1, chosen = -1;
long biggestDiff = -1;
for (i = 0; i < card; i++)
{
if (taken[i] == 0)
{
long diff = (Rectangle.JoinArea(group0, b[i]) - groupArea0)
- (Rectangle.JoinArea(group1, b[i]) - groupArea1);
if (diff > biggestDiff || -diff > biggestDiff)
{
chosen = i;
if (diff < 0)
{
betterGroup = 0;
biggestDiff = -diff;
}
else
{
betterGroup = 1;
biggestDiff = diff;
}
}
}
}
Debug.Assert(chosen >= 0);
if (betterGroup == 0)
{
group0.Join(b[chosen]);
groupArea0 = group0.Area();
taken[chosen] = 1;
pg.setBranch(groupCard0++, b[chosen], branch.GetRaw(chosen));
}
else
{
groupCard1 += 1;
group1.Join(b[chosen]);
groupArea1 = group1.Area();
taken[chosen] = 2;
}
}
//
// If one group gets too full, then remaining rectangle are
// split between two groups in such way to balance cards of two groups.
//
if (groupCard0 + groupCard1 < card + 1)
{
for (i = 0; i < card; i++)
{
if (taken[i] == 0)
{
if (groupCard0 >= groupCard1)
{
taken[i] = 2;
groupCard1 += 1;
}
else
{
taken[i] = 1;
pg.setBranch(groupCard0++, b[i], branch.GetRaw(i));
}
}
}
}
pg.n = groupCard0;
n = groupCard1;
for (i = 0, j = 0; i < groupCard1; j++)
{
if (taken[j] == 2)
{
setBranch(i++, b[j], branch.GetRaw(j));
}
}
// truncate rest of link
branch.Length = groupCard1;
branch.Length = card;
return pg;
}
RtreePage addBranch(Storage storage, Rectangle r, object obj)
{
if (n < card)
{
setBranch(n++, r, obj);
return null;
}
else
{
return splitPage(storage, r, obj);
}
}
void setBranch(int i, Rectangle r, object obj)
{
b[i] = r;
branch[i] = obj;
}
internal void find(Rectangle r, ArrayList result, int level)
{
if (--level != 0)
{ /* this is an internal node in the tree */
for (int i = 0; i < n; i++)
{
if (r.Intersects(b[i]))
{
((RtreePage)branch[i]).find(r, result, level);
}
}
}
else
{ /* this is a leaf node */
for (int i = 0; i < n; i++)
{
if (r.Intersects(b[i]))
{
result.Add(branch[i]);
}
}
}
}