/// <summary>
/// Create copy of the rectangle
/// </summary>
public RectangleR2(RectangleR2 r)
{
this.top = r.top;
this.left = r.left;
this.bottom = r.bottom;
this.right = r.right;
}
internal RectangleR2 cover()
{
RectangleR2 r = new RectangleR2(b[0]);
for (int i = 1; i < n; i++)
{
r.Join(b[i]);
}
return r;
}
internal RtreeR2Page(IDatabase db, IPersistent obj, RectangleR2 r)
{
branch = db.CreateLink<IPersistent>(card);
branch.Length = card;
b = new RectangleR2[card];
setBranch(0, new RectangleR2(r), obj);
n = 1;
for (int i = 1; i < card; i++)
{
b[i] = new RectangleR2();
}
}
internal RtreeR2Page(IDatabase db, RtreeR2Page root, RtreeR2Page p)
{
branch = db.CreateLink<IPersistent>(card);
branch.Length = card;
b = new RectangleR2[card];
n = 2;
setBranch(0, root.cover(), root);
setBranch(1, p.cover(), p);
for (int i = 2; i < card; i++)
{
b[i] = new RectangleR2();
}
}
internal void find(RectangleR2 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]))
{
((RtreeR2Page)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]);
}
}
}
}
internal RtreeR2Page insert(IDatabase db, RectangleR2 r, IPersistent obj, int level)
{
Modify();
if (--level != 0)
{
// not leaf page
int i, mini = 0;
double minIncr = Double.MaxValue;
double minArea = Double.MaxValue;
for (i = 0; i < n; i++)
{
double area = b[i].Area();
double incr = RectangleR2.JoinArea(b[i], r) - area;
if (incr < minIncr)
{
minIncr = incr;
minArea = area;
mini = i;
}
else if (incr == minIncr && area < minArea)
{
minArea = area;
mini = i;
}
}
RtreeR2Page p = (RtreeR2Page)branch[mini];
RtreeR2Page q = p.insert(db, 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(db, q.cover(), q);
}
}
else
{
return addBranch(db, new RectangleR2(r), obj);
}
}
RtreeR2Page splitPage(IDatabase db, RectangleR2 r, IPersistent obj)
{
int i, j, seed0 = 0, seed1 = 0;
double[] rectArea = new double[card + 1];
double waste;
double worstWaste = Double.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();
}
RectangleR2 bp = r;
for (i = 0; i < card; i++)
{
for (j = i + 1; j <= card; j++)
{
waste = RectangleR2.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];
RectangleR2 group0, group1;
double groupArea0, groupArea1;
int groupCard0, groupCard1;
RtreeR2Page pg;
taken[seed1 - 1] = 2;
group1 = new RectangleR2(b[seed1 - 1]);
if (seed0 == 0)
{
group0 = new RectangleR2(r);
pg = new RtreeR2Page(db, obj, r);
}
else
{
group0 = new RectangleR2(b[seed0 - 1]);
pg = new RtreeR2Page(db, 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;
double biggestDiff = -1;
for (i = 0; i < card; i++)
{
if (taken[i] == 0)
{
double diff = (RectangleR2.JoinArea(group0, b[i]) - groupArea0)
- (RectangleR2.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));
}
}
return pg;
}
void setBranch(int i, RectangleR2 r, IPersistent obj)
{
b[i] = r;
branch[i] = obj;
}
RtreeR2Page addBranch(IDatabase db, RectangleR2 r, IPersistent obj)
{
if (n < card)
{
setBranch(n++, r, obj);
return null;
}
else
{
return splitPage(db, r, obj);
}
}
internal int remove(RectangleR2 r, IPersistent obj, int level, ArrayList reinsertList)
{
if (--level != 0)
{
for (int i = 0; i < n; i++)
{
if (r.Intersects(b[i]))
{
RtreeR2Page pg = (RtreeR2Page)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;
}
/// <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(RectangleR2 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>
/// Checks if this rectangle intersects with specified rectangle
/// </summary>
public bool Intersects(RectangleR2 r)
{
return left <= r.right && top <= r.bottom && right >= r.left && bottom >= r.top;
}
public bool EqualsTo(RectangleR2 other)
{
if (Left != other.Left)
return false;
if (Right != other.Right)
return false;
if (Top != other.Top)
return false;
if (Bottom != other.Bottom)
return false;
return true;
}
/// <summary>
/// Checks if this rectangle contains the specified rectangle
/// </summary>
public bool Contains(RectangleR2 r)
{
return left <= r.left && top <= r.top && right >= r.right && bottom >= r.bottom;
}
/// <summary>
/// Area of covered rectangle for two sepcified rectangles
/// </summary>
public static double JoinArea(RectangleR2 a, RectangleR2 b)
{
double left = (a.left < b.left) ? a.left : b.left;
double right = (a.right > b.right) ? a.right : b.right;
double top = (a.top < b.top) ? a.top : b.top;
double bottom = (a.bottom > b.bottom) ? a.bottom : b.bottom;
return (bottom - top) * (right - left);
}
/// <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 RectangleR2 Join(RectangleR2 a, RectangleR2 b)
{
RectangleR2 r = new RectangleR2(a);
r.Join(b);
return r;
}
