/// <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(RectangleRn r)
{
for (int i = 0, n = coords.Length / 2; i < n; i++)
{
coords[i] = Math.Min(coords[i], r.coords[i]);
coords[i + n] = Math.Max(coords[i + n], r.coords[i + n]);
}
}
internal RtreeRnPage(Storage storage, object obj, RectangleRn r)
{
branch = storage.CreateLink(card);
branch.Length = card;
b = new RectangleRn[card];
setBranch(0, new RectangleRn(r), obj);
n = 1;
}
/// <summary>
/// Area of covered rectangle for two sepcified rectangles
/// </summary>
public static double JoinArea(RectangleRn a, RectangleRn b)
{
double area = 1.0;
for (int i = 0, n = a.coords.Length/2; i < n; i++) {
double min = Math.Min(a.coords[i], b.coords[i]);
double max = Math.Max(a.coords[n + i], b.coords[n + i]);
area *= max - min;
}
return area;
}
/// <summary>
/// Checks if this rectangle contains the specified rectangle
/// </summary>
public bool Contains(RectangleRn r)
{
for (int i = 0, n = coords.Length / 2; i < n; i++)
{
if (coords[i] > r.coords[i] || coords[i + n] < r.coords[i + n])
{
return(false);
}
}
return(true);
}
/// <summary>
/// Area of covered rectangle for two sepcified rectangles
/// </summary>
public static double JoinArea(RectangleRn a, RectangleRn b)
{
double area = 1.0;
for (int i = 0, n = a.coords.Length / 2; i < n; i++)
{
double min = Math.Min(a.coords[i], b.coords[i]);
double max = Math.Max(a.coords[n + i], b.coords[n + i]);
area *= max - min;
}
return(area);
}
public RectangleRn WrappingRectangle()
{
Line line = new Line(points[0], points[1]);
RectangleRn wr = line.WrappingRectangle();
for (int i = 1; i < points.Length; i++)
{
line = new Line(points[i], points[(i + 1) % points.Length]);
wr.Join(line.WrappingRectangle());
}
return(wr);
}
public void Unpack(ObjectReader reader)
{
n = reader.ReadInt32();
branch = (Link)reader.ReadObject();
card = branch.Count;
int nDims = ((Page.pageSize-ObjectHeader.Sizeof-12)/card - 4) / 16;
double[] coords = new double[nDims*2];
b = new RectangleRn[card];
for (int i = 0; i < n; i++) {
for (int j = 0; j < nDims; j++) {
coords[j] = reader.ReadDouble();
coords[j+nDims] = reader.ReadDouble();
}
b[i] = new RectangleRn(coords);
}
}
internal RtreeRnPage insert(Storage storage, RectangleRn r, object 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 = RectangleRn.JoinArea(b[i], r) - area;
if (incr < minIncr)
{
minIncr = incr;
minArea = area;
mini = i;
}
else if (incr == minIncr && area < minArea)
{
minArea = area;
mini = i;
}
}
RtreeRnPage p = (RtreeRnPage)branch[mini];
RtreeRnPage 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 RectangleRn(r), obj);
}
}
public RectangleRn WrappingRectangle()
{
Euler euler = new Euler();
euler.phi = phi;
euler.theta = theta;
euler.psi = psi;
euler.psi_a = Euler.AXIS_Z;
euler.theta_a = Euler.AXIS_X;
euler.phi_a = Euler.AXIS_Z;
if (FP.zero(length))
{
Point3D beg3d = new Point3D();
Point3D end3d = new Point3D();
euler.transform(beg3d, new Point3D(0.0, 0.0));
euler.transform(end3d, new Point3D(length, 0.0));
RectangleRn r = beg3d.toRectangle();
end3d.addToRectangle(r);
return(r);
}
else
{
double l, ls, lc;
Point3D[] v = new Point3D[4];
Point3D tv = new Point3D();
l = length / 2.0;
ls = Math.Sin(l);
lc = Math.Cos(l);
euler.phi += l;
v[0] = new Point3D(lc, lc < 0 ? -1.0 : -ls, 0.0);
v[1] = new Point3D(1.0, lc < 0 ? -1.0 : -ls, 0.0);
v[2] = new Point3D(lc, lc < 0 ? +1.0 : +ls, 0.0);
v[3] = new Point3D(1.0, lc < 0 ? +1.0 : +ls, 0.0);
Point3D min = new Point3D(1.0, 1.0, 1.0);
Point3D max = new Point3D(-1.0, -1.0, -1.0);
for (int i = 0; i < 4; i++)
{
euler.transform(tv, v[i]);
if (tv.x < -1.0)
{
min.x = -1.0;
}
else if (tv.x > 1.0)
{
max.x = 1.0;
}
else
{
if (tv.x < min.x)
{
min.x = tv.x;
}
if (tv.x > max.x)
{
max.x = tv.x;
}
}
if (tv.y < -1.0)
{
min.y = -1.0;
}
else if (tv.y > 1.0)
{
max.y = 1.0;
}
else
{
if (tv.y < min.y)
{
min.y = tv.y;
}
if (tv.y > max.y)
{
max.y = tv.y;
}
}
if (tv.z < -1.0)
{
min.z = -1.0;
}
else if (tv.z > 1.0)
{
max.z = 1.0;
}
else
{
if (tv.z < min.z)
{
min.z = tv.z;
}
if (tv.z > max.z)
{
max.z = tv.z;
}
}
}
return(new RectangleRn(new double[] { min.x, min.y, min.z, max.x, max.y, max.z }));
}
}
internal void addToRectangle(RectangleRn r)
{
addToRectangle(r, x, y, z);
}
/// <summary>
/// Create copy of the rectangle
/// </summary>
public RectangleRn(RectangleRn r)
{
coords = new double[r.coords.Length];
Array.Copy(r.coords, 0, coords, 0, coords.Length);
}
void setBranch(int i, RectangleRn r, object obj)
{
b[i] = r;
branch[i] = obj;
}
/// <summary>
/// Checks if this rectangle contains the specified rectangle
/// </summary>
public bool Contains(RectangleRn r)
{
for (int i = 0, n = coords.Length/2; i < n; i++) {
if (coords[i] > r.coords[i] || coords[i+n] < r.coords[i+n]) {
return false;
}
}
return true;
}
/// <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 RectangleRn Join(RectangleRn a, RectangleRn b)
{
RectangleRn r = new RectangleRn(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(RectangleRn r)
{
for (int i = 0, n = coords.Length/2; i < n; i++)
{
coords[i] = Math.Min(coords[i], r.coords[i]);
coords[i+n] = Math.Max(coords[i+n], r.coords[i+n]);
}
}
internal void find(RectangleRn 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]))
{
((RtreeRnPage)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 static void addToRectangle(RectangleRn r, double ra, double dec) {
double x = Math.Cos(ra)*Math.Cos(dec);
double y = Math.Sin(ra)*Math.Cos(dec);
double z = Math.Sin(dec);
addToRectangle(r, x, y, z);
}
RtreeRnPage addBranch(Storage storage, RectangleRn r, object obj)
{
if (n < card)
{
setBranch(n++, r, obj);
return null;
}
else
{
return splitPage(storage, r, obj);
}
}
RtreeRnPage splitPage(Storage storage, RectangleRn r, object 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();
}
RectangleRn bp = r;
for (i = 0; i < card; i++)
{
for (j = i+1; j <= card; j++)
{
waste = RectangleRn.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];
RectangleRn group0, group1;
double groupArea0, groupArea1;
int groupCard0, groupCard1;
RtreeRnPage pg;
taken[seed1-1] = 2;
group1 = new RectangleRn(b[seed1-1]);
if (seed0 == 0)
{
group0 = new RectangleRn(r);
pg = new RtreeRnPage(storage, obj, r);
}
else
{
group0 = new RectangleRn(b[seed0-1]);
pg = new RtreeRnPage(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 - card/2
&& groupCard1 < card + 1 - card/2)
{
int betterGroup = -1, chosen = -1;
double biggestDiff = -1;
for (i = 0; i < card; i++)
{
if (taken[i] == 0)
{
double diff = (RectangleRn.JoinArea(group0, b[i]) - groupArea0)
- (RectangleRn.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;
}
internal RectangleRn cover()
{
RectangleRn r = new RectangleRn(b[0]);
for (int i = 1; i < n; i++)
{
r.Join(b[i]);
}
return r;
}
internal void addToRectangle(RectangleRn r) {
addToRectangle(r, x, y, z);
}
/// <summary>
/// Create copy of the rectangle
/// </summary>
public RectangleRn(RectangleRn r)
{
coords = new double[r.coords.Length];
Array.Copy(r.coords, 0, coords, 0, coords.Length);
}
internal static void addToRectangle(RectangleRn r, double x, double y, double z) {
if (x < r.coords[0]) {
r.coords[0] = x;
}
if (y < r.coords[1]) {
r.coords[1] = y;
}
if (z < r.coords[2]) {
r.coords[2] = z;
}
if (x > r.coords[3]) {
r.coords[3] = x;
}
if (y > r.coords[4]) {
r.coords[4] = y;
}
if (z > r.coords[5]) {
r.coords[5] = z;
}
}
internal int remove(RectangleRn r, object obj, int level, ArrayList reinsertList)
{
if (--level != 0)
{
for (int i = 0; i < n; i++)
{
if (r.Intersects(b[i]))
{
RtreeRnPage pg = (RtreeRnPage)branch[i];
int reinsertLevel = pg.remove(r, obj, level, reinsertList);
if (reinsertLevel >= 0)
{
if (pg.n >= card/2)
{
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;
}
