public static double LeftBreakPoint(RedBlackTree arc, double directrix)
{
var site = arc.Site;
var rfocx = site.X;
var rfocy = site.Y;
var pby2 = rfocy - directrix;
if (pby2 == 0)
{
return(rfocx);
}
var lArc = arc.P;
if (lArc == null)
{
return(double.MinValue);
}
site = lArc.Site;
var lfocx = site.X;
var lfocy = site.Y;
var plby2 = lfocy - directrix;
if (plby2 == 0)
{
return(lfocx);
}
var hl = lfocx - rfocx;
var aby2 = 1 / pby2 - 1 / plby2;
var b = hl / plby2;
if (aby2 != 0)
{
return((-b + Math.Sqrt(b * b - 2 * aby2 * (hl * hl / (-2 * plby2) - lfocy + plby2 / 2 + rfocy - pby2 / 2))) / aby2 + rfocx);
}
return((rfocx + lfocx) / 2);
}
public static void AddBeach(ref Dictionary <int, Cell> cells, ref RedBlackTree circles, ref RedBlackTree beaches, ref List <Edge> edges, Point site)
{
var x = site.X;
var directrix = site.Y;
RedBlackTree lArc = null;
RedBlackTree rArc = null;
var dxl = 0d;
var dxr = 0d;
var node = beaches._;
while (node != null)
{
dxl = LeftBreakPoint(node, directrix) - x;
if (dxl > Diagram.Epsilon)
{
node = node.L;
}
else
{
dxr = x - RightBreakPoint(node, directrix);
if (dxr > Diagram.Epsilon)
{
if (node.R == null)
{
lArc = node;
break;
}
node = node.R;
}
else
{
if (dxl > -Diagram.Epsilon)
{
lArc = node.P;
rArc = node;
}
else if (dxr > -Diagram.Epsilon)
{
lArc = node;
rArc = node.N;
}
else
{
lArc = rArc = node;
}
break;
}
}
}
Cell.CreateCell(ref cells, site);
var newArc = CreateBeach(site);
beaches.Insert(lArc, newArc);
if (lArc == null && rArc == null)
{
return;
}
if (lArc == rArc)
{
Circle.DetachCircle(ref circles, lArc);
rArc = CreateBeach(lArc.Site);
beaches.Insert(newArc, rArc);
newArc.Edge = rArc.Edge = Edge.CreateEdge(ref cells, ref edges, lArc.Site, newArc.Site);
Circle.AttachCircle(ref circles, lArc);
Circle.AttachCircle(ref circles, rArc);
return;
}
if (rArc == null)
{ // && lArc
newArc.Edge = Edge.CreateEdge(ref cells, ref edges, lArc.Site, newArc.Site);
return;
}
// else lArc !== rArc
Circle.DetachCircle(ref circles, lArc);
Circle.DetachCircle(ref circles, rArc);
var lSite = lArc.Site;
var ax = lSite.X;
var ay = lSite.Y;
var bx = site.X - ax;
var by = site.Y - ay;
var rSite = rArc.Site;
var cx = rSite.X - ax;
var cy = rSite.Y - ay;
var d = 2 * (bx * cy - by * cx);
var hb = bx * bx + by * by;
var hc = cx * cx + cy * cy;
var vertex = new Point((cy * hb - by * hc) / d + ax, (bx * hc - cx * hb) / d + ay);
rArc.Edge = Edge.SetEdgeEnd(rArc.Edge, lSite, rSite, vertex);
newArc.Edge = Edge.CreateEdge(ref cells, ref edges, lSite, site, null, vertex);
rArc.Edge = Edge.CreateEdge(ref cells, ref edges, site, rSite, null, vertex);
Circle.AttachCircle(ref circles, lArc);
Circle.AttachCircle(ref circles, rArc);
}
public static void RemoveBeach(ref Dictionary <int, Cell> cells, ref List <Edge> edges, ref RedBlackTree beaches, ref RedBlackTree circles, RedBlackTree beach)
{
var circle = beach.Circle;
var x = circle.X;
var y = circle.CY;
var vertex = new Point(x, y);
var previous = beach.P;
var next = beach.N;
var disappearing = new List <RedBlackTree>()
{
beach
};
DetachBeach(ref circles, ref beaches, beach);
var lArc = previous;
while (lArc.Circle != null && Math.Abs(x - lArc.Circle.X) < Diagram.Epsilon && Math.Abs(y - lArc.Circle.CY) < Diagram.Epsilon)
{
previous = lArc.P;
disappearing.Insert(0, lArc);
DetachBeach(ref circles, ref beaches, lArc);
lArc = previous;
}
disappearing.Insert(0, lArc);
Circle.DetachCircle(ref circles, lArc);
var rArc = next;
while (rArc.Circle != null && Math.Abs(x - rArc.Circle.X) < Diagram.Epsilon && Math.Abs(y - rArc.Circle.CY) < Diagram.Epsilon)
{
next = rArc.N;
disappearing.Add(rArc);
DetachBeach(ref circles, ref beaches, rArc);
rArc = next;
}
disappearing.Add(rArc);
Circle.DetachCircle(ref circles, rArc);
int nArcs = disappearing.Count;
int iArc;
for (iArc = 1; iArc < nArcs; ++iArc)
{
rArc = disappearing[iArc];
lArc = disappearing[iArc - 1];
rArc.Edge = Edge.SetEdgeEnd(rArc.Edge, lArc.Site, rArc.Site, vertex);
}
lArc = disappearing[0];
rArc = disappearing[nArcs - 1];
rArc.Edge = Edge.CreateEdge(ref cells, ref edges, lArc.Site, rArc.Site, null, vertex);
Circle.AttachCircle(ref circles, lArc);
Circle.AttachCircle(ref circles, rArc);
}
public static void DetachBeach(ref RedBlackTree circles, ref RedBlackTree beaches, RedBlackTree beach)
{
Circle.DetachCircle(ref circles, beach);
beaches.Remove(beach);
Beach.BeachPool.Add(beach);
beach.Reset();
}
public void Insert(RedBlackTree after, RedBlackTree node)
{
RedBlackTree parent = null;
RedBlackTree grandpa = null;
RedBlackTree uncle = null;
if (after != null)
{
node.P = after;
node.N = after.N;
if (after.N != null)
{
after.N.P = node;
}
after.N = node;
if (after.R != null)
{
after = after.R;
while (after.L != null)
{
after = after.L;
}
after.L = node;
}
else
{
after.R = node;
}
parent = after;
}
else if (this._ != null)
{
after = RedBlackFirst(this._);
node.P = null;
node.N = after;
after.P = after.L = node;
parent = after;
}
else
{
node.P = node.N = null;
this._ = node;
parent = null;
}
node.L = node.R = null;
node.U = parent;
node.C = true;
after = node;
while (parent != null && parent.C)
{
grandpa = parent.U;
if (parent == grandpa.L)
{
uncle = grandpa.R;
if (uncle != null && uncle.C)
{
parent.C = uncle.C = false;
grandpa.C = true;
after = grandpa;
}
else
{
if (after == parent.R)
{
RedBlackRotateLeft(this, parent);
after = parent;
parent = after.U;
}
parent.C = false;
grandpa.C = true;
RedBlackRotateRight(this, grandpa);
}
}
else
{
uncle = grandpa.L;
if (uncle != null && uncle.C)
{
parent.C = uncle.C = false;
grandpa.C = true;
after = grandpa;
}
else
{
if (after == parent.L)
{
RedBlackRotateRight(this, parent);
after = parent;
parent = after.U;
}
parent.C = false;
grandpa.C = true;
RedBlackRotateLeft(this, grandpa);
}
}
parent = after.U;
}
this._.C = false;
}
public void Reset()
{
U = L = R = P = N = null;
C = false;
}
public void Remove(RedBlackTree node)
{
if (node.N != null)
{
node.N.P = node.P;
}
if (node.P != null)
{
node.P.N = node.N;
}
node.N = node.P = null;
RedBlackTree parent = node.U;
RedBlackTree sibling = null;
RedBlackTree left = node.L;
RedBlackTree right = node.R;
RedBlackTree next = null;
bool red = false;
if (left == null)
{
next = right;
}
else if (right == null)
{
next = left;
}
else
{
next = RedBlackFirst(right);
}
if (parent != null)
{
if (parent.L == node)
{
parent.L = next;
}
else
{
parent.R = next;
}
}
else
{
this._ = next;
}
if (left != null && right != null)
{
red = next.C;
next.C = node.C;
next.L = left;
left.U = next;
if (next != right)
{
parent = next.U;
next.U = node.U;
node = next.R;
parent.L = node;
next.R = right;
right.U = next;
}
else
{
next.U = parent;
parent = next;
node = next.R;
}
}
else
{
red = node.C;
node = next;
}
if (node != null)
{
node.U = parent;
}
if (red)
{
return;
}
if (node != null && node.C)
{
node.C = false; return;
}
do
{
if (node == this._)
{
break;
}
if (node == parent.L)
{
sibling = parent.R;
if (sibling.C)
{
sibling.C = false;
parent.C = true;
RedBlackRotateLeft(this, parent);
sibling = parent.R;
}
if ((sibling.L != null && sibling.L.C) ||
(sibling.R != null && sibling.R.C))
{
if (sibling.R == null || !sibling.R.C)
{
sibling.L.C = false;
sibling.C = true;
RedBlackRotateRight(this, sibling);
sibling = parent.R;
}
sibling.C = parent.C;
parent.C = sibling.R.C = false;
RedBlackRotateLeft(this, parent);
node = this._;
break;
}
}
else
{
sibling = parent.L;
if (sibling.C)
{
sibling.C = false;
parent.C = true;
RedBlackRotateRight(this, parent);
sibling = parent.L;
}
if ((sibling.L != null && sibling.L.C) ||
(sibling.R != null && sibling.R.C))
{
if (sibling.L == null || !sibling.L.C)
{
sibling.R.C = false;
sibling.C = true;
RedBlackRotateLeft(this, sibling);
sibling = parent.L;
}
sibling.C = parent.C;
parent.C = sibling.L.C = false;
RedBlackRotateRight(this, parent);
node = this._;
break;
}
}
sibling.C = true;
node = parent;
parent = parent.U;
} while (!node.C);
if (node != null)
{
node.C = false;
}
}
public static void AttachCircle(ref RedBlackTree circles, RedBlackTree arc)
{
var lArc = arc.P;
var rArc = arc.N;
if (lArc == null || rArc == null)
{
return;
}
var lSite = lArc.Site;
var cSite = arc.Site;
var rSite = rArc.Site;
if (lSite == rSite)
{
return;
}
var bx = cSite.X;
var by = cSite.Y;
var ax = lSite.X - bx;
var ay = lSite.Y - by;
var cx = rSite.X - bx;
var cy = rSite.Y - by;
var d = 2 * (ax * cy - ay * cx);
if (d >= -Diagram.Epsilon2)
{
return;
}
var ha = ax * ax + ay * ay;
var hc = cx * cx + cy * cy;
var x = (cy * ha - ay * hc) / d;
var y = (ax * hc - cx * ha) / d;
RedBlackTree circle = null;
if (Circle.CirclePool.Any())
{
circle = Circle.CirclePool.Last();
Circle.CirclePool.Remove(circle);
}
else
{
circle = new RedBlackTree();
}
circle.Arc = arc;
circle.Site = cSite;
circle.X = x + bx;
circle.Y = (circle.CY = y + by) + Math.Sqrt(x * x + y * y); // y bottom
arc.Circle = circle;
RedBlackTree before = null;
var node = circles._;
while (node != null)
{
if (circle.Y < node.Y || (circle.Y == node.Y && circle.X <= node.X))
{
if (node.L != null)
{
node = node.L;
}
else
{
before = node.P; break;
}
}
else
{
if (node.R != null)
{
node = node.R;
}
else
{
before = node; break;
}
}
}
circles.Insert(before, circle);
if (before == null)
{
FirstCircle = circle;
}
}
