/// <summary>
/// Determines if the Point is to the right of the HalfEdge.
/// </summary>
/// <param name="el">edge</param>
/// <param name="p">point</param>
/// <returns>1 if p is to the right of HalfEdge</returns>
private static bool IsRightOf(HalfEdge el, Point2D p)
{
bool above;
var e = el.Edge;
var topsite = e.Reg[1];
var rightOfSite = p.X > topsite.X;
if (rightOfSite && (el.Midpoint == 0))
{
return(true);
}
if (!rightOfSite && (el.Midpoint == 1))
{
return(false);
}
if (DoubleComparison.IsEqual(e.A, 1.0))
{
var dyp = p.Y - topsite.Y;
var dxp = p.X - topsite.X;
var fast = false;
if ((!rightOfSite && (e.B < 0.0)) || (rightOfSite && (e.B >= 0.0)))
{
above = dyp >= e.B * dxp;
fast = above;
}
else
{
above = p.X + p.Y * e.B > e.C;
if (e.B < 0.0)
{
above = !above;
}
if (!above)
{
fast = true;
}
}
if (fast)
{
return(el.Midpoint == 0 ? above : !above);
}
var dxs = topsite.X - e.Reg[0].X;
above = e.B * (dxp * dxp - dyp * dyp) < dxs * dyp * (1.0 + 2.0 * dxp / dxs + e.B * e.B);
if (e.B < 0.0)
{
above = !above;
}
}
else
{
var yl = e.C - e.A * p.X;
var t1 = p.Y - yl;
var t2 = p.X - topsite.X;
var t3 = yl - topsite.Y;
above = t1 * t1 > t2 * t2 + t3 * t3;
}
return(el.Midpoint == 0 ? above : !above);
}
// push the HalfEdge into the ordered linked list of vertices
internal void PQinsert(HalfEdge he, Point2D v, double offset)
{
HalfEdge next;
he.Vertex = v;
he.YStar = v.Y + offset;
var last = _hash[0];
_min = 0;
while (((next = last.NextSite) != null) && ((he.YStar > next.YStar) || (DoubleComparison.IsEqual(he.YStar, next.YStar) && (v.X > next.Vertex.X))))
{
last = next;
}
he.NextSite = last.NextSite;
last.NextSite = he;
_count++;
}
/// <summary>
/// Creates a new site where the HalfEdges intersect.
/// </summary>
/// <param name="el1">HalfEdge to intersect</param>
/// <param name="el2">HalfEdge to intersect</param>
/// <returns>new site/point at intersection</returns>
private static Point2D Intersect(HalfEdge el1, HalfEdge el2)
{
Edge e;
HalfEdge el;
var e1 = el1.Edge;
var e2 = el2.Edge;
if ((e1 == null) || (e2 == null) || (e1.Reg[1] == e2.Reg[1]))
{
return(null);
}
var d = e1.A * e2.B - e1.B * e2.A;
//This checks for the value being basically zero
if ((-0.0000000001 < d) && (d < 0.0000000001))
{
return(null);
}
var xint = (e1.C * e2.B - e2.C * e1.B) / d;
var yint = (e2.C * e1.A - e1.C * e2.A) / d;
if ((e1.Reg[1].Y < e2.Reg[1].Y) || (DoubleComparison.IsEqual(e1.Reg[1].Y, e2.Reg[1].Y) &&
(e1.Reg[1].X < e2.Reg[1].X)))
{
el = el1;
e = e1;
}
else
{
el = el2;
e = e2;
}
return(((xint >= e.Reg[1].X) && (el.Midpoint == 0)) || ((xint < e.Reg[1].X) && (el.Midpoint == 1)) ? null : new Point2D(xint, yint));
}
/// <summary>
/// Starts fortune's algorithm.
/// </summary>
private void Voronoi()
{
Point2D newintstar = null;
HalfEdge leftBound;
var queue = new PriorityQueue(NumSites);
_bottomsite = NextSite();
var list = new EdgeList(NumSites);
var newsite = NextSite();
while (true)
{
Point2D bot;
Point2D p;
HalfEdge rbnd;
HalfEdge bisector;
Edge e;
if (!queue.IsEmpty())
{
newintstar = queue.Min();
}
//if the lowest site has a smaller y value than the lowest vector intersection, process the site
//otherwise process the vector intersection
if ((newsite != null) && (queue.IsEmpty() || (newintstar == null) || (newsite.Y < newintstar.Y) || (DoubleComparison.IsEqual(newsite.Y, newintstar.Y) && (newsite.X < newintstar.X))))
{ /* new site is smallest - this is a site event*/
leftBound = list.LeftBound(newsite); //get the first HalfEdge to the LEFT of the new site
rbnd = leftBound.Right; //get the first HalfEdge to the RIGHT of the new site
bot = Rightreg(leftBound); //if this HalfEdge has no edge, , bot = bottom site (whatever that is)
e = Bisect(bot, newsite); //create a new edge that bisects
bisector = new HalfEdge(e, 0); //create a new HalfEdge, setting its elPm field to 0
EdgeList.ElInsert(leftBound, bisector); //insert this new bisector edge between the left and right vectors in a linked list
if ((p = Intersect(leftBound, bisector)) != null) //if the new bisector intersects with the left edge, remove the left edge's vertex, and put in the new one
{
queue.PQinsert(queue.Delete(leftBound), p, p.Distance(newsite));
}
leftBound = bisector;
bisector = new HalfEdge(e, 1); //create a new HalfEdge, setting its elPm field to 1
EdgeList.ElInsert(leftBound, bisector); //insert the new HE to the right of the original bisector earlier in the IF stmt
if ((p = Intersect(bisector, rbnd)) != null) //if this new bisector intersects with the
{
queue.PQinsert(bisector, p, p.Distance(newsite)); //push the HE into the ordered linked list of vertices
}
newsite = NextSite();
}
else if (!queue.IsEmpty())
{ /* intersection is smallest - this is a vector event */
leftBound = queue.ExtractMin(); //pop the HalfEdge with the lowest vector off the ordered list of vectors
var llbnd = leftBound.Left;
rbnd = leftBound.Right; //get the HalfEdge to the right of the above HE
var rrbnd = rbnd.Right;
bot = Leftreg(leftBound); //get the Site to the left of the left HE which it bisects
var top = Rightreg(rbnd);
var leftBoundVertex = leftBound.Vertex;
Endpoint(leftBound.Edge, leftBound.Midpoint, leftBoundVertex); //set the endpoint of the left HalfEdge to be this vector
Endpoint(rbnd.Edge, rbnd.Midpoint, leftBoundVertex); //set the endpoint of the right HalfEdge to be this vector
list.Delete(leftBound); //mark the lowest HE for deletion - can't delete yet because there might be pointers to it in Hash Map
queue.Delete(rbnd); //remove all vertex events to do with the right HE
list.Delete(rbnd); //mark the right HE for deletion - can't delete yet because there might be pointers to it in Hash Map
var pm = 0;
if (bot.Y > top.Y)
{ //if the site to the left of the event is higher than the Site to the right of it, then swap them and set the 'pm' variable to 1
var temp = bot;
bot = top;
top = temp;
pm = 1;
}
e = Bisect(bot, top); //Create Edge between the two Sites
bisector = new HalfEdge(e, pm); //Create a HE from the Edge 'e', and make it point to that edge with its elEdge field
EdgeList.ElInsert(llbnd, bisector); //Insert the new bisector to the right of the left HE
Endpoint(e, 1 - pm, leftBoundVertex); //Set one endpoint to the new edge to be the vector point 'v'
//If left HE and the new bisector don't intersect, then delete the left HE, and reinsert
if ((p = Intersect(llbnd, bisector)) != null)
{
queue.PQinsert(queue.Delete(llbnd), p, p.Distance(bot));
}
//If right HE and the new bisector don't intersect, then reinsert it
if ((p = Intersect(bisector, rrbnd)) != null)
{
queue.PQinsert(bisector, p, p.Distance(bot));
}
}
else
{
break;
}
}
for (leftBound = list.LeftEnd.Right; leftBound != list.RightEnd; leftBound = leftBound.Right)
{
ClipLine(leftBound.Edge);
}
}
private void ClipLine(Edge e)
{
double x1;
double x2;
double y1;
double y2;
//if the distance between the two points this line was created from is less than
//the square root of 2, then ignore it
if (e.Reg[0].Distance(e.Reg[1]) < 1.41421356)
{
return;
}
var s1 = DoubleComparison.IsEqual(e.A, 1.0) && (e.B >= 0.0) ? e.EndPoints[1] : e.EndPoints[0];
var s2 = DoubleComparison.IsEqual(e.A, 1.0) && (e.B >= 0.0) ? e.EndPoints[0] : e.EndPoints[1];
if (DoubleComparison.IsEqual(e.A, 1.0))
{
y1 = (s1 != null) && (s1.Y > 1) ? s1.Y : 1;
y1 = y1 > ImageHeight ? ImageHeight : y1;
x1 = e.C - e.B * y1;
y2 = (s2 != null) && (s2.Y < ImageHeight) ? s2.Y : ImageHeight;
y2 = y2 < 1 ? 1 : y2;
x2 = e.C - e.B * y2;
if (((x1 > ImageWidth) && (x2 > ImageWidth)) || ((x1 < 1) && (x2 < 1)))
{
return;
}
x1 = x1 > ImageWidth ? ImageWidth : x1;
x1 = x1 < 1 ? 1 : x1;
y1 = (x1 > ImageWidth) || (x1 < 1) ? (e.C - x1) / e.B : y1;
x2 = x2 > ImageWidth ? ImageWidth : x2;
x2 = x2 < 1 ? 1 : x2;
y2 = (x2 > ImageWidth) || (x2 < 1) ? (e.C - x2) / e.B : y2;
}
else
{
x1 = (s1 != null) && (s1.X > 1) ? s1.X : 1;
x1 = x1 > ImageWidth ? ImageWidth : x1;
y1 = e.C - e.A * x1;
x2 = (s2 != null) && (s2.X < ImageWidth) ? s2.X : ImageWidth;
x2 = x2 < 1 ? 1 : x2;
y2 = e.C - e.A * x2;
if (((y1 > ImageHeight) & (y2 > ImageHeight)) | ((y1 < 1) & (y2 < 1)))
{
return;
}
y1 = y1 > ImageHeight ? ImageHeight : y1;
y1 = y1 < 1 ? 1 : y1;
x1 = (y1 > ImageHeight) || (y1 < 1) ? (e.C - y1) / e.A : x1;
y2 = y2 > ImageHeight ? ImageHeight : y2;
y2 = y2 < 1 ? 1 : y2;
x2 = (y2 > ImageHeight) || (y2 < 1) ? (e.C - y2) / e.A : x2;
}
PushGraphEdge(x1, y1, x2, y2);
}
