////////////////////////////////////////////////////////////////////////////////////////////////////
/// <summary> Insert a new parabola into the beachline when the beachline spans the X axis. </summary>
/// <remarks>
/// This is the normal case. We insert our new parabola and split the parabola above our site in
/// two. This means one new leaf node is created for leftmost of the two nodes in the split (the
/// old lfn is recycled to become the right node of the split). Also a new internal node to
/// parent all this.
/// </remarks>
/// <param name="lfnOld"> Parabola above the new site. </param>
/// <param name="lfnNewParabola"> parabola for the new site. </param>
/// <param name="innSubRoot">
/// Parent node of both lfnOld and lfnNewParabola represneting
/// the breakpoint between them.
/// </param>
////////////////////////////////////////////////////////////////////////////////////////////////////
private static void InsertAtDifferentY(LeafNode lfnOld, LeafNode lfnNewParabola, InternalNode innSubRoot)
{
// The old lfn will become the new right half of the split but we need a new leaf node
// for the left half of the split...
var lfnLeftHalf = new LeafNode(lfnOld.Poly);
var innSubRootLeftChild = new InternalNode(lfnOld.Poly, lfnNewParabola.Poly);
var edge = new FortuneEdge();
// This is all fairly straightforward (albeit dense) insertion of a node into a binary tree.
innSubRoot.RightChild = lfnOld;
innSubRoot.LeftChild = innSubRootLeftChild;
innSubRoot.SetEdge(edge);
innSubRoot.AddEdgeToPolygons(edge);
innSubRootLeftChild.LeftChild = lfnLeftHalf;
innSubRootLeftChild.RightChild = lfnNewParabola;
innSubRootLeftChild.SetEdge(edge);
lfnNewParabola.LeftAdjacentLeaf = lfnLeftHalf;
lfnNewParabola.RightAdjacentLeaf = lfnOld;
lfnLeftHalf.LeftAdjacentLeaf = lfnOld.LeftAdjacentLeaf;
lfnLeftHalf.RightAdjacentLeaf = lfnNewParabola;
if (lfnOld.LeftAdjacentLeaf != null)
{
lfnOld.LeftAdjacentLeaf.RightAdjacentLeaf = lfnLeftHalf;
}
lfnOld.LeftAdjacentLeaf = lfnNewParabola;
edge.SetPolys(innSubRoot.PolyRight, innSubRoot.PolyLeft);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
/// <summary> Handle the top N nodes located on a single horizontal line. </summary>
/// <remarks>
/// This only handles the corner case where the top N nodes are on the same horizontal
/// line. In that case the parabolas from previous points are vertically straight up and only
/// project to a single point on the x axis so that the beachline is a series of points rather
/// than a series of parabolas. When that is the case we can't "intersect" new points with
/// parabolas that span the x axis. After the scanline passes that initial set of topmost points,
/// there will always be a parabola which projects to the entire x axis so no need for this
/// special handling. Normally, we produce two new parabolas at a site event like this - the new
/// parabola for the site itself and the new parabola produced when we split the parabola above
/// us. In this case there is no parabola above us so we only produce one new parabola - the one
/// inserted by the site.
/// </remarks>
/// <param name="lfn"> LeafNode of the (degenerate) parabola nearest us. </param>
/// <param name="lfnNewParabola"> LeafNode we're inserting. </param>
/// <param name="innParent"> Parent of lfnOld. </param>
/// <param name="innSubRoot"> Root of the tree. </param>
/// <param name="fLeftChild"> Left child of innParent. </param>
////////////////////////////////////////////////////////////////////////////////////////////////////
private static void NdInsertAtSameY(
LeafNode lfn,
LeafNode lfnNewParabola,
InternalNode innParent,
InternalNode innSubRoot,
bool fLeftChild)
{
// Locals
LeafNode lfnLeft, lfnRight;
var lfnAdjacentParabolaLeft = lfn.LeftAdjacentLeaf;
var lfnAdjacentParabolaRight = lfn.RightAdjacentLeaf;
if (lfnNewParabola.Poly.VoronoiPoint.X < lfn.Poly.VoronoiPoint.X)
{
lfnLeft = lfnNewParabola;
lfnRight = lfn;
}
else
{
//! Note: I don't think this case ever occurs in practice since we pull events off with higher
//! x coordinates before events with lower x coordinates
lfnLeft = lfn;
lfnRight = lfnNewParabola;
}
innSubRoot.PolyLeft = lfnLeft.Poly;
innSubRoot.PolyRight = lfnRight.Poly;
innSubRoot.LeftChild = lfnLeft;
innSubRoot.RightChild = lfnRight;
var edge = new FortuneEdge();
innSubRoot.SetEdge(edge);
innSubRoot.AddEdgeToPolygons(edge);
lfnLeft.LeftAdjacentLeaf = lfnAdjacentParabolaLeft;
lfnLeft.RightAdjacentLeaf = lfnRight;
lfnRight.LeftAdjacentLeaf = lfnLeft;
lfnRight.RightAdjacentLeaf = lfnAdjacentParabolaRight;
if (innParent != null)
{
if (fLeftChild)
{
innParent.PolyLeft = lfnRight.Poly;
}
else
{
innParent.PolyRight = lfnLeft.Poly;
}
}
edge.SetPolys(innSubRoot.PolyRight, innSubRoot.PolyLeft);
}