public AdvancingFront( AdvancingFrontNode head, AdvancingFrontNode tail )
{
this.Head = head;
this.Tail = tail;
this.Search = head;
AddNode(head);
AddNode(tail);
}
public void RemoveNode( AdvancingFrontNode node )
{
}
/// <summary>
/// We will traverse the entire advancing front and fill it to form a convex hull.
/// </summary>
private static void TurnAdvancingFrontConvex( DTSweepContext tcx, AdvancingFrontNode b, AdvancingFrontNode c )
{
AdvancingFrontNode first = b;
while (c != tcx.Front.Tail) {
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = c;
if (TriangulationUtil.Orient2d(b.Point, c.Point, c.Next.Point) == Orientation.CCW) {
// [b,c,d] Concave - fill around c
Fill(tcx, c);
c = c.Next;
} else {
// [b,c,d] Convex
if (b != first && TriangulationUtil.Orient2d(b.Prev.Point, b.Point, c.Point) == Orientation.CCW) {
// [a,b,c] Concave - fill around b
Fill(tcx, b);
b = b.Prev;
} else {
// [a,b,c] Convex - nothing to fill
b = c;
c = c.Next;
}
}
}
}
/// <summary>
/// Creates a new front triangle and legalize it
/// </summary>
private static AdvancingFrontNode NewFrontTriangle( DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node )
{
AdvancingFrontNode newNode;
DelaunayTriangle triangle;
triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
newNode = new AdvancingFrontNode(point) {Next = node.Next, Prev = node};
node.Next.Prev = newNode;
node.Next = newNode;
tcx.AddNode(newNode); // XXX: BST
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = newNode;
if (!Legalize(tcx, triangle)) tcx.MapTriangleToNodes(triangle);
return newNode;
}
private static bool IsShallow( DTSweepContext tcx, AdvancingFrontNode node )
{
double height;
if (tcx.Basin.leftHighest) {
height = tcx.Basin.leftNode.Point.Y - node.Point.Y;
} else {
height = tcx.Basin.rightNode.Point.Y - node.Point.Y;
}
if (tcx.Basin.width > height) {
return true;
}
return false;
}
/// <summary>
/// ???
/// </summary>
/// <param name="node">middle node</param>
/// <returns>the angle between 3 front nodes</returns>
private static double HoleAngle( AdvancingFrontNode node )
{
// XXX: do we really need a signed angle for holeAngle?
// could possible save some cycles here
/* Complex plane
* ab = cosA +i*sinA
* ab = (ax + ay*i)(bx + by*i) = (ax*bx + ay*by) + i(ax*by-ay*bx)
* atan2(y,x) computes the principal value of the argument function
* applied to the complex number x+iy
* Where x = ax*bx + ay*by
* y = ax*by - ay*bx
*/
double px = node.Point.X;
double py = node.Point.Y;
double ax = node.Next.Point.X - px;
double ay = node.Next.Point.Y - py;
double bx = node.Prev.Point.X - px;
double by = node.Prev.Point.Y - py;
return Math.Atan2(ax * by - ay * bx, ax * bx + ay * by);
}
private static void EdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
try {
tcx.EdgeEvent.ConstrainedEdge = edge;
tcx.EdgeEvent.Right = edge.P.X > edge.Q.X;
if (tcx.IsDebugEnabled) { tcx.DTDebugContext.PrimaryTriangle = node.Triangle; }
if (IsEdgeSideOfTriangle(node.Triangle, edge.P, edge.Q)) return;
// For now we will do all needed filling
// TODO: integrate with flip process might give some better performance
// but for now this avoid the issue with cases that needs both flips and fills
FillEdgeEvent(tcx, edge, node);
EdgeEvent(tcx, edge.P, edge.Q, node.Triangle, edge.Q);
} catch ( PointOnEdgeException e) {
//Debug.WriteLine( String.Format( "Warning: Skipping Edge: {0}", e.Message ) );
throw;
}
}
public void AddNode( AdvancingFrontNode node )
{
}
private static void FillRightAboveEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
while (node.Next.Point.X < edge.P.X) {
if (tcx.IsDebugEnabled) { tcx.DTDebugContext.ActiveNode = node; }
// Check if next node is below the edge
Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P);
if (o1 == Orientation.CCW) {
FillRightBelowEdgeEvent(tcx, edge, node);
} else {
node = node.Next;
}
}
}
private static void FillLeftConcaveEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
Fill(tcx, node.Prev);
if (node.Prev.Point != edge.P) {
// Next above or below edge?
if (TriangulationUtil.Orient2d(edge.Q, node.Prev.Point, edge.P) == Orientation.CW) {
// Below
if (TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point) == Orientation.CW) {
// Next is concave
FillLeftConcaveEdgeEvent(tcx, edge, node);
} else {
// Next is convex
}
}
}
}
private static void FillEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
if (tcx.EdgeEvent.Right) {
FillRightAboveEdgeEvent(tcx, edge, node);
} else {
FillLeftAboveEdgeEvent(tcx, edge, node);
}
}
/// <summary>
/// Recursive algorithm to fill a Basin with triangles
/// </summary>
private static void FillBasinReq( DTSweepContext tcx, AdvancingFrontNode node )
{
if (IsShallow(tcx, node)) return; // if shallow stop filling
Fill(tcx, node);
if (node.Prev == tcx.Basin.leftNode && node.Next == tcx.Basin.rightNode) {
return;
} else if (node.Prev == tcx.Basin.leftNode) {
Orientation o = TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point);
if (o == Orientation.CW) return;
node = node.Next;
} else if (node.Next == tcx.Basin.rightNode) {
Orientation o = TriangulationUtil.Orient2d(node.Point, node.Prev.Point, node.Prev.Prev.Point);
if (o == Orientation.CCW) return;
node = node.Prev;
} else {
// Continue with the neighbor node with lowest Y value
if (node.Prev.Point.Y < node.Next.Point.Y) {
node = node.Prev;
} else {
node = node.Next;
}
}
FillBasinReq(tcx, node);
}
/// <summary>
/// Fills a basin that has formed on the Advancing Front to the right
/// of given node.<br>
/// First we decide a left,bottom and right node that forms the
/// boundaries of the basin. Then we do a reqursive fill.
/// </summary>
/// <param name="tcx"></param>
/// <param name="node">starting node, this or next node will be left node</param>
private static void FillBasin( DTSweepContext tcx, AdvancingFrontNode node )
{
if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW) {
// tcx.basin.leftNode = node.next.next;
tcx.Basin.leftNode = node;
} else {
tcx.Basin.leftNode = node.Next;
}
// Find the bottom and right node
tcx.Basin.bottomNode = tcx.Basin.leftNode;
while (tcx.Basin.bottomNode.HasNext && tcx.Basin.bottomNode.Point.Y >= tcx.Basin.bottomNode.Next.Point.Y) tcx.Basin.bottomNode = tcx.Basin.bottomNode.Next;
if (tcx.Basin.bottomNode == tcx.Basin.leftNode) return; // No valid basin
tcx.Basin.rightNode = tcx.Basin.bottomNode;
while (tcx.Basin.rightNode.HasNext && tcx.Basin.rightNode.Point.Y < tcx.Basin.rightNode.Next.Point.Y) tcx.Basin.rightNode = tcx.Basin.rightNode.Next;
if (tcx.Basin.rightNode == tcx.Basin.bottomNode) return; // No valid basins
tcx.Basin.width = tcx.Basin.rightNode.Point.X - tcx.Basin.leftNode.Point.X;
tcx.Basin.leftHighest = tcx.Basin.leftNode.Point.Y > tcx.Basin.rightNode.Point.Y;
FillBasinReq(tcx, tcx.Basin.bottomNode);
}
/// <summary>
/// Fills holes in the Advancing Front
/// </summary>
private static void FillAdvancingFront( DTSweepContext tcx, AdvancingFrontNode n )
{
AdvancingFrontNode node;
double angle;
// Fill right holes
node = n.Next;
while (node.HasNext) {
angle = HoleAngle(node);
if (angle > PiDiv2 || angle < -PiDiv2) break;
Fill(tcx, node);
node = node.Next;
}
// Fill left holes
node = n.Prev;
while (node.HasPrev) {
angle = HoleAngle(node);
if (angle > PiDiv2 || angle < -PiDiv2) break;
Fill(tcx, node);
node = node.Prev;
}
// Fill right basins
if (n.HasNext && n.Next.HasNext) {
angle = BasinAngle(n);
if (angle < PI_3div4) FillBasin(tcx, n);
}
}
/// <summary>
/// Adds a triangle to the advancing front to fill a hole.
/// </summary>
/// <param name="tcx"></param>
/// <param name="node">middle node, that is the bottom of the hole</param>
private static void Fill( DTSweepContext tcx, AdvancingFrontNode node )
{
DelaunayTriangle triangle = new DelaunayTriangle(node.Prev.Point, node.Point, node.Next.Point);
// TODO: should copy the cEdge value from neighbor triangles
// for now cEdge values are copied during the legalize
triangle.MarkNeighbor(node.Prev.Triangle);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
// Update the advancing front
node.Prev.Next = node.Next;
node.Next.Prev = node.Prev;
tcx.RemoveNode(node);
// If it was legalized the triangle has already been mapped
if (!Legalize(tcx, triangle)) tcx.MapTriangleToNodes(triangle);
}
private AdvancingFrontNode LocateNode( double x )
{
AdvancingFrontNode node = FindSearchNode(x);
if (x < node.Value) {
while ((node = node.Prev) != null)
if (x >= node.Value) {
Search = node;
return node;
}
} else {
while ((node = node.Next) != null)
if (x < node.Value) {
Search = node.Prev;
return node.Prev;
}
}
return null;
}
private static void FillRightBelowEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
if (tcx.IsDebugEnabled) tcx.DTDebugContext.ActiveNode = node;
if (node.Point.X < edge.P.X) { // needed?
if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW) {
// Concave
FillRightConcaveEdgeEvent(tcx, edge, node);
} else {
// Convex
FillRightConvexEdgeEvent(tcx, edge, node);
// Retry this one
FillRightBelowEdgeEvent(tcx, edge, node);
}
}
}
private static void FillRightConvexEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
{
// Next concave or convex?
if (TriangulationUtil.Orient2d(node.Next.Point, node.Next.Next.Point, node.Next.Next.Next.Point) == Orientation.CCW) {
// Concave
FillRightConcaveEdgeEvent(tcx, edge, node.Next);
} else {
// Convex
// Next above or below edge?
if (TriangulationUtil.Orient2d(edge.Q, node.Next.Next.Point, edge.P) == Orientation.CCW) {
// Below
FillRightConvexEdgeEvent(tcx, edge, node.Next);
} else {
// Above
}
}
}
/// <summary>
/// This implementation will use simple node traversal algorithm to find a point on the front
/// </summary>
public AdvancingFrontNode LocatePoint( TriangulationPoint point )
{
double px = point.X;
AdvancingFrontNode node = FindSearchNode(px);
double nx = node.Point.X;
if (px == nx) {
if (point != node.Point) {
// We might have two nodes with same x value for a short time
if (point == node.Prev.Point) {
node = node.Prev;
} else if (point == node.Next.Point) {
node = node.Next;
} else {
throw new Exception("Failed to find Node for given afront point");
}
}
} else if (px < nx) {
while ((node = node.Prev) != null) if (point == node.Point) break;
} else {
while ((node = node.Next) != null) if (point == node.Point) break;
}
Search = node;
return node;
}
/// <summary>
/// The basin angle is decided against the horizontal line [1,0]
/// </summary>
private static double BasinAngle( AdvancingFrontNode node )
{
double ax = node.Point.X - node.Next.Next.Point.X;
double ay = node.Point.Y - node.Next.Next.Point.Y;
return Math.Atan2(ay, ax);
}