public static bool InScanArea(
TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc, TriangulationPoint pd)
{
double pdx = pd.X;
double pdy = pd.Y;
double adx = pa.X - pdx;
double ady = pa.Y - pdy;
double bdx = pb.X - pdx;
double bdy = pb.Y - pdy;
double adxbdy = adx * bdy;
double bdxady = bdx * ady;
double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if (oabd <= 0)
{
return false;
}
double cdx = pc.X - pdx;
double cdy = pc.Y - pdy;
double cdxady = cdx * ady;
double adxcdy = adx * cdy;
double ocad = cdxady - adxcdy;
// ocad = orient2d(pc,pa,pd);
if (ocad <= 0)
{
return false;
}
return true;
}
public PointOnEdgeException(string message, TriangulationPoint a, TriangulationPoint b, TriangulationPoint c)
: base(message)
{
this.A = a;
this.B = b;
this.C = c;
}
/// <summary>
/// Requirements:
/// 1. a,b and c form a triangle.
/// 2. a and d is know to be on opposite side of bc
/// <code>
/// a
/// +
/// / \
/// / \
/// b/ \c
/// +-------+
/// / B \
/// / \
/// </code>
/// Facts:
/// d has to be in area B to have a chance to be inside the circle formed by a,b and c
/// d is outside B if orient2d(a,b,d) or orient2d(c,a,d) is CW
/// This preknowledge gives us a way to optimize the incircle test
/// </summary>
/// <param name="pa">triangle point, opposite d</param>
/// <param name="pb">triangle point</param>
/// <param name="pc">triangle point</param>
/// <param name="pd">point opposite a</param>
/// <returns>true if d is inside circle, false if on circle edge</returns>
public static bool SmartIncircle( TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc, TriangulationPoint pd ) {
double pdx = pd.X;
double pdy = pd.Y;
double adx = pa.X - pdx;
double ady = pa.Y - pdy;
double bdx = pb.X - pdx;
double bdy = pb.Y - pdy;
double adxbdy = adx * bdy;
double bdxady = bdx * ady;
double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if (oabd <= 0) return false;
double cdx = pc.X - pdx;
double cdy = pc.Y - pdy;
double cdxady = cdx * ady;
double adxcdy = adx * cdy;
double ocad = cdxady - adxcdy;
// ocad = orient2d(pc,pa,pd);
if (ocad <= 0) return false;
double bdxcdy = bdx * cdy;
double cdxbdy = cdx * bdy;
double alift = adx * adx + ady * ady;
double blift = bdx * bdx + bdy * bdy;
double clift = cdx * cdx + cdy * cdy;
double det = alift * (bdxcdy - cdxbdy) + blift * ocad + clift * oabd;
return det > 0;
}
/// <summary>
/// Give two points in any order. Will always be ordered so
/// that q.y > p.y and q.x > p.x if same y value
/// </summary>
public DTSweepConstraint(TriangulationPoint p1, TriangulationPoint p2)
{
this.P = p1;
this.Q = p2;
if (p1.Y > p2.Y)
{
this.Q = p1;
this.P = p2;
}
else if (p1.Y == p2.Y)
{
if (p1.X > p2.X)
{
this.Q = p1;
this.P = p2;
}
else if (p1.X == p2.X)
{
// logger.info( "Failed to create constraint {}={}", p1, p2 );
// throw new DuplicatePointException( p1 + "=" + p2 );
// return;
}
}
this.Q.AddEdge(this);
}
/// <summary>
/// Give two points in any order. Will always be ordered so
/// that q.y > p.y and q.x > p.x if same y value
/// </summary>
public DTSweepConstraint(TriangulationPoint p1, TriangulationPoint p2)
{
P = p1;
Q = p2;
if (p1.y > p2.y)
{
Q = p1;
P = p2;
}
else if (p1.y == p2.y)
{
if (p1.x > p2.x)
{
Q = p1;
P = p2;
}
else if (p1.x == p2.x)
{
// logger.info( "Failed to create constraint {}={}", p1, p2 );
// throw new DuplicatePointException( p1 + "=" + p2 );
// return;
}
}
Q.AddEdge(this);
}
public PointOnEdgeException( string message, TriangulationPoint a, TriangulationPoint b, TriangulationPoint c )
: base(message)
{
A=a;
B=b;
C=c;
}
/// Forumla to calculate signed area
/// Positive if CCW
/// Negative if CW
/// 0 if collinear
/// A[P1,P2,P3] = (x1*y2 - y1*x2) + (x2*y3 - y2*x3) + (x3*y1 - y3*x1)
/// = (x1-x3)*(y2-y3) - (y1-y3)*(x2-x3)
public static Orientation Orient2d( TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc )
{
double detleft = (pa.X - pc.X) * (pb.Y - pc.Y);
double detright = (pa.Y - pc.Y) * (pb.X - pc.X);
double val = detleft - detright;
if (val > -EPSILON && val < EPSILON) {
return Orientation.Collinear;
} else if (val > 0) {
return Orientation.CCW;
}
return Orientation.CW;
}
//TODO: Port note - different implementation
public int IndexCW(TriangulationPoint p)
{
int index = IndexOf(p);
switch (index)
{
case 0:
return 2;
case 1:
return 0;
default:
return 1;
}
}
/*
public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
TriangulationPoint pd)
{
double pdx = pd.X;
double pdy = pd.Y;
double adx = pa.X - pdx;
double ady = pa.Y - pdy;
double bdx = pb.X - pdx;
double bdy = pb.Y - pdy;
double adxbdy = adx*bdy;
double bdxady = bdx*ady;
double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if (oabd <= 0)
{
return false;
}
double cdx = pc.X - pdx;
double cdy = pc.Y - pdy;
double cdxady = cdx*ady;
double adxcdy = adx*cdy;
double ocad = cdxady - adxcdy;
// ocad = orient2d(pc,pa,pd);
if (ocad <= 0)
{
return false;
}
return true;
}
*/
public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc, TriangulationPoint pd)
{
double oadb = (pa.X - pb.X) * (pd.Y - pb.Y) - (pd.X - pb.X) * (pa.Y - pb.Y);
if (oadb >= -EPSILON)
{
return false;
}
double oadc = (pa.X - pc.X) * (pd.Y - pc.Y) - (pd.X - pc.X) * (pa.Y - pc.Y);
if (oadc <= EPSILON)
{
return false;
}
return true;
}
/// <summary>
/// We use a balancing tree to locate a node smaller or equal to given key value (in theory)
/// </summary>
public AdvancingFrontNode LocateNode(TriangulationPoint point)
{
return LocateNode(point.X);
}
/// <summary>
/// After a flip we have two triangles and know that only one will still be
/// intersecting the edge. So decide which to contiune with and legalize the other
/// </summary>
/// <param name="tcx"></param>
/// <param name="o">should be the result of an TriangulationUtil.orient2d( eq, op, ep )</param>
/// <param name="t">triangle 1</param>
/// <param name="ot">triangle 2</param>
/// <param name="p">a point shared by both triangles</param>
/// <param name="op">another point shared by both triangles</param>
/// <returns>returns the triangle still intersecting the edge</returns>
static DelaunayTriangle NextFlipTriangle(DTSweepContext tcx, Orientation o, DelaunayTriangle t, DelaunayTriangle ot, TriangulationPoint p, TriangulationPoint op)
{
int edgeIndex;
if (o == Orientation.CCW)
{
// ot is not crossing edge after flip
edgeIndex = ot.EdgeIndex(p, op);
ot.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, ot);
ot.EdgeIsDelaunay.Clear();
return(t);
}
// t is not crossing edge after flip
edgeIndex = t.EdgeIndex(p, op);
t.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, t);
t.EdgeIsDelaunay.Clear();
return(ot);
}
static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
}
if (t.GetConstrainedEdgeAcross(p))
{
throw new Exception("Intersecting Constraints");
}
bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
if (inScanArea)
{
// Lets rotate shared edge one vertex CW
RotateTrianglePair(t, p, ot, op);
tcx.MapTriangleToNodes(t);
tcx.MapTriangleToNodes(ot);
if (p == eq && op == ep)
{
if (eq == tcx.EdgeEvent.ConstrainedEdge.Q &&
ep == tcx.EdgeEvent.ConstrainedEdge.P)
{
//if (tcx.IsDebugEnabled) Console.WriteLine("[FLIP] - constrained edge done"); // TODO: remove
t.MarkConstrainedEdge(ep, eq);
ot.MarkConstrainedEdge(ep, eq);
Legalize(tcx, t);
Legalize(tcx, ot);
}
else
{
//if (tcx.IsDebugEnabled) Console.WriteLine("[FLIP] - subedge done"); // TODO: remove
// XXX: I think one of the triangles should be legalized here?
}
}
else
{
//if (tcx.IsDebugEnabled)
// Console.WriteLine("[FLIP] - flipping and continuing with triangle still crossing edge");
// TODO: remove
Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
t = NextFlipTriangle(tcx, o, t, ot, p, op);
FlipEdgeEvent(tcx, ep, eq, t, p);
}
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
/// Forumla to calculate signed area
/// Positive if CCW
/// Negative if CW
/// 0 if collinear
/// A[P1,P2,P3] = (x1*y2 - y1*x2) + (x2*y3 - y2*x3) + (x3*y1 - y3*x1)
/// = (x1-x3)*(y2-y3) - (y1-y3)*(x2-x3)
public static Orientation Orient2d(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc)
{
double detleft = (pa.X - pc.X) * (pb.Y - pc.Y);
double detright = (pa.Y - pc.Y) * (pb.X - pc.X);
double val = detleft - detright;
if (val > -EPSILON && val < EPSILON)
{
return(Orientation.Collinear);
}
else if (val > 0)
{
return(Orientation.CCW);
}
return(Orientation.CW);
}
/// <summary>
/// Creates a new front triangle and legalize it
/// </summary>
private static AdvancingFrontNode NewFrontTriangle(DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node)
{
DelaunayTriangle triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
triangle.MarkNeighbor(node.Triangle);
tcx.Triangles.Add(triangle);
AdvancingFrontNode newNode = new AdvancingFrontNode(point);
newNode.Next = node.Next;
newNode.Prev = node;
node.Next.Prev = newNode;
node.Next = newNode;
tcx.AddNode(newNode); // XXX: BST
if (!Legalize(tcx, triangle))
{
tcx.MapTriangleToNodes(triangle);
}
return newNode;
}
static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
{
if (IsEdgeSideOfTriangle(triangle, ep, eq))
{
return;
}
TriangulationPoint p1 = triangle.PointCCW(point);
Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
if (o1 == Orientation.Collinear)
{
if (triangle.Contains(eq, p1))
{
triangle.MarkConstrainedEdge(eq, p1);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p1;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p1, triangle, p1);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("EdgeEvent - Point on constrained edge");
}
return;
}
TriangulationPoint p2 = triangle.PointCW(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear)
{
if (triangle.Contains(eq, p2))
{
triangle.MarkConstrainedEdge(eq, p2);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p2;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p2, triangle, p2);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
if (tcx.IsDebugEnabled)
{
Debug.WriteLine("EdgeEvent - Point on constrained edge");
}
return;
}
if (o1 == o2)
{
// Need to decide if we are rotating CW or CCW to get to a triangle
// that will cross edge
if (o1 == Orientation.CW)
{
triangle = triangle.NeighborCCW(point);
}
else
{
triangle = triangle.NeighborCW(point);
}
EdgeEvent(tcx, ep, eq, triangle, point);
}
else
{
// This triangle crosses constraint so lets flippin start!
FlipEdgeEvent(tcx, ep, eq, triangle, point);
}
}
public bool Contains(TriangulationPoint p, TriangulationPoint q)
{
return(Contains(p) && Contains(q));
}
private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
}
if (t.GetConstrainedEdgeAcross(p))
{
throw new Exception("Intersecting Constraints");
}
bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
if (inScanArea)
{
// Lets rotate shared edge one vertex CW
RotateTrianglePair(t, p, ot, op);
tcx.MapTriangleToNodes(t);
tcx.MapTriangleToNodes(ot);
if (p == eq && op == ep)
{
if (eq == tcx.EdgeEvent.ConstrainedEdge.Q
&& ep == tcx.EdgeEvent.ConstrainedEdge.P)
{
t.MarkConstrainedEdge(ep, eq);
ot.MarkConstrainedEdge(ep, eq);
Legalize(tcx, t);
Legalize(tcx, ot);
}
else
{
// XXX: I think one of the triangles should be legalized here?
}
}
else
{
// TODO: remove
Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
t = NextFlipTriangle(tcx, o, t, ot, p, op);
FlipEdgeEvent(tcx, ep, eq, t, p);
}
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
EdgeEvent(tcx, ep, eq, t, p);
}
}
/// <summary>
/// Give two points in any order. Will always be ordered so
/// that q.y > p.y and q.x > p.x if same y value
/// </summary>
public DTSweepConstraint(TriangulationPoint p1, TriangulationPoint p2)
: base(p1, p2)
{
Q.AddEdge(this);
}
public bool Contains(TriangulationPoint p)
{
return(p == Points[0] || p == Points[1] || p == Points[2]);
}
/// <summary>
/// We use a balancing tree to locate a node smaller or equal to given key value
/// </summary>
public AdvancingFrontNode LocateNode(TriangulationPoint point)
{
return(LocateNode(point.X));
}
public AdvancingFrontNode(TriangulationPoint point)
{
Point = point;
Value = point.X;
}
/// <summary>
/// Requirements:
/// 1. a,b and c form a triangle.
/// 2. a and d is know to be on opposite side of bc
/// <code>
/// a
/// +
/// / \
/// / \
/// b/ \c
/// +-------+
/// / B \
/// / \
/// </code>
/// Facts:
/// d has to be in area B to have a chance to be inside the circle formed by a,b and c
/// d is outside B if orient2d(a,b,d) or orient2d(c,a,d) is CW
/// This preknowledge gives us a way to optimize the incircle test
/// </summary>
/// <param name="pa">triangle point, opposite d</param>
/// <param name="pb">triangle point</param>
/// <param name="pc">triangle point</param>
/// <param name="pd">point opposite a</param>
/// <returns>true if d is inside circle, false if on circle edge</returns>
public static bool SmartIncircle(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
TriangulationPoint pd)
{
double pdx = pd.X;
double pdy = pd.Y;
double adx = pa.X - pdx;
double ady = pa.Y - pdy;
double bdx = pb.X - pdx;
double bdy = pb.Y - pdy;
double adxbdy = adx * bdy;
double bdxady = bdx * ady;
double oabd = adxbdy - bdxady;
// oabd = orient2d(pa,pb,pd);
if (oabd <= 0)
{
return(false);
}
double cdx = pc.X - pdx;
double cdy = pc.Y - pdy;
double cdxady = cdx * ady;
double adxcdy = adx * cdy;
double ocad = cdxady - adxcdy;
// ocad = orient2d(pc,pa,pd);
if (ocad <= 0)
{
return(false);
}
double bdxcdy = bdx * cdy;
double cdxbdy = cdx * bdy;
double alift = adx * adx + ady * ady;
double blift = bdx * bdx + bdy * bdy;
double clift = cdx * cdx + cdy * cdy;
double det = alift * (bdxcdy - cdxbdy) + blift * ocad + clift * oabd;
return(det > 0);
}
/// <summary>
/// Rotates a triangle pair one vertex CW
/// n2 n2
/// P +-----+ P +-----+
/// | t /| |\ t |
/// | / | | \ |
/// n1| / |n3 n1| \ |n3
/// | / | after CW | \ |
/// |/ oT | | oT \|
/// +-----+ oP +-----+
/// n4 n4
/// </summary>
private static void RotateTrianglePair(DelaunayTriangle t, TriangulationPoint p, DelaunayTriangle ot, TriangulationPoint op)
{
DelaunayTriangle n1 = t.NeighborCCW(p);
DelaunayTriangle n2 = t.NeighborCW(p);
DelaunayTriangle n3 = ot.NeighborCCW(op);
DelaunayTriangle n4 = ot.NeighborCW(op);
bool ce1 = t.GetConstrainedEdgeCCW(p);
bool ce2 = t.GetConstrainedEdgeCW(p);
bool ce3 = ot.GetConstrainedEdgeCCW(op);
bool ce4 = ot.GetConstrainedEdgeCW(op);
bool de1 = t.GetDelaunayEdgeCCW(p);
bool de2 = t.GetDelaunayEdgeCW(p);
bool de3 = ot.GetDelaunayEdgeCCW(op);
bool de4 = ot.GetDelaunayEdgeCW(op);
t.Legalize(p, op);
ot.Legalize(op, p);
// Remap dEdge
ot.SetDelaunayEdgeCCW(p, de1);
t.SetDelaunayEdgeCW(p, de2);
t.SetDelaunayEdgeCCW(op, de3);
ot.SetDelaunayEdgeCW(op, de4);
// Remap cEdge
ot.SetConstrainedEdgeCCW(p, ce1);
t.SetConstrainedEdgeCW(p, ce2);
t.SetConstrainedEdgeCCW(op, ce3);
ot.SetConstrainedEdgeCW(op, ce4);
// Remap neighbors
// XXX: might optimize the markNeighbor by keeping track of
// what side should be assigned to what neighbor after the
// rotation. Now mark neighbor does lots of testing to find
// the right side.
t.Neighbors.Clear();
ot.Neighbors.Clear();
if (n1 != null) ot.MarkNeighbor(n1);
if (n2 != null) t.MarkNeighbor(n2);
if (n3 != null) t.MarkNeighbor(n3);
if (n4 != null) ot.MarkNeighbor(n4);
t.MarkNeighbor(ot);
}
static bool AngleExceedsPlus90DegreesOrIsNegative(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
{
double angle = Angle(origin, pa, pb);
bool exceedsPlus90DegreesOrIsNegative = (angle > PI_div2) || (angle < 0);
return(exceedsPlus90DegreesOrIsNegative);
}
private static bool AngleExceedsPlus90DegreesOrIsNegative(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
{
double angle = Angle(origin, pa, pb);
bool exceedsPlus90DegreesOrIsNegative = (angle > PI_div2) || (angle < 0);
return exceedsPlus90DegreesOrIsNegative;
}
public int IndexOf( TriangulationPoint p )
{
int i = points.IndexOf( p );
if( i == -1 ) throw new Exception( "Calling index with a point that doesn't exist in triangle" );
return i;
}
private static bool IsEdgeSideOfTriangle(DelaunayTriangle triangle, TriangulationPoint ep, TriangulationPoint eq)
{
int index = triangle.EdgeIndex(ep, eq);
if (index != -1)
{
triangle.MarkConstrainedEdge(index);
triangle = triangle.Neighbors[index];
if (triangle != null)
{
triangle.MarkConstrainedEdge(ep, eq);
}
return true;
}
return false;
}
static bool AngleExceeds90Degrees(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
{
double angle = Angle(origin, pa, pb);
bool exceeds90Degrees = ((angle > PI_div2) || (angle < -PI_div2));
return(exceeds90Degrees);
}
/// <summary>
/// After a flip we have two triangles and know that only one will still be
/// intersecting the edge. So decide which to contiune with and legalize the other
/// </summary>
/// <param name="tcx"></param>
/// <param name="o">should be the result of an TriangulationUtil.orient2d( eq, op, ep )</param>
/// <param name="t">triangle 1</param>
/// <param name="ot">triangle 2</param>
/// <param name="p">a point shared by both triangles</param>
/// <param name="op">another point shared by both triangles</param>
/// <returns>returns the triangle still intersecting the edge</returns>
private static DelaunayTriangle NextFlipTriangle(DTSweepContext tcx, Orientation o, DelaunayTriangle t, DelaunayTriangle ot, TriangulationPoint p, TriangulationPoint op)
{
int edgeIndex;
if (o == Orientation.CCW)
{
// ot is not crossing edge after flip
edgeIndex = ot.EdgeIndex(p, op);
ot.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, ot);
ot.EdgeIsDelaunay.Clear();
return t;
}
// t is not crossing edge after flip
edgeIndex = t.EdgeIndex(p, op);
t.EdgeIsDelaunay[edgeIndex] = true;
Legalize(tcx, t);
t.EdgeIsDelaunay.Clear();
return ot;
}
/// <summary>
/// Scan part of the FlipScan algorithm
/// When a triangle pair isn't flippable we will scan for the next
/// point that is inside the flip triangle scan area. When found
/// we generate a new flipEdgeEvent
/// </summary>
/// <param name="tcx"></param>
/// <param name="ep">last point on the edge we are traversing</param>
/// <param name="eq">first point on the edge we are traversing</param>
/// <param name="flipTriangle">the current triangle sharing the point eq with edge</param>
/// <param name="t"></param>
/// <param name="p"></param>
static void FlipScanEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle flipTriangle, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new Exception("[BUG:FIXME] FLIP failed due to missing triangle");
}
bool inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCW(eq), flipTriangle.PointCW(eq), op);
if (inScanArea)
{
// flip with new edge op->eq
FlipEdgeEvent(tcx, eq, op, ot, op);
// TODO: Actually I just figured out that it should be possible to
// improve this by getting the next ot and op before the the above
// flip and continue the flipScanEdgeEvent here
// set new ot and op here and loop back to inScanArea test
// also need to set a new flipTriangle first
// Turns out at first glance that this is somewhat complicated
// so it will have to wait.
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
}
}
/// <summary>
/// When we need to traverse from one triangle to the next we need
/// the point in current triangle that is the opposite point to the next
/// triangle.
/// </summary>
static TriangulationPoint NextFlipPoint(TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle ot, TriangulationPoint op)
{
Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
if (o2d == Orientation.CW)
{
// Right
return(ot.PointCCW(op));
}
else if (o2d == Orientation.CCW)
{
// Left
return(ot.PointCW(op));
}
else
{
// TODO: implement support for point on constraint edge
throw new PointOnEdgeException("Point on constrained edge not supported yet");
}
}
public override TriangulationConstraint NewConstraint(TriangulationPoint a, TriangulationPoint b)
{
return new DTSweepConstraint(a, b);
}
/// <param name="t">Opposite triangle</param>
/// <param name="p">The point in t that isn't shared between the triangles</param>
public TriangulationPoint OppositePoint(DelaunayTriangle t, TriangulationPoint p)
{
Debug.Assert(t != this, "self-pointer error");
return(PointCW(t.PointCW(p)));
}
/*
* public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc,
* TriangulationPoint pd)
* {
* double pdx = pd.X;
* double pdy = pd.Y;
* double adx = pa.X - pdx;
* double ady = pa.Y - pdy;
* double bdx = pb.X - pdx;
* double bdy = pb.Y - pdy;
*
* double adxbdy = adx*bdy;
* double bdxady = bdx*ady;
* double oabd = adxbdy - bdxady;
* // oabd = orient2d(pa,pb,pd);
* if (oabd <= 0)
* {
* return false;
* }
*
* double cdx = pc.X - pdx;
* double cdy = pc.Y - pdy;
*
* double cdxady = cdx*ady;
* double adxcdy = adx*cdy;
* double ocad = cdxady - adxcdy;
* // ocad = orient2d(pc,pa,pd);
* if (ocad <= 0)
* {
* return false;
* }
* return true;
* }
*/
public static bool InScanArea(TriangulationPoint pa, TriangulationPoint pb, TriangulationPoint pc, TriangulationPoint pd)
{
double oadb = (pa.X - pb.X) * (pd.Y - pb.Y) - (pd.X - pb.X) * (pa.Y - pb.Y);
if (oadb >= -EPSILON)
{
return(false);
}
double oadc = (pa.X - pc.X) * (pd.Y - pc.Y) - (pd.X - pc.X) * (pa.Y - pc.Y);
if (oadc <= EPSILON)
{
return(false);
}
return(true);
}
public DelaunayTriangle( TriangulationPoint p1, TriangulationPoint p2, TriangulationPoint p3 )
{
points[0] = p1;
points[1] = p2;
points[2] = p3;
}
public DelaunayTriangle NeighborCCW(TriangulationPoint point)
{
return(Neighbors[(Points.IndexOf(point) + 2) % 3]);
}
public DelaunayTriangle NeighborAcross(TriangulationPoint point)
{
return(Neighbors[Points.IndexOf(point)]);
}
public TriangulationPoint PointCW(TriangulationPoint point)
{
return(Points[(IndexOf(point) + 2) % 3]);
}
public void AddSteinerPoint(TriangulationPoint point)
{
if (_steinerPoints == null)
{
_steinerPoints = new List<TriangulationPoint>();
}
_steinerPoints.Add(point);
}
/// <summary>
/// Legalize triangle by rotating clockwise around oPoint
/// </summary>
/// <param name="oPoint">The origin point to rotate around</param>
/// <param name="nPoint">???</param>
public void Legalize(TriangulationPoint oPoint, TriangulationPoint nPoint)
{
RotateCW();
Points[IndexCCW(oPoint)] = nPoint;
}
private static Vector3 ConvertToVertexPosition(TriangulationPoint point, Vector3 normal, float normalComponent)
{
if (normal.X != 0 && normal.Y == 0 && normal.Z == 0)
{
return new Vector3(normalComponent, point.Yf, point.Xf);
}
if (normal.X == 0 && normal.Y != 0 && normal.Z == 0)
{
return new Vector3(point.Xf, normalComponent, point.Yf);
}
if (normal.X == 0 && normal.Y == 0 && normal.Z != 0)
{
return new Vector3(point.Xf, point.Yf, normalComponent);
}
return new Vector3(0, 0, 0);
}
public bool GetConstrainedEdgeCW(TriangulationPoint p)
{
return(EdgeIsConstrained[(IndexOf(p) + 1) % 3]);
}
public override void PrepareTriangulation(Triangulatable t)
{
base.PrepareTriangulation(t);
double xmax, xmin;
double ymax, ymin;
xmax = xmin = Points[0].x;
ymax = ymin = Points[0].y;
// Calculate bounds. Should be combined with the sorting
foreach (TriangulationPoint p in Points)
{
if (p.x > xmax)
xmax = p.x;
if (p.x < xmin)
xmin = p.x;
if (p.y > ymax)
ymax = p.y;
if (p.y < ymin)
ymin = p.y;
}
double deltaX = ALPHA*(xmax - xmin);
double deltaY = ALPHA*(ymax - ymin);
TriangulationPoint p1 = new TriangulationPoint(xmax + deltaX, ymin - deltaY);
TriangulationPoint p2 = new TriangulationPoint(xmin - deltaX, ymin - deltaY);
Head = p1;
Tail = p2;
// long time = System.nanoTime();
// Sort the points along y-axis
Points.Sort(_comparator);
// logger.info( "Triangulation setup [{}ms]", ( System.nanoTime() - time ) / 1e6 );
}
public bool GetConstrainedEdgeAcross(TriangulationPoint p)
{
return(EdgeIsConstrained[IndexOf(p)]);
}
/// <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 = this.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;
}
}
}
this.Search = node;
return node;
}
public void SetConstrainedEdgeCW(TriangulationPoint p, bool ce)
{
EdgeIsConstrained[(IndexOf(p) + 1) % 3] = ce;
}
/// <summary>
/// Find closes node to the left of the new point and
/// create a new triangle. If needed new holes and basins
/// will be filled to.
/// </summary>
private static AdvancingFrontNode PointEvent(DTSweepContext tcx, TriangulationPoint point)
{
AdvancingFrontNode node = tcx.LocateNode(point);
AdvancingFrontNode newNode = NewFrontTriangle(tcx, point, node);
// Only need to check +epsilon since point never have smaller
// x value than node due to how we fetch nodes from the front
if (point.X <= node.Point.X + TriangulationUtil.EPSILON)
{
Fill(tcx, node);
}
tcx.AddNode(newNode);
FillAdvancingFront(tcx, newNode);
return newNode;
}
public void SetConstrainedEdgeAcross(TriangulationPoint p, bool ce)
{
EdgeIsConstrained[IndexOf(p)] = ce;
}
private static bool AngleExceeds90Degrees(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
{
double angle = Angle(origin, pa, pb);
bool exceeds90Degrees = ((angle > PI_div2) || (angle < -PI_div2));
return exceeds90Degrees;
}
public bool GetDelaunayEdgeCW(TriangulationPoint p)
{
return(EdgeIsDelaunay[(IndexOf(p) + 1) % 3]);
}
private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
{
if (IsEdgeSideOfTriangle(triangle, ep, eq))
return;
TriangulationPoint p1 = triangle.PointCCW(point);
Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
if (o1 == Orientation.Collinear)
{
if (triangle.Contains(eq, p1))
{
triangle.MarkConstrainedEdge(eq, p1);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p1;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p1, triangle, p1);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
return;
}
TriangulationPoint p2 = triangle.PointCW(point);
Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
if (o2 == Orientation.Collinear)
{
if (triangle.Contains(eq, p2))
{
triangle.MarkConstrainedEdge(eq, p2);
// We are modifying the constraint maybe it would be better to
// not change the given constraint and just keep a variable for the new constraint
tcx.EdgeEvent.ConstrainedEdge.Q = p2;
triangle = triangle.NeighborAcross(point);
EdgeEvent(tcx, ep, p2, triangle, p2);
}
else
{
throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
}
return;
}
if (o1 == o2)
{
// Need to decide if we are rotating CW or CCW to get to a triangle
// that will cross edge
if (o1 == Orientation.CW)
{
triangle = triangle.NeighborCCW(point);
}
else
{
triangle = triangle.NeighborCW(point);
}
EdgeEvent(tcx, ep, eq, triangle, point);
}
else
{
// This triangle crosses constraint so lets flippin start!
FlipEdgeEvent(tcx, ep, eq, triangle, point);
}
}
public bool GetDelaunayEdgeAcross(TriangulationPoint p)
{
return(EdgeIsDelaunay[IndexOf(p)]);
}
/// <summary>
/// Scan part of the FlipScan algorithm<br>
/// When a triangle pair isn't flippable we will scan for the next
/// point that is inside the flip triangle scan area. When found
/// we generate a new flipEdgeEvent
/// </summary>
/// <param name="tcx"></param>
/// <param name="ep">last point on the edge we are traversing</param>
/// <param name="eq">first point on the edge we are traversing</param>
/// <param name="flipTriangle">the current triangle sharing the point eq with edge</param>
/// <param name="t"></param>
/// <param name="p"></param>
private static void FlipScanEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle flipTriangle, DelaunayTriangle t, TriangulationPoint p)
{
DelaunayTriangle ot = t.NeighborAcross(p);
TriangulationPoint op = ot.OppositePoint(t, p);
if (ot == null)
{
// If we want to integrate the fillEdgeEvent do it here
// With current implementation we should never get here
throw new Exception("[BUG:FIXME] FLIP failed due to missing triangle");
}
bool inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCW(eq), flipTriangle.PointCW(eq), op);
if (inScanArea)
{
// flip with new edge op->eq
FlipEdgeEvent(tcx, eq, op, ot, op);
// TODO: Actually I just figured out that it should be possible to
// improve this by getting the next ot and op before the the above
// flip and continue the flipScanEdgeEvent here
// set new ot and op here and loop back to inScanArea test
// also need to set a new flipTriangle first
// Turns out at first glance that this is somewhat complicated
// so it will have to wait.
}
else
{
TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
}
}
public void SetDelaunayEdgeCW(TriangulationPoint p, bool ce)
{
EdgeIsDelaunay[(IndexOf(p) + 1) % 3] = ce;
}
private static double Angle(TriangulationPoint origin, TriangulationPoint pa, TriangulationPoint pb)
{
/* 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 = origin.X;
double py = origin.Y;
double ax = pa.X - px;
double ay = pa.Y - py;
double bx = pb.X - px;
double by = pb.Y - py;
double x = ax * by - ay * bx;
double y = ax * bx + ay * by;
double angle = Math.Atan2(x, y);
return angle;
}
public void SetDelaunayEdgeAcross(TriangulationPoint p, bool ce)
{
EdgeIsDelaunay[IndexOf(p)] = ce;
}
/// <summary>
/// When we need to traverse from one triangle to the next we need
/// the point in current triangle that is the opposite point to the next
/// triangle.
/// </summary>
private static TriangulationPoint NextFlipPoint(TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle ot, TriangulationPoint op)
{
Orientation o2d = TriangulationUtil.Orient2d(eq, op, ep);
if (o2d == Orientation.CW)
{
// Right
return ot.PointCCW(op);
}
else if (o2d == Orientation.CCW)
{
// Left
return ot.PointCW(op);
}
else
{
// TODO: implement support for point on constraint edge
throw new PointOnEdgeException("Point on constrained edge not supported yet");
}
}
public DelaunayTriangle(TriangulationPoint p1, TriangulationPoint p2, TriangulationPoint p3)
{
Points[0] = p1;
Points[1] = p2;
Points[2] = p3;
}
public AdvancingFrontNode(TriangulationPoint point)
{
this.Point = point;
Value = point.X;
}
static bool IsEdgeSideOfTriangle(DelaunayTriangle triangle, TriangulationPoint ep, TriangulationPoint eq)
{
int index = triangle.EdgeIndex(ep, eq);
if (index != -1)
{
triangle.MarkConstrainedEdge(index);
triangle = triangle.Neighbors[index];
if (triangle != null)
{
triangle.MarkConstrainedEdge(ep, eq);
}
return(true);
}
return(false);
}
