PerimeterEdge ShortcutTwoListElements(PerimeterEdge a)
{
var b = a.Next;
Debug.Assert(a.End == b.Start);
var t = new CdtTriangle(a.Start, a.End, b.End, a.Edge, b.Edge,
createEdgeDelegate);
Triangles.Insert(t);
var newEdge = t.Edges[2];
Debug.Assert(newEdge.IsAdjacent(a.Start) && newEdge.IsAdjacent(b.End));
LegalizeEdge(a.Start, t.OppositeEdge(a.Start));
t = newEdge.CcwTriangle ?? newEdge.CwTriangle;
LegalizeEdge(b.End, t.OppositeEdge(b.End));
var c = new PerimeterEdge(newEdge)
{
Start = a.Start, End = b.End
};
a.Prev.Next = c;
c.Prev = a.Prev;
c.Next = b.Next;
b.Next.Prev = c;
return(c);
}
static bool CheckTriangle(CdtTriangle t)
{
if (Point.GetTriangleOrientationWithNoEpsilon(t.Sites[0].Point, t.Sites[1].Point, t.Sites[2].Point) != TriangleOrientation.Counterclockwise)
{
return(false);
}
for (int i = 0; i < 3; i++)
{
var e = t.Edges[i];
var a = t.Sites[i];
var b = t.Sites[i + 1];
if (!e.IsAdjacent(a) || !e.IsAdjacent(b))
{
return(false);
}
if (e.upperSite == a)
{
if (e.CcwTriangle != t)
{
return(false);
}
}
else if (e.CwTriangle != t)
{
return(false);
}
}
return(true);
}
internal static bool EdgeIsPierced(CdtEdge e, Point source, Point target, CdtTriangle cdtTriangle)
{
var area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, source, target);
var area1 = Point.SignedDoubledTriangleArea(e.lowerSite.Point, source, target);
if (ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) > 0)
{
return(false);
}
area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, source);
area1 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, target);
if (ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) > 0)
{
return(false);
}
var otherT = e.GetOtherTriangle(cdtTriangle);
if (otherT == null)
{
return(true);
}
var otherSite = otherT.OppositeSite(e);
area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, otherSite.Point);
return(ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) >= 0);
}
void TriangulatePolygon(int start, int end, List <CdtSite> polygon, CdtSite a, CdtSite b, bool reverseTrangleWhenCompare)
{
// if(CdtSweeper.db)
// CdtSweeper.ShowFront(triangles,front, Enumerable.Range(start, end-start+1).Select(i=> new Ellipse(10,10,polygon[i].Point)).ToArray(), new[]{new LineSegment(a.Point,b.Point)});
var c = polygon[start];
int cIndex = start;
for (int i = start + 1; i <= end; i++)
{
var v = polygon[i];
if (LocalInCircle(v, a, b, c, reverseTrangleWhenCompare))
{
cIndex = i;
c = v;
}
}
var t = new CdtTriangle(a, b, c, createEdgeDelegate);
triangles.Insert(t);
addedTriangles.Add(t);
if (start < cIndex)
{
TriangulatePolygon(start, cIndex - 1, polygon, a, c, reverseTrangleWhenCompare);
}
if (cIndex < end)
{
TriangulatePolygon(cIndex + 1, end, polygon, c, b, reverseTrangleWhenCompare);
}
}
static bool PointBelongsToInteriorOfTriangle(Point point, CdtTriangle cdtTriangle) {
for (int i = 0; i < 3; i++)
if (Point.GetTriangleOrientation(cdtTriangle.Sites[i].Point, cdtTriangle.Sites[i + 1].Point,
point) != TriangleOrientation.Counterclockwise)
return false;
return true;
}
private bool GetCenterOfDescribedCircle(CdtTriangle triangle, out Point x)
{
var p0 = (triangle.Sites[0].Point + triangle.Sites[1].Point) / 2;
var p1 = p0 + (triangle.Sites[0].Point - triangle.Sites[1].Point).Rotate(-Math.PI/2);
var p2 = (triangle.Sites[1].Point + triangle.Sites[2].Point) / 2;
var p3 = p0 + (triangle.Sites[1].Point - triangle.Sites[2].Point).Rotate(-Math.PI/2);
return Point.LineLineIntersection(p0, p1, p2, p3, out x);
}
static bool SeparatedByEdge(CdtTriangle triangle, int i, CdtSite site)
{
var e = triangle.Edges[i];
var s = triangle.Sites[i + 2];
var a0 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(s.Point, e.upperSite.Point, e.lowerSite.Point));
var a1 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(site.Point, e.upperSite.Point, e.lowerSite.Point));
return(a0 * a1 <= 0);
}
static bool SeparatedByConstrainedEdge(CdtTriangle triangle, CdtSite site)
{
for (int i = 0; i < 3; i++)
{
if (SeparatedByEdge(triangle, i, site))
{
return(true);
}
}
return(false);
}
internal CdtSweeper(List<CdtSite> listOfSites, CdtSite p_1, CdtSite p_2,
Func<CdtSite, CdtSite, CdtEdge> createEdgeDelegate) {
this.listOfSites=listOfSites;
var firstTriangle=new CdtTriangle(p_1, p_2, listOfSites[0], createEdgeDelegate);
Triangles.Insert( firstTriangle );
front.Insert(new CdtFrontElement(p_1, firstTriangle.Edges[2] ));
front.Insert(new CdtFrontElement(listOfSites[0], firstTriangle.Edges[1]));
this.p_1 = p_1;
this.p_2 = p_2;
this.createEdgeDelegate = createEdgeDelegate;
//ShowFront();
}
internal static PointLocation PointLocationForTriangle(Point p, CdtTriangle triangle) {
bool seenBoundary = false;
for (int i = 0; i < 3; i++) {
var area = Point.SignedDoubledTriangleArea(p, triangle.Sites[i].Point, triangle.Sites[i + 1].Point);
if (area < -ApproximateComparer.DistanceEpsilon)
return PointLocation.Outside;
if (area < ApproximateComparer.DistanceEpsilon)
seenBoundary = true;
}
return seenBoundary ? PointLocation.Boundary : PointLocation.Inside;
}
IEnumerable <CdtEdge> ThreadThroughTriangles(Point start, Point end, CdtTriangle triangle, CdtEdge piercedEdge)
{
var ret = new List <CdtEdge>();
do
{
if (piercedEdge.upperSite.Owner != piercedEdge.lowerSite.Owner)
{
ret.Add(piercedEdge);
}
}while (FindNextPierced(start, end, ref triangle, ref piercedEdge));
return(ret);
}
// /// <summary>
// /// returns CdtEdges crossed by the segment a.Point, b.Point
// /// </summary>
// /// <param name="prevA">if prevA is not a null, that means the path is passing through prevA and might need to include
// /// the edge containing a.Point if such exists</param>
// /// <param name="a"></param>
// /// <param name="b"></param>
// /// <returns></returns>
// internal IEnumerable<CdtEdge> GetCdtEdgesCrossedBySegment(PolylinePoint prevA, PolylinePoint a, PolylinePoint b) {
// count++;
// if (dd) {
// var l = new List<DebugCurve> {
// new DebugCurve("red", new Ellipse(5, 5, a.Point)),
// new DebugCurve("blue", new Ellipse(5, 5, b.Point)),
// new DebugCurve("blue", new LineSegment(a.Point, b.Point))
// };
//
// l.AddRange(
// GetTriangles().Select(
// tr => new DebugCurve(100, 1, "green", new Polyline(tr.Sites.Select(v => v.Point)) {Closed = true})));
// LayoutAlgorithmSettings.ShowDebugCurvesEnumeration(l);
//
// }
// var ret = new List<CdtEdge>();
// CdtEdge piercedEdge;
// CdtTriangle t = GetFirstTriangleAndPiercedEdge(a, b, out piercedEdge);
// if (ProperCrossing(a, b, piercedEdge))
// ret.Add(piercedEdge);
//
// ret.AddRange(ContinueThreadingThroughTriangles(a,b,t, piercedEdge));
//
// return ret;
// }
/*
* static bool ProperCrossing(Point a, Point b, CdtEdge cdtEdge) {
* return cdtEdge != null && cdtEdge.upperSite.Owner != cdtEdge.lowerSite.Owner &&
* CrossEdgeInterior(cdtEdge, a, b);
* }
*/
// static int count;
// static bool db { get { return count == 125; }}
/*
* static CdtEdge GetPiercedEdge(Point a, Point b, CdtTriangle triangle) {
* Debug.Assert(!triangle.Sites.Any(s=>ApproximateComparer.Close(a, s.Point)));
* var a0 = Point.GetTriangleOrientation(a, triangle.Sites[0].Point, triangle.Sites[1].Point);
* if (a0 == TriangleOrientation.Clockwise)return null;
*
* var a1 = Point.GetTriangleOrientation(a,triangle.Sites[1].Point, triangle.Sites[2].Point);
* if (a1 == TriangleOrientation.Clockwise)return null;
*
* var a2 = Point.GetTriangleOrientation(a,triangle.Sites[2].Point, triangle.Sites[3].Point);
* if (a2 == TriangleOrientation.Clockwise)return null;
*
* if (a0 == TriangleOrientation.Counterclockwise &&
* Point.GetTriangleOrientation(b, triangle.Sites[0].Point, triangle.Sites[1].Point) == TriangleOrientation.Clockwise)
* return triangle.Edges[0];
* if (a1 == TriangleOrientation.Counterclockwise &&
* Point.GetTriangleOrientation(b, triangle.Sites[1].Point, triangle.Sites[2].Point) == TriangleOrientation.Clockwise)
* return triangle.Edges[1];
* if (a2 == TriangleOrientation.Counterclockwise &&
* Point.GetTriangleOrientation(b, triangle.Sites[2].Point, triangle.Sites[3].Point) == TriangleOrientation.Clockwise)
* return triangle.Edges[2];
*
* return null;
* }
*/
/*
* static bool CheckIntersectionStartingFromSide(int i, CdtTriangle triangle, Point a, Point b) {
* var edgeDir = triangle.Sites[i + 1].Point - triangle.Sites[i].Point;
* var edgePerp = edgeDir.Rotate90Ccw();
* return ((b - a)*edgePerp)*((triangle.Sites[i + 2].Point - a)*edgePerp) > 0;
* }
*/
internal static bool PointIsInsideOfTriangle(Point point, CdtTriangle t)
{
for (int i = 0; i < 3; i++)
{
var a = t.Sites[i].Point;
var b = t.Sites[i + 1].Point;
if (Point.SignedDoubledTriangleArea(point, a, b) < -ApproximateComparer.DistanceEpsilon)
{
return(false);
}
}
return(true);
}
/// <summary>
/// returns null iff the edge overlap an obstacle
/// </summary>
Dictionary<Polyline, Tuple<Point, Point>> FindCloseObstaclesForBundle(CdtTriangle startTriangle, Point start,
Point end, Set<Polyline> obstaclesToIgnore,
double upperBound) {
var obstacles = new Dictionary<Polyline, Tuple<Point, Point>>();
List<CdtTriangle> list;
if (!ThreadLineSegmentThroughTriangles(startTriangle, start, end, obstaclesToIgnore, out list))
return null;
if (!ComputeForcesForBundles && !bundlingSettings.HighestQuality)
return obstacles;
var checkedSites = new HashSet<CdtSite>();
foreach (var t in list) {
foreach (var s in t.Sites) {
if (!checkedSites.Add(s)) continue;
var poly = (Polyline) s.Owner;
if (obstaclesToIgnore.Contains(poly)) continue;
PolylinePoint pp = FindPolylinePoint(poly, s.Point);
double par11, par12, par21, par22;
double d12 = LineSegment.MinDistBetweenLineSegments(pp.Point, pp.NextOnPolyline.Point, start, end,
out par11, out par12);
double d22 = LineSegment.MinDistBetweenLineSegments(pp.Point, pp.PrevOnPolyline.Point, start, end,
out par21, out par22);
Point r1, r2;
double dist;
if (d12 < d22) {
dist = d12;
if (dist > upperBound) continue;
r1 = pp.Point + (pp.NextOnPolyline.Point - pp.Point)*par11;
r2 = start + (end - start)*par12;
}
else {
dist = d22;
if (dist > upperBound) continue;
r1 = pp.Point + (pp.PrevOnPolyline.Point - pp.Point)*par21;
r2 = start + (end - start)*par22;
}
//if (dist > upperBound) continue;
Tuple<Point, Point> currentValue;
if (!obstacles.TryGetValue(poly, out currentValue))
obstacles.Add(poly, new Tuple<Point, Point>(r1, r2));
}
}
return obstacles;
}
internal CdtSweeper(List <CdtSite> listOfSites, CdtSite p_1, CdtSite p_2,
Func <CdtSite, CdtSite, CdtEdge> createEdgeDelegate)
{
this.listOfSites = listOfSites;
var firstTriangle = new CdtTriangle(p_1, p_2, listOfSites[0], createEdgeDelegate);
Triangles.Insert(firstTriangle);
front.Insert(new CdtFrontElement(p_1, firstTriangle.Edges[2]));
front.Insert(new CdtFrontElement(listOfSites[0], firstTriangle.Edges[1]));
this.p_1 = p_1;
this.p_2 = p_2;
this.createEdgeDelegate = createEdgeDelegate;
//ShowFront();
}
void AddVoronoiCite(CdtTriangle triangle)
{
Point p;
var goodTriangle = GetCenterOfDescribedCircle(triangle, out p);
if (!goodTriangle)
return;
if (!BoundingBox.Contains(p))
return;
var rect=new Rectangle(p);
rect.Pad(eps);
if (voronoiSiteTree.GetAllIntersecting(rect).Count() > 0)
return;
voronoiSiteTree.Add(rect, p);
}
void RemovePiercedTriangle(CdtTriangle t)
{
triangles.Remove(t);
foreach (var e in t.Edges)
{
if (e.CwTriangle == t)
{
e.CwTriangle = null;
}
else
{
e.CcwTriangle = null;
}
}
removedTriangles.Add(t);
}
static void ShowFlip(CdtSite pi, CdtTriangle t, CdtTriangle ot)
{
List <DebugCurve> ls = new List <DebugCurve>();
ls.Add(new DebugCurve(new Ellipse(2, 2, pi.Point)));
for (int i = 0; i < 3; i++)
{
var e = t.Edges[i];
ls.Add(new DebugCurve(100, 1, "red", new LineSegment(e.upperSite.Point, e.lowerSite.Point)));
}
for (int i = 0; i < 3; i++)
{
var e = ot.Edges[i];
ls.Add(new DebugCurve(100, 1, "blue", new LineSegment(e.upperSite.Point, e.lowerSite.Point)));
}
ls.Add(new DebugCurve(Circumcircle(t.Sites[0].Point, t.Sites[1].Point, t.Sites[2].Point)));
LayoutAlgorithmSettings.ShowDebugCurvesEnumeration(ls);
}
internal static void RemoveTriangleWithEdges(Set <CdtTriangle> cdtTriangles, CdtTriangle t)
{
cdtTriangles.Remove(t);
foreach (var e in t.Edges)
{
if (e.CwTriangle == t)
{
e.CwTriangle = null;
}
else
{
e.CcwTriangle = null;
}
if (e.CwTriangle == null && e.CcwTriangle == null)
{
e.upperSite.Edges.Remove(e);
}
}
}
void TestTriangle(CdtTriangle triangle, Set <CdtSite> usedSites)
{
var tsites = triangle.Sites;
foreach (var site in usedSites)
{
if (!tsites.Contains(site))
{
if (!SeparatedByConstrainedEdge(triangle, site) && InCircle(site, tsites[0], tsites[1], tsites[2]))
{
List <ICurve> redCurves = new List <ICurve>();
redCurves.Add(new Ellipse(2, 2, site.Point));
List <ICurve> blueCurves = new List <ICurve>();
blueCurves.Add(Circumcircle(tsites[0].Point, tsites[1].Point, tsites[2].Point));
ShowFront(Triangles, front, redCurves, blueCurves);
}
}
}
}
void FindPiercedTriangle(RBNode <CdtFrontElement> v)
{
var e = v.Item.Edge;
var t = e.CcwTriangle ?? e.CwTriangle;
var eIndex = t.Edges.Index(e);
for (int i = 1; i <= 2; i++)
{
var ei = t.Edges[i + eIndex];
var signedArea0 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(ei.lowerSite.Point, a.Point, b.Point));
var signedArea1 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(ei.upperSite.Point, a.Point, b.Point));
if (signedArea1 * signedArea0 <= 0)
{
piercedTriangle = t;
piercedEdge = ei;
break;
}
}
}
void Init()
{
// if (CdtSweeper.D)
// CdtSweeper.ShowFront(triangles, front, new[] {new LineSegment(a.Point, b.Point)},null);
//new[] {new LineSegment(piercedEdge.upperSite.Point, piercedEdge.lowerSite.Point)});
var frontElemNodeRightOfA = CdtSweeper.FindNodeInFrontBySite(front, a);
var frontElemNodeLeftOfA = front.Previous(frontElemNodeRightOfA);
if (Point.PointToTheLeftOfLine(b.Point, frontElemNodeLeftOfA.Item.LeftSite.Point, frontElemNodeLeftOfA.Item.RightSite.Point))
{
piercedToTheLeftFrontElemNode = frontElemNodeLeftOfA;
}
else if (Point.PointToTheRightOfLine(b.Point, frontElemNodeRightOfA.Item.RightSite.Point, frontElemNodeRightOfA.Item.LeftSite.Point))
{
piercedToTheRightFrontElemNode = frontElemNodeRightOfA;
}
else
{
foreach (var e in a.Edges)
{
var t = e.CcwTriangle;
if (t == null)
{
continue;
}
if (Point.PointToTheLeftOfLine(b.Point, e.lowerSite.Point, e.upperSite.Point))
{
continue;
}
var eIndex = t.Edges.Index(e);
var site = t.Sites[eIndex + 2];
if (Point.PointToTheLeftOfLineOrOnLine(b.Point, site.Point, e.upperSite.Point))
{
piercedEdge = t.Edges[eIndex + 1];
piercedTriangle = t;
// CdtSweeper.ShowFront(triangles, front, new[] { new LineSegment(e.upperSite.Point, e.lowerSite.Point) },
// new[] { new LineSegment(piercedEdge.upperSite.Point, piercedEdge.lowerSite.Point) });
break;
}
}
}
}
void TriangulatePolygon(int start, int end, List<CdtSite> polygon, CdtSite a, CdtSite b, bool reverseTrangleWhenCompare) {
// if(CdtSweeper.db)
// CdtSweeper.ShowFront(triangles,front, Enumerable.Range(start, end-start+1).Select(i=> new Ellipse(10,10,polygon[i].Point)).ToArray(), new[]{new LineSegment(a.Point,b.Point)});
var c = polygon[start];
int cIndex = start;
for (int i = start + 1; i <= end; i++) {
var v = polygon[i];
if (LocalInCircle(v, a, b, c, reverseTrangleWhenCompare)) {
cIndex = i;
c = v;
}
}
var t = new CdtTriangle(a, b, c, createEdgeDelegate);
triangles.Insert(t);
addedTriangles.Add(t);
if (start < cIndex)
TriangulatePolygon(start, cIndex - 1, polygon, a, c, reverseTrangleWhenCompare);
if (cIndex < end)
TriangulatePolygon(cIndex + 1, end, polygon, c, b, reverseTrangleWhenCompare);
}
/// <summary>
/// aNode is to the left of bNode, and they are consecutive
/// </summary>
/// <param name="aNode"></param>
/// <param name="bNode"></param>
RBNode <CdtFrontElement> ShortcutTwoFrontElements(RBNode <CdtFrontElement> aNode, RBNode <CdtFrontElement> bNode)
{
var aElem = aNode.Item;
var bElem = bNode.Item;
Debug.Assert(aElem.RightSite == bElem.LeftSite);
CdtTriangle t = new CdtTriangle(aElem.LeftSite, aElem.RightSite, bElem.RightSite, aElem.Edge, bElem.Edge,
createEdgeDelegate);
Triangles.Insert(t);
front.DeleteNodeInternal(aNode);
//now bNode might b not valid anymore
front.Remove(bElem);
var newEdge = t.Edges[2];
Debug.Assert(newEdge.IsAdjacent(aElem.LeftSite) && newEdge.IsAdjacent(bElem.RightSite));
LegalizeEdge(aElem.LeftSite, t.OppositeEdge(aElem.LeftSite));
t = newEdge.CcwTriangle ?? newEdge.CwTriangle;
LegalizeEdge(bElem.RightSite, t.OppositeEdge(bElem.RightSite));
return(front.Insert(new CdtFrontElement(aElem.LeftSite, newEdge)));
}
bool FindNextPierced(Point start, Point end, ref CdtTriangle t, ref CdtEdge piercedEdge)
{
t = piercedEdge.GetOtherTriangle(t);
if (t == null)
{
return(false);
}
var i = t.Edges.Index(piercedEdge);
for (int j = i + 1; j <= i + 2; j++)
{
var pe = t.Edges[j];
piercedEdge = PiercedEdgeQuery(pe, start, end, t);
if (piercedEdge != null)
{
// CdtSweeper.ShowFront(trs, null,
// new []{new LineSegment(e.SourcePoint,e.TargetPoint)}, new []{new LineSegment(pe.upperSite.Point,pe.lowerSite.Point)});
break;
}
}
return(!PointIsInsideOfTriangle(end, t));
}
void PrepareNextStateAfterPiercedEdge()
{
var t = piercedEdge.CwTriangle ?? piercedEdge.CcwTriangle;
var eIndex = t.Edges.Index(piercedEdge);
for (int i = 1; i <= 2; i++)
{
var e = t.Edges[i + eIndex];
var signedArea0 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(e.lowerSite.Point, a.Point, b.Point));
var signedArea1 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(e.upperSite.Point, a.Point, b.Point));
if (signedArea1 * signedArea0 <= 0)
{
if (e.CwTriangle != null && e.CcwTriangle != null)
{
piercedTriangle = t;
piercedEdge = e;
break;
}
//e has to belong to the front, and its triangle has to be removed
piercedTriangle = null;
piercedEdge = null;
var leftSite = e.upperSite.Point.X < e.lowerSite.Point.X ? e.upperSite : e.lowerSite;
var frontElem = CdtSweeper.FindNodeInFrontBySite(front, leftSite);
Debug.Assert(frontElem != null);
if (leftSite.Point.X < a.Point.X)
{
piercedToTheLeftFrontElemNode = frontElem;
}
else
{
piercedToTheRightFrontElemNode = frontElem;
}
RemovePiercedTriangle(e.CwTriangle ?? e.CcwTriangle);
break;
}
}
}
void InsertAndLegalizeTriangle(CdtSite pi, CdtFrontElement frontElement)
{
if (Point.GetTriangleOrientationWithNoEpsilon(pi.Point, frontElement.LeftSite.Point, frontElement.RightSite.Point) != TriangleOrientation.Collinear)
{
var tr = new CdtTriangle(pi, frontElement.Edge, createEdgeDelegate);
Triangles.Insert(tr);
LegalizeEdge(pi, tr.Edges[0]);
}
else //we need to split the triangle below the element in to two triangles and legalize the old edges
//we also delete, that is forget, the frontElement.Edge
{
var e = frontElement.Edge;
e.upperSite.Edges.Remove(e);
var t = e.CcwTriangle ?? e.CwTriangle;
var oppositeSite = t.OppositeSite(e);
RemoveTriangleButLeaveEdges(triangles, t);
t = new CdtTriangle(frontElement.LeftSite, oppositeSite, pi, createEdgeDelegate);
var t1 = new CdtTriangle(frontElement.RightSite, oppositeSite, pi, createEdgeDelegate);
triangles.Insert(t);
triangles.Insert(t1);
LegalizeEdge(pi, t.OppositeEdge(pi));
LegalizeEdge(pi, t1.OppositeEdge(pi));
}
}
static bool CheckTriangle(CdtTriangle t) {
if (Point.GetTriangleOrientationWithNoEpsilon(t.Sites[0].Point, t.Sites[1].Point, t.Sites[2].Point) != TriangleOrientation.Counterclockwise) {
return false;
}
for (int i = 0; i < 3; i++) {
var e = t.Edges[i];
var a = t.Sites[i];
var b = t.Sites[i+1];
if (!e.IsAdjacent(a) || !e.IsAdjacent(b)) return false;
if (e.upperSite == a) {
if (e.CcwTriangle != t)
return false;
}
else if (e.CwTriangle != t)
return false;
}
return true;
}
CdtEdge GetPiercedEdgeInSiteTriangle(CdtTriangle t, CdtSite site, Point target)
{
var e = t.OppositeEdge(site);
return(PiercedEdgeQuery(e, site.Point, target, t));
}
void TestTriangle(CdtTriangle triangle, Set<CdtSite> usedSites) {
var tsites=triangle.Sites;
foreach (var site in usedSites) {
if (!tsites.Contains(site)) {
if (!SeparatedByConstrainedEdge(triangle, site) && InCircle(site, tsites[0], tsites[1], tsites[2])) {
List<ICurve> redCurves=new List<ICurve>();
redCurves.Add(new Ellipse(2, 2, site.Point));
List<ICurve> blueCurves = new List<ICurve>();
blueCurves.Add(Circumcircle(tsites[0].Point,tsites[1].Point,tsites[2].Point));
ShowFront(Triangles, front, redCurves, blueCurves);
}
}
}
}
bool FindNextPierced(Point start, Point end, ref CdtTriangle t, ref CdtEdge piercedEdge) {
t = piercedEdge.GetOtherTriangle(t);
if (t == null)
return false;
var i = t.Edges.Index(piercedEdge);
for (int j = i + 1; j <= i + 2; j++) {
var pe = t.Edges[j];
piercedEdge = PiercedEdgeQuery(pe, start, end, t);
if (piercedEdge != null) {
// CdtSweeper.ShowFront(trs, null,
// new []{new LineSegment(e.SourcePoint,e.TargetPoint)}, new []{new LineSegment(pe.upperSite.Point,pe.lowerSite.Point)});
break;
}
}
return !PointIsInsideOfTriangle(end, t);
}
static bool SeparatedByConstrainedEdge(CdtTriangle triangle, CdtSite site) {
for (int i = 0; i < 3; i++)
if (SeparatedByEdge(triangle, i, site))
return true;
return false;
}
static internal HitTestBehavior Test(Point pnt, CdtTriangle t) {
return Cdt.PointIsInsideOfTriangle(pnt, t) ? HitTestBehavior.Stop : HitTestBehavior.Continue;
}
static bool SeparatedByEdge(CdtTriangle triangle, int i, CdtSite site) {
var e = triangle.Edges[i];
var s = triangle.Sites[i+2];
var a0 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(s.Point, e.upperSite.Point, e.lowerSite.Point));
var a1 = ApproximateComparer.Sign(Point.SignedDoubledTriangleArea(site.Point, e.upperSite.Point, e.lowerSite.Point));
return a0 * a1 <= 0;
}
void InsertAndLegalizeTriangle(CdtSite pi, CdtFrontElement frontElement) {
if (Point.GetTriangleOrientationWithNoEpsilon(pi.Point, frontElement.LeftSite.Point, frontElement.RightSite.Point) != TriangleOrientation.Collinear) {
var tr = new CdtTriangle(pi, frontElement.Edge, createEdgeDelegate);
Triangles.Insert(tr);
LegalizeEdge(pi, tr.Edges[0]);
} else { //we need to split the triangle below the element in to two triangles and legalize the old edges
//we also delete, that is forget, the frontElement.Edge
var e = frontElement.Edge;
e.upperSite.Edges.Remove(e);
var t=e.CcwTriangle??e.CwTriangle;
var oppositeSite = t.OppositeSite(e);
RemoveTriangleButLeaveEdges(triangles, t);
t=new CdtTriangle(frontElement.LeftSite, oppositeSite, pi, createEdgeDelegate);
var t1 = new CdtTriangle(frontElement.RightSite, oppositeSite, pi, createEdgeDelegate);
triangles.Insert(t);
triangles.Insert(t1);
LegalizeEdge(pi, t.OppositeEdge(pi));
LegalizeEdge(pi,t1.OppositeEdge(pi));
}
}
/// <summary>
/// aNode is to the left of bNode, and they are consecutive
/// </summary>
/// <param name="aNode"></param>
/// <param name="bNode"></param>
RBNode<CdtFrontElement> ShortcutTwoFrontElements(RBNode<CdtFrontElement> aNode, RBNode<CdtFrontElement> bNode) {
var aElem = aNode.Item;
var bElem = bNode.Item;
Debug.Assert(aElem.RightSite == bElem.LeftSite);
CdtTriangle t = new CdtTriangle(aElem.LeftSite, aElem.RightSite, bElem.RightSite, aElem.Edge, bElem.Edge,
createEdgeDelegate);
Triangles.Insert(t);
front.DeleteNodeInternal(aNode);
//now bNode might b not valid anymore
front.Remove(bElem);
var newEdge = t.Edges[2];
Debug.Assert(newEdge.IsAdjacent( aElem.LeftSite) && newEdge.IsAdjacent(bElem.RightSite));
LegalizeEdge(aElem.LeftSite, t.OppositeEdge(aElem.LeftSite));
t=newEdge.CcwTriangle ?? newEdge.CwTriangle;
LegalizeEdge(bElem.RightSite, t.OppositeEdge(bElem.RightSite));
return front.Insert(new CdtFrontElement(aElem.LeftSite, newEdge));
}
PerimeterEdge ShortcutTwoListElements(PerimeterEdge a) {
var b = a.Next;
Debug.Assert(a.End == b.Start);
var t = new CdtTriangle(a.Start, a.End, b.End, a.Edge, b.Edge,
createEdgeDelegate);
Triangles.Insert(t);
var newEdge = t.Edges[2];
Debug.Assert(newEdge.IsAdjacent(a.Start) && newEdge.IsAdjacent(b.End));
LegalizeEdge(a.Start, t.OppositeEdge(a.Start));
t = newEdge.CcwTriangle ?? newEdge.CwTriangle;
LegalizeEdge(b.End, t.OppositeEdge(b.End));
var c = new PerimeterEdge(newEdge) { Start = a.Start, End = b.End };
a.Prev.Next = c;
c.Prev = a.Prev;
c.Next = b.Next;
b.Next.Prev = c;
return c;
}
private void AddTriangleToCanvas(CdtTriangle t) {
var color = new System.Windows.Media.Color();
color.A = 100;
color.B = 255;
var wpfTriangle = new Polygon {
Stroke = new SolidColorBrush(color),
StrokeEndLineCap = PenLineCap.Round,
StrokeStartLineCap = PenLineCap.Round,
StrokeLineJoin = PenLineJoin.Round,
StrokeThickness = scroller.GetScale()
};
PointCollection trianglePoints = new PointCollection();
trianglePoints.Add(ToWpfPoint( t.Sites[0].Point));
trianglePoints.Add(ToWpfPoint(t.Sites[1].Point));
trianglePoints.Add(ToWpfPoint(t.Sites[2].Point));
wpfTriangle.Points = trianglePoints;
diagram.Canvas.Children.Add(wpfTriangle);
}
internal static void RemoveTriangleButLeaveEdges(Set<CdtTriangle> cdtTriangles, CdtTriangle t) {
cdtTriangles.Remove(t);
foreach (var e in t.Edges)
if (e.CwTriangle == t)
e.CwTriangle = null;
else
e.CcwTriangle = null;
}
///<summary>
///</summary>
///<param name="triangle"></param>
///<returns></returns>
public CdtTriangle GetOtherTriangle(CdtTriangle triangle) {
return ccwTriangle == triangle ? cwTriangle : ccwTriangle;
}
internal static void RemoveTriangleWithEdges(Set<CdtTriangle> cdtTriangles, CdtTriangle t) {
cdtTriangles.Remove(t);
foreach (var e in t.Edges) {
if (e.CwTriangle == t)
e.CwTriangle = null;
else e.CcwTriangle = null;
if (e.CwTriangle == null && e.CcwTriangle == null)
e.upperSite.Edges.Remove(e);
}
}
CdtEdge GetPiercedEdgeInSiteTriangle(CdtTriangle t, CdtSite site, Point target) {
var e = t.OppositeEdge(site);
return PiercedEdgeQuery(e, site.Point, target, t);
}
CdtEdge PiercedEdgeQuery(CdtEdge e, Point source, Point target, CdtTriangle cdtTriangle) {
return EdgeIsPierced(e, source, target, cdtTriangle) ? e : null;
}
static IEnumerable<CdtTriangle> FindStartTriangle(CdtTriangle[] trs, Point p) {
foreach (CdtTriangle t in trs) {
PointLocation loc = CdtIntersections.PointLocationInsideTriangle(p, t);
if (loc != PointLocation.Outside)
yield return t;
}
}
static void AddTriangleToListOfDebugCurves(List<DebugCurve> debugCurves, CdtTriangle triangle, byte transparency,
double width, string color) {
foreach (CdtEdge cdtEdge in triangle.Edges) {
debugCurves.Add(new DebugCurve(transparency, width, color,
new LineSegment(cdtEdge.upperSite.Point, cdtEdge.lowerSite.Point)));
}
}
IEnumerable<CdtEdge> ThreadThroughTriangles(Point start, Point end, CdtTriangle triangle, CdtEdge piercedEdge) {
var ret = new List<CdtEdge>();
do {
if (piercedEdge.upperSite.Owner != piercedEdge.lowerSite.Owner)
ret.Add(piercedEdge);
}
while (FindNextPierced(start, end, ref triangle, ref piercedEdge));
return ret;
}
CdtEdge PiercedEdgeQuery(CdtEdge e, Point source, Point target, CdtTriangle cdtTriangle)
{
return(EdgeIsPierced(e, source, target, cdtTriangle) ? e : null);
}
/*
static CdtEdge GetPiercedEdge(Point a, Point b, CdtTriangle triangle) {
Debug.Assert(!triangle.Sites.Any(s=>ApproximateComparer.Close(a, s.Point)));
var a0 = Point.GetTriangleOrientation(a, triangle.Sites[0].Point, triangle.Sites[1].Point);
if (a0 == TriangleOrientation.Clockwise)return null;
var a1 = Point.GetTriangleOrientation(a,triangle.Sites[1].Point, triangle.Sites[2].Point);
if (a1 == TriangleOrientation.Clockwise)return null;
var a2 = Point.GetTriangleOrientation(a,triangle.Sites[2].Point, triangle.Sites[3].Point);
if (a2 == TriangleOrientation.Clockwise)return null;
if (a0 == TriangleOrientation.Counterclockwise &&
Point.GetTriangleOrientation(b, triangle.Sites[0].Point, triangle.Sites[1].Point) == TriangleOrientation.Clockwise)
return triangle.Edges[0];
if (a1 == TriangleOrientation.Counterclockwise &&
Point.GetTriangleOrientation(b, triangle.Sites[1].Point, triangle.Sites[2].Point) == TriangleOrientation.Clockwise)
return triangle.Edges[1];
if (a2 == TriangleOrientation.Counterclockwise &&
Point.GetTriangleOrientation(b, triangle.Sites[2].Point, triangle.Sites[3].Point) == TriangleOrientation.Clockwise)
return triangle.Edges[2];
return null;
}
*/
/*
static bool CheckIntersectionStartingFromSide(int i, CdtTriangle triangle, Point a, Point b) {
var edgeDir = triangle.Sites[i + 1].Point - triangle.Sites[i].Point;
var edgePerp = edgeDir.Rotate90Ccw();
return ((b - a)*edgePerp)*((triangle.Sites[i + 2].Point - a)*edgePerp) > 0;
}
*/
internal static bool PointIsInsideOfTriangle(Point point, CdtTriangle t) {
for (int i = 0; i < 3; i++) {
var a = t.Sites[i].Point;
var b = t.Sites[i + 1].Point;
if (Point.SignedDoubledTriangleArea(point, a, b) < -ApproximateComparer.DistanceEpsilon)
return false;
}
return true;
}
private void FillRemovedConnectedRegion(CdtTriangle t, Set<CdtTriangle> removedTriangles) {
if (removedTriangles.Contains(t))
return;
var q = new Queue<CdtTriangle>();
q.Enqueue(t);
while (q.Count > 0) {
t = q.Dequeue();
removedTriangles.Insert(t);
foreach(var e in t.Edges)
if (!e.Constrained) {
var tr = e.GetOtherTriangle(t);
if (tr!=null && !removedTriangles.Contains(tr))
q.Enqueue(tr);
}
}
}
internal static bool EdgeIsPierced(CdtEdge e, Point source, Point target, CdtTriangle cdtTriangle) {
var area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, source, target);
var area1 = Point.SignedDoubledTriangleArea(e.lowerSite.Point, source, target);
if (ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) > 0)
return false;
area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, source);
area1 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, target);
if (ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) > 0)
return false;
var otherT = e.GetOtherTriangle(cdtTriangle);
if (otherT == null)
return true;
var otherSite = otherT.OppositeSite(e);
area0 = Point.SignedDoubledTriangleArea(e.upperSite.Point, e.lowerSite.Point, otherSite.Point);
return (ApproximateComparer.Sign(area0) * ApproximateComparer.Sign(area1) >= 0);
}
internal static void RemoveTriangleButLeaveEdges(Set <CdtTriangle> cdtTriangles, CdtTriangle t)
{
cdtTriangles.Remove(t);
foreach (var e in t.Edges)
{
if (e.CwTriangle == t)
{
e.CwTriangle = null;
}
else
{
e.CcwTriangle = null;
}
}
}
static void ShowFlip(CdtSite pi, CdtTriangle t, CdtTriangle ot) {
List<DebugCurve> ls=new List<DebugCurve>();
ls.Add(new DebugCurve(new Ellipse(2,2, pi.Point)));
for(int i=0;i<3;i++) {
var e=t.Edges[i];
ls.Add(new DebugCurve(100, 1, "red", new LineSegment(e.upperSite.Point,e.lowerSite.Point)));
}
for (int i = 0; i < 3; i++)
{
var e = ot.Edges[i];
ls.Add(new DebugCurve(100, 1, "blue", new LineSegment(e.upperSite.Point, e.lowerSite.Point)));
}
ls.Add(new DebugCurve(Circumcircle(t.Sites[0].Point, t.Sites[1].Point, t.Sites[2].Point)));
LayoutAlgorithmSettings.ShowDebugCurvesEnumeration(ls);
}
static List<DebugCurve> ThreadOnTriangle(Point start, Point end, CdtTriangle t) {
var l = new List<DebugCurve> {new DebugCurve(10, "red", new LineSegment(start, end))};
AddTriangleToListOfDebugCurves(l, t, 100, 3, "brown");
var threader = new CdtThreader(t, start, end);
foreach (var triangle in threader.Triangles()) {
AddTriangleToListOfDebugCurves(l, triangle, 100, 3, "black");
// CdtSweeper.ShowFront(trs, null, new ICurve[] { new LineSegment(start, end), new Polyline(triangle.Sites.Select(s => s.Point)) { Closed = true } }, new []{new LineSegment(threader.CurrentPiercedEdge.lowerSite.Point,threader.CurrentPiercedEdge.upperSite.Point) });
}
return l;
}
