public PointFr?Intersection(LineSegmentFr that)
{
if (StartPoint.Equals(that.EndPoint))
{
return(StartPoint);
}
if (EndPoint.Equals(that.StartPoint))
{
return(EndPoint);
}
if (StartPoint.Equals(that.StartPoint))
{
return(Line.Slope.Equals(that.Line.Slope) ? (PointFr?)null : StartPoint);
}
if (EndPoint.Equals(that.EndPoint))
{
return(Line.Slope.Equals(that.Line.Slope) ? (PointFr?)null : EndPoint);
}
var p = Line.Intersection(that.Line);
if (p == null || !Contains((PointFr)p) || !that.Contains((PointFr)p))
{
return(null);
}
return(p);
}
} // test bada współliniowość, a nie czy punkt jest zawarty w odcinku
public static Fraction PointFrOrientationTest(PointFr point, LineSegmentFr segment)
{
var p0 = point;
var p1 = segment.StartPoint;
var p2 = segment.EndPoint;
return((p1.X - p0.X) * (p2.Y - p0.Y) - (p1.Y - p0.Y) * (p2.X - p0.X));
}
public List <PointFr> Intersections(LineSegmentFr segment)
{
return
(Edges(true)
.Select(segment.Intersection)
.Where(intersection => intersection != null)
.Select(intersection => (PointFr)intersection).ToList());
}
public PointFr Center()
{
var segment = new LineSegmentFr(StartPoint, EndPoint, true);
var dX = segment.EndPoint.X - segment.StartPoint.X;
var dY = segment.EndPoint.Y - segment.StartPoint.Y;
return(new PointFr(segment.StartPoint.X + dX / 2, segment.StartPoint.Y + dY / 2));
}
public static bool IsInsideConvexPolygon(PointFr point, PolygonFr polygon)
{
var vertices = polygon.Vertices.ToList(); // wierzchołki posortowane przeciwnie do wskazówek zegara względem wnętrza wielokąta
var edges = polygon.Edges().ToList();
if (vertices.Count < 3)
{
throw new ArgumentException("Polygon can't have less than 3 vertices");
}
if (ConvexHullJarvis(vertices).Count != vertices.Count) // Powinno wystarczyć Count
{
throw new ArgumentException("Polygon must be convex");
}
if (vertices.Count == 3)
{
return(!edges.Any(point.IsRightOf));
}
var polyCenter = polygon.Center;
if (polyCenter == null)
{
throw new Exception("Can't calculate center of the Polygon");
}
var mid = (PointFr)polyCenter;
while (edges.Count > 1)
{
var testSegment = new LineSegmentFr(mid, edges[edges.Count / 2].StartPoint);
if (point.IsRightOf(testSegment))
{
edges = edges.Take(edges.Count / 2).ToList();
}
else if (point.IsLeftOf(testSegment))
{
edges = edges.Skip(edges.Count / 2).ToList();
}
else if (testSegment.Contains(point))
{
return(true);
}
else
{
throw new Exception("Invalid calculations performed, it should never happen");
}
}
return(!point.IsRightOf(edges.Single())); // czyli IsLeftOf + Contains, jeżeli jest we wierzchołku to będzie spełniony ostatni warunek z while'a
}
public bool IntersectsStrict(LineSegmentFr that) // nie uwzględnia stykających się wierzchołków
{
if (!Intersects(that))
{
return(false);
}
return(!Contains(that.StartPoint) && !Contains(that.EndPoint) &&
!that.Contains(StartPoint) && !that.Contains(EndPoint));
//var pn = Line.Intersection(that.Line);
//if (pn == null) return false;
//var p = (PointFr) pn;
//return
// Line.Contains(p)
// && (MinX == MaxX ? p.X >= MinX : p.X > MinX)
// && (MinX == MaxX ? p.X <= MaxX : p.X < MaxX)
// && (MinY == MaxY ? p.Y >= MinY : p.Y > MinY)
// && (MinY == MaxY ? p.Y <= MaxY : p.Y < MaxY)
// && that.Line.Contains(p)
// && (that.MinX == that.MaxX ? p.X >= that.MinX : p.X > that.MinX)
// && (that.MinX == that.MaxX ? p.X <= that.MaxX : p.X < that.MaxX)
// && (that.MinY == that.MaxY ? p.Y >= that.MinY : p.Y > that.MinY)
// && (that.MinY == that.MaxY ? p.Y <= that.MaxY : p.Y < that.MaxY);
}
private static List <LineSegmentFr> MergeTriangulationDnQ(List <LineSegmentFr> leftTri, List <LineSegmentFr> rightTri)
{
var leftPoints = leftTri.SelectMany(p => p.EndPoints()).OrderBy(p => p.Y).ThenByDescending(p => p.X).Distinct().ToList();
var rightPoints = rightTri.SelectMany(p => p.EndPoints()).OrderBy(p => p.Y).ThenBy(p => p.X).Distinct().ToList();
var triangulation = leftTri.Concat(rightTri).ToList();
var baseLREdge = new LineSegmentFr(leftPoints.First(), rightPoints.First(), true);
var allPoints = leftPoints.Concat(rightPoints).ToList();
while (allPoints.Any(p => p.IsRightOf(baseLREdge)))
{
var newBaseLREdgeC1 = new LineSegmentFr(baseLREdge.StartPoint, allPoints.First(p => p.IsRightOf(baseLREdge)), true);
var newBaseLREdgeC2 = new LineSegmentFr(baseLREdge.EndPoint, allPoints.First(p => p.IsRightOf(baseLREdge)), true);
if (baseLREdge.StartPoint.Y < baseLREdge.EndPoint.Y)
{
baseLREdge = triangulation.Contains(newBaseLREdgeC1) ? newBaseLREdgeC2 : newBaseLREdgeC1;
}
else
{
baseLREdge = triangulation.Contains(newBaseLREdgeC2) ? newBaseLREdgeC1 : newBaseLREdgeC2;
}
}
triangulation.Add(baseLREdge);
PointFr?rightCandidate;
PointFr?leftCandidate;
do
{
rightCandidate = null;
leftCandidate = null;
var rightCandidates = AngularSortDescending(rightPoints, baseLREdge.EndPoint, false, baseLREdge.StartPoint);
for (var i = 0; i < rightCandidates.Count; i++)
{
var rc = rightCandidates[i];
if (rc.IsRightOf(baseLREdge))
{
break;
}
if (i + 1 >= rightCandidates.Count ||
!new TriangleFr(baseLREdge.StartPoint, baseLREdge.EndPoint, rc).ContainsInCircumcircle(
rightCandidates[i + 1]))
{
if (rightTri.Any(s => s.IntersectsStrict(new LineSegmentFr(baseLREdge.StartPoint, rc, true))))
{
continue;
}
rightCandidate = rc;
break;
}
rightTri.RemoveAll(s => s == new LineSegmentFr(baseLREdge.EndPoint, rc, true));
triangulation.RemoveAll(s => s == new LineSegmentFr(baseLREdge.EndPoint, rc, true));
}
var leftCandidates = AngularSort(leftPoints, baseLREdge.StartPoint, false, baseLREdge.EndPoint);
for (var i = 0; i < leftCandidates.Count; i++)
{
var lc = leftCandidates[i];
if (lc.IsRightOf(baseLREdge))
{
break;
}
if (i + 1 >= leftCandidates.Count ||
!new TriangleFr(baseLREdge.StartPoint, baseLREdge.EndPoint, lc).ContainsInCircumcircle(
leftCandidates[i + 1]))
{
if (leftTri.Any(s => s.IntersectsStrict(new LineSegmentFr(baseLREdge.EndPoint, lc, true))))
{
continue;
}
leftCandidate = lc;
break;
}
leftTri.RemoveAll(s => s == new LineSegmentFr(baseLREdge.StartPoint, lc, true));
triangulation.RemoveAll(s => s == new LineSegmentFr(baseLREdge.StartPoint, lc, true));
}
if (leftCandidate != null && rightCandidate != null)
{
if (new TriangleFr(baseLREdge.StartPoint, baseLREdge.EndPoint, (PointFr)rightCandidate)
.ContainsInCircumcircle((PointFr)leftCandidate))
{
triangulation.Add(new LineSegmentFr(baseLREdge.EndPoint, (PointFr)leftCandidate, true));
}
else if (
new TriangleFr(baseLREdge.StartPoint, baseLREdge.EndPoint, (PointFr)leftCandidate)
.ContainsInCircumcircle((PointFr)rightCandidate))
{
triangulation.Add(new LineSegmentFr(baseLREdge.StartPoint, (PointFr)rightCandidate, true));
}
else // cztery punkty leżą na jednym okręgu
{
triangulation.Add(new LineSegmentFr(baseLREdge.EndPoint, (PointFr)leftCandidate, true));
}
}
else if (leftCandidate != null)
{
triangulation.Add(new LineSegmentFr(baseLREdge.EndPoint, (PointFr)leftCandidate, true));
}
else if (rightCandidate != null)
{
triangulation.Add(new LineSegmentFr(baseLREdge.StartPoint, (PointFr)rightCandidate, true));
}
baseLREdge = triangulation.Last();
}while (leftCandidate != null || rightCandidate != null);
return(triangulation);
}
public bool Intersects(LineSegmentFr segment)
{
return(Intersections(segment).Any());
}
public bool IsLeftOf(LineSegmentFr segment)
{
return(PointFrOrientationTest(this, segment) > 0);
}
public bool IsRightOf(LineSegmentFr segment)
{
return(PointFrOrientationTest(this, segment) < 0);
}
public bool isShorterThan(LineSegmentFr that)
{
return(LengthSquared() < that.LengthSquared());
}
public bool IsLongerThan(LineSegmentFr that)
{
return(LengthSquared() > that.LengthSquared());
}
public bool IsEqualLength(LineSegmentFr that)
{
return(LengthSquared().Equals(that.LengthSquared()));
}
public bool Intersects(LineSegmentFr that)
{
return(Intersection(that) != null);
}
public bool Intersects(LineSegmentFr that)
{
return(that.Intersects(this));
}
public PointFr?Intersection(LineSegmentFr segment)
{
return(segment.Intersection(this));
}