public bool Intersects(OrientedLineSegment otherLineSegment)
{
if (otherLineSegment is null)
{
throw new ArgumentNullException(nameof(otherLineSegment));
}
return(Intersect(this, otherLineSegment));
}
/// <summary>
/// Returns a boolean value indicating whether the quiver is plane, i.e., whether the
/// arrows (drawn as straight lines) are pairwise non-intersecting.
/// </summary>
/// <returns>A boolean value indicating whether the quiver is plane.</returns>
public static bool IsPlane <TVertex>(this IReadOnlyUndirectedGraph <TVertex> graph) where TVertex : IEquatable <TVertex>, IVertexInPlane
{
// Remark: Deconstructing lambda arguments does not seem to be possible as of this writing. In other words,
// the following would not work:
// ... .Where( ((e1, e2)) => e1 != e2 )
foreach (var(edge1, edge2) in Utility.CartesianProduct(graph.Edges, graph.Edges).Where(p => p.Item1 != p.Item2))
{
var lineSegment1 = new OrientedLineSegment(edge1.Vertex1.Position, edge1.Vertex2.Position);
var lineSegment2 = new OrientedLineSegment(edge2.Vertex1.Position, edge2.Vertex2.Position);
if (lineSegment1.IntersectsProperly(lineSegment2))
{
return(false);
}
}
return(true);
}
/// <summary>
/// Determines whether two line segments intersect.
/// </summary>
/// <param name="lineSegment1">The first line segment.</param>
/// <param name="lineSegment2">The second line segment.</param>
/// <returns></returns>
/// <remarks>
/// <para>See <see href="https://www.cdn.geeksforgeeks.org/check-if-two-given-line-segments-intersect/"/>
/// for the inner workings of this method (details which I have not worked out myself).</para></remarks>
public static bool Intersect(OrientedLineSegment lineSegment1, OrientedLineSegment lineSegment2)
{
if (lineSegment1 is null)
{
throw new ArgumentNullException(nameof(lineSegment1));
}
if (lineSegment2 is null)
{
throw new ArgumentNullException(nameof(lineSegment2));
}
if (lineSegment1.Start == lineSegment1.End)
{
throw new NotImplementedException(); // Haven't checked that the method works in this case
}
if (lineSegment2.Start == lineSegment2.End)
{
throw new NotImplementedException(); // Haven't checked that the method works in this case
}
var ls1 = lineSegment1;
var ls2 = lineSegment2;
var o1 = PlaneUtility.GetOrientation(ls1.Start, ls1.End, ls2.Start);
var o2 = PlaneUtility.GetOrientation(ls1.Start, ls1.End, ls2.End);
var o3 = PlaneUtility.GetOrientation(ls2.Start, ls2.End, ls1.Start);
var o4 = PlaneUtility.GetOrientation(ls2.Start, ls2.End, ls1.End);
if (o1 != o2 && o3 != o4)
{
return(true);
}
if (o1 == TripletOrientation.Collinear && LineSegmentContainsPoint(ls1, ls2.Start))
{
return(true);
}
if (o2 == TripletOrientation.Collinear && LineSegmentContainsPoint(ls1, ls2.End))
{
return(true);
}
if (o3 == TripletOrientation.Collinear && LineSegmentContainsPoint(ls2, ls1.Start))
{
return(true);
}
if (o4 == TripletOrientation.Collinear && LineSegmentContainsPoint(ls2, ls1.End))
{
return(true);
}
return(false);
// Idea (obsolete in favor of the above I guess):
// Look at the common range of, say, the x-coordinates
// If empty, then return false
// If equal at either endpoint, return true (because they intersect in the endpoint)
// If the first line segment is below/above the other in one endpoint and above/below the other in the other, return true
// Else return false
// The above doesn't work when one of the lines is vertical though
// Assumes that p is on the line determined by ls (this assumes that ls is non-degenerate)
bool LineSegmentContainsPoint(OrientedLineSegment ls, Point p)
{
return(Math.Min(ls.Start.X, ls.End.X) <= p.X &&
p.X <= Math.Max(ls.Start.X, ls.End.X) &&
Math.Min(ls.Start.Y, ls.End.Y) <= p.Y &&
p.Y <= Math.Max(ls.Start.Y, ls.End.Y));
}
}
public bool IsEqualToAsUnorientedLineSegments(OrientedLineSegment otherLineSegment)
{
return(this == otherLineSegment || this == otherLineSegment.Reverse());
}
/// <summary>
/// Determines whether two line segments intersect properly, in the sense that the
/// interiors of the line segments intersect.
/// </summary>
/// <param name="lineSegment1">The first line segment.</param>
/// <param name="lineSegment2">The second line segment.</param>
/// <returns></returns>
public static bool IntersectProperly(OrientedLineSegment lineSegment1, OrientedLineSegment lineSegment2)
{
if (lineSegment1 is null)
{
throw new ArgumentNullException(nameof(lineSegment1));
}
if (lineSegment2 is null)
{
throw new ArgumentNullException(nameof(lineSegment2));
}
if (lineSegment1.Start == lineSegment1.End)
{
return(false); // The interior of a degenerate line segment is empty
}
if (lineSegment2.Start == lineSegment2.End)
{
return(false); // The interior of a degenerate line segment is empty
}
var ls1 = lineSegment1;
var ls2 = lineSegment2;
var o1 = PlaneUtility.GetOrientation(ls1.Start, ls1.End, ls2.Start);
var o2 = PlaneUtility.GetOrientation(ls1.Start, ls1.End, ls2.End);
var o3 = PlaneUtility.GetOrientation(ls2.Start, ls2.End, ls1.Start);
var o4 = PlaneUtility.GetOrientation(ls2.Start, ls2.End, ls1.End);
// The line segments are collinear
if (o1 == TripletOrientation.Collinear && o2 == TripletOrientation.Collinear)
{
return(ls1.IsEqualToAsUnorientedLineSegments(ls2) ||
LineSegmentInteriorContainsPoint(ls1, ls2.Start) ||
LineSegmentInteriorContainsPoint(ls1, ls2.End) ||
LineSegmentInteriorContainsPoint(ls2, ls1.Start) ||
LineSegmentInteriorContainsPoint(ls2, ls1.End));
}
// The line segments are not collinear, so if any three points are collinear, the line segments just "touch"
// each other, which does not constitute a proper intersection
if (o1 == TripletOrientation.Collinear || o2 == TripletOrientation.Collinear || o3 == TripletOrientation.Collinear || o4 == TripletOrientation.Collinear)
{
return(false);
}
// Then just do "the usual" check
return(o1 != o2 && o3 != o4);
// Assumes that p is on the line determined by ls (this assumes that ls is non-degenerate)
bool LineSegmentContainsPoint(OrientedLineSegment ls, Point p)
{
return(Math.Min(ls.Start.X, ls.End.X) <= p.X &&
p.X <= Math.Max(ls.Start.X, ls.End.X) &&
Math.Min(ls.Start.Y, ls.End.Y) <= p.Y &&
p.Y <= Math.Max(ls.Start.Y, ls.End.Y));
}
// Assumes that p is on the line determined by ls (this assumes that ls is non-degenerate)
bool LineSegmentInteriorContainsPoint(OrientedLineSegment ls, Point p)
{
return(LineSegmentContainsPoint(ls, p) && p != ls.Start && p != ls.End);
}
}
