private ConvexPolygon2D(IReadOnlyList <CartesianPoint> vertices)
{
this.Vertices = vertices;
var edges = new LineSegment2D[vertices.Count];
for (int i = 0; i < vertices.Count; ++i)
{
edges[i] = new LineSegment2D(vertices[i], vertices[(i + 1) % vertices.Count]);
}
this.Edges = edges;
}
public PolygonPointPosition FindRelativePositionOfPoint(CartesianPoint point)
{
int edgesPassingThroughPoint = 0;
for (int i = 0; i < Vertices.Count; ++i)
{
var edge = new LineSegment2D(Vertices[i], Vertices[(i + 1) % Vertices.Count]); //TODO: Perhaps I should use the DirectedSegment2D, which is faster for the use
if (edge.FindRelativePositionOfPoint(point) == LineSegment2D.SegmentPointPosition.PointOnSegment)
{
++edgesPassingThroughPoint;
}
}
if (edgesPassingThroughPoint == 1)
{
return(PolygonPointPosition.OnEdge);
}
else if (edgesPassingThroughPoint == 2)
{
return(PolygonPointPosition.OnVertex);
}
else if (IsPointInsidePolygon(point))
{
return(PolygonPointPosition.Inside);
}
else
if (IsPointInsidePolygon(point))
{
return(PolygonPointPosition.Inside);
}
else
{
return(PolygonPointPosition.Outside);
}
//TODO: IsPointInsidePolygon(point) is undefined the point is on the boundary, so the following doesn't always work.
//if (IsPointInsidePolygon(point)) return PolygonPointPosition.Inside;
//{
// int edgesPassingThroughPoint = 0;
// for (int i = 0; i < Vertices.Count; ++i)
// {
// var edge = new LineSegment2D(Vertices[i], Vertices[(i + 1) % Vertices.Count]); //TODO: Perhaps I should use the DirectedSegment2D, which is faster for the use
// if (edge.FindRelativePositionOfPoint(point) == LineSegment2D.SegmentPointPosition.PointOnSegment)
// {
// ++edgesPassingThroughPoint;
// }
// }
// if (edgesPassingThroughPoint == 0) return PolygonPointPosition.Outside;
// else if (edgesPassingThroughPoint == 1) return PolygonPointPosition.OnEdge;
// else if (edgesPassingThroughPoint == 2) return PolygonPointPosition.OnVertex;
// else throw new Exception("This should not have happened.");
//}
}
/// <summary>
/// See <see cref="http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect"/>
/// </summary>
/// <param name="segment"></param>
/// <param name="intersectionPoint"></param>
/// <returns></returns>
public SegmentSegmentPosition IntersectionWith(LineSegment2D segment, out CartesianPoint intersectionPoint)
{
//TODO: optimize this:
// a) Cache the vector representation of "this".Perhaps there could be a private vector representation class
//b) Perhaps some cases can be ignored/lumped together.E.g. for colinear
//c) Perhaps working with the double values instead of vector structs saves a lot of accesses.
//TODO: handle extreme cases:
// a) One segment's end lies on the other segment
// b) One segment's end coincides with one of the other segment's ends, but otherwise they do not overlap
// c) These cases probably need some tolerance checks.This requires attention since intersection points
// outside the element will create unwanted triangulations.
//Create vectors p, r, q, s
var p = Vector2.Create(this.Start.X, this.Start.Y);
var r = Vector2.Create(this.End.X - this.Start.X, this.End.Y - this.Start.Y);
var q = Vector2.Create(segment.Start.X, segment.Start.Y);
var s = Vector2.Create(segment.End.X - segment.Start.X, segment.End.Y - segment.Start.Y);
// Find the cross products r x s and (q-p)*r
double rCrossS = r.CrossProduct(s);
var qMinusP = q - p;
double qMinusPCrossR = qMinusP.CrossProduct(r);
if (rCrossS == 0) // TODO: use tolerance here
{
if (qMinusPCrossR == 0) // TODO: use tolerance here
{
double rDotR = r * r;
double t0 = (qMinusP * r) / rDotR;
double t1 = t0 + (s * r) / rDotR;
LineSegment1D this1D = (new LineSegment1D(0.0, 1.0));
LineSegment1D.SegmentSegmentPosition intersection1D =
this1D.IntesectionWith(new LineSegment1D(t0, t1));
if (intersection1D == LineSegment1D.SegmentSegmentPosition.Disjoint)
{
intersectionPoint = null;
return(LineSegment2D.SegmentSegmentPosition.CollinearDisjoint);
}
else if (intersection1D == LineSegment1D.SegmentSegmentPosition.Overlapping)
{
intersectionPoint = null;
return(LineSegment2D.SegmentSegmentPosition.Overlapping);
}
else // TODO: handle this case
{
throw new NotImplementedException("The two segments are colinear and meet only at one point");
}
}
else
{
intersectionPoint = null;
return(SegmentSegmentPosition.Parallel);
}
}
else
{
double t = qMinusP.CrossProduct(s) / rCrossS;
double u = qMinusPCrossR / rCrossS;
if ((t >= 0.0) && (t <= 1.0) && (u >= 0.0) && (u <= 1.0))
{
var solution = p + t * r;
intersectionPoint = new CartesianPoint(solution[0], solution[1]);
return(SegmentSegmentPosition.Intersecting);
}
else
{
intersectionPoint = null;
return(SegmentSegmentPosition.Disjoint);
}
}
}
//Perhaps I can override the intersects method and project the other segment onto the local system!
public LineSegment2D.SegmentSegmentPosition IntersectionWith(LineSegment2D segment,
out CartesianPoint intersectionPoint)
{
return(segment.IntersectionWith(new LineSegment2D(Start, End), out intersectionPoint));
}
