/// <summary>
/// True if the two segments intersect
/// </summary>
/// <param name="that">The other segment</param>
/// <returns></returns>
internal bool Intersects(OverlayLineSegment that)
{
//Console.WriteLine("Checking intersection of THIS segment " + this.ToString());
//Console.WriteLine("with THAT segment " + that.ToString());
// Quick check to see if the bounding box of either line segment intersects.
//if (BoundingBox.IntersectsWith(that.BoundingBox))
//{
// If the bounding boxes DO intersect, the segments themselves MAY intersect
// If the lines overlap, they do intersect
if (Overlaps(that))
return true;
// If the lines do not overlap, and the bounding box of this point
// contains the intersection point, then they DO intersect
var intersectionPoint = IntersectionPoint(that);
//Console.WriteLine("Intersection point calculated to be ({0}, {1})", IntersectionPoint.Latitude, IntersectionPoint.Longitude);
if ((intersectionPoint != null) && (GeoRect.Contains(intersectionPoint) && that.GeoRect.Contains(intersectionPoint)))
return true;
//if (IntersectionPoint.Longitude < BoundingBox.Left)
// Console.WriteLine("Intersection point is LEFT of the bounding box by {0}", BoundingBox.Left - IntersectionPoint.Longitude);
//if (IntersectionPoint.Longitude > BoundingBox.Right)
// Console.WriteLine("Intersection point is RIGHT of the bounding box by {0}", IntersectionPoint.Longitude - BoundingBox.Right);
//if (IntersectionPoint.Latitude > BoundingBox.Top)
// Console.WriteLine("Intersection point is ABOVE the bounding box by {0}", IntersectionPoint.Latitude - BoundingBox.Top);
//if (IntersectionPoint.Latitude < BoundingBox.Bottom)
// Console.WriteLine("Intersection point is BELOW the bounding box by {0}", BoundingBox.Bottom - IntersectionPoint.Latitude);
//}
// If none of the above conditions were previously met, the segments DO NOT intersect
return false;
}
public Geo IntersectionPoint(OverlayLineSegment that)
{
if (IsParallelTo(that))
{
if (IsColinearWith(that))
{
if (GeoRect.Contains(that[0])) return that[0];
if (GeoRect.Contains(that[1])) return that[1];
if (that.GeoRect.Contains(this[0])) return this[0];
if (that.GeoRect.Contains(this[1])) return this[1];
}
return null;
//throw new GeometricException(
// "OverlayLineSegment: Lines are parallel but not colinear, they do not intersect");
}
// After we pass the above tests, we know the lines represented by our segments DO intersect somewhere
// Now we will figure out exactly where.
if (IsVertical)
return new Geo(that.Y(this[0].Longitude), this[0].Longitude);
if (that.IsVertical)
return new Geo(Y(that[0].Longitude), that[0].Longitude);
//if (this.IsHorizontal)
// return new PointF(that.X(this.Points[0].Y), this.Points[0].Y);
// Algebra to solve for the x-coordinate intersection point
// set the y-coordinates equal to each other:
// this.m*x + this.b = that.m*x + that.b
// subtract that.m*x from both sides, yielding:
// (this.m - that.m)*x + this.b = that.b
// subtract this.b from both sides, yielding:
// (this.m - that.m)*x = that.b - this.b
// divide both sides by this.m - that.m, yielding:
// x = (that.b - this.b) / (this.m - that.m)
var xIntersect = (that._b - _b)/(_m - that._m);
// now that we have xIntersect, we solve for y by plugging in xIntersect into
// either one of our line equations. Arbitrarily, we'll pick the first one.
var yIntersect = Y(xIntersect);
return new Geo(yIntersect, xIntersect);
//return new PointF((float)xIntersect, (float)yIntersect);
}
/// <summary>
/// True if the two segments are parallel to each other
/// </summary>
/// <param name="that">The other segment</param>
/// <returns></returns>
internal bool IsParallelTo(OverlayLineSegment that)
{
if (IsVertical && that.IsVertical)
return true;
if (Math.Abs(_m - that._m) < 0.0001)
return true;
return false;
}
/// <summary>
/// True if the two segments are on the same line (not necessarily overlapping)
/// </summary>
/// <param name="that">The other segment</param>
/// <returns></returns>
internal bool IsColinearWith(OverlayLineSegment that)
{
if (IsVertical && that.IsVertical)
{
if (Math.Abs(_geos[0].Longitude - that._geos[0].Longitude) < 0.0001)
return true;
}
if (IsParallelTo(that))
{
if (Math.Abs(_b - that._b) < 0.0001)
return true;
}
return false;
}
/// <summary>
/// True if the two segments overlap
/// </summary>
/// <param name="that">The other segment</param>
/// <returns></returns>
internal bool Overlaps(OverlayLineSegment that)
{
// For two segments to overlap, they must first be colinear
if (IsColinearWith(that))
{
// If they are colinear, check if our bounding box contains either of the other segment's endpoints
if (GeoRect.Contains(that._geos[0]) ||
(GeoRect.Contains(that._geos[1])))
// If it does, we overlap the other segment
return true;
// If it doesn't, then check if the other segment overlaps us. This can happen if the other segment
// completely contains us, and is also longer than us. If that turns out to be the case, then one or
// both of our endpoints will be contained in the other segment's bounding box.
if (that.GeoRect.Contains(_geos[0]) ||
(that.GeoRect.Contains(_geos[1])))
// If it does, we overlap the other segment
return true;
}
return false;
}
/// <summary>
/// Takes a start location and a proposed end location, and returns a reflected end location
/// If the proposed end location is outside of the current figure, the end location is reflected
/// by the normal to the intersecting segment, and returned to the caller. If the proposed end
/// location is inside the current figure, then it is simply returned to the caller.
/// </summary>
/// <param name="startLocation">Start location for the current proposed move</param>
/// <param name="proposedEndLocation">End location for the current proposed move</param>
/// <param name="proposedCourse"> </param>
/// <returns>Actual end location that remains inside the figure, which may be reflected from the
/// proposed end location provided if the proposed end location lies outside the figure</returns>
public override Geo Reflect(Geo startLocation, Geo proposedEndLocation, out Course proposedCourse)
{
//Geo start = new Geo(StartLocation);
//Geo end = new Geo(ProposedEndLocation);
#if MATLAB_DEBUG_OUTPUT
MatlabDumpVertices();
#endif
proposedCourse = new Course(startLocation, proposedEndLocation);
if (Contains(proposedEndLocation))
return proposedEndLocation;
//start.Move(ProposedCourse.ReciprocalDegrees, 1000);
//end.Move(ProposedCourse.Degrees, 1000);
#if MATLAB_DEBUG_OUTPUT
Console.WriteLine("Course=zeros(2,2);\nCourse(1,:)=[{0} {1}];\nCourse(2,:)=[{2} {3}];",
startLocation.Longitude, startLocation.Latitude,
proposedEndLocation.Longitude, proposedEndLocation.Latitude);
#endif
var proposedCourseSegment = new OverlayLineSegment(startLocation, proposedEndLocation);
for (var i = 0; i < Segments.Count(); i++)
{
var intersect = proposedCourseSegment.IntersectionPoint(Segments[i]);
#if MATLAB_DEBUG_OUTPUT
Console.WriteLine("Intersects({0},:)=[{1} {2}];", i + 1, intersect.Longitude, intersect.Latitude);
#endif
//if (intersect == null) continue;
if (!proposedCourseSegment.Contains(intersect) || !Segments[i].Contains(intersect)) continue;
proposedCourse = proposedCourse.Reflect(Normals[i]);
var distance = startLocation.DistanceKilometers(proposedEndLocation);
var result = startLocation.Offset(Geo.KilometersToRadians(distance), proposedCourse.Radians);
return result;
}
#if MATLAB_DEBUG_OUTPUT
Console.WriteLine("figure;");
Console.WriteLine("plot(Vertices(:, 1), Vertices(:, 2), 'g-*');");
Console.WriteLine("hold on;");
Console.WriteLine("plot(Course(:, 1), Course(:, 2), 'r-o');");
Console.WriteLine("plot(Intersects(:, 1), Intersects(:, 2), 'bx');");
Console.WriteLine("legend('Area Boundary', 'Course Segment under review', 'Calculated intersection points');");
#endif
throw new GeometricException("The proposed course didn't intersect with any of the edges of the figure");
}