//
// Returns the exact transversal between the intersections
//
public Segment AcquireTransversal(Intersection thatInter)
{
// The two intersections should not be at the same vertex
if (intersect.Equals(thatInter.intersect))
{
return(null);
}
Segment common = CommonSegment(thatInter);
if (common == null)
{
return(null);
}
// A legitimate transversal must belong to both intersections (is a subsegment of one of the lines)
Segment transversal = new Segment(this.intersect, thatInter.intersect);
Segment thisTransversal = this.GetCollinearSegment(transversal);
Segment thatTransversal = thatInter.GetCollinearSegment(transversal);
if (!thisTransversal.HasSubSegment(transversal))
{
return(null);
}
if (!thatTransversal.HasSubSegment(transversal))
{
return(null);
}
return(transversal);
}
//
// Returns the exact transversal between the intersections
//
public Segment AcquireTransversal(Intersection thatInter)
{
// The two intersections should not be at the same vertex
if (intersect.Equals(thatInter.intersect)) return null;
Segment common = CommonSegment(thatInter);
if (common == null) return null;
// A legitimate transversal must belong to both intersections (is a subsegment of one of the lines)
Segment transversal = new Segment(this.intersect, thatInter.intersect);
Segment thisTransversal = this.GetCollinearSegment(transversal);
Segment thatTransversal = thatInter.GetCollinearSegment(transversal);
if (!thisTransversal.HasSubSegment(transversal)) return null;
if (!thatTransversal.HasSubSegment(transversal)) return null;
return transversal;
}
// leftTop rightTop
// | |
// offleft ____|_________|_____ offRight
// | |
// | |
// leftBottom rightBottom
//
private static List<EdgeAggregator> GenerateDualCrossings(Parallel parallel, Intersection crossingInterLeft, Intersection crossingInterRight)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = crossingInterLeft.AcquireTransversal(crossingInterRight);
//
// Find offLeft and offRight
//
Segment crossingLeftParallel = crossingInterLeft.OtherSegment(transversal);
Segment crossingRightParallel = crossingInterRight.OtherSegment(transversal);
//
// Determine which points are on the same side of the transversal.
//
Segment testingCrossSegment = new Segment(crossingLeftParallel.Point1, crossingRightParallel.Point1);
Point intersection = transversal.FindIntersection(testingCrossSegment);
Point leftTop = crossingLeftParallel.Point1;
Point leftBottom = crossingLeftParallel.Point2;
Point rightTop = null;
Point rightBottom = null;
if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
rightTop = crossingRightParallel.Point2;
rightBottom = crossingRightParallel.Point1;
}
else
{
rightTop = crossingRightParallel.Point1;
rightBottom = crossingRightParallel.Point2;
}
// Point that is outside of the parallel lines and transversal
Segment leftTransversal = crossingInterLeft.GetCollinearSegment(transversal);
Segment rightTransversal = crossingInterRight.GetCollinearSegment(transversal);
Point offLeft = Segment.Between(crossingInterLeft.intersect, leftTransversal.Point1, crossingInterRight.intersect) ? leftTransversal.Point1 : leftTransversal.Point2;
Point offRight = Segment.Between(crossingInterRight.intersect, crossingInterLeft.intersect, rightTransversal.Point1) ? rightTransversal.Point1 : rightTransversal.Point2;
//
// Generate the new congruences
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(leftTop, crossingInterLeft.intersect, crossingInterRight.intersect),
new Angle(rightBottom, crossingInterRight.intersect, crossingInterLeft.intersect));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(rightTop, crossingInterRight.intersect, crossingInterLeft.intersect),
new Angle(leftBottom, crossingInterLeft.intersect, crossingInterRight.intersect));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, crossingInterLeft, crossingInterRight);
}
//
// Take the angle congruence and bisector and create the AngleBisector relation
// \
// \
// B ---------V---------A
// \
// \
// C
//
private static List<EdgeAggregator> InstantiateToDef(Point intersectionPoint, Intersection inter, CongruentSegments cs)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Does the given point of intersection apply to this actual intersection object
if (!intersectionPoint.Equals(inter.intersect)) return newGrounded;
// The entire segment AB
Segment overallSegment = new Segment(cs.cs1.OtherPoint(intersectionPoint), cs.cs2.OtherPoint(intersectionPoint));
// The segment must align completely with one of the intersection segments
Segment interCollinearSegment = inter.GetCollinearSegment(overallSegment);
if (interCollinearSegment == null) return newGrounded;
// Does this intersection have the entire segment AB
if (!inter.HasSegment(overallSegment)) return newGrounded;
Segment bisector = inter.OtherSegment(overallSegment);
Segment bisectedSegment = inter.GetCollinearSegment(overallSegment);
// Check if the bisected segment extends is the exact same segment as the overall segment AB
if (!bisectedSegment.StructurallyEquals(overallSegment))
{
if (overallSegment.PointLiesOnAndBetweenEndpoints(bisectedSegment.Point1) &&
overallSegment.PointLiesOnAndBetweenEndpoints(bisectedSegment.Point2)) return newGrounded;
}
SegmentBisector newSB = new SegmentBisector(inter, bisector);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(cs);
newGrounded.Add(new EdgeAggregator(antecedent, newSB, annotation));
return newGrounded;
}
// Corresponding angles if:
//
// left _____________ right
// | |
// | |
// off1 off2
//
// Inter 1 Inter 2
//
private static List<EdgeAggregator> InstantiatePiIntersection(Parallel parallel, Intersection inter1, Point off1, Intersection inter2, Point off2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = inter1.AcquireTransversal(inter2);
Segment nonParallel1 = inter1.GetCollinearSegment(transversal);
Segment nonParallel2 = inter2.GetCollinearSegment(transversal);
Point left = Segment.Between(inter1.intersect, nonParallel1.Point1, inter2.intersect) ? nonParallel1.Point1 : nonParallel1.Point2;
Point right = Segment.Between(inter2.intersect, inter1.intersect, nonParallel2.Point1) ? nonParallel2.Point1 : nonParallel2.Point2;
//
// Generate the new congruences
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
// CTA: Hack to avoid an exception being thrown during testing.
try
{
GeometricCongruentAngles gca1 = new GeometricCongruentAngles(new Angle(left, inter1.intersect, off1),
new Angle(inter1.intersect, inter2.intersect, off2));
newAngleRelations.Add(gca1);
GeometricCongruentAngles gca2 = new GeometricCongruentAngles(new Angle(right, inter2.intersect, off2),
new Angle(inter2.intersect, inter1.intersect, off1));
newAngleRelations.Add(gca2);
}
catch (Exception)
{
return newGrounded;
}
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Creates a Topped F-Shape
// top
// offLeft __________ offEnd <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
// bottom
//
// Returns: <bottom, off>
public KeyValuePair <Intersection, Point> CreatesToppedFShape(Intersection thatInter)
{
KeyValuePair <Intersection, Point> nullPair = new KeyValuePair <Intersection, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Avoid both standing on an endpoint OR crossing
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint())
{
return(nullPair);
}
if (this.Crossing() || thatInter.Crossing())
{
return(nullPair);
}
Segment transversal = this.AcquireTransversal(thatInter);
Intersection standsOnTop = null;
Intersection standsOnBottom = null;
// Top has 2 points on the transversal; bottom has 3
Segment nonTransversalThis = this.OtherSegment(transversal);
Segment nonTransversalThat = thatInter.OtherSegment(transversal);
if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThis.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThis.Point2))
{
// |
// ____| <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point2))
{
return(nullPair);
}
standsOnBottom = this;
standsOnTop = thatInter;
}
else if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point2))
{
standsOnBottom = this;
standsOnTop = thatInter;
}
else
{
return(nullPair);
}
// Check that the bottom extends the transversal
if (!standsOnBottom.GetCollinearSegment(transversal).HasStrictSubSegment(transversal))
{
return(nullPair);
}
Point off = standsOnBottom.OtherSegment(transversal).OtherPoint(standsOnBottom.intersect);
return(new KeyValuePair <Intersection, Point>(standsOnBottom, off));
}