public override bool Equals(Object obj)
{
GeometricParallel gp = obj as GeometricParallel;
if (gp == null)
{
return(false);
}
return(base.Equals(obj));
}
private static List<EdgeAggregator> InstantiateToTheorem(Trapezoid trapezoid, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// If median has not been checked, check now
if (!trapezoid.IsMedianChecked()) trapezoid.FindMedian();
// Generate only if the median is valid (exists in the original figure)
if (!trapezoid.IsMedianValid()) return newGrounded;
GeometricParallel newParallel1 = new GeometricParallel(trapezoid.median, trapezoid.oppBaseSegment);
GeometricParallel newParallel2 = new GeometricParallel(trapezoid.median, trapezoid.baseSegment);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, newParallel1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, newParallel2, annotation));
return newGrounded;
}
private static List<EdgeAggregator> CheckAndGenerateCorrespondingAnglesImplyParallel(Intersection inter1, Intersection inter2, CongruentAngles conAngles)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The two intersections should not be at the same vertex
if (inter1.intersect.Equals(inter2.intersect)) return newGrounded;
Segment transversal = inter1.CommonSegment(inter2);
if (transversal == null) return newGrounded;
Angle angleI = inter1.GetInducedNonStraightAngle(conAngles);
Angle angleJ = inter2.GetInducedNonStraightAngle(conAngles);
//
// Do we have valid intersections and congruent angle pairs
//
if (angleI == null || angleJ == null) return newGrounded;
//
// Check to see if they are, in fact, Corresponding Angles
//
Segment parallelCand1 = inter1.OtherSegment(transversal);
Segment parallelCand2 = inter2.OtherSegment(transversal);
// The resultant candidate parallel segments shouldn't share any vertices
if (parallelCand1.SharedVertex(parallelCand2) != null) return newGrounded;
// Numeric hack to discount any non-parallel segments
if (!parallelCand1.IsParallelWith(parallelCand2)) return newGrounded;
// A sanity check that the '4th' point does not lie on the other intersection (thus creating an obvious triangle and thus not parallel lines)
Point fourthPoint1 = parallelCand1.OtherPoint(inter1.intersect);
Point fourthPoint2 = parallelCand2.OtherPoint(inter2.intersect);
if (fourthPoint1 != null && fourthPoint2 != null)
{
if (parallelCand1.PointLiesOn(fourthPoint2) || parallelCand2.PointLiesOn(fourthPoint1)) return newGrounded;
}
// Both angles should NOT be in the interioir OR the exterioir; a combination is needed.
bool ang1Interior = angleI.OnInteriorOf(inter1, inter2);
bool ang2Interior = angleJ.OnInteriorOf(inter1, inter2);
if (ang1Interior && ang2Interior) return newGrounded;
if (!ang1Interior && !ang2Interior) return newGrounded;
//
// Are these angles on the same side of the transversal?
//
//
// Make a simple transversal from the two intersection points
Segment simpleTransversal = new Segment(inter1.intersect, inter2.intersect);
// Find the rays the lie on the transversal
Segment rayNotOnTransversalI = angleI.OtherRayEquates(simpleTransversal);
Segment rayNotOnTransversalJ = angleJ.OtherRayEquates(simpleTransversal);
Point pointNotOnTransversalNorVertexI = rayNotOnTransversalI.OtherPoint(angleI.GetVertex());
Point pointNotOnTransversalNorVertexJ = rayNotOnTransversalJ.OtherPoint(angleJ.GetVertex());
// Create a segment from these two points so we can compare distances
Segment crossing = new Segment(pointNotOnTransversalNorVertexI, pointNotOnTransversalNorVertexJ);
//
// Will this crossing segment actually intersect the real transversal in the middle of the two segments It should NOT.
//
Point intersection = transversal.FindIntersection(crossing);
if (Segment.Between(intersection, inter1.intersect, inter2.intersect)) return newGrounded;
//
// Now we have an alternate interior scenario
//
GeometricParallel newParallel = new GeometricParallel(parallelCand1, parallelCand2);
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter1);
antecedent.Add(inter2);
antecedent.Add(conAngles);
newGrounded.Add(new EdgeAggregator(antecedent, newParallel, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateFromTrapezoid(Trapezoid trapezoid, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine the parallel opposing sides and output that.
//
GeometricParallel newParallel = new GeometricParallel(trapezoid.baseSegment, trapezoid.oppBaseSegment);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, newParallel, annotation));
return newGrounded;
}
private static List<EdgeAggregator> CheckAndGenerateSameSideInteriorImplyParallel(Intersection inter1, Intersection inter2, Supplementary supp)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Get the transversal (shared segment), if it exists
Segment transversal = inter1.AcquireTransversal(inter2);
if (transversal == null) return newGrounded;
Angle angleI = inter1.GetInducedNonStraightAngle(supp);
Angle angleJ = inter2.GetInducedNonStraightAngle(supp);
//
// Do we have valid intersections and congruent angle pairs
//
if (angleI == null || angleJ == null) return newGrounded;
//
// Check to see if they are, in fact, alternate interior angles respectively
//
// Are the angles within the interior
Segment parallelCand1 = inter1.OtherSegment(transversal);
Segment parallelCand2 = inter2.OtherSegment(transversal);
if (!angleI.OnInteriorOf(inter1, inter2) || !angleJ.OnInteriorOf(inter1, inter2)) return newGrounded;
//
// Are these angles on the opposite side of the transversal?
//
// Make a simple transversal from the two intersection points
Segment simpleTransversal = new Segment(inter1.intersect, inter2.intersect);
// Find the rays the lie on the transversal
Segment rayNotOnTransversalI = angleI.OtherRayEquates(simpleTransversal);
Segment rayNotOnTransversalJ = angleJ.OtherRayEquates(simpleTransversal);
Point pointNotOnTransversalNorVertexI = rayNotOnTransversalI.OtherPoint(angleI.GetVertex());
Point pointNotOnTransversalNorVertexJ = rayNotOnTransversalJ.OtherPoint(angleJ.GetVertex());
// Create a segment from these two points so we can compare distances
Segment crossing = new Segment(pointNotOnTransversalNorVertexI, pointNotOnTransversalNorVertexJ);
//
// Will this crossing segment intersect the real transversal in the middle of the two segments? If it DOES NOT, it is same side
//
Point intersection = transversal.FindIntersection(crossing);
if (Segment.Between(intersection, inter1.intersect, inter2.intersect)) return newGrounded;
//
// Now we have an alternate interior scenario
//
GeometricParallel newParallel = new GeometricParallel(parallelCand1, parallelCand2);
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter1);
antecedent.Add(inter2);
antecedent.Add(supp);
newGrounded.Add(new EdgeAggregator(antecedent, newParallel, annotation));
return newGrounded;
}
