//
// Implements transitivity with equations
// Congruent(Triangle(A, B, C), Triangle(D, E, F)), Congruent(Triangle(L, M, N), Triangle(D, E, F)) -> Congruent(Triangle(A, B, C), Triangle(L, M, N))
//
// This includes CongruentSegments and CongruentAngles
//
// Generation of new equations is restricted to the following rules; let G be Geometric and A algebriac
// G + G -> A
// G + A -> A
// A + A -X> A <- Not allowed
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.TRANSITIVE_CONGRUENT_TRIANGLES;
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is GeometricCongruentTriangles)
{
GeometricCongruentTriangles newGCTS = clause as GeometricCongruentTriangles;
if (newGCTS.IsReflexive())
{
return(newGrounded);
}
foreach (GeometricCongruentTriangles oldGCTS in candidateGeoCongruentTriangles)
{
newGrounded.AddRange(InstantiateTransitive(oldGCTS, newGCTS));
}
foreach (AlgebraicCongruentTriangles oldACTS in candidateAlgCongruentTriangles)
{
newGrounded.AddRange(InstantiateTransitive(oldACTS, newGCTS));
}
candidateGeoCongruentTriangles.Add(newGCTS);
}
else if (clause is AlgebraicCongruentTriangles)
{
AlgebraicCongruentTriangles newACTS = clause as AlgebraicCongruentTriangles;
if (newACTS.IsReflexive())
{
return(newGrounded);
}
foreach (GeometricCongruentTriangles oldGCTS in candidateGeoCongruentTriangles)
{
newGrounded.AddRange(InstantiateTransitive(oldGCTS, newACTS));
}
candidateAlgCongruentTriangles.Add(newACTS);
}
return(newGrounded);
}
public static List <EdgeAggregator> InstantiateTransitive(CongruentTriangles cts1, CongruentTriangles cts2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
Dictionary <Point, Point> firstTriangleCorrespondence = cts1.HasTriangle(cts2.ct1);
Dictionary <Point, Point> secondTriangleCorrespondence = cts1.HasTriangle(cts2.ct2);
// Same Congruence
if (firstTriangleCorrespondence != null && secondTriangleCorrespondence != null)
{
return(newGrounded);
}
// No relationship between congruences
if (firstTriangleCorrespondence == null && secondTriangleCorrespondence == null)
{
return(newGrounded);
}
// Acquiring the triangle that links the congruences
Triangle linkTriangle = firstTriangleCorrespondence != null ? cts2.ct1 : cts2.ct2;
List <Point> linkPts = linkTriangle.points;
Dictionary <Point, Point> otherCorrGCTSpts = cts1.OtherTriangle(linkTriangle);
Dictionary <Point, Point> otherCorrCTSpts = cts2.OtherTriangle(linkTriangle);
// Link the other triangles together in a new congruence
Dictionary <Point, Point> newCorrespondence = new Dictionary <Point, Point>();
foreach (Point linkPt in linkPts)
{
Point otherGpt;
if (!otherCorrGCTSpts.TryGetValue(linkPt, out otherGpt))
{
throw new ArgumentException("Something strange happened in Triangle correspondence.");
}
Point otherCpt;
if (!otherCorrCTSpts.TryGetValue(linkPt, out otherCpt))
{
throw new ArgumentException("Something strange happened in Triangle correspondence.");
}
newCorrespondence.Add(otherGpt, otherCpt);
}
List <Point> triOne = new List <Point>();
List <Point> triTwo = new List <Point>();
foreach (KeyValuePair <Point, Point> pair in newCorrespondence)
{
triOne.Add(pair.Key);
triTwo.Add(pair.Value);
}
//
// Create the new congruence
//
AlgebraicCongruentTriangles acts = new AlgebraicCongruentTriangles(new Triangle(triOne), new Triangle(triTwo));
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(cts1);
antecedent.Add(cts2);
newGrounded.Add(new EdgeAggregator(antecedent, acts, annotation));
return(newGrounded);
}
