////
//// Constructs the coverage relationship amongst all figure components
////
//private static void HandleAllFigureIntrinsicFacts(List<GroundedClause> figure)
//{
// for (int f1 = 0; f1 < figure.Count; f1++)
// {
// for (int f2 = 0; f2 < figure.Count; f2++)
// {
// if (f1 != f2)
// {
// if (figure[f1].Covers(figure[f2])) figure[f1].AddComponent(figure[f2].clauseId);
// }
// }
// }
//}
//
// Preprocess the given clauses
//
private static void HandleAllGivens(List <GroundedClause> figure, List <GroundedClause> givens)
{
////
//// Link the boolean facts to the intrinsic facts through coverage (implication)
////
//foreach (GroundedClause given in givens)
//{
// foreach (GroundedClause component in figure)
// {
// if (given.Covers(component))
// {
// given.AddComponent(component.clauseId);
// given.AddComponentList(component.figureComponents);
// }
// }
//}
//
// Are any of the givens congruent relationships?
//
foreach (GroundedClause clause in givens)
{
if (clause is CongruentTriangles)
{
CongruentTriangles conTris = clause as CongruentTriangles;
if (conTris.VerifyCongruentTriangles())
{
// indicate that these triangles are congruent to prevent future 'reproving' congruent
conTris.ProcessGivens();
}
// This is not a valid congruence.
else
{
// Remove?
}
}
//else if (clause is SimilarTriangles)
//{
// SimilarTriangles simTris = clause as SimilarTriangles;
// if (simTris.VerifyCongruentTriangles())
// {
// // indicate that these triangles are congruent to prevent future 'reproving' congruent
// simTris.ProcessGivens();
// }
// // This is not a valid similarity.
// else
// {
// // Remove?
// }
//}
}
}
//
// Acquires all of the applicable congruent segments; then checks HL
//
private static List <EdgeAggregator> CollectAndCheckHL(RightTriangle rt1, RightTriangle rt2,
CongruentSegments css1, CongruentSegments css2,
GroundedClause original1, GroundedClause original2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// The Congruence pairs must relate the two triangles
if (!css1.LinksTriangles(rt1, rt2) || !css2.LinksTriangles(rt1, rt2))
{
return(newGrounded);
}
// One of the congruence pairs must relate the hypotenuses
Segment hypotenuse1 = rt1.OtherSide(rt1.rightAngle);
Segment hypotenuse2 = rt2.OtherSide(rt2.rightAngle);
// Determine the specific congruence pair that relates the hypotenuses
CongruentSegments hypotenuseCongruence = null;
CongruentSegments nonHypotenuseCongruence = null;
if (css1.HasSegment(hypotenuse1) && css1.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css1;
nonHypotenuseCongruence = css2;
}
else if (css2.HasSegment(hypotenuse1) && css2.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css2;
nonHypotenuseCongruence = css1;
}
else
{
return(newGrounded);
}
// Sanity check that the non hypotenuse congruence pair does not contain hypotenuse
if (nonHypotenuseCongruence.HasSegment(hypotenuse1) || nonHypotenuseCongruence.HasSegment(hypotenuse2))
{
return(newGrounded);
}
//
// We now have a hypotenuse leg situation; acquire the point-to-point congruence mapping
//
List <Point> triangleOne = new List <Point>();
List <Point> triangleTwo = new List <Point>();
// Right angle vertices correspond
triangleOne.Add(rt1.rightAngle.GetVertex());
triangleTwo.Add(rt2.rightAngle.GetVertex());
Point nonRightVertexRt1 = rt1.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse1);
Point nonRightVertexRt2 = rt2.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse2);
triangleOne.Add(nonRightVertexRt1);
triangleTwo.Add(nonRightVertexRt2);
triangleOne.Add(hypotenuse1.OtherPoint(nonRightVertexRt1));
triangleTwo.Add(hypotenuse2.OtherPoint(nonRightVertexRt2));
//
// Construct the new deduced relationships
//
GeometricCongruentTriangles ccts = new GeometricCongruentTriangles(new Triangle(triangleOne),
new Triangle(triangleTwo));
// Hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(css1);
antecedent.Add(css2);
newGrounded.Add(new EdgeAggregator(antecedent, ccts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(ccts, triangleOne, triangleTwo));
return(newGrounded);
}
//
// Main instantiation function for all figures stated in the given list; worklist technique to construct the graph
//
public Hypergraph <GroundedClause, Hypergraph.EdgeAnnotation> Instantiate(List <ConcreteAST.GroundedClause> figure, List <ConcreteAST.GroundedClause> givens)
{
// The worklist initialized to initial set of ground clauses from the figure
List <GroundedClause> worklist = new List <GroundedClause>(figure);
worklist.AddRange(givens);
// Add all initial elements to the graph
figure.ForEach(g => { graph.AddNode(g); g.SetID(graph.Size()); });
givens.ForEach(g => { graph.AddNode(g); g.SetID(graph.Size()); });
// Indicate all figure-based information is intrinsic; this needs to verified with the UI
figure.ForEach(f => f.MakeIntrinsic());
// For problem generation, indicate that all given information is intrinsic
givens.ForEach(g => g.MakeGiven());
// Calculates Coverage of the figure
//HandleAllFigureIntrinsicFacts(figure);
HandleAllGivens(figure, givens);
//
// Process all new clauses until the worklist is empty
//
int numSequentialEquations = 0;
while (worklist.Any())
{
// Acquire the first element from the list for processing
GroundedClause clause = worklist[0];
worklist.RemoveAt(0);
if (Utilities.DEBUG)
{
Debug.WriteLine("Working on: " + clause.clauseId + " " + clause.ToString());
}
//
// Cutoff counter; seek a bunch of equations in sequence.
//
int NUMEQUATIONS_FOR_CUTOFF = 50;
if (clause is Equation || clause.IsAlgebraic() || clause is Supplementary)
{
numSequentialEquations++;
}
else
{
numSequentialEquations = 0;
}
if (numSequentialEquations >= NUMEQUATIONS_FOR_CUTOFF)
{
return(graph);
}
if (graph.Size() > 800)
{
return(graph);
}
//
// Apply the clause to all applicable instantiators
//
if (clause is Point)
{
Point.Record(clause);
}
else if (clause is Angle)
{
// A list of all problem angles
Angle.Record(clause);
if (clause is RightAngle)
{
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
}
HandleDeducedClauses(worklist, ExteriorAngleEqualSumRemoteAngles.Instantiate(clause));
// HandleDeducedClauses(worklist, AngleAdditionAxiom.Instantiate(clause));
//HandleDeducedClauses(worklist, ConcreteAngle.Instantiate(null, clause));
//HandleDeducedClauses(worklist, AngleBisector.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
// Circle
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, CentralAngleEqualInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, TwoInterceptedArcsHaveCongruentAngles.Instantiate(clause));
}
else if (clause is Arc)
{
Arc.Record(clause);
if (clause is Semicircle)
{
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
}
}
else if (clause is Segment)
{
HandleDeducedClauses(worklist, Segment.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
Segment.Record(clause);
}
else if (clause is InMiddle)
{
HandleDeducedClauses(worklist, SegmentAdditionAxiom.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
}
else if (clause is ArcInMiddle)
{
// HandleDeducedClauses(worklist, ArcAdditionAxiom.Instantiate(clause));
}
else if (clause is Intersection)
{
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
if (clause is PerpendicularBisector)
{
HandleDeducedClauses(worklist, PerpendicularBisectorDefinition.Instantiate(clause));
}
else if (clause is Perpendicular)
{
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
}
else
{
HandleDeducedClauses(worklist, VerticalAnglesTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, AltIntCongruentAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, SameSideSuppleAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CorrespondingAnglesOfParallelLines.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentCorrespondingAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAdjacentAnglesImplyPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplyAltIntCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplySameSideInteriorSupplementary.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, TwoChordsAnglesHalfSumInterceptedArc.Instantiate(clause));
}
}
else if (clause is Complementary)
{
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
}
else if (clause is Altitude)
{
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
}
else if (clause is AngleBisector)
{
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
}
else if (clause is Supplementary)
{
HandleDeducedClauses(worklist, SameSideSuppleAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryAndCongruentImplyRightAngles.Instantiate(clause));
}
else if (clause is SegmentRatio)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
}
else if (clause is Equation)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, SegmentRatio.InstantiateEquation(clause));
if (clause is AngleEquation)
{
HandleDeducedClauses(worklist, AnglesOfEqualMeasureAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
}
// If a geometric equation was constructed, it may not have been checked for proportionality
if ((clause as Equation).IsGeometric())
{
HandleDeducedClauses(worklist, ProportionalAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentRatio.InstantiateEquation(clause));
}
}
else if (clause is Midpoint)
{
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointTheorem.Instantiate(clause));
}
else if (clause is Collinear)
{
HandleDeducedClauses(worklist, StraightAngleDefinition.Instantiate(clause));
}
else if (clause is Median)
{
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
}
else if (clause is SegmentBisector)
{
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
}
else if (clause is Parallel)
{
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, CorrespondingAnglesOfParallelLines.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplyAltIntCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelImplySameSideInteriorSupplementary.Instantiate(clause));
// Quadrilaterals
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
}
else if (clause is SegmentRatioEquation)
{
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, SSSSimilarity.Instantiate(clause));
// HandleDeducedClauses(worklist, SegmentRatio.InstantiateProportion(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
}
else if (clause is ProportionalAngles)
{
HandleDeducedClauses(worklist, ProportionalAngles.InstantiateProportion(clause));
}
else if (clause is CongruentTriangles)
{
HandleDeducedClauses(worklist, CongruentTriangles.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveCongruentTriangles.Instantiate(clause));
}
else if (clause is CongruentAngles)
{
HandleDeducedClauses(worklist, SupplementaryAndCongruentImplyRightAngles.Instantiate(clause));
HandleDeducedClauses(worklist, TwoPairsCongruentAnglesImplyThirdPairCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, AngleAdditionAxiom.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAnglesInTriangleImplyCongruentSides.Instantiate(clause));
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AASimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AltIntCongruentAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentCorrespondingAnglesImplyParallel.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAdjacentAnglesImplyPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, RelationsOfCongruentAnglesAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SupplementaryDefinition.Instantiate(clause));
// Quadrilaterals
HandleDeducedClauses(worklist, BothPairsOppAnglesCongruentImpliesParallelogram.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, MinorArcsCongruentIfCentralAnglesCongruent.Instantiate(clause));
}
else if (clause is CongruentSegments)
{
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SSS.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentSidesInTriangleImplyCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSegmentsImplySegmentRatioDefinition.Instantiate(clause));
// For quadrilaterals
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppSidesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
// Circles
HandleDeducedClauses(worklist, CongruentCircleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentArcsHaveCongruentChords.Instantiate(clause));
}
else if (clause is Triangle)
{
Triangle.Record(clause);
//HandleDeducedClauses(worklist, SumAnglesInTriangle.Instantiate(clause));
HandleDeducedClauses(worklist, Angle.InstantiateReflexiveAngles(clause));
HandleDeducedClauses(worklist, Triangle.Instantiate(clause));
HandleDeducedClauses(worklist, SSS.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, ASA.Instantiate(clause));
HandleDeducedClauses(worklist, AAS.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleEqualSumRemoteAngles.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentAnglesInTriangleImplyCongruentSides.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSidesInTriangleImplyCongruentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SASSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, SSSSimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, AASimilarity.Instantiate(clause));
HandleDeducedClauses(worklist, TriangleProportionality.Instantiate(clause));
HandleDeducedClauses(worklist, AcuteAnglesInRightTriangleComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TwoPairsCongruentAnglesImplyThirdPairCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CongruentSegmentsImplySegmentRatioDefinition.Instantiate(clause));
if (clause is IsoscelesTriangle)
{
HandleDeducedClauses(worklist, IsoscelesTriangleTheorem.Instantiate(clause));
// CTA: Needs to worl with Equilateral Triangles as well
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
}
if (clause is EquilateralTriangle)
{
HandleDeducedClauses(worklist, EquilateralTriangleHasSixtyDegreeAngles.Instantiate(clause));
}
}
else if (clause is Quadrilateral)
{
Quadrilateral.Record(clause);
if (clause is Quadrilateral)
{
if ((clause as Quadrilateral).IsStrictQuadrilateral())
{
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppSidesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, OnePairOppSidesCongruentParallelImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, BothPairsOppAnglesCongruentImpliesParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
}
}
if (clause is Parallelogram)
{
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, OppositeSidesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, OppositeAnglesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
}
if (clause is Trapezoid)
{
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidParallelToBases.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidHalfSumBases.Instantiate(clause));
}
if (clause is IsoscelesTrapezoid)
{
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, BaseAnglesIsoscelesTrapezoidCongruent.Instantiate(clause));
}
if (clause is Rhombus)
{
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusBisectRhombusAngles.Instantiate(clause));
}
if (clause is Square)
{
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
}
if (clause is Rectangle)
{
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRectangleAreCongruent.Instantiate(clause));
}
if (clause is Kite)
{
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfKiteArePerpendicular.Instantiate(clause));
}
}
else if (clause is Strengthened)
{
HandleDeducedClauses(worklist, IsoscelesTriangleTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, AcuteAnglesInRightTriangleComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, AngleBisectorIsPerpendicularBisectorInIsosceles.Instantiate(clause));
HandleDeducedClauses(worklist, EquilateralTriangleHasSixtyDegreeAngles.Instantiate(clause));
HandleDeducedClauses(worklist, SASCongruence.Instantiate(clause));
HandleDeducedClauses(worklist, HypotenuseLeg.Instantiate(clause));
// For strengthening an intersection to a perpendicular
HandleDeducedClauses(worklist, PerpendicularImplyCongruentAdjacentAngles.Instantiate(clause));
HandleDeducedClauses(worklist, AdjacentAnglesPerpendicularImplyComplementary.Instantiate(clause));
HandleDeducedClauses(worklist, AltitudeDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, TransversalPerpendicularToParallelImplyBothPerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularBisectorDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SegmentBisectorDefinition.Instantiate(clause));
// InMiddle Strengthened to Midpoint
HandleDeducedClauses(worklist, MidpointDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, MidpointTheorem.Instantiate(clause));
HandleDeducedClauses(worklist, MedianDefinition.Instantiate(clause));
// Right Angle
HandleDeducedClauses(worklist, RightAngleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ComplementaryDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RightTriangleDefinition.Instantiate(clause));
// Correlating isoceles triangles with right triangles.
CoordinateRightIsoscelesTriangles.Instantiate(clause);
// For quadrilateral definitions
HandleDeducedClauses(worklist, TrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, IsoscelesTrapezoidDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, SquareDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, KiteDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, ParallelogramDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RectangleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, RhombusDefinition.Instantiate(clause));
// Quad Theorems
HandleDeducedClauses(worklist, OppositeSidesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, OppositeAnglesOfParallelogramAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsParallelogramBisectEachOther.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsBisectEachOtherImplyParallelogram.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRectangleAreCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfKiteArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusArePerpendicular.Instantiate(clause));
HandleDeducedClauses(worklist, DiagonalsOfRhombusBisectRhombusAngles.Instantiate(clause));
HandleDeducedClauses(worklist, BaseAnglesIsoscelesTrapezoidCongruent.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidParallelToBases.Instantiate(clause));
HandleDeducedClauses(worklist, MedianTrapezoidHalfSumBases.Instantiate(clause));
// Circle
HandleDeducedClauses(worklist, AngleInscribedSemiCircleIsRight.Instantiate(clause));
HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
}
else if (clause is CircleIntersection)
{
HandleDeducedClauses(worklist, DiameterPerpendicularToChordBisectsChordAndArc.Instantiate(clause));
HandleDeducedClauses(worklist, PerpendicularToRadiusIsTangent.Instantiate(clause));
}
else if (clause is Tangent)
{
// HandleDeducedClauses(worklist, ChordTangentAngleHalfInterceptedArc.Instantiate(clause));
// HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, TangentPerpendicularToRadius.Instantiate(clause));
HandleDeducedClauses(worklist, TangentsToCircleFromPointAreCongruent.Instantiate(clause));
}
else if (clause is CongruentArcs)
{
HandleDeducedClauses(worklist, TransitiveSubstitution.Instantiate(clause)); // Simplifies as well
HandleDeducedClauses(worklist, CongruentArcsHaveCongruentChords.Instantiate(clause));
HandleDeducedClauses(worklist, MinorArcsCongruentIfCentralAnglesCongruent.Instantiate(clause));
}
else if (clause is Circle)
{
Circle.Record(clause);
HandleDeducedClauses(worklist, CircleDefinition.Instantiate(clause));
HandleDeducedClauses(worklist, CentralAngleEqualInterceptedArc.Instantiate(clause));
//HandleDeducedClauses(worklist, ExteriorAngleHalfDifferenceInterceptedArcs.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedAngleHalfInterceptedArc.Instantiate(clause));
//HandleDeducedClauses(worklist, TwoChordsAnglesHalfSumInterceptedArc.Instantiate(clause));
HandleDeducedClauses(worklist, InscribedQuadrilateralOppositeSupplementary.Instantiate(clause));
HandleDeducedClauses(worklist, TwoInterceptedArcsHaveCongruentAngles.Instantiate(clause));
}
else if (clause is CongruentCircles)
{
HandleDeducedClauses(worklist, CongruentCircleDefinition.Instantiate(clause));
}
}
return(graph);
}
//
// Checks for SAS given the 5 values
//
private static List <EdgeAggregator> InstantiateSAS(Triangle tri1, Triangle tri2, CongruentSegments css1, CongruentSegments css2, CongruentAngles cas)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
//
// All congruence pairs must minimally relate the triangles
//
if (!css1.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
if (!css2.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
if (!cas.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
// Is this angle an 'extension' of the actual triangle angle? If so, acquire the normalized version of
// the angle, using only the triangle vertices to represent the angle
Angle angleTri1 = tri1.NormalizeAngle(tri1.AngleBelongs(cas));
Angle angleTri2 = tri2.NormalizeAngle(tri2.AngleBelongs(cas));
Segment seg1Tri1 = tri1.GetSegment(css1);
Segment seg1Tri2 = tri2.GetSegment(css1);
Segment seg2Tri1 = tri1.GetSegment(css2);
Segment seg2Tri2 = tri2.GetSegment(css2);
if (!angleTri1.IsIncludedAngle(seg1Tri1, seg2Tri1) || !angleTri2.IsIncludedAngle(seg1Tri2, seg2Tri2))
{
return(newGrounded);
}
//
// Construct the corrsesponding points between the triangles
//
List <Point> triangleOne = new List <Point>();
List <Point> triangleTwo = new List <Point>();
triangleOne.Add(angleTri1.GetVertex());
triangleTwo.Add(angleTri2.GetVertex());
triangleOne.Add(seg1Tri1.OtherPoint(angleTri1.GetVertex()));
triangleTwo.Add(seg1Tri2.OtherPoint(angleTri2.GetVertex()));
triangleOne.Add(seg2Tri1.OtherPoint(angleTri1.GetVertex()));
triangleTwo.Add(seg2Tri2.OtherPoint(angleTri2.GetVertex()));
//
// Construct the new clauses: congruent triangles and CPCTC
//
GeometricCongruentTriangles gcts = new GeometricCongruentTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
// Hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(css1);
antecedent.Add(css2);
antecedent.Add(cas);
newGrounded.Add(new EdgeAggregator(antecedent, gcts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(gcts, triangleOne, triangleTwo));
return(newGrounded);
}
//
// Checks for SSS given the 5 values
//
private static List <EdgeAggregator> InstantiateSSS(Triangle tri1, Triangle tri2, CongruentSegments css1, CongruentSegments css2, CongruentSegments css3)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
//
// All congruence pairs must minimally relate the triangles
//
if (!css1.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
if (!css2.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
if (!css3.LinksTriangles(tri1, tri2))
{
return(newGrounded);
}
Segment seg1Tri1 = tri1.GetSegment(css1);
Segment seg1Tri2 = tri2.GetSegment(css1);
Segment seg2Tri1 = tri1.GetSegment(css2);
Segment seg2Tri2 = tri2.GetSegment(css2);
Segment seg3Tri1 = tri1.GetSegment(css3);
Segment seg3Tri2 = tri2.GetSegment(css3);
//
// The vertices of both triangles must all be distinct and cover the triangle completely.
//
Point vertex1Tri1 = seg1Tri1.SharedVertex(seg2Tri1);
Point vertex2Tri1 = seg2Tri1.SharedVertex(seg3Tri1);
Point vertex3Tri1 = seg1Tri1.SharedVertex(seg3Tri1);
if (vertex1Tri1 == null || vertex2Tri1 == null || vertex3Tri1 == null)
{
return(newGrounded);
}
if (vertex1Tri1.StructurallyEquals(vertex2Tri1) ||
vertex1Tri1.StructurallyEquals(vertex3Tri1) ||
vertex2Tri1.StructurallyEquals(vertex3Tri1))
{
return(newGrounded);
}
Point vertex1Tri2 = seg1Tri2.SharedVertex(seg2Tri2);
Point vertex2Tri2 = seg2Tri2.SharedVertex(seg3Tri2);
Point vertex3Tri2 = seg1Tri2.SharedVertex(seg3Tri2);
if (vertex1Tri2 == null || vertex2Tri2 == null || vertex3Tri2 == null)
{
return(newGrounded);
}
if (vertex1Tri2.StructurallyEquals(vertex2Tri2) ||
vertex1Tri2.StructurallyEquals(vertex3Tri2) ||
vertex2Tri2.StructurallyEquals(vertex3Tri2))
{
return(newGrounded);
}
//
// Construct the corresponding points between the triangles
//
List <Point> triangleOne = new List <Point>();
List <Point> triangleTwo = new List <Point>();
triangleOne.Add(vertex1Tri1);
triangleTwo.Add(vertex1Tri2);
triangleOne.Add(vertex2Tri1);
triangleTwo.Add(vertex2Tri2);
triangleOne.Add(vertex3Tri1);
triangleTwo.Add(vertex3Tri2);
//
// Construct the new clauses: congruent triangles and CPCTC
//
GeometricCongruentTriangles gcts = new GeometricCongruentTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
// Hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(css1);
antecedent.Add(css2);
antecedent.Add(css3);
newGrounded.Add(new EdgeAggregator(antecedent, gcts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(gcts, triangleOne, triangleTwo));
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);
}
