//
// 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);
}
//
//
//
private static List <EdgeAggregator> IfCongruencesApplyToTrianglesGenerate(Triangle ct1, Triangle ct2, CongruentSegments css1, CongruentSegments css2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
//
// The congruent relationships need to link the given triangles
//
if (!css1.LinksTriangles(ct1, ct2))
{
return(newGrounded);
}
if (!css2.LinksTriangles(ct1, ct2))
{
return(newGrounded);
}
Segment seg1Tri1 = ct1.GetSegment(css1);
Segment seg2Tri1 = ct1.GetSegment(css2);
Segment seg1Tri2 = ct2.GetSegment(css1);
Segment seg2Tri2 = ct2.GetSegment(css2);
// Avoid redundant segments, if it arises
if (seg1Tri1.StructurallyEquals(seg2Tri1))
{
return(newGrounded);
}
if (seg1Tri2.StructurallyEquals(seg2Tri2))
{
return(newGrounded);
}
//
// Proportional Segments (we generate only as needed to avoid bloat in the hypergraph (assuming they are used by both triangles)
// We avoid generating proportions if they are truly congruences.
//
List <GroundedClause> propAntecedent = new List <GroundedClause>();
propAntecedent.Add(css1);
propAntecedent.Add(css2);
SegmentRatio ratio1 = new SegmentRatio(seg1Tri1, seg1Tri2);
SegmentRatio ratio2 = new SegmentRatio(seg2Tri1, seg2Tri2);
GeometricSegmentRatioEquation newEq = new GeometricSegmentRatioEquation(ratio1, ratio2);
newGrounded.Add(new EdgeAggregator(propAntecedent, newEq, annotation));
////
//// Only generate if ratios are not 1.
////
//GeometricSegmentRatio newProp = null;
//if (!Utilities.CompareValues(seg1Tri1.Length, seg1Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg1Tri1, seg1Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg1Tri1.Length, seg2Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg1Tri1, seg2Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg2Tri1.Length, seg1Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg2Tri1, seg1Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg2Tri1.Length, seg2Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg2Tri1, seg2Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
return(newGrounded);
}
private static List <EdgeAggregator> CheckAndGenerateProportionality(Triangle tri, Intersection inter1,
Intersection inter2, Parallel parallel)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// The two intersections should not be at the same vertex
if (inter1.intersect.Equals(inter2.intersect))
{
return(newGrounded);
}
//
// Do these intersections share a segment? That is, do they share the transversal?
//
Segment transversal = inter1.AcquireTransversal(inter2);
if (transversal == null)
{
return(newGrounded);
}
//
// Is the transversal a side of the triangle? It should not be.
//
if (tri.LiesOn(transversal))
{
return(newGrounded);
}
//
// Determine if one parallel segment is a side of the triangle (which must occur)
//
Segment coinciding = tri.DoesParallelCoincideWith(parallel);
if (coinciding == null)
{
return(newGrounded);
}
// The transversal and common segment must be distinct
if (coinciding.IsCollinearWith(transversal))
{
return(newGrounded);
}
//
// Determine if the simplified transversal is within the parallel relationship.
//
Segment parallelTransversal = parallel.OtherSegment(coinciding);
Segment simpleParallelTransversal = new Segment(inter1.intersect, inter2.intersect);
if (!parallelTransversal.IsCollinearWith(simpleParallelTransversal))
{
return(newGrounded);
}
// A
// /\
// / \
// / \
// off1 /------\ off2
// / \
// B /__________\ C
//
// Both intersections should create a T-shape.
//
Point off1 = inter1.CreatesTShape();
Point off2 = inter2.CreatesTShape();
if (off1 == null || off2 == null)
{
return(newGrounded);
}
// Get the intersection segments which should coincide with the triangle sides
KeyValuePair <Segment, Segment> otherSides = tri.OtherSides(coinciding);
// The intersections may be outside this triangle
if (otherSides.Key == null || otherSides.Value == null)
{
return(newGrounded);
}
Segment side1 = inter1.OtherSegment(transversal);
Segment side2 = inter2.OtherSegment(transversal);
// Get the actual sides of the triangle
Segment triangleSide1 = null;
Segment triangleSide2 = null;
if (side1.IsCollinearWith(otherSides.Key) && side2.IsCollinearWith(otherSides.Value))
{
triangleSide1 = otherSides.Key;
triangleSide2 = otherSides.Value;
}
else if (side1.IsCollinearWith(otherSides.Value) && side2.IsCollinearWith(otherSides.Key))
{
triangleSide1 = otherSides.Value;
triangleSide2 = otherSides.Key;
}
else
{
return(newGrounded);
}
// Verify the opposing parts of the T are on the opposite sides of the triangle
if (!triangleSide1.PointLiesOnAndExactlyBetweenEndpoints(off2))
{
return(newGrounded);
}
if (!triangleSide2.PointLiesOnAndExactlyBetweenEndpoints(off1))
{
return(newGrounded);
}
//
// Construct the new proprtional relationship and resultant equation
//
Point sharedVertex = triangleSide1.SharedVertex(triangleSide2);
SegmentRatio newProp1 = new SegmentRatio(new Segment(sharedVertex, off2), triangleSide1);
SegmentRatio newProp2 = new SegmentRatio(new Segment(sharedVertex, off1), triangleSide2);
GeometricSegmentRatioEquation newEq = new GeometricSegmentRatioEquation(newProp1, newProp2);
// Construct hyperedge
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(tri);
antecedent.Add(inter1);
antecedent.Add(inter2);
antecedent.Add(parallel);
newGrounded.Add(new EdgeAggregator(antecedent, newEq, annotation));
return(newGrounded);
}
//
// Of all the congruent segment pairs, choose a subset of 3. Exhaustively check all; if they work, return the set.
//
private static List <EdgeAggregator> CheckForSSS(Triangle ct1, Triangle ct2, SegmentRatioEquation sre1, SegmentRatioEquation sre2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
//
// The proportional relationships need to link the given triangles
//
if (!sre1.LinksTriangles(ct1, ct2))
{
return(newGrounded);
}
if (!sre2.LinksTriangles(ct1, ct2))
{
return(newGrounded);
}
//
// Both equations must share a fraction (ratio)
//
if (!sre1.SharesRatio(sre2))
{
return(newGrounded);
}
//
// Collect all of the applicable segments
//
SegmentRatio shared = sre1.GetSharedRatio(sre2);
SegmentRatio other1 = sre1.GetOtherRatio(shared);
SegmentRatio other2 = sre2.GetOtherRatio(shared);
Segment seg1Tri1 = ct1.GetSegment(shared);
Segment seg2Tri1 = ct1.GetSegment(other1);
Segment seg3Tri1 = ct1.GetSegment(other2);
if (seg1Tri1 == null || seg2Tri1 == null || seg3Tri1 == null)
{
return(newGrounded);
}
Segment seg1Tri2 = ct2.GetSegment(shared);
Segment seg2Tri2 = ct2.GetSegment(other1);
Segment seg3Tri2 = ct2.GetSegment(other2);
if (seg1Tri2 == null || seg2Tri2 == null || seg3Tri2 == null)
{
return(newGrounded);
}
// Avoid redundant segments, if they arise
if (seg1Tri1.StructurallyEquals(seg2Tri1) || seg1Tri1.StructurallyEquals(seg3Tri1) || seg2Tri1.StructurallyEquals(seg3Tri1))
{
return(newGrounded);
}
if (seg1Tri2.StructurallyEquals(seg2Tri2) || seg1Tri2.StructurallyEquals(seg3Tri2) || seg2Tri2.StructurallyEquals(seg3Tri2))
{
return(newGrounded);
}
//
// Collect the corresponding points
//
List <KeyValuePair <Point, Point> > pointPairs = new List <KeyValuePair <Point, Point> >();
pointPairs.Add(new KeyValuePair <Point, Point>(seg1Tri1.SharedVertex(seg2Tri1), seg1Tri2.SharedVertex(seg2Tri2)));
pointPairs.Add(new KeyValuePair <Point, Point>(seg1Tri1.SharedVertex(seg3Tri1), seg1Tri2.SharedVertex(seg3Tri2)));
pointPairs.Add(new KeyValuePair <Point, Point>(seg2Tri1.SharedVertex(seg3Tri1), seg2Tri2.SharedVertex(seg3Tri2)));
List <GroundedClause> simTriAntecedent = new List <GroundedClause>();
simTriAntecedent.Add(ct1);
simTriAntecedent.Add(ct2);
simTriAntecedent.Add(sre1);
simTriAntecedent.Add(sre2);
newGrounded.AddRange(SASSimilarity.GenerateCorrespondingParts(pointPairs, simTriAntecedent, annotation));
return(newGrounded);
}