private static List<EdgeAggregator> InstantiateTheorem(Angle a1, Angle a2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Acquire all circles in which the angles are inscribed
List<Circle> circles1 = Circle.IsInscribedAngle(a1);
List<Circle> circles2 = Circle.IsInscribedAngle(a2);
//Acquire the common circles in which both angles are inscribed
List<Circle> circles = (circles1.Intersect(circles2)).ToList();
//For each common circle, check for equivalent itercepted arcs
foreach (Circle c in circles)
{
Arc i1 = Arc.GetInterceptedArc(c, a1);
Arc i2 = Arc.GetInterceptedArc(c, a2);
if (i1.StructurallyEquals(i2))
{
GeometricCongruentAngles gcas = new GeometricCongruentAngles(a1, a2);
//For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(c);
antecedent.Add(a1);
antecedent.Add(a2);
antecedent.Add(i1);
newGrounded.Add(new EdgeAggregator(antecedent, gcas, annotation));
}
}
return newGrounded;
}
public static List<EdgeAggregator> InstantiateTheorem(GroundedClause original, IsoscelesTriangle isoTri)
{
GeometricCongruentAngles newCongSegs = new GeometricCongruentAngles(isoTri.baseAngleOppositeLeg1, isoTri.baseAngleOppositeLeg2);
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(original);
return Utilities.MakeList<EdgeAggregator>(new EdgeAggregator(antecedent, newCongSegs, annotation));
}
private static List<EdgeAggregator> InstantiateToTheorem(IsoscelesTrapezoid trapezoid, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
GeometricCongruentAngles gcas1 = new GeometricCongruentAngles(trapezoid.bottomLeftBaseAngle, trapezoid.bottomRightBaseAngle);
GeometricCongruentAngles gcas2 = new GeometricCongruentAngles(trapezoid.topLeftBaseAngle, trapezoid.topRightBaseAngle);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, gcas1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gcas2, annotation));
return newGrounded;
}
// V---------------A
// / \
// / \
// / \
// B C
//
// AngleBisector(Angle(A, V, B), Segment(V, C)) -> Congruent(Angle, A, V, C), Angle(C, V, B))
//
private static List<EdgeAggregator> InstantiateBisector(AngleBisector ab)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Create the two adjacent angles
Point vertex = ab.angle.GetVertex();
Point interiorPt = ab.angle.IsOnInteriorExplicitly(ab.bisector.Point1) ? ab.bisector.Point1 : ab.bisector.Point2;
Angle adj1 = new Angle(ab.angle.ray1.OtherPoint(vertex), vertex, interiorPt);
Angle adj2 = new Angle(ab.angle.ray2.OtherPoint(vertex), vertex, interiorPt);
GeometricCongruentAngles cas = new GeometricCongruentAngles(adj1, adj2);
// For hypergraph
newGrounded.Add(new EdgeAggregator(Utilities.MakeList<GroundedClause>(ab), cas, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateTheorem(Parallelogram parallelogram, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Determine the CongruentSegments opposing sides and output that.
GeometricCongruentAngles gcas1 = new GeometricCongruentAngles(parallelogram.topLeftAngle, parallelogram.bottomRightAngle);
GeometricCongruentAngles gcas2 = new GeometricCongruentAngles(parallelogram.bottomLeftAngle, parallelogram.topRightAngle);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, gcas1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gcas2, annotation));
return newGrounded;
}
//
// Intersect(X, Segment(A, B), Segment(C, D)) -> Congruent(Angle(A, X, C), Angle(B, X, D)),
// Congruent(Angle(A, X, D), Angle(C, X, B))
//
public static List<EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.VERTICAL_ANGLES;
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Intersection inter = c as Intersection;
if (inter == null) return newGrounded;
//
// Verify that this intersection is composed of two overlapping segments
// That is, we do not allow a segment to stand on another:
// \
// \
// \
// ______\_______
//
if (inter.StandsOn()) return newGrounded;
//
// Congruent(Angle(A, X, C), Angle(B, X, D))
//
List<GroundedClause> antecedent1 = Utilities.MakeList<GroundedClause>(inter);
Angle ang1Set1 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point1, inter.intersect, inter.rhs.Point1));
Angle ang2Set1 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point2, inter.intersect, inter.rhs.Point2));
antecedent1.Add(ang1Set1);
antecedent1.Add(ang2Set1);
GeometricCongruentAngles cca1 = new GeometricCongruentAngles(ang1Set1, ang2Set1);
cca1.MakeIntrinsic(); // This is an 'obvious' notion so it should be intrinsic to any figure
newGrounded.Add(new EdgeAggregator(antecedent1, cca1, annotation));
//
// Congruent(Angle(A, X, D), Angle(C, X, B))
//
List<GroundedClause> antecedent2 = Utilities.MakeList<GroundedClause>(inter);
Angle ang1Set2 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point1, inter.intersect, inter.rhs.Point2));
Angle ang2Set2 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point2, inter.intersect, inter.rhs.Point1));
antecedent2.Add(ang1Set2);
antecedent2.Add(ang2Set2);
GeometricCongruentAngles cca2 = new GeometricCongruentAngles(ang1Set2, ang2Set2);
cca2.MakeIntrinsic(); // This is an 'obvious' notion so it should be intrinsic to any figure
newGrounded.Add(new EdgeAggregator(antecedent2, cca2, annotation));
return newGrounded;
}
public static GenericInstantiator.EdgeAggregator GenerateAngleCongruence(Triangle tri, Angle angle)
{
//
// If we have already generated a reflexive congruence, avoid regenerating
//
foreach (Angle oldSharedAngle in knownSharedAngles)
{
if (oldSharedAngle.Equates(angle))
{
return(null);
}
}
// Generate
GeometricCongruentAngles gcas = new GeometricCongruentAngles(angle, angle);
// This is an 'obvious' notion so it should be intrinsic to any figure
gcas.MakeIntrinsic();
return(new GenericInstantiator.EdgeAggregator(Utilities.MakeList <GroundedClause>(Angle.AcquireFigureAngle(angle)), gcas, reflexAnnotation));
}
//
// Creates a basic S-Shape with standsOnEndpoints
//
// ______ offThat
// |
// offThis ______|
//
// Return <offThis, offThat>
private static List<EdgeAggregator> GenerateSimpleS(Parallel parallel, Intersection inter1, Point offThis, Intersection inter2, Point offThat)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(offThat, inter2.intersect, inter1.intersect),
new Angle(offThis, inter1.intersect, inter2.intersect));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
// leftTop rightTop
// | |
// |_________|
// | |
// | |
// leftBottom rightBottom
//
private static List<EdgeAggregator> GenerateH(Parallel parallel, Intersection crossingInterLeft, Intersection crossingInterRight)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = crossingInterLeft.AcquireTransversal(crossingInterRight);
//
// Find tops and bottoms
//
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;
}
//
// 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);
}
// offCross
// |
// leftCross ______|______ rightCross
// |
// leftStands _____|_____ rightStands
//
private static List<EdgeAggregator> GenerateFlying(Parallel parallel, Intersection inter1, Intersection inter2, Point offCross)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine which is the crossing intersection and which stands on the endpoints
//
Intersection crossingInter = null;
Intersection standsInter = null;
if (inter1.Crossing())
{
crossingInter = inter1;
standsInter = inter2;
}
else if (inter2.Crossing())
{
crossingInter = inter2;
standsInter = inter1;
}
// Determine the side of the crossing needed for the angle
Segment transversal = inter1.AcquireTransversal(inter2);
Segment parallelStands = standsInter.OtherSegment(transversal);
Segment parallelCrossing = crossingInter.OtherSegment(transversal);
// Determine point orientation in the plane
Point leftStands = parallelStands.Point1;
Point rightStands = parallelStands.Point2;
Point leftCross = null;
Point rightCross = null;
Segment crossingTester = new Segment(leftStands, parallelCrossing.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
leftCross = parallelCrossing.Point2;
rightCross = parallelCrossing.Point1;
}
else
{
leftCross = parallelCrossing.Point1;
rightCross = parallelCrossing.Point2;
}
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(rightCross, crossingInter.intersect, standsInter.intersect),
new Angle(leftStands, standsInter.intersect, crossingInter.intersect));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(leftCross, crossingInter.intersect, standsInter.intersect),
new Angle(rightStands, standsInter.intersect, crossingInter.intersect));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
private static List<EdgeAggregator> IndirectRelations(CongruentAngles cas, AnglePairRelation relation1, AnglePairRelation relation2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Do we have the same type of relation?
if (relation1.GetType() != relation2.GetType()) return newGrounded;
//
// Determine the shared values amongst the relations
//
Angle shared1 = relation1.AngleShared(cas);
if (shared1 == null) return newGrounded;
Angle shared2 = cas.OtherAngle(shared1);
if (!relation2.HasAngle(shared2)) return newGrounded;
Angle otherAngle1 = relation1.OtherAngle(shared1);
Angle otherAngle2 = relation2.OtherAngle(shared2);
// Avoid generating a reflexive relationship
if (otherAngle1.Equates(otherAngle2)) return newGrounded;
//
// Congruent(Angle(1), Angle(3))
//
// The other two angles from the relation pairs are then congruent
GeometricCongruentAngles gcas = new GeometricCongruentAngles(otherAngle1, otherAngle2);
// Avoid direct cyclic congruent angle generation
if (cas.StructurallyEquals(gcas)) return newGrounded;
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(cas);
antecedent.Add(relation1);
antecedent.Add(relation2);
//
// AnglePairRelation(Angle(1), Angle(4)),
// AnglePairRelation(Angle(2), Angle(3)),
//
if (relation1 is Complementary && relation2 is Complementary)
{
Complementary comp1 = new Complementary(shared1, otherAngle2);
Complementary comp2 = new Complementary(shared2, otherAngle1);
newGrounded.Add(new EdgeAggregator(antecedent, comp1, compAnnotation));
newGrounded.Add(new EdgeAggregator(antecedent, comp2, compAnnotation));
}
else if (relation1 is Supplementary && relation2 is Supplementary)
{
Supplementary supp1 = new Supplementary(shared1, otherAngle2);
Supplementary supp2 = new Supplementary(shared2, otherAngle1);
newGrounded.Add(new EdgeAggregator(antecedent, supp1, suppAnnotation));
newGrounded.Add(new EdgeAggregator(antecedent, supp2, suppAnnotation));
}
else
{
throw new ArgumentException("RelationsOfCongruent:: Expected a supplementary or complementary angle, not " + relation1.GetType());
}
newGrounded.Add(new EdgeAggregator(antecedent, gcas, relation1 is Complementary ? compAnnotation : suppAnnotation));
return newGrounded;
}
private static List<EdgeAggregator> DirectRelations(AnglePairRelation relation1, AnglePairRelation relation2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Do we have the same type of relation?
if (relation1.GetType() != relation2.GetType()) return newGrounded;
// Acquire the shared angle
Angle shared = relation1.AngleShared(relation2);
if (shared == null) return newGrounded;
Angle otherAngle1 = relation1.OtherAngle(shared);
Angle otherAngle2 = relation2.OtherAngle(shared);
// Avoid generating a reflexive relationship
if (otherAngle1.Equates(otherAngle2)) return newGrounded;
// The other two angles are then congruent
GeometricCongruentAngles gcas = new GeometricCongruentAngles(otherAngle1, otherAngle2);
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(relation1);
antecedent.Add(relation2);
newGrounded.Add(new EdgeAggregator(antecedent, gcas, relation1 is Complementary ? compAnnotation : suppAnnotation));
return newGrounded;
}
// offCross
// |
// ______|______ rightCrossing
// |
// |_____ offStands
// |
// |
// bottomStands
private static List<EdgeAggregator> InstantiateExtendedChairIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Point offCross)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine which is the crossing intersection and which stands on the endpoints
//
Intersection crossingInter = null;
Intersection standsInter = null;
if (inter1.Crossing())
{
crossingInter = inter1;
standsInter = inter2;
}
else if (inter2.Crossing())
{
crossingInter = inter2;
standsInter = inter1;
}
//
// Determination of Points
//
Point offStands = standsInter.CreatesTShape();
Segment transversal = inter1.AcquireTransversal(inter2);
Segment transversalStands = standsInter.GetCollinearSegment(transversal);
Point bottomStands = Segment.Between(standsInter.intersect, transversalStands.Point1, crossingInter.intersect) ? transversalStands.Point1 : transversalStands.Point2;
// Which side for rightCrossing
Segment parallelCrossing = crossingInter.OtherSegment(transversal);
Segment crossingTester = new Segment(offStands, parallelCrossing.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
Point rightCrossing = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelCrossing.Point2 : parallelCrossing.Point1;
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(bottomStands, standsInter.intersect, offStands),
new Angle(standsInter.intersect, crossingInter.intersect, rightCrossing));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(offStands, standsInter.intersect, crossingInter.intersect),
new Angle(rightCrossing, crossingInter.intersect, offCross));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Generate the three pairs of congruent segments.
//
private static List<EdgeAggregator> InstantiateFromDefinition(EquilateralTriangle tri, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
//
// Create the 3 sets of congruent segments.
//
for (int s = 0; s < tri.orderedSides.Count; s++)
{
GeometricCongruentSegments gcs = new GeometricCongruentSegments(tri.orderedSides[s], tri.orderedSides[(s+1) % tri.orderedSides.Count]);
newGrounded.Add(new EdgeAggregator(antecedent, gcs, annotation));
}
//
// Create the 3 congruent angles.
//
for (int a = 0; a < tri.angles.Count; a++)
{
GeometricCongruentAngles gcas = new GeometricCongruentAngles(tri.angles[a], tri.angles[(a + 1) % tri.angles.Count]);
newGrounded.Add(new EdgeAggregator(antecedent, gcas, annotation));
}
//
// Create the 3 equations for the measure of each angle being 60 degrees.
//
for (int a = 0; a < tri.angles.Count; a++)
{
GeometricAngleEquation gae = new GeometricAngleEquation(tri.angles[a], new NumericValue(60));
newGrounded.Add(new EdgeAggregator(antecedent, gae, annotation));
}
return newGrounded;
}
//
// Just generate the new angle congruence
//
private static List<EdgeAggregator> InstantiateToCongruence(Triangle tri, CongruentSegments css)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
if (!tri.HasSegment(css.cs1) || !tri.HasSegment(css.cs2)) return newGrounded;
GeometricCongruentAngles newConAngs = new GeometricCongruentAngles(tri.GetOppositeAngle(css.cs1), tri.GetOppositeAngle(css.cs2));
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(css);
antecedent.Add(tri);
newGrounded.Add(new EdgeAggregator(antecedent, newConAngs, annotation));
return newGrounded;
}
// Corresponding angles if (we have 8 points here)
//
// InterLeft InterRight
// | |
// offLeft __|__________|__ offRight
// | |
// | |
//
private static List<EdgeAggregator> InstantiateCompleteIntersection(Parallel parallel, Intersection crossingInterLeft, Intersection crossingInterRight)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = crossingInterLeft.AcquireTransversal(crossingInterRight);
//
// Find off1 and off2
//
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 crossingLeftTop = crossingLeftParallel.Point1;
Point crossingLeftBottom = crossingLeftParallel.Point2;
Point crossingRightTop = null;
Point crossingRightBottom = null;
if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
crossingRightTop = crossingRightParallel.Point2;
crossingRightBottom = crossingRightParallel.Point1;
}
else
{
crossingRightTop = crossingRightParallel.Point1;
crossingRightBottom = crossingRightParallel.Point2;
}
// Point that is outside of the parallel lines and transversal
Segment leftTransversal = crossingInterLeft.GetCollinearSegment(transversal);
Segment rightTransversal = crossingInterRight.GetCollinearSegment(transversal);
Point offCrossingLeft = Segment.Between(crossingInterLeft.intersect, leftTransversal.Point1, crossingInterRight.intersect) ? leftTransversal.Point1 : leftTransversal.Point2;
Point offCrossingRight = 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(crossingLeftTop, crossingInterLeft.intersect, crossingInterRight.intersect),
new Angle(crossingRightTop, crossingInterRight.intersect, offCrossingRight));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(crossingLeftTop, crossingInterLeft.intersect, offCrossingLeft),
new Angle(crossingRightTop, crossingInterRight.intersect, crossingInterLeft.intersect));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(crossingLeftBottom, crossingInterLeft.intersect, offCrossingLeft),
new Angle(crossingRightBottom, crossingInterRight.intersect, crossingInterLeft.intersect));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(crossingLeftBottom, crossingInterLeft.intersect, crossingInterRight.intersect),
new Angle(crossingRightBottom, crossingInterRight.intersect, offCrossingRight));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, crossingInterLeft, crossingInterRight);
}
// top
// o
// offStands oooooooe
// e
//offEndpoint eeeeeee
// o
// bottom
// Returns: <offEndpoint, offStands>
private static List<EdgeAggregator> InstantiateSimplePiIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Point offEndpoint, Point offStands)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine which is the endpoint and stands intersections
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (inter1.StandsOnEndpoint() && inter2.StandsOn())
{
endpointInter = inter1;
standsInter = inter2;
}
else if (inter2.StandsOnEndpoint() && inter1.StandsOn())
{
endpointInter = inter2;
standsInter = inter1;
}
else return newGrounded;
//
// Determine the top and bottom points
//
Segment transversal = inter1.AcquireTransversal(inter2);
Segment transversalStands = standsInter.GetCollinearSegment(transversal);
Point top = null;
Point bottom = null;
if (Segment.Between(standsInter.intersect, transversalStands.Point1, endpointInter.intersect))
{
top = transversalStands.Point1;
bottom = transversalStands.Point2;
}
else
{
top = transversalStands.Point2;
bottom = transversalStands.Point1;
}
//
// Generate the new congruences
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(top, standsInter.intersect, offStands),
new Angle(standsInter.intersect, endpointInter.intersect, offEndpoint));
newAngleRelations.Add(gca);
gca = new GeometricCongruentAngles(new Angle(bottom, endpointInter.intersect, offEndpoint),
new Angle(endpointInter.intersect, standsInter.intersect, offStands));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
// 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 shape like a crazy person flying
//
// top top
// | |
// larger |_____|___ off
// | |
// | |
//
// Similar to H-shape with an extended point
// Returns the 'larger' intersection that contains the point: off
private static List<EdgeAggregator> InstantiateFlyingIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Intersection larger, Point off)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Intersection smallerInter = inter1.Equals(larger) ? inter2 : inter1;
Segment transversal = inter1.AcquireTransversal(inter2);
Segment parallel1 = inter1.OtherSegment(transversal);
Segment parallel2 = inter2.OtherSegment(transversal);
Point largerTop = parallel1.Point1;
Point largerBottom = parallel1.Point2;
Point otherTop = null;
Point otherBottom = null;
Segment crossingTester = new Segment(parallel1.Point1, parallel2.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
// opposite sides
if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
otherTop = parallel2.Point2;
otherBottom = parallel2.Point1;
}
// same sides
else
{
otherTop = parallel2.Point1;
otherBottom = parallel2.Point2;
}
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca1 = new GeometricCongruentAngles(new Angle(off, smallerInter.intersect, otherTop),
new Angle(smallerInter.intersect, larger.intersect, largerTop));
newAngleRelations.Add(gca1);
GeometricCongruentAngles gca2 = new GeometricCongruentAngles(new Angle(off, smallerInter.intersect, otherBottom),
new Angle(smallerInter.intersect, larger.intersect, largerBottom));
newAngleRelations.Add(gca2);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
// Corresponding angles if:
//
// up <- may not occur
// |_____ offEnd
// |
// |_____ offStands
// |
// |
// down
//
private static List<EdgeAggregator> InstantiateFIntersection(Parallel parallel, Intersection inter1, Point off1, Intersection inter2, Point off2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Point offEnd = null;
Point offStands = null;
Intersection endpt = null;
Intersection stands = null;
if (inter1.StandsOnEndpoint())
{
endpt = inter1;
offEnd = off1;
stands = inter2;
offStands = off2;
}
else if (inter2.StandsOnEndpoint())
{
endpt = inter2;
offEnd = off2;
stands = inter1;
offStands = off1;
}
Segment transversal = inter1.AcquireTransversal(inter2);
Segment nonParallelEndpt = endpt.GetCollinearSegment(transversal);
Segment nonParallelStands = stands.GetCollinearSegment(transversal);
Point down = null;
Point up = null;
if (Segment.Between(stands.intersect, nonParallelStands.Point1, endpt.intersect))
{
down = nonParallelStands.Point1;
up = nonParallelStands.Point2;
}
else
{
down = nonParallelStands.Point2;
up = nonParallelStands.Point1;
}
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
if (!down.Equals(stands.intersect))
{
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(offEnd, endpt.intersect, stands.intersect),
new Angle(offStands, stands.intersect, down));
newAngleRelations.Add(gca);
}
if (!up.Equals(endpt.intersect))
{
GeometricCongruentAngles gcaOptional = new GeometricCongruentAngles(new Angle(up, endpt.intersect, offEnd),
new Angle(endpt.intersect, stands.intersect, offStands));
newAngleRelations.Add(gcaOptional);
}
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Creates a Topped F-Shape
// top
// oppSide __________ <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
// bottom
//
// Returns: <bottom, off>
private static List<EdgeAggregator> GenerateToppedFShape(Parallel parallel, Intersection inter1, Intersection inter2, Intersection bottom, Point off)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Intersection top = inter1.Equals(bottom) ? inter2 : inter1;
// Determine the side of the top intersection needed for the angle
Segment transversal = inter1.AcquireTransversal(inter2);
Segment parallelTop = top.OtherSegment(transversal);
Segment parallelBottom = bottom.OtherSegment(transversal);
Segment crossingTester = new Segment(off, parallelTop.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
Point oppSide = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelTop.Point1 : parallelTop.Point2;
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(off, bottom.intersect, top.intersect),
new Angle(oppSide, top.intersect, bottom.intersect));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Chair Corresponding
//
// | | |
// |_____|____ leftInter |_________ tipOfT
// | | |
// | | |
// off tipOfT
//
// bottomInter
private static List<EdgeAggregator> InstantiateChairIntersection(Parallel parallel, Intersection inter1, Point off, Intersection inter2, Point bottomTip)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = inter1.AcquireTransversal(inter2);
Point tipOfT1 = inter1.CreatesTShape();
Point tipOfT2 = inter2.CreatesTShape();
Point leftTip = null;
Intersection leftInter = null;
Intersection bottomInter = null;
if (transversal.PointLiesOn(tipOfT1))
{
leftInter = inter1;
bottomInter = inter2;
leftTip = tipOfT1;
}
// thatInter is leftInter
else if (transversal.PointLiesOn(tipOfT2))
{
leftInter = inter2;
bottomInter = inter1;
leftTip = tipOfT2;
}
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
// CTA: Hack fix to alleviate exception thrown from improper congruent constructions.
GeometricCongruentAngles gca = null;
try
{
gca = new GeometricCongruentAngles(new Angle(leftTip, bottomInter.intersect, bottomTip),
new Angle(bottomInter.intersect, leftInter.intersect, off));
}
catch (Exception e)
{
if (Utilities.DEBUG) System.Diagnostics.Debug.WriteLine(e.ToString());
return newGrounded;
}
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Creates a shape like an extended t
// offCross offCross
// | |
// _____|____ sameSide sameSide ______|______
// | |
// |_____ offStands offStands _____|
//
// Returns <offStands, offCross>
private static List<EdgeAggregator> InstantiateCrossedTIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Point offStands, Point offCross)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine which is the crossing intersection and which stands on the endpoints
//
Intersection crossingInter = null;
Intersection standsInter = null;
if (inter1.Crossing() && inter2.StandsOnEndpoint())
{
crossingInter = inter1;
standsInter = inter2;
}
else if (inter2.Crossing() && inter1.StandsOnEndpoint())
{
crossingInter = inter2;
standsInter = inter1;
}
// Determine the side of the crossing needed for the angle
Segment transversal = inter1.AcquireTransversal(inter2);
Segment parallelStands = standsInter.OtherSegment(transversal);
Segment parallelCrossing = crossingInter.OtherSegment(transversal);
Segment crossingTester = new Segment(offStands, parallelCrossing.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
Point sameSide = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelCrossing.Point2 : parallelCrossing.Point1;
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(offStands, standsInter.intersect, crossingInter.intersect),
new Angle(sameSide, crossingInter.intersect, offCross));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
private static List<EdgeAggregator> CheckAndGeneratePerpendicularImplyCongruentAdjacent(Perpendicular perp, Angle angle1, Angle angle2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
if (!Utilities.CompareValues(angle1.measure, angle2.measure)) return newGrounded;
// The given angles must belong to the intersection. That is, the vertex must align and all rays must overlay the intersection.
if (!(perp.InducesNonStraightAngle(angle1) && perp.InducesNonStraightAngle(angle1))) return newGrounded;
//
// Now we have perpendicular -> congruent angles scenario
//
GeometricCongruentAngles gcas = new GeometricCongruentAngles(angle1, angle2);
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(perp);
antecedent.Add(angle1);
antecedent.Add(angle2);
newGrounded.Add(new EdgeAggregator(antecedent, gcas, annotation));
return newGrounded;
}
// Corresponding angles if:
// sameSide offRightEnd
// standsOn (o) o e
// o e standsOnEndpoint (e)
// offLeftEnd eeeoeeeeeeee
// o
// o
//
// Returns <offLeftEnd, offRightEnd>
//
private static List<EdgeAggregator> InstantiateSimpleTIntersection(Parallel parallel, Intersection inter1, Intersection inter2, Point offLeftEnd, Point offRightEnd)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Determine which is the endpoint and stands intersections
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (inter1.StandsOnEndpoint() && inter2.StandsOn())
{
endpointInter = inter1;
standsInter = inter2;
}
else if (inter2.StandsOnEndpoint() && inter1.StandsOn())
{
endpointInter = inter2;
standsInter = inter1;
}
else return newGrounded;
// Determine the sameSide point
Segment transversal = inter1.AcquireTransversal(inter2);
Segment parallelStands = standsInter.OtherSegment(transversal);
Segment crossingTester = new Segment(offRightEnd, parallelStands.Point1);
Point intersection = transversal.FindIntersection(crossingTester);
Point sameSide = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelStands.Point2 : parallelStands.Point1;
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
GeometricCongruentAngles gca = new GeometricCongruentAngles(new Angle(offLeftEnd, standsInter.intersect, sameSide),
new Angle(standsInter.intersect, endpointInter.intersect, offRightEnd));
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
public static GenericInstantiator.EdgeAggregator GenerateAngleCongruence(Triangle tri, Angle angle)
{
//
// If we have already generated a reflexive congruence, avoid regenerating
//
foreach (Angle oldSharedAngle in knownSharedAngles)
{
if (oldSharedAngle.Equates(angle)) return null;
}
// Generate
GeometricCongruentAngles gcas = new GeometricCongruentAngles(angle, angle);
// This is an 'obvious' notion so it should be intrinsic to any figure
gcas.MakeIntrinsic();
return new GenericInstantiator.EdgeAggregator(Utilities.MakeList<GroundedClause>(Angle.AcquireFigureAngle(angle)), gcas, reflexAnnotation);
}
// A
// /)
// / )
// / )
// center: O )
// \ )
// \ )
// \)
// C
//
// D
// /)
// / )
// / )
// center: Q )
// \ )
// \ )
// \)
// F
//
// Congruent(Arc(A, C), Arc(D, F)) -> Congruent(Angle(AOC), Angle(DQF))
//
private static List<EdgeAggregator> InstantiateConversePartOfTheorem(CongruentArcs cas)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Get the radii (and determine if the exist in the figure)
//
Segment radius11;
Segment radius12;
cas.ca1.GetRadii(out radius11, out radius12);
if (radius11 == null || radius12 == null) return newGrounded;
Segment radius21;
Segment radius22;
cas.ca2.GetRadii(out radius21, out radius22);
if (radius21 == null || radius22 == null) return newGrounded;
//
// Acquire the central angles from the respoitory
//
Angle central1 = Angle.AcquireFigureAngle(new Angle(radius11, radius12));
Angle central2 = Angle.AcquireFigureAngle(new Angle(radius21, radius22));
if (central1 == null || central2 == null) return newGrounded;
GeometricCongruentAngles gcas = new GeometricCongruentAngles(central1, central2);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(central1);
antecedent.Add(central2);
antecedent.Add(cas);
newGrounded.Add(new EdgeAggregator(antecedent, gcas, converseAnnotation));
return newGrounded;
}