public static List<GenericInstantiator.EdgeAggregator> GeneratePerpendicularBisector(GroundedClause tri, AngleBisector ab, Intersection inter)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
IsoscelesTriangle isoTri = (tri is Strengthened ? (tri as Strengthened).strengthened : tri) as IsoscelesTriangle;
if (tri is EquilateralTriangle)
{
}
// Does the Angle Bisector occur at the vertex angle (non-base angles) of the Isosceles triangle?
try
{
if (!ab.angle.GetVertex().Equals(isoTri.GetVertexAngle().GetVertex())) return newGrounded;
}
catch (Exception e)
{
System.Diagnostics.Debug.WriteLine(e.ToString());
}
// Is the intersection point between the endpoints of the base of the triangle?
if (!Segment.Between(inter.intersect, isoTri.baseSegment.Point1, isoTri.baseSegment.Point2)) return newGrounded;
// Does this intersection define this angle bisector situation? That is, the bisector and base must align with the intersection
if (!inter.ImpliesRay(ab.bisector)) return newGrounded;
if (!inter.HasSegment(isoTri.baseSegment)) return newGrounded;
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri);
antecedent.Add(ab);
antecedent.Add(inter);
// PerpendicularBisector(M, Segment(M, C), Segment(A, B))
Strengthened newPerpB = new Strengthened(inter, new PerpendicularBisector(inter, ab.bisector));
newGrounded.Add(new EdgeAggregator(antecedent, newPerpB, annotation));
return newGrounded;
}
// \ A
// \
// \
// center: O / P
// /
// / B
//
// Tangent(Circle(O), Segment(B, P)),
// Tangent(Circle(O), Segment(A, P)),
// Intersection(AP, BP) -> Congruent(Segment(A, P), Segment(P, B))
//
private static List<EdgeAggregator> InstantiateTheorem(Tangent tangent1, Tangent tangent2, Intersection inter, GroundedClause original1, GroundedClause original2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Do the tangents apply to the same circle?
if (!tangent1.intersection.theCircle.StructurallyEquals(tangent2.intersection.theCircle)) return newGrounded;
// Do the tangents have components the are part of the third intersection
if (!inter.HasSegment((tangent1.intersection as CircleSegmentIntersection).segment)) return newGrounded;
if (!inter.HasSegment((tangent2.intersection as CircleSegmentIntersection).segment)) return newGrounded;
Segment segment1 = Segment.GetFigureSegment(inter.intersect, tangent1.intersection.intersect);
Segment segment2 = Segment.GetFigureSegment(inter.intersect, tangent2.intersection.intersect);
GeometricCongruentSegments gcs = new GeometricCongruentSegments(segment1, segment2);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(inter);
newGrounded.Add(new EdgeAggregator(antecedent, gcs, annotation));
return newGrounded;
}
//
// A \
// \ B
// \ /
// O \/ X
// /\
// / \
// C / D
//
// Two tangents:
// Intersection(X, AD, BC), Tangent(Circle(O), BC), Tangent(Circle(O), AD) -> 2 * Angle(AXC) = MajorArc(AC) - MinorArc(AC)
//
public static List<EdgeAggregator> InstantiateTwoTangentsTheorem(Tangent tangent1, Tangent tangent2, Intersection inter, GroundedClause original1, GroundedClause original2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
CircleSegmentIntersection tan1 = tangent1.intersection as CircleSegmentIntersection;
CircleSegmentIntersection tan2 = tangent2.intersection as CircleSegmentIntersection;
if (tan1.StructurallyEquals(tan2)) return newGrounded;
// Do the tangents apply to the same circle?
if (!tan1.theCircle.StructurallyEquals(tan2.theCircle)) return newGrounded;
Circle circle = tan1.theCircle;
// Do these tangents work with this intersection?
if (!inter.HasSegment(tan1.segment) || !inter.HasSegment(tan2.segment)) return newGrounded;
// Overkill? Do the tangents intersect at the same point as the intersection's intersect point?
if (!tan1.segment.FindIntersection(tan2.segment).StructurallyEquals(inter.intersect)) return newGrounded;
//
// Get the arcs
//
Arc minorArc = new MinorArc(circle, tan1.intersect, tan2.intersect);
Arc majorArc = new MajorArc(circle, tan1.intersect, tan2.intersect);
Angle theAngle = new Angle(tan1.intersect, inter.intersect, tan2.intersect);
//
// Construct the new relationship
//
NumericValue two = new NumericValue(2);
GeometricAngleArcEquation gaaeq = new GeometricAngleArcEquation(new Multiplication(two, theAngle), new Subtraction(majorArc, minorArc));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(inter);
antecedent.Add(majorArc);
antecedent.Add(minorArc);
newGrounded.Add(new EdgeAggregator(antecedent, gaaeq, annotation));
return newGrounded;
}
//
// A \
// \ B
// \ /
// O \/ X
// /\
// / \
// C / D
//
// One Secant, One Tangent
// Intersection(X, AD, BC), Tangent(Circle(O), BC) -> 2 * Angle(AXC) = MajorArc(AC) - MinorArc(AC)
//
public static List<EdgeAggregator> InstantiateOneSecantOneTangentTheorem(Intersection inter, Tangent tangent, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
CircleSegmentIntersection tan = tangent.intersection as CircleSegmentIntersection;
// Is the tangent segment part of the intersection?
if (!inter.HasSegment(tan.segment)) return newGrounded;
// Acquire the chord that the intersection creates.
Segment secant = inter.OtherSegment(tan.segment);
Circle circle = tan.theCircle;
Segment chord = circle.ContainsChord(secant);
// Check if this segment never intersects the circle or doesn't create a chord.
if (chord == null) return newGrounded;
//
// Get the near / far points out of the chord
//
Point closeChordPt = null;
Point farChordPt = null;
if (Segment.Between(chord.Point1, chord.Point2, inter.intersect))
{
closeChordPt = chord.Point1;
farChordPt = chord.Point2;
}
else
{
closeChordPt = chord.Point2;
farChordPt = chord.Point1;
}
//
// Acquire the arcs
//
// Get the close arc first which we know exactly how it is constructed AND that it's a minor arc.
Arc closeArc = Arc.GetFigureMinorArc(circle, closeChordPt, tan.intersect);
// The far arc MAY be a major arc; if it is, the first candidate arc will contain the close arc.
Arc farArc = Arc.GetFigureMinorArc(circle, farChordPt, tan.intersect);
if (farArc.HasMinorSubArc(closeArc))
{
farArc = Arc.GetFigureMajorArc(circle, farChordPt, tan.intersect);
}
Angle theAngle = Angle.AcquireFigureAngle(new Angle(closeChordPt, inter.intersect, tan.intersect));
//
// Construct the new relationship
//
NumericValue two = new NumericValue(2);
GeometricAngleArcEquation gaaeq = new GeometricAngleArcEquation(new Multiplication(two, theAngle), new Subtraction(farArc, closeArc));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
antecedent.Add(closeArc);
antecedent.Add(farArc);
newGrounded.Add(new EdgeAggregator(antecedent, gaaeq, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateFromAltitude(Intersection inter, Altitude altitude)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The intersection should contain the altitude segment
if (!inter.HasSegment(altitude.segment)) return newGrounded;
// The triangle should contain the other segment in the intersection
Segment triangleSide = altitude.triangle.CoincidesWithASide(inter.OtherSegment(altitude.segment));
if (triangleSide == null) return newGrounded;
if (!inter.OtherSegment(altitude.segment).HasSubSegment(triangleSide)) return newGrounded;
//
// Create the Perpendicular relationship
//
Strengthened streng = new Strengthened(inter, new Perpendicular(inter));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(altitude);
newGrounded.Add(new EdgeAggregator(antecedent, streng, annotation));
return newGrounded;
}
// ) | B
// ) |
// O )| S
// ) |
// ) |
// ) | A
// Tangent(Circle(O, R), Segment(A, B)), Intersection(OS, AB) -> Perpendicular(Segment(A,B), Segment(O, S))
//
private static List<EdgeAggregator> InstantiateTheorem(Tangent tangent, Intersection inter, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
CircleSegmentIntersection tanInter = tangent.intersection as CircleSegmentIntersection;
// Does this tangent segment apply to this intersection?
if (!inter.HasSegment(tanInter.segment)) return newGrounded;
// Get the radius--if it exists
Segment radius = null;
Segment garbage = null;
tanInter.GetRadii(out radius, out garbage);
if (radius == null) return newGrounded;
// Does this radius apply to this intersection?
if (!inter.HasSubSegment(radius)) return newGrounded;
Strengthened newPerp = new Strengthened(inter, new Perpendicular(inter));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
newGrounded.Add(new EdgeAggregator(antecedent, newPerp, annotation));
return newGrounded;
}
//
// Take the angle congruence and bisector and create the AngleBisector relation
// \
// \
// B ---------V---------A
// \
// \
// C
//
private static List<EdgeAggregator> InstantiateToDef(Point intersectionPoint, Intersection inter, CongruentSegments cs)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Does the given point of intersection apply to this actual intersection object
if (!intersectionPoint.Equals(inter.intersect)) return newGrounded;
// The entire segment AB
Segment overallSegment = new Segment(cs.cs1.OtherPoint(intersectionPoint), cs.cs2.OtherPoint(intersectionPoint));
// The segment must align completely with one of the intersection segments
Segment interCollinearSegment = inter.GetCollinearSegment(overallSegment);
if (interCollinearSegment == null) return newGrounded;
// Does this intersection have the entire segment AB
if (!inter.HasSegment(overallSegment)) return newGrounded;
Segment bisector = inter.OtherSegment(overallSegment);
Segment bisectedSegment = inter.GetCollinearSegment(overallSegment);
// Check if the bisected segment extends is the exact same segment as the overall segment AB
if (!bisectedSegment.StructurallyEquals(overallSegment))
{
if (overallSegment.PointLiesOnAndBetweenEndpoints(bisectedSegment.Point1) &&
overallSegment.PointLiesOnAndBetweenEndpoints(bisectedSegment.Point2)) return newGrounded;
}
SegmentBisector newSB = new SegmentBisector(inter, bisector);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(cs);
newGrounded.Add(new EdgeAggregator(antecedent, newSB, annotation));
return newGrounded;
}
// A
// |)
// | )
// | )
// Q------- O---X---) D
// | )
// | )
// |)
// C
//
// Perpendicular(Segment(Q, D), Segment(A, C)) -> Congruent(Arc(A, D), Arc(D, C)) -> Congruent(Segment(AX), Segment(XC))
//
private static List<EdgeAggregator> InstantiateTheorem(Intersection inter, CircleSegmentIntersection arcInter, Perpendicular perp, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Does this intersection apply to this perpendicular?
//
if (!inter.intersect.StructurallyEquals(perp.intersect)) return newGrounded;
// Is this too restrictive?
if (!((inter.HasSegment(perp.lhs) && inter.HasSegment(perp.rhs)) && (perp.HasSegment(inter.lhs) && perp.HasSegment(inter.rhs)))) return newGrounded;
//
// Does this perpendicular intersection apply to a given circle?
//
// Acquire the circles for which the segments are secants.
List<Circle> secantCircles1 = Circle.GetSecantCircles(perp.lhs);
List<Circle> secantCircles2 = Circle.GetSecantCircles(perp.rhs);
List<Circle> intersection = Utilities.Intersection<Circle>(secantCircles1, secantCircles2);
if (!intersection.Any()) return newGrounded;
//
// Find the single, unique circle that has as chords the components of the perpendicular intersection
//
Circle theCircle = null;
Segment chord1 = null;
Segment chord2 = null;
foreach (Circle circle in intersection)
{
chord1 = circle.GetChord(perp.lhs);
chord2 = circle.GetChord(perp.rhs);
if (chord1 != null && chord2 != null)
{
theCircle = circle;
break;
}
}
Segment diameter = chord1.Length > chord2.Length ? chord1 : chord2;
Segment chord = chord1.Length < chord2.Length ? chord1 : chord2;
//
// Does the arc intersection apply?
//
if (!arcInter.HasSegment(diameter)) return newGrounded;
if (!theCircle.StructurallyEquals(arcInter.theCircle)) return newGrounded;
//
// Create the bisector
//
Strengthened sb = new Strengthened(inter, new SegmentBisector(inter, diameter));
Strengthened ab = new Strengthened(arcInter, new ArcSegmentBisector(arcInter));
// For hypergraph
List<GroundedClause> antecedentArc = new List<GroundedClause>();
antecedentArc.Add(arcInter);
antecedentArc.Add(original);
antecedentArc.Add(theCircle);
newGrounded.Add(new EdgeAggregator(antecedentArc, ab, annotation));
List<GroundedClause> antecedentSegment = new List<GroundedClause>();
antecedentSegment.Add(inter);
antecedentSegment.Add(original);
antecedentSegment.Add(theCircle);
newGrounded.Add(new EdgeAggregator(antecedentSegment, sb, annotation));
return newGrounded;
}