public Kite(Segment left, Segment right, Segment top, Segment bottom,
bool tlDiag = false, bool brDiag = false, Intersection inter = null)
: base(left, right, top, bottom)
{
if (Utilities.CompareValues(left.Length, top.Length) && Utilities.CompareValues(right.Length, bottom.Length))
{
pairASegment1 = left;
pairASegment2 = top;
pairBSegment1 = right;
pairBSegment2 = bottom;
}
else if (Utilities.CompareValues(left.Length, bottom.Length) && Utilities.CompareValues(right.Length, top.Length))
{
pairASegment1 = left;
pairASegment2 = bottom;
pairBSegment1 = right;
pairBSegment2 = top;
}
else
{
throw new ArgumentException("Quadrilateral does not define a kite; no two adjacent sides are equal lengths: " + this);
}
//Set the diagonal and intersection values
if (!tlDiag) this.SetTopLeftDiagonalInValid();
if (!brDiag) this.SetBottomRightDiagonalInValid();
this.SetIntersection(inter);
}
public Square(Segment left, Segment right, Segment top, Segment bottom,
bool tlDiag = false, bool brDiag = false, Intersection inter = null)
: base(left, right, top, bottom)
{
if (!Utilities.CompareValues(topLeftAngle.measure, 90))
{
throw new ArgumentException("Quadrilateral is not a Square; angle does not measure 90^o: " + topLeftAngle);
}
if (!Utilities.CompareValues(topRightAngle.measure, 90))
{
throw new ArgumentException("Quadrilateral is not a Square; angle does not measure 90^o: " + topRightAngle);
}
if (!Utilities.CompareValues(bottomLeftAngle.measure, 90))
{
throw new ArgumentException("Quadrilateral is not a Square; angle does not measure 90^o: " + bottomLeftAngle);
}
if (!Utilities.CompareValues(bottomRightAngle.measure, 90))
{
throw new ArgumentException("Quadrilateral is not a Square; angle does not measure 90^o: " + bottomRightAngle);
}
//Set the diagonal and intersection values
if (!tlDiag) this.SetTopLeftDiagonalInValid();
if (!brDiag) this.SetBottomRightDiagonalInValid();
this.SetIntersection(inter);
}
//
// If a common segment exists (a transversal that cuts across both intersections), return that common segment
//
public Segment CommonSegment(Intersection thatInter)
{
if (lhs.StructurallyEquals(thatInter.lhs) || lhs.IsCollinearWith(thatInter.lhs)) return lhs;
if (lhs.StructurallyEquals(thatInter.rhs) || lhs.IsCollinearWith(thatInter.rhs)) return lhs;
if (rhs.StructurallyEquals(thatInter.lhs) || rhs.IsCollinearWith(thatInter.lhs)) return rhs;
if (rhs.StructurallyEquals(thatInter.rhs) || rhs.IsCollinearWith(thatInter.rhs)) return rhs;
return null;
}
public Perpendicular(Intersection inter)
: base(inter.intersect, inter.lhs, inter.rhs)
{
// Check if truly perpendicular
if (lhs.CoordinatePerpendicular(rhs) == null)
{
throw new ArgumentException("Intersection is not perpendicular: " + inter.ToString());
}
originalInter = inter;
}
//
// 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);
}
public Rectangle(Segment a, Segment b, Segment c, Segment d,
bool tlDiag = false, bool brDiag = false, Intersection inter = null)
: base(a, b, c, d)
{
foreach (Angle angle in angles)
{
if (!Utilities.CompareValues(angle.measure, 90))
{
throw new ArgumentException("Quadrilateral is not a Rectangle; angle does not measure 90^o: " + angle);
}
}
//Set the diagonal and intersection values
if (!tlDiag) this.SetTopLeftDiagonalInValid();
if (!brDiag) this.SetBottomRightDiagonalInValid();
this.SetIntersection(inter);
}
//
// Returns the exact transversal between the intersections
//
public Segment AcquireTransversal(Intersection thatInter)
{
// The two intersections should not be at the same vertex
if (intersect.Equals(thatInter.intersect)) return null;
Segment common = CommonSegment(thatInter);
if (common == null) return null;
// A legitimate transversal must belong to both intersections (is a subsegment of one of the lines)
Segment transversal = new Segment(this.intersect, thatInter.intersect);
Segment thisTransversal = this.GetCollinearSegment(transversal);
Segment thatTransversal = thatInter.GetCollinearSegment(transversal);
if (!thisTransversal.HasSubSegment(transversal)) return null;
if (!thatTransversal.HasSubSegment(transversal)) return null;
return transversal;
}
private static List<EdgeAggregator> CheckAndGenerateCongruentAdjacentImplyPerpendicular(Intersection intersection, CongruentAngles conAngles)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The given angles must belong to the intersection. That is, the vertex must align and all rays must overlay the intersection.
if (!intersection.InducesBothAngles(conAngles)) return newGrounded;
//
// Now we have perpendicular scenario
//
Strengthened streng = new Strengthened(intersection, new Perpendicular(intersection));
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(intersection);
antecedent.Add(conAngles);
newGrounded.Add(new EdgeAggregator(antecedent, streng, annotation));
return newGrounded;
}
//TODO: Need to find a way to determine the validity of diagonals, and to find the intersection if both diagonals are valid
//These values are determined for base quadrilaterals by the Implied Component Calculator in the UI parser, but are never
//computed for the specialized quads
public Rhombus(Segment left, Segment right, Segment top, Segment bottom,
bool tlDiag = false, bool brDiag = false, Intersection inter = null)
: base(left, right, top, bottom)
{
if (!Utilities.CompareValues(top.Length, left.Length))
{
throw new ArgumentException("Quadrilateral is not a Rhombus; sides are not equal length: " + top + " " + left);
}
if (!Utilities.CompareValues(top.Length, right.Length))
{
throw new ArgumentException("Quadrilateral is not a Rhombus; sides are not equal length: " + top + " " + right);
}
if (!Utilities.CompareValues(top.Length, bottom.Length))
{
throw new ArgumentException("Quadrilateral is not a Rhombus; sides are not equal length: " + top + " " + bottom);
}
//Set the diagonal and intersection values
if (!tlDiag) this.SetTopLeftDiagonalInValid();
if (!brDiag) this.SetBottomRightDiagonalInValid();
this.SetIntersection(inter);
}
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;
}
// 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);
}
public SegmentBisector(Intersection b, Segment bisec)
: base()
{
bisected = b;
bisector = bisec;
}
// top
// o
// offStands oooooooe
// e
//offEndpoint eeeeeee
// o
// bottom
// Returns: <offEndpoint, offStands>
public KeyValuePair <Point, Point> CreatesSimplePIShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Restrict to desired combination
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
//
// Determine which is the stands and which is the endpoint
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else if (thatInter.StandsOnEndpoint() && this.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else
{
return(nullPair);
}
//
// Avoid Some shapes
//
Segment transversal = this.AcquireTransversal(thatInter);
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;
}
// Avoid: ____ Although this shouldn't happen since both intersections do not stand on endpoints
// ____|
//
// Also avoid Simple F-Shape
//
if (transversal.HasPoint(top) || transversal.HasPoint(bottom))
{
return(nullPair);
}
// Determine S shape
Point offStands = standsInter.CreatesTShape();
Segment parallelEndpoint = endpointInter.OtherSegment(transversal);
Point offEndpoint = parallelEndpoint.OtherPoint(endpointInter.intersect);
Segment crossingTester = new Segment(offStands, offEndpoint);
Point intersection = transversal.FindIntersection(crossingTester);
// S-shape // PI-Shape
return(transversal.PointLiesOnAndBetweenEndpoints(intersection) ? nullPair : new KeyValuePair <Point, Point>(offEndpoint, offStands));
}
//
// Acquire all intersections from the maximal segment list
//
private void ConstructMaximalSegmentSegmentIntersections()
{
for (int s1 = 0; s1 < maximalSegments.Count - 1; s1++)
{
for (int s2 = s1 + 1; s2 < maximalSegments.Count; s2++)
{
// An intersection should not be between collinear segments
if (!maximalSegments[s1].IsCollinearWith(maximalSegments[s2]))
{
// The point must be 'between' both segment endpoints
Point numericInter = maximalSegments[s1].FindIntersection(maximalSegments[s2]);
if (maximalSegments[s1].PointLiesOnAndBetweenEndpoints(numericInter) &&
maximalSegments[s2].PointLiesOnAndBetweenEndpoints(numericInter))
{
// The actual point in the figure
Point knownPt = GeometryTutorLib.Utilities.GetStructurally<Point>(allFigurePoints, numericInter);
Intersection newInter = new Intersection(knownPt, maximalSegments[s1], maximalSegments[s2]);
GeometryTutorLib.Utilities.AddStructurallyUnique<Intersection>(ssIntersections, newInter);
}
}
}
}
}
public void SetIntersection(Intersection diag)
{
diagonalIntersection = diag;
}
private static List<EdgeAggregator> MakeRelations(List<CongruentAngles> newAngleRelations, Parallel parallel, Intersection inter1, Intersection inter2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(parallel);
antecedent.Add(inter1);
antecedent.Add(inter2);
foreach (CongruentAngles newAngles in newAngleRelations)
{
newGrounded.Add(new EdgeAggregator(antecedent, newAngles, annotation));
}
return newGrounded;
}
//
// Creates an F-Shape
// top
// _____ offEnd <--- Stands on Endpt
// |
// |_____ offStands <--- Stands on
// |
// |
// bottom
// Order of non-collinear points is order of intersections: <this, that>
public KeyValuePair <Point, Point> CreatesFShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Avoid both standing on an endpoint
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
Intersection endpt = null;
Intersection standsOn = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpt = this;
standsOn = thatInter;
}
else if (thatInter.StandsOnEndpoint() && this.StandsOn())
{
endpt = thatInter;
standsOn = this;
}
else
{
return(nullPair);
}
Segment transversal = this.AcquireTransversal(thatInter);
Segment transversalStands = standsOn.GetCollinearSegment(transversal);
//
// Determine Top and bottom to avoid PI shape
//
Point top = null;
Point bottom = null;
if (Segment.Between(standsOn.intersect, transversalStands.Point1, endpt.intersect))
{
bottom = transversalStands.Point1;
top = transversalStands.Point2;
}
else
{
bottom = transversalStands.Point2;
top = transversalStands.Point1;
}
// Avoid: ____ Although this shouldn't happen since both intersections do not stand on endpoints
// ____|
if (transversal.HasPoint(top) && transversal.HasPoint(bottom))
{
return(nullPair);
}
// Also avoid Simple PI-Shape
//
if (!transversal.HasPoint(top) && !transversal.HasPoint(bottom))
{
return(nullPair);
}
// Find the two points that make the points of the F
Segment parallelEndPt = endpt.OtherSegment(transversal);
Segment parallelStands = standsOn.OtherSegment(transversal);
Point offEnd = transversal.PointLiesOn(parallelEndPt.Point1) ? parallelEndPt.Point2 : parallelEndPt.Point1;
Point offStands = transversal.PointLiesOn(parallelStands.Point1) ? parallelStands.Point2 : parallelStands.Point1;
// Check this is not a crazy F
// _____
// |
// ____|
// |
// |
Point intersection = transversal.FindIntersection(new Segment(offEnd, offStands));
if (transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
return(nullPair);
}
// Return in the order of 'off' points: <this, that>
return(this.Equals(endpt) ? new KeyValuePair <Point, Point>(offEnd, offStands) : new KeyValuePair <Point, Point>(offStands, offEnd));
}
//
// Creates a Topped F-Shape
// top
// offLeft __________ offEnd <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
// bottom
//
// Returns: <bottom, off>
public KeyValuePair <Intersection, Point> CreatesToppedFShape(Intersection thatInter)
{
KeyValuePair <Intersection, Point> nullPair = new KeyValuePair <Intersection, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Avoid both standing on an endpoint OR crossing
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint())
{
return(nullPair);
}
if (this.Crossing() || thatInter.Crossing())
{
return(nullPair);
}
Segment transversal = this.AcquireTransversal(thatInter);
Intersection standsOnTop = null;
Intersection standsOnBottom = null;
// Top has 2 points on the transversal; bottom has 3
Segment nonTransversalThis = this.OtherSegment(transversal);
Segment nonTransversalThat = thatInter.OtherSegment(transversal);
if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThis.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThis.Point2))
{
// |
// ____| <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point2))
{
return(nullPair);
}
standsOnBottom = this;
standsOnTop = thatInter;
}
else if (transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point1) ||
transversal.PointLiesOnAndBetweenEndpoints(nonTransversalThat.Point2))
{
standsOnBottom = this;
standsOnTop = thatInter;
}
else
{
return(nullPair);
}
// Check that the bottom extends the transversal
if (!standsOnBottom.GetCollinearSegment(transversal).HasStrictSubSegment(transversal))
{
return(nullPair);
}
Point off = standsOnBottom.OtherSegment(transversal).OtherPoint(standsOnBottom.intersect);
return(new KeyValuePair <Intersection, Point>(standsOnBottom, off));
}
//
// 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);
}
//
// 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;
}
//
// 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);
}
//
// 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;
}
private static List<EdgeAggregator> CheckAndGenerateParallelImplyAlternateInterior(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;
// Determine the transversal
Segment transversal = inter1.AcquireTransversal(inter2);
if (transversal == null) return newGrounded;
//
// Ensure the non-traversal segments align with the parallel segments
//
Segment parallel1 = inter1.OtherSegment(transversal);
Segment parallel2 = inter2.OtherSegment(transversal);
// The non-transversals should not be the same (coinciding)
if (parallel1.IsCollinearWith(parallel2)) return newGrounded;
Segment coincidingParallel1 = parallel.CoincidesWith(parallel1);
Segment coincidingParallel2 = parallel.CoincidesWith(parallel2);
// The pair of non-transversals needs to align exactly with the parallel pair of segments
if (coincidingParallel1 == null || coincidingParallel2 == null) return newGrounded;
// Both intersections should not be referring to an intersection point on the same parallel segment
if (parallel.segment1.PointLiesOn(inter1.intersect) && parallel.segment1.PointLiesOn(inter2.intersect)) return newGrounded;
if (parallel.segment2.PointLiesOn(inter1.intersect) && parallel.segment2.PointLiesOn(inter2.intersect)) return newGrounded;
// The resultant candidate parallel segments shouldn't share any vertices
if (coincidingParallel1.SharedVertex(coincidingParallel2) != null) return newGrounded;
if (inter1.StandsOnEndpoint() && inter2.StandsOnEndpoint())
{
//
// Creates a basic S-Shape with standsOnEndpoints
//
// offThis ______
// |
// offThat ______|
//
// Return <offThis, offThat>
KeyValuePair<Point, Point> cShapePoints = inter1.CreatesBasicCShape(inter2);
if (cShapePoints.Key != null && cShapePoints.Value != null) return newGrounded;
//
// Creates a basic S-Shape with standsOnEndpoints
//
// ______ offThat _______
// | \
// offThis ______| _____\
//
// Return <offThis, offThat>
KeyValuePair<Point, Point> sShapePoints = inter1.CreatesBasicSShape(inter2);
if (sShapePoints.Key != null && sShapePoints.Value != null)
{
return GenerateSimpleS(parallel, inter1, sShapePoints.Key, inter2, sShapePoints.Value);
}
return newGrounded;
}
// _______/________
// /
// /
// ______/_______
// /
if (inter1.Crossing() && inter2.Crossing()) return GenerateDualCrossings(parallel, inter1, inter2);
// No alt int in this case:
// Creates an F-Shape
// top
// _____ offEnd <--- Stands on Endpt
// |
// |_____ offStands <--- Stands on
// |
// |
// bottom
KeyValuePair<Point, Point> fShapePoints = inter1.CreatesFShape(inter2);
if (fShapePoints.Key != null && fShapePoints.Value != null) return newGrounded;
// Alt. Int if an H-Shape
//
// | |
// |_____|
// | |
// | |
//
if (inter1.CreatesHShape(inter2)) return GenerateH(parallel, inter1, inter2);
// Creates an S-Shape
//
// |______
// |
// ______|
// |
//
// Order of non-collinear points is order of intersections: <this, that>
KeyValuePair<Point, Point> standardSShapePoints = inter1.CreatesStandardSShape(inter2);
if (standardSShapePoints.Key != null && standardSShapePoints.Value != null)
{
return GenerateSimpleS(parallel, inter1, standardSShapePoints.Key, inter2, standardSShapePoints.Value);
}
// Corresponding if a flying-Shape
//
// | |
// |_____|___ offCross
// | |
// | |
//
Point offCross = inter1.CreatesFlyingShapeWithCrossing(inter2);
if (offCross != null)
{
return GenerateFlying(parallel, inter1, inter2, offCross);
}
//
// Creates a shape like an extended t
// offCross offCross
// | |
// _____|____ ______|______
// | |
// |_____ offStands offStands _____|
//
// Returns <offStands, offCross>
KeyValuePair<Point, Point> tShapePoints = inter1.CreatesCrossedTShape(inter2);
if (tShapePoints.Key != null && tShapePoints.Value != null)
{
return GenerateCrossedT(parallel, inter1, inter2, tShapePoints.Key, tShapePoints.Value);
}
//
// Creates a Topped F-Shape
// top
// offLeft __________ offEnd <--- Stands on
// |
// |_____ off <--- Stands on
// |
// |
// bottom
//
// Returns: <bottom, off>
KeyValuePair<Intersection, Point> toppedFShapePoints = inter1.CreatesToppedFShape(inter2);
if (toppedFShapePoints.Key != null && toppedFShapePoints.Value != null)
{
return GenerateToppedFShape(parallel, inter1, inter2, toppedFShapePoints.Key, toppedFShapePoints.Value);
}
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;
}
//
// Generate all covering intersection clauses; that is, generate maximal intersections (a subset of all intersections)
//
private void CalculateIntersections()
{
//
// Iterate over all polygons
//
for (int sidesIndex = Polygon.MIN_POLY_INDEX; sidesIndex < Polygon.MAX_EXC_POLY_INDEX; sidesIndex++)
{
foreach (Polygon poly in polygons[sidesIndex])
{
//
// Add intersection clauses for all sides the polygon
//
List<Segment> sides = poly.orderedSides;
for (int s1 = 0; s1 < sides.Count - 1; s1++)
{
for (int s2 = s1 + 1; s2 < sides.Count; s2++)
{
// The shared vertex must be a vertex of the polygon
Point vertex = sides[s1].SharedVertex(sides[s2]);
if (vertex != null && poly.points.Contains(vertex))
{
GeometryTutorLib.Utilities.AddStructurallyUnique(ssIntersections, new Intersection(vertex, sides[s1], sides[s2]));
}
}
}
//
// Handle quadrilateral diagonals
//
if (poly is Quadrilateral)
{
Quadrilateral quad = poly as Quadrilateral;
if (GetMaximalProblemSegment(quad.bottomLeftTopRightDiagonal) == null)
{
quad.SetBottomRightDiagonalInValid();
}
if (GetMaximalProblemSegment(quad.topLeftBottomRightDiagonal) == null)
{
quad.SetTopLeftDiagonalInValid();
}
// If both diagonals exist in the figure, create an intersection and provide the quadrilateral with the intersection.
if (quad.TopLeftDiagonalIsValid() && quad.BottomRightDiagonalIsValid())
{
// The calculated intersection
Point inter = quad.bottomLeftTopRightDiagonal.FindIntersection(quad.topLeftBottomRightDiagonal);
// The actual point in the figure
Point knownPt = GeometryTutorLib.Utilities.GetStructurally<Point>(allFigurePoints, inter);
if (knownPt == null)
{
throw new Exception("Expected to find the point (did not):");
}
Intersection diagInter = new Intersection(knownPt, quad.bottomLeftTopRightDiagonal, quad.topLeftBottomRightDiagonal);
GeometryTutorLib.Utilities.AddStructurallyUnique<Intersection>(ssIntersections, diagInter);
quad.SetIntersection(diagInter);
}
}
}
}
CalculateMaximalMinimalSegments();
ConstructMaximalSegmentSegmentIntersections();
}
//public PerpendicularBisector(Point i, Segment l, Segment bisector, string just) : base(i, l, bisector, just)
//{
// this.bisector = bisector;
//}
public PerpendicularBisector(Intersection inter, Segment bisector) : base(inter)
{
this.bisector = bisector;
}
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;
}
//
// Creates a Chair
//
// | | |
// |_____|____ leftInter |_________ tipOfT
// | | |
// | | |
// off tipOfT
//
// bottomInter
//
// <leftInter, bottomInter>
// Returns the legs of the chair in specific ordering: <off, bottomTip>
public KeyValuePair <Point, Point> CreatesChairShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn())
{
return(nullPair);
}
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint())
{
return(nullPair);
}
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
Intersection leftInter = null;
Intersection bottomInter = null;
// Avoid:
// |
// |______
// | |
// | |
// this is leftInter
Point bottomTip = null;
if (transversal.PointLiesOn(thisTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT))
{
return(nullPair);
}
leftInter = this;
bottomInter = thatInter;
bottomTip = thisTipOfT;
}
// thatInter is leftInter
else if (transversal.PointLiesOn(thatTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT))
{
return(nullPair);
}
leftInter = thatInter;
bottomInter = this;
bottomTip = thisTipOfT;
}
// Otherwise, this indicates a PI-shaped scenario
else
{
return(nullPair);
}
//
// Returns the bottom of the legs of the chair
//
Segment parallelLeft = leftInter.OtherSegment(transversal);
Segment crossingTester = new Segment(parallelLeft.Point1, bottomTip);
Point intersection = transversal.FindIntersection(crossingTester);
Point off = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelLeft.Point2 : parallelLeft.Point1;
return(new KeyValuePair <Point, Point>(off, bottomTip));
}
//
// A \
// \ B
// \ /
// O \/ X
// /\
// / \
// C / D
//
// Two Secants
// Intersection(X, AD, BC) -> 2 * Angle(AXC) = MajorArc(AC) - MinorArc(AC)
//
public static List<EdgeAggregator> InstantiateTwoSecantsTheorem(Intersection inter, Circle circle)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Is this intersection explicitly outside the circle? That is, the point of intersection exterior?
if (!circle.PointIsExterior(inter.intersect)) return newGrounded;
//
// Get the chords
//
Segment chord1 = circle.ContainsChord(inter.lhs);
Segment chord2 = circle.ContainsChord(inter.rhs);
if (chord1 == null || chord2 == null) return newGrounded;
Point closeChord1Pt = null;
Point closeChord2Pt = null;
Point farChord1Pt = null;
Point farChord2Pt = null;
if (Segment.Between(chord1.Point1, chord1.Point2, inter.intersect))
{
closeChord1Pt = chord1.Point1;
farChord1Pt = chord1.Point2;
}
else
{
closeChord1Pt = chord1.Point2;
farChord1Pt = chord1.Point1;
}
if (Segment.Between(chord2.Point1, chord2.Point2, inter.intersect))
{
closeChord2Pt = chord2.Point1;
farChord2Pt = chord2.Point2;
}
else
{
closeChord2Pt = chord2.Point2;
farChord2Pt = chord2.Point1;
}
//
// Get the arcs
//
Arc closeArc = Arc.GetFigureMinorArc(circle, closeChord1Pt, closeChord2Pt);
Arc farArc = Arc.GetFigureMinorArc(circle, farChord1Pt, farChord2Pt);
Angle theAngle = Angle.AcquireFigureAngle(new Angle(closeChord1Pt, inter.intersect, closeChord2Pt));
//
// Construct the new relationship
//
NumericValue two = new NumericValue(2);
//GeometricAngleEquation gaeq = new GeometricAngleEquation(new Multiplication(two, theAngle), new Subtraction(farArc, closeArc));
GeometricAngleArcEquation gaaeq = new GeometricAngleArcEquation(new Multiplication(two, theAngle), new Subtraction(farArc, closeArc));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(circle);
antecedent.Add(closeArc);
antecedent.Add(farArc);
newGrounded.Add(new EdgeAggregator(antecedent, gaaeq, annotation));
return newGrounded;
}
private static List<GroundedClause> MakeAntecedent(Intersection inter, Angle angle1, Angle angle2)
{
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(inter);
antecedent.Add(angle1);
antecedent.Add(angle2);
return antecedent;
}
private static List<EdgeAggregator> CheckAndGenerateCorrespondingAnglesImplyParallel(Intersection inter1, Intersection inter2, CongruentAngles conAngles)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The two intersections should not be at the same vertex
if (inter1.intersect.Equals(inter2.intersect)) return newGrounded;
Segment transversal = inter1.CommonSegment(inter2);
if (transversal == null) return newGrounded;
Angle angleI = inter1.GetInducedNonStraightAngle(conAngles);
Angle angleJ = inter2.GetInducedNonStraightAngle(conAngles);
//
// Do we have valid intersections and congruent angle pairs
//
if (angleI == null || angleJ == null) return newGrounded;
//
// Check to see if they are, in fact, Corresponding Angles
//
Segment parallelCand1 = inter1.OtherSegment(transversal);
Segment parallelCand2 = inter2.OtherSegment(transversal);
// The resultant candidate parallel segments shouldn't share any vertices
if (parallelCand1.SharedVertex(parallelCand2) != null) return newGrounded;
// Numeric hack to discount any non-parallel segments
if (!parallelCand1.IsParallelWith(parallelCand2)) return newGrounded;
// A sanity check that the '4th' point does not lie on the other intersection (thus creating an obvious triangle and thus not parallel lines)
Point fourthPoint1 = parallelCand1.OtherPoint(inter1.intersect);
Point fourthPoint2 = parallelCand2.OtherPoint(inter2.intersect);
if (fourthPoint1 != null && fourthPoint2 != null)
{
if (parallelCand1.PointLiesOn(fourthPoint2) || parallelCand2.PointLiesOn(fourthPoint1)) return newGrounded;
}
// Both angles should NOT be in the interioir OR the exterioir; a combination is needed.
bool ang1Interior = angleI.OnInteriorOf(inter1, inter2);
bool ang2Interior = angleJ.OnInteriorOf(inter1, inter2);
if (ang1Interior && ang2Interior) return newGrounded;
if (!ang1Interior && !ang2Interior) return newGrounded;
//
// Are these angles on the same side of the transversal?
//
//
// Make a simple transversal from the two intersection points
Segment simpleTransversal = new Segment(inter1.intersect, inter2.intersect);
// Find the rays the lie on the transversal
Segment rayNotOnTransversalI = angleI.OtherRayEquates(simpleTransversal);
Segment rayNotOnTransversalJ = angleJ.OtherRayEquates(simpleTransversal);
Point pointNotOnTransversalNorVertexI = rayNotOnTransversalI.OtherPoint(angleI.GetVertex());
Point pointNotOnTransversalNorVertexJ = rayNotOnTransversalJ.OtherPoint(angleJ.GetVertex());
// Create a segment from these two points so we can compare distances
Segment crossing = new Segment(pointNotOnTransversalNorVertexI, pointNotOnTransversalNorVertexJ);
//
// Will this crossing segment actually intersect the real transversal in the middle of the two segments It should NOT.
//
Point intersection = transversal.FindIntersection(crossing);
if (Segment.Between(intersection, inter1.intersect, inter2.intersect)) return newGrounded;
//
// Now we have an alternate interior scenario
//
GeometricParallel newParallel = new GeometricParallel(parallelCand1, parallelCand2);
// Construct hyperedge
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter1);
antecedent.Add(inter2);
antecedent.Add(conAngles);
newGrounded.Add(new EdgeAggregator(antecedent, newParallel, annotation));
return newGrounded;
}
// A B
// \ /
// \ /
// \/
// /\ X
// / \
// / \
// C D
//
// Intersection(X, Segment(A, D), Segment(B, C)) -> Supplementary(Angle(A, X, B), Angle(B, X, D))
// Supplementary(Angle(B, X, D), Angle(D, X, C))
// Supplementary(Angle(D, X, C), Angle(C, X, A))
// Supplementary(Angle(C, X, A), Angle(A, X, B))
//
public static List<EdgeAggregator> InstantiateToSupplementary(Intersection inter)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The situation looks like this:
// |
// |
// |_______
//
if (inter.StandsOnEndpoint()) return newGrounded;
// The situation looks like this:
// |
// |
// _____|_______
//
if (inter.StandsOn())
{
Point up = null;
Point left = null;
Point right = null;
if (inter.lhs.HasPoint(inter.intersect))
{
up = inter.lhs.OtherPoint(inter.intersect);
left = inter.rhs.Point1;
right = inter.rhs.Point2;
}
else
{
up = inter.rhs.OtherPoint(inter.intersect);
left = inter.lhs.Point1;
right = inter.lhs.Point2;
}
// Gets the single angle object from the original figure
Angle newAngle1 = Angle.AcquireFigureAngle(new Angle(left, inter.intersect, up));
Angle newAngle2 = Angle.AcquireFigureAngle(new Angle(right, inter.intersect, up));
Supplementary supp = new Supplementary(newAngle1, newAngle2);
supp.SetNotASourceNode();
supp.SetNotAGoalNode();
supp.SetClearDefinition();
newGrounded.Add(new EdgeAggregator(MakeAntecedent(inter, supp.angle1, supp.angle2), supp, annotation));
}
//
// The situation is standard and results in 4 supplementary relationships
//
else
{
Angle newAngle1 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point1, inter.intersect, inter.rhs.Point1));
Angle newAngle2 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point1, inter.intersect, inter.rhs.Point2));
Angle newAngle3 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point2, inter.intersect, inter.rhs.Point1));
Angle newAngle4 = Angle.AcquireFigureAngle(new Angle(inter.lhs.Point2, inter.intersect, inter.rhs.Point2));
List<Supplementary> newSupps = new List<Supplementary>();
newSupps.Add(new Supplementary(newAngle1, newAngle2));
newSupps.Add(new Supplementary(newAngle2, newAngle4));
newSupps.Add(new Supplementary(newAngle3, newAngle4));
newSupps.Add(new Supplementary(newAngle3, newAngle1));
foreach (Supplementary supp in newSupps)
{
supp.SetNotASourceNode();
supp.SetNotAGoalNode();
supp.SetClearDefinition();
newGrounded.Add(new EdgeAggregator(MakeAntecedent(inter, supp.angle1, supp.angle2), supp, annotation));
}
}
return newGrounded;
}
//public PerpendicularBisector(Point i, Segment l, Segment bisector, string just) : base(i, l, bisector, just)
//{
// this.bisector = bisector;
//}
public PerpendicularBisector(Intersection inter, Segment bisector)
: base(inter)
{
this.bisector = bisector;
}
//
// A \ / B
// \ /
// \ /
// O \/ X
// /\
// / \
// C / \ D
//
// Intersection(Segment(AD), Segment(BC)) -> 2 * Angle(CXA) = Arc(A, C) + Arc(B, D),
// 2 * Angle(BXD) = Arc(A, C) + Arc(B, D),
// 2 * Angle(AXB) = Arc(A, B) + Arc(C, D),
// 2 * Angle(CXD) = Arc(A, B) + Arc(C, D)
//
public static List<EdgeAggregator> InstantiateTheorem(Intersection inter, Circle circle)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Is this intersection explicitly inside the circle? That is, the point of intersection interior?
if (!circle.PointIsInterior(inter.intersect)) return newGrounded;
//
// Get the chords
//
Segment chord1 = circle.GetChord(inter.lhs);
Segment chord2 = circle.GetChord(inter.rhs);
if (chord1 == null || chord2 == null) return newGrounded;
//
// Group 1
//
Arc arc1 = Arc.GetFigureMinorArc(circle, chord1.Point1, chord2.Point1);
Angle angle1 = Angle.AcquireFigureAngle(new Angle(chord1.Point1, inter.intersect, chord2.Point1));
Arc oppArc1 = Arc.GetFigureMinorArc(circle, chord1.Point2, chord2.Point2);
Angle oppAngle1 = Angle.AcquireFigureAngle(new Angle(chord1.Point2, inter.intersect, chord2.Point2));
//
// Group 2
//
Arc arc2 = Arc.GetFigureMinorArc(circle, chord1.Point1, chord2.Point2);
Angle angle2 = Angle.AcquireFigureAngle(new Angle(chord1.Point1, inter.intersect, chord2.Point2));
Arc oppArc2 = Arc.GetFigureMinorArc(circle, chord1.Point2, chord2.Point1);
Angle oppAngle2 = Angle.AcquireFigureAngle(new Angle(chord1.Point2, inter.intersect, chord2.Point1));
//
// Construct each of the 4 equations.
//
NumericValue two = new NumericValue(2);
GeometricAngleArcEquation gaeq1 = new GeometricAngleArcEquation(new Multiplication(two, angle1), new Addition(arc1, oppArc1));
GeometricAngleArcEquation gaeq2 = new GeometricAngleArcEquation(new Multiplication(two, oppAngle1), new Addition(arc1, oppArc1));
GeometricAngleArcEquation gaeq3 = new GeometricAngleArcEquation(new Multiplication(two, angle2), new Addition(arc2, oppArc2));
GeometricAngleArcEquation gaeq4 = new GeometricAngleArcEquation(new Multiplication(two, oppAngle2), new Addition(arc2, oppArc2));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(circle);
newGrounded.Add(new EdgeAggregator(antecedent, gaeq1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gaeq2, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gaeq3, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gaeq4, annotation));
return newGrounded;
}
