//
// Since we are cutting segments into sections, there is a direct relationship between the split side lengths for each side.
//
protected void GetGranularMidpointEquations(out List <Equation> eqs, out List <Congruent> congs)
{
eqs = new List <Equation>();
congs = new List <Congruent>();
//
// Each sub-segment is equal to each other on each side.
//
for (int side = 0; side < sideSubsegments.Length; side++)
{
for (int s1 = 0; s1 < sideSubsegments[side].Count - 1; s1++)
{
for (int s2 = s1 + 1; s2 < sideSubsegments[side].Count; s2++)
{
congs.Add(new GeometricCongruentSegments(sideSubsegments[side][s1], sideSubsegments[side][s2]));
}
}
}
//
// Each sub-segment is equation to a fraction of the side length.
//
int factor = (int)Math.Pow(2, NUM_MID_SEGMENT_POINTS);
NumericValue factorVal = new NumericValue(factor);
if (factor != sideSubsegments[0].Count)
{
throw new Exception("Disagreement with the number of sub-segments in polygon");
}
for (int side = 0; side < sideSubsegments.Length; side++)
{
foreach (Segment subSeg in sideSubsegments[side])
{
// Factor * sub-segment = whole side
eqs.Add(new GeometricSegmentEquation(new Multiplication(factorVal, subSeg), orderedSides[side]));
}
}
}
//
// Triangle(A, B, C) -> m\angle ABC + m\angle CAB + m\angle BCA = 180^o
//
public static List<EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.SUM_ANGLES_IN_TRIANGLE_180;
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Triangle tri = c as Triangle;
if (tri == null) return newGrounded;
// Generate, by definition the sum of the three angles equal 180^o
Angle a1 = new Angle(tri.Point1, tri.Point2, tri.Point3);
Angle a2 = new Angle(tri.Point3, tri.Point1, tri.Point2);
Angle a3 = new Angle(tri.Point2, tri.Point3, tri.Point1);
Addition add = new Addition(a1, a2);
Addition overallAdd = new Addition(add, a3);
NumericValue value = new NumericValue(180); // Sum is 180^o
GeometricAngleEquation eq = new GeometricAngleEquation(overallAdd, value);
List<GroundedClause> antecedent = Utilities.MakeList<GroundedClause>(tri);
newGrounded.Add(new EdgeAggregator(antecedent, eq, 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
//
// 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;
}
//
// 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;
}
//
// Check for (basically) atomic equations involving one unknown and constants otherwise.
//
private static FlatEquation SimplifyForMultipliersAndConstants(FlatEquation inEq)
{
if (inEq.lhsExps.Count != 1 || inEq.rhsExps.Count != 1) return inEq;
//
// Figure out what we're looking at.
//
NumericValue value = null;
GroundedClause unknown = null;
if (inEq.lhsExps[0] is NumericValue)
{
value = inEq.lhsExps[0] as NumericValue;
unknown = inEq.rhsExps[0];
}
else if (inEq.rhsExps[0] is NumericValue)
{
value = inEq.rhsExps[0] as NumericValue;
unknown = inEq.lhsExps[0];
}
// Not the type of equation we were looking for.
else return inEq;
//
// Divide both sides to simplify.
//
if (unknown.multiplier != 1)
{
NumericValue newValue = new NumericValue(value.DoubleValue / unknown.multiplier);
// reset the multiplier
unknown.multiplier = 1;
return new FlatEquation(Utilities.MakeList<GroundedClause>(unknown), Utilities.MakeList<GroundedClause>(newValue));
}
// Nothing happened so return original
return inEq;
}
//
// 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;
}