public override bool Equals(Object obj)
{
MajorArc arc = obj as MajorArc;
if (arc == null)
{
return(false);
}
// Check equality of MajorArc Major / major points?
return(base.Equals(obj));
}
// Checking for structural equality (is it the same segment) excluding the multiplier
public override bool StructurallyEquals(object obj)
{
MajorArc arc = obj as MajorArc;
if (arc == null)
{
return(false);
}
return(this.theCircle.StructurallyEquals(arc.theCircle) && ((this.endpoint1.StructurallyEquals(arc.endpoint1) &&
this.endpoint2.StructurallyEquals(arc.endpoint2)) ||
(this.endpoint1.StructurallyEquals(arc.endpoint2) &&
this.endpoint2.StructurallyEquals(arc.endpoint1))));
}
public static Arc GetFigureMajorArc(Circle circle, Point pt1, Point pt2)
{
MajorArc candArc = new MajorArc(circle, pt1, pt2);
// Search for exact segment first
foreach (MajorArc arc in figureMajorArcs)
{
if (arc.StructurallyEquals(candArc))
{
return(arc);
}
}
return(null);
}
public override bool CoordinateCongruent(Figure that)
{
MajorArc thatArc = that as MajorArc;
if (thatArc == null)
{
return(false);
}
if (!theCircle.CoordinateCongruent(thatArc.theCircle))
{
return(false);
}
return(Utilities.CompareValues(this.GetMajorArcMeasureDegrees(), thatArc.GetMajorArcMeasureDegrees()));
}
private static Arc GetInscribedInterceptedArc(Circle circle, Angle angle)
{
Point endpt1, endpt2;
Point pt1, pt2;
circle.FindIntersection(angle.ray1, out pt1, out pt2);
endpt1 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
circle.FindIntersection(angle.ray2, out pt1, out pt2);
endpt2 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
// Need to check if the angle is a diameter and create a semicircle
Segment chord = new Segment(endpt1, endpt2);
if (circle.DefinesDiameter(chord))
{
Point opp = circle.Midpoint(endpt1, endpt2, angle.GetVertex());
Semicircle semi = new Semicircle(circle, endpt1, endpt2, circle.OppositePoint(opp), chord);
//Find a defined semicircle of the figure that lies on the same side
Semicircle sameSideSemi = figureSemicircles.Where(s => semi.SameSideSemicircle(s)).FirstOrDefault();
//If none were found, should we throw an exception or just return the original semi?
if (sameSideSemi == null)
{
return(semi);
}
else
{
return(sameSideSemi);
}
}
//Initially assume intercepted arc is the minor arc
Arc intercepted = null;
intercepted = new MinorArc(circle, endpt1, endpt2);
//Verify assumption, create major arc if necessary
if (Arc.BetweenMinor(angle.GetVertex(), intercepted))
{
intercepted = new MajorArc(circle, endpt1, endpt2);
}
return(intercepted);
}
//Demonstrates: ExteriorAngleHalfDifferenceInterceptedArcs : two tangents
//Demonstrates: Tangents from point are congruent
public Test05(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle
Point o = new Point("O", 0, 0); points.Add(o);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
//Intersection point for two tangents
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for tangent line ac, intersection at b
Point a = new Point("A", -8, 0.25); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Points for tangent line ec, intersection at d
Point e = new Point("E", 8, 0.25); points.Add(e);
Point d = new Point("D", 3, 4); points.Add(d);
//Create point for another arc (Arc(DF)) of equal measure to (1/2)*(MajorArc(BD)-MinorArc(BD))
MinorArc minor = new MinorArc(circleO, b, d);
MajorArc major = new MajorArc(circleO, b, d);
double measure = (major.GetMajorArcMeasureDegrees() - minor.GetMinorArcMeasureDegrees()) / 2;
//Get theta for D and E
Circle unit = new Circle(o, 1.0);
Point inter1, trash;
unit.FindIntersection(new Segment(o, d), out inter1, out trash);
if (inter1.X < 0) inter1 = trash;
double dThetaDegrees = (System.Math.Acos(inter1.X)) * (180 / System.Math.PI);
double fThetaRadians = (dThetaDegrees - measure) * (System.Math.PI / 180);
//Get coordinates for E
Point unitPnt = new Point("", System.Math.Cos(fThetaRadians), System.Math.Sin(fThetaRadians));
Point f;
circleO.FindIntersection(new Segment(o, unitPnt), out f, out trash);
if (f.X < 0) f = trash;
f = new Point("F", f.X, f.Y); points.Add(f);
//Should now be able to form segments for a central angle of equal measure to (1/2)*(Arc(AB)-Arc(CD))
Segment od = new Segment(o, d); segments.Add(od);
Segment of = new Segment(o, f); segments.Add(of);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(b);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(c);
pnts.Add(d);
pnts.Add(e);
collinear.Add(new Collinear(pnts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ac = (Segment)parser.Get(new Segment(a, c));
Segment ce = (Segment)parser.Get(new Segment(c, e));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(b, circleO, ac));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, circleO, ce));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
MinorArc a1 = (MinorArc)parser.Get(new MinorArc(circleO, b, d));
MajorArc a2 = (MajorArc)parser.Get(new MajorArc(circleO, b, d));
MinorArc centralAngleArc = (MinorArc)parser.Get(new MinorArc(circleO, d, f));
given.Add(new GeometricArcEquation(new Multiplication(new NumericValue(2), centralAngleArc), new Subtraction(a2, a1)));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, c, e)), (Angle)parser.Get(new Angle(d, o, f))));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(b, c)), (Segment)parser.Get(new Segment(c, d))));
}
private static Arc GetInscribedInterceptedArc(Circle circle, Angle angle)
{
Point endpt1, endpt2;
Point pt1, pt2;
circle.FindIntersection(angle.ray1, out pt1, out pt2);
endpt1 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
circle.FindIntersection(angle.ray2, out pt1, out pt2);
endpt2 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
// Need to check if the angle is a diameter and create a semicircle
Segment chord = new Segment(endpt1, endpt2);
if (circle.DefinesDiameter(chord))
{
Point opp = circle.Midpoint(endpt1, endpt2, angle.GetVertex());
Semicircle semi = new Semicircle(circle, endpt1, endpt2, circle.OppositePoint(opp), chord);
//Find a defined semicircle of the figure that lies on the same side
Semicircle sameSideSemi = figureSemicircles.Where(s => semi.SameSideSemicircle(s)).FirstOrDefault();
//If none were found, should we throw an exception or just return the original semi?
if (sameSideSemi == null) return semi;
else return sameSideSemi;
}
//Initially assume intercepted arc is the minor arc
Arc intercepted = null;
intercepted = new MinorArc(circle, endpt1, endpt2);
//Verify assumption, create major arc if necessary
if (Arc.BetweenMinor(angle.GetVertex(), intercepted)) intercepted = new MajorArc(circle, endpt1, endpt2);
return intercepted;
}
public static Arc GetFigureMajorArc(Circle circle, Point pt1, Point pt2)
{
MajorArc candArc = new MajorArc(circle, pt1, pt2);
// Search for exact segment first
foreach (MajorArc arc in figureMajorArcs)
{
if (arc.StructurallyEquals(candArc)) return arc;
}
return null;
}
// A
// /)
// / )
// / )
// center: O )
// \ )
// \ )
// \)
// C
//
// D
// /)
// / )
// / )
// center: Q )
// \ )
// \ )
// \)
// F
//
// Congruent(Segment(AC), Segment(DF)) -> Congruent(Arc(A, C), Arc(D, F))
//
private static List<EdgeAggregator> InstantiateForwardPartOfTheorem(CongruentSegments cas)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Acquire the circles for which the segments are chords.
//
List<Circle> circles1 = Circle.GetChordCircles(cas.cs1);
List<Circle> circles2 = Circle.GetChordCircles(cas.cs2);
//
// Make all possible combinations of arcs congruent
//
foreach (Circle circle1 in circles1)
{
// Create the appropriate type of arcs from the chord and the circle
List<Semicircle> c1semi = null;
MinorArc c1minor = null;
MajorArc c1major = null;
if (circle1.DefinesDiameter(cas.cs1))
{
c1semi = CreateSemiCircles(circle1, cas.cs1);
}
else
{
c1minor = new MinorArc(circle1, cas.cs1.Point1, cas.cs1.Point2);
c1major = new MajorArc(circle1, cas.cs1.Point1, cas.cs1.Point2);
}
foreach (Circle circle2 in circles2)
{
//The two circles must be the same or congruent
if (circle1.radius == circle2.radius)
{
List<Semicircle> c2semi = null;
MinorArc c2minor = null;
MajorArc c2major = null;
List<GeometricCongruentArcs> congruencies = new List<GeometricCongruentArcs>();
if (circle2.DefinesDiameter(cas.cs2))
{
c2semi = CreateSemiCircles(circle2, cas.cs2);
congruencies.AddRange(EquateSemiCircles(c1semi, c2semi));
}
else
{
c2minor = new MinorArc(circle2, cas.cs2.Point1, cas.cs2.Point2);
c2major = new MajorArc(circle2, cas.cs2.Point1, cas.cs2.Point2);
congruencies.Add(new GeometricCongruentArcs(c1minor, c2minor));
congruencies.Add(new GeometricCongruentArcs(c1major, c2major));
}
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(cas.cs1);
antecedent.Add(cas.cs2);
antecedent.Add(cas);
foreach (GeometricCongruentArcs gcas in congruencies)
{
newGrounded.Add(new EdgeAggregator(antecedent, gcas, forwardAnnotation));
}
}
}
}
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;
}
private void CreateMajorMinorArcs(Circle circle, int p1, int p2)
{
List<Point> minorArcPoints;
List<Point> majorArcPoints;
PartitionArcPoints(circle, p1, p2, out minorArcPoints, out majorArcPoints);
MinorArc newMinorArc = new MinorArc(circle, circle.pointsOnCircle[p1], circle.pointsOnCircle[p2], minorArcPoints, majorArcPoints);
MajorArc newMajorArc = new MajorArc(circle, circle.pointsOnCircle[p1], circle.pointsOnCircle[p2], minorArcPoints, majorArcPoints);
Sector newMinorSector = new Sector(newMinorArc);
Sector newMajorSector = new Sector(newMajorArc);
if (!GeometryTutorLib.Utilities.HasStructurally<MinorArc>(minorArcs, newMinorArc))
{
minorArcs.Add(newMinorArc);
minorSectors.Add(newMinorSector);
majorSectors.Add(newMajorSector);
angles.Add(new Angle(circle.pointsOnCircle[p1], circle.center, circle.pointsOnCircle[p2]));
}
if (!GeometryTutorLib.Utilities.HasStructurally<MajorArc>(majorArcs, newMajorArc))
{
majorArcs.Add(newMajorArc);
majorSectors.Add(newMajorSector);
}
circle.AddMinorArc(newMinorArc);
circle.AddMajorArc(newMajorArc);
circle.AddMinorSector(newMinorSector);
circle.AddMajorSector(newMajorSector);
// Generate ArcInMiddle clauses for minor arc and major arc
for (int imIndex = 0; imIndex < newMinorArc.arcMinorPoints.Count; imIndex++)
{
GeometryTutorLib.Utilities.AddStructurallyUnique<ArcInMiddle>(arcInMiddle, new ArcInMiddle(newMinorArc.arcMinorPoints[imIndex], newMinorArc));
}
for (int imIndex = 0; imIndex < newMajorArc.arcMajorPoints.Count; imIndex++)
{
GeometryTutorLib.Utilities.AddStructurallyUnique<ArcInMiddle>(arcInMiddle, new ArcInMiddle(newMajorArc.arcMajorPoints[imIndex], newMajorArc));
}
}
public void AddMajorArc(MajorArc mArc)
{
majorArcs.Add(mArc);
}
