private static List<EdgeAggregator> InstantiateToDefinition(CongruentSegments css)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Find all the circles for which the two segments are radii.
//
List<Circle> circlesCSS1 = Circle.GetFigureCirclesByRadius(css.cs1);
List<Circle> circlesCSS2 = Circle.GetFigureCirclesByRadius(css.cs2);
//
// Since the radii are congruent, the circles are therefore congruent.
//
foreach (Circle cc1 in circlesCSS1)
{
foreach (Circle cc2 in circlesCSS2)
{
// Avoid generating refexive relationships(?)
if (!cc1.StructurallyEquals(cc2))
{
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(css);
antecedent.Add(cc1);
antecedent.Add(cc2);
GeometricCongruentCircles gccs = new GeometricCongruentCircles(cc1, cc2);
newGrounded.Add(new EdgeAggregator(antecedent, gccs, annotation));
}
}
}
return newGrounded;
}
// Return the shared segment in both congruences
public Segment SegmentShared(CongruentSegments thatCC)
{
if (SharesNumClauses(thatCC) != 1)
{
return(null);
}
return(smallerSegment.Equals(thatCC.cs1) || smallerSegment.Equals(thatCC.cs2) ? smallerSegment : largerSegment);
}
// Return the shared segment in both congruences
public Segment SegmentShared(CongruentSegments thatCC)
{
if (SharesNumClauses(thatCC) != 1)
{
return(null);
}
return(cs1.Equals(thatCC.cs1) || cs1.Equals(thatCC.cs2) ? cs1 : cs2);
}
public static bool AcquireCongruences(KnownMeasurementsAggregator known, List <GroundedClause> clauses)
{
bool addedKnown = false;
foreach (GeometryTutorLib.ConcreteAST.GroundedClause clause in clauses)
{
GeometryTutorLib.ConcreteAST.CongruentSegments cs = clause as GeometryTutorLib.ConcreteAST.CongruentSegments;
if (cs != null && !cs.IsReflexive())
{
double length1 = known.GetSegmentLength(cs.cs1);
double length2 = known.GetSegmentLength(cs.cs2);
if (length1 >= 0 && length2 < 0)
{
if (known.AddSegmentLength(cs.cs2, length1))
{
addedKnown = true;
}
}
if (length1 <= 0 && length2 > 0)
{
if (known.AddSegmentLength(cs.cs1, length2))
{
addedKnown = true;
}
}
// else: both known
}
GeometryTutorLib.ConcreteAST.CongruentAngles cas = clause as GeometryTutorLib.ConcreteAST.CongruentAngles;
if (cas != null && !cas.IsReflexive())
{
double measure1 = known.GetAngleMeasure(cas.ca1);
double measure2 = known.GetAngleMeasure(cas.ca2);
if (measure1 >= 0 && measure2 < 0)
{
if (known.AddAngleMeasureDegree(cas.ca2, measure1))
{
addedKnown = true;
}
}
if (measure1 <= 0 && measure2 > 0)
{
if (known.AddAngleMeasureDegree(cas.ca1, measure2))
{
addedKnown = true;
}
}
// else: both known
}
}
return(addedKnown);
}
public override bool Equals(Object obj)
{
CongruentSegments ccs = obj as CongruentSegments;
if (ccs == null)
{
return(false);
}
return((cs1.Equals(ccs.cs1) && cs2.Equals(ccs.cs2)) || (cs1.Equals(ccs.cs2) && cs2.Equals(ccs.cs1)) && base.Equals(obj));
}
// Return the number of shared segments in both congruences
public int SharesNumClauses(CongruentSegments thatCS)
{
//CongruentSegments css = thatPS as CongruentSegments;
//if (css == null) return 0;
int numShared = smallerSegment.Equals(thatCS.cs1) || smallerSegment.Equals(thatCS.cs2) ? 1 : 0;
numShared += largerSegment.Equals(thatCS.cs1) || largerSegment.Equals(thatCS.cs2) ? 1 : 0;
return(numShared);
}
public override bool StructurallyEquals(Object obj)
{
CongruentSegments ccs = obj as CongruentSegments;
if (ccs == null)
{
return(false);
}
return((cs1.StructurallyEquals(ccs.cs1) && cs2.StructurallyEquals(ccs.cs2)) ||
(cs1.StructurallyEquals(ccs.cs2) && cs2.StructurallyEquals(ccs.cs1)));
}
public Segment SharedSegment(CongruentSegments ccs)
{
if (ccs.cs1.StructurallyEquals(this.cs1) || ccs.cs2.StructurallyEquals(this.cs1))
{
return(this.cs1);
}
if (ccs.cs1.StructurallyEquals(this.cs2) || ccs.cs2.StructurallyEquals(this.cs2))
{
return(this.cs2);
}
return(null);
}
//
// Are the legs congruent (for an isosceles trapezoid)?
//
public bool CreatesCongruentLegs(CongruentSegments css)
{
if (leftLeg.StructurallyEquals(css.cs1) && rightLeg.StructurallyEquals(css.cs2))
{
return(true);
}
if (leftLeg.StructurallyEquals(css.cs2) && rightLeg.StructurallyEquals(css.cs1))
{
return(true);
}
return(false);
}
// Return the number of shared segments in both congruences
public override int SharesNumClauses(Congruent thatCC)
{
CongruentSegments ccss = thatCC as CongruentSegments;
if (ccss == null)
{
return(0);
}
int numShared = cs1.Equals(ccss.cs1) || cs1.Equals(ccss.cs2) ? 1 : 0;
numShared += cs2.Equals(ccss.cs1) || cs2.Equals(ccss.cs2) ? 1 : 0;
return(numShared);
}
//
// 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;
}
public static List <GenericInstantiator.EdgeAggregator> CreateTransitiveCongruence(Congruent congruent1, Congruent congruent2)
{
List <GenericInstantiator.EdgeAggregator> newGrounded = new List <GenericInstantiator.EdgeAggregator>();
//
// Create the antecedent clauses
//
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(congruent1);
antecedent.Add(congruent2);
//
// Create the consequent clause
//
Congruent newCC = null;
if (congruent1 is CongruentSegments)
{
CongruentSegments css1 = congruent1 as CongruentSegments;
CongruentSegments css2 = congruent2 as CongruentSegments;
Segment shared = css1.SegmentShared(css2);
newCC = new AlgebraicCongruentSegments(css1.OtherSegment(shared), css2.OtherSegment(shared));
}
else if (congruent1 is CongruentAngles)
{
CongruentAngles cas1 = congruent1 as CongruentAngles;
CongruentAngles cas2 = congruent2 as CongruentAngles;
Angle shared = cas1.AngleShared(cas2);
newCC = new AlgebraicCongruentAngles(cas1.OtherAngle(shared), cas2.OtherAngle(shared));
}
if (newCC == null)
{
System.Diagnostics.Debug.WriteLine("");
throw new NullReferenceException("Unexpected Problem in Atomic substitution...");
}
newGrounded.Add(new GenericInstantiator.EdgeAggregator(antecedent, newCC, annotation));
return(newGrounded);
}
//
// Are the legs congruent (for an isosceles trapezoid)?
//
public bool CreatesCongruentLegs(CongruentSegments css)
{
if (leftLeg.StructurallyEquals(css.cs1) && rightLeg.StructurallyEquals(css.cs2)) return true;
if (leftLeg.StructurallyEquals(css.cs2) && rightLeg.StructurallyEquals(css.cs1)) return true;
return false;
}
public bool SharedVertex(CongruentSegments ccs)
{
return(ccs.cs1.SharedVertex(cs1) != null || ccs.cs1.SharedVertex(cs2) != null ||
ccs.cs2.SharedVertex(cs1) != null || ccs.cs2.SharedVertex(cs2) != null);
}
//
// Does this congruent pair apply to this quadrilateral?
//
public bool HasOppositeCongruentSides(CongruentSegments cs)
{
return(AreOppositeSides(cs.cs1, cs.cs2));
}
// 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;
}
//
// Does this congruent pair apply to this quadrilateral?
//
public bool HasOppositeCongruentSides(CongruentSegments cs)
{
return AreOppositeSides(cs.cs1, cs.cs2);
}
//
// Acquires all of the applicable congruent segments; then checks HL
//
private static List<EdgeAggregator> ReconfigureAndCheck(RightTriangle rt1, RightTriangle rt2, CongruentSegments css1, CongruentSegments css2)
{
return CollectAndCheckHL(rt1, rt2, css1, css2, rt1, rt2);
}
private static List<EdgeAggregator> InstantiateToIsoscelesTrapezoid(Trapezoid trapezoid, CongruentSegments css, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Does this paralle set apply to this triangle?
if (!trapezoid.CreatesCongruentLegs(css)) return newGrounded;
//
// Create the new IsoscelesTrapezoid object
//
Strengthened newIsoscelesTrapezoid = new Strengthened(trapezoid, new IsoscelesTrapezoid(trapezoid));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
antecedent.Add(css);
newGrounded.Add(new EdgeAggregator(antecedent, newIsoscelesTrapezoid, annotation));
return newGrounded;
}
// Of the congruent pair, return the segment that applies to this triangle
public Segment GetSegment(CongruentSegments ccss)
{
if (HasSegment(ccss.cs1)) return ccss.cs1;
if (HasSegment(ccss.cs2)) return ccss.cs2;
return null;
}
// Return the number of shared segments in both congruences
public int SharesNumClauses(CongruentSegments thatCS)
{
//CongruentSegments css = thatPS as CongruentSegments;
//if (css == null) return 0;
int numShared = smallerSegment.Equals(thatCS.cs1) || smallerSegment.Equals(thatCS.cs2) ? 1 : 0;
numShared += largerSegment.Equals(thatCS.cs1) || largerSegment.Equals(thatCS.cs2) ? 1 : 0;
return numShared;
}
//
// 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;
}
// Return the shared segment in both congruences
public Segment SegmentShared(CongruentSegments thatCC)
{
if (SharesNumClauses(thatCC) != 1) return null;
return smallerSegment.Equals(thatCC.cs1) || smallerSegment.Equals(thatCC.cs2) ? smallerSegment : largerSegment;
}
private static List<EdgeAggregator> InstantiateToDefinition(Triangle tri, CongruentSegments cs1, CongruentSegments cs2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Do these congruences relate one common segment?
Segment shared = cs1.SharedSegment(cs2);
if (shared == null) return newGrounded;
//
// Do these congruences apply to this triangle?
//
if (!tri.HasSegment(cs1.cs1) || !tri.HasSegment(cs1.cs2)) return newGrounded;
if (!tri.HasSegment(cs2.cs1) || !tri.HasSegment(cs2.cs2)) return newGrounded;
//
// These cannot be reflexive congruences.
//
if (cs1.IsReflexive() || cs2.IsReflexive()) return newGrounded;
//
// Are the non-shared segments unique?
//
Segment other1 = cs1.OtherSegment(shared);
Segment other2 = cs2.OtherSegment(shared);
if (other1.StructurallyEquals(other2)) return newGrounded;
//
// Generate the new equialteral clause
//
Strengthened newStrengthened = new Strengthened(tri, new EquilateralTriangle(tri));
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(cs1);
antecedent.Add(cs2);
antecedent.Add(tri);
newGrounded.Add(new EdgeAggregator(antecedent, newStrengthened, annotation));
return newGrounded;
}
//
// Congruent(Segment(A, M), Segment(M, B)) -> Midpoint(M, Segment(A, B))
//
private static List<EdgeAggregator> InstantiateToMidpoint(InMiddle im, CongruentSegments css)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Point midpoint = css.cs1.SharedVertex(css.cs2);
// Does this InMiddle relate to the congruent segments?
if (!im.point.StructurallyEquals(midpoint)) return newGrounded;
// Do the congruent segments combine into a single segment equating to the InMiddle?
Segment overallSegment = new Segment(css.cs1.OtherPoint(midpoint), css.cs2.OtherPoint(midpoint));
if (!im.segment.StructurallyEquals(overallSegment)) return newGrounded;
Strengthened newMidpoint = new Strengthened(im, new Midpoint(im));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(im);
antecedent.Add(css);
newGrounded.Add(new EdgeAggregator(antecedent, newMidpoint, annotation));
return newGrounded;
}
//
//
//
private static List<EdgeAggregator> IfCongruencesApplyToTrianglesGenerate(Triangle ct1, Triangle ct2, CongruentSegments css1, CongruentSegments css2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// The congruent relationships need to link the given triangles
//
if (!css1.LinksTriangles(ct1, ct2)) return newGrounded;
if (!css2.LinksTriangles(ct1, ct2)) return newGrounded;
Segment seg1Tri1 = ct1.GetSegment(css1);
Segment seg2Tri1 = ct1.GetSegment(css2);
Segment seg1Tri2 = ct2.GetSegment(css1);
Segment seg2Tri2 = ct2.GetSegment(css2);
// Avoid redundant segments, if it arises
if (seg1Tri1.StructurallyEquals(seg2Tri1)) return newGrounded;
if (seg1Tri2.StructurallyEquals(seg2Tri2)) return newGrounded;
//
// Proportional Segments (we generate only as needed to avoid bloat in the hypergraph (assuming they are used by both triangles)
// We avoid generating proportions if they are truly congruences.
//
List<GroundedClause> propAntecedent = new List<GroundedClause>();
propAntecedent.Add(css1);
propAntecedent.Add(css2);
SegmentRatio ratio1 = new SegmentRatio(seg1Tri1, seg1Tri2);
SegmentRatio ratio2 = new SegmentRatio(seg2Tri1, seg2Tri2);
GeometricSegmentRatioEquation newEq = new GeometricSegmentRatioEquation(ratio1, ratio2);
newGrounded.Add(new EdgeAggregator(propAntecedent, newEq, annotation));
////
//// Only generate if ratios are not 1.
////
//GeometricSegmentRatio newProp = null;
//if (!Utilities.CompareValues(seg1Tri1.Length, seg1Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg1Tri1, seg1Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg1Tri1.Length, seg2Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg1Tri1, seg2Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg2Tri1.Length, seg1Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg2Tri1, seg1Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
//if (!Utilities.CompareValues(seg2Tri1.Length, seg2Tri2.Length))
//{
// newProp = new GeometricSegmentRatio(seg2Tri1, seg2Tri2);
// newGrounded.Add(new EdgeAggregator(propAntecedent, newProp, annotation));
//}
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToTheorem(Quadrilateral quad, CongruentSegments cs, Parallel parallel)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentSides(cs)) return newGrounded;
if (!quad.HasOppositeParallelSides(parallel)) return newGrounded;
// Do the congruent segments coincide with these parallel segments?
if (!parallel.segment1.HasSubSegment(cs.cs1) && !parallel.segment2.HasSubSegment(cs.cs1)) return newGrounded;
if (!parallel.segment1.HasSubSegment(cs.cs2) && !parallel.segment2.HasSubSegment(cs.cs2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs);
antecedent.Add(parallel);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
//
// Does this parallel set apply to this quadrilateral?
//
public bool HasAdjacentCongruentSides(CongruentSegments cs)
{
return AreAdjacentSides(cs.cs1, cs.cs2);
}
public Segment SharedSegment(CongruentSegments ccs)
{
if (ccs.cs1.StructurallyEquals(this.cs1) || ccs.cs2.StructurallyEquals(this.cs1)) return this.cs1;
if (ccs.cs1.StructurallyEquals(this.cs2) || ccs.cs2.StructurallyEquals(this.cs2)) return this.cs2;
return null;
}
//
// Acquires all of the applicable congruent segments; then checks HL
//
private static List<EdgeAggregator> CollectAndCheckHL(RightTriangle rt1, RightTriangle rt2,
CongruentSegments css1, CongruentSegments css2,
GroundedClause original1, GroundedClause original2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The Congruence pairs must relate the two triangles
if (!css1.LinksTriangles(rt1, rt2) || !css2.LinksTriangles(rt1, rt2)) return newGrounded;
// One of the congruence pairs must relate the hypotenuses
Segment hypotenuse1 = rt1.OtherSide(rt1.rightAngle);
Segment hypotenuse2 = rt2.OtherSide(rt2.rightAngle);
// Determine the specific congruence pair that relates the hypotenuses
CongruentSegments hypotenuseCongruence = null;
CongruentSegments nonHypotenuseCongruence = null;
if (css1.HasSegment(hypotenuse1) && css1.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css1;
nonHypotenuseCongruence = css2;
}
else if (css2.HasSegment(hypotenuse1) && css2.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css2;
nonHypotenuseCongruence = css1;
}
else return newGrounded;
// Sanity check that the non hypotenuse congruence pair does not contain hypotenuse
if (nonHypotenuseCongruence.HasSegment(hypotenuse1) || nonHypotenuseCongruence.HasSegment(hypotenuse2)) return newGrounded;
//
// We now have a hypotenuse leg situation; acquire the point-to-point congruence mapping
//
List<Point> triangleOne = new List<Point>();
List<Point> triangleTwo = new List<Point>();
// Right angle vertices correspond
triangleOne.Add(rt1.rightAngle.GetVertex());
triangleTwo.Add(rt2.rightAngle.GetVertex());
Point nonRightVertexRt1 = rt1.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse1);
Point nonRightVertexRt2 = rt2.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse2);
triangleOne.Add(nonRightVertexRt1);
triangleTwo.Add(nonRightVertexRt2);
triangleOne.Add(hypotenuse1.OtherPoint(nonRightVertexRt1));
triangleTwo.Add(hypotenuse2.OtherPoint(nonRightVertexRt2));
//
// Construct the new deduced relationships
//
GeometricCongruentTriangles ccts = new GeometricCongruentTriangles(new Triangle(triangleOne),
new Triangle(triangleTwo));
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(css1);
antecedent.Add(css2);
newGrounded.Add(new EdgeAggregator(antecedent, ccts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(ccts, triangleOne, triangleTwo));
return newGrounded;
}
public bool SharedVertex(CongruentSegments ccs)
{
return ccs.cs1.SharedVertex(cs1) != null || ccs.cs1.SharedVertex(cs2) != null ||
ccs.cs2.SharedVertex(cs1) != null || ccs.cs2.SharedVertex(cs2) != null;
}
private static List<EdgeAggregator> ReconfigureAndCheck(Strengthened streng1, Strengthened streng2, CongruentSegments css1, CongruentSegments css2)
{
return CollectAndCheckHL(streng1.strengthened as RightTriangle, streng2.strengthened as RightTriangle, css1, css2, streng1, streng2);
}
// Return the shared segment in both congruences
public Segment SegmentShared(CongruentSegments thatCC)
{
if (SharesNumClauses(thatCC) != 1) return null;
return cs1.Equals(thatCC.cs1) || cs1.Equals(thatCC.cs2) ? cs1 : cs2;
}
//
// Does this parallel set apply to this quadrilateral?
//
public bool HasAdjacentCongruentSides(CongruentSegments cs)
{
return(AreAdjacentSides(cs.cs1, cs.cs2));
}
//
// Checks for ASA given the 5 values
//
private static List<EdgeAggregator> InstantiateAAS(Triangle tri1, Triangle tri2,
CongruentAngles cas1, CongruentAngles cas2, CongruentSegments css)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// All congruence pairs must minimally relate the triangles
//
if (!cas1.LinksTriangles(tri1, tri2)) return newGrounded;
if (!cas2.LinksTriangles(tri1, tri2)) return newGrounded;
if (!css.LinksTriangles(tri1, tri2)) return newGrounded;
// Is this angle an 'extension' of the actual triangle angle? If so, acquire the normalized version of
// the angle, using only the triangle vertices to represent the angle
Angle angle1Tri1 = tri1.NormalizeAngle(tri1.AngleBelongs(cas1));
Angle angle1Tri2 = tri2.NormalizeAngle(tri2.AngleBelongs(cas1));
Angle angle2Tri1 = tri1.NormalizeAngle(tri1.AngleBelongs(cas2));
Angle angle2Tri2 = tri2.NormalizeAngle(tri2.AngleBelongs(cas2));
// The angles for each triangle must be distinct
if (angle1Tri1.Equals(angle2Tri1) || angle1Tri2.Equals(angle2Tri2)) return newGrounded;
Segment segTri1 = tri1.GetSegment(css);
Segment segTri2 = tri2.GetSegment(css);
// ASA situations
if (segTri1.IsIncludedSegment(angle1Tri1, angle2Tri1)) return newGrounded;
if (segTri2.IsIncludedSegment(angle1Tri2, angle2Tri2)) return newGrounded;
// The segments for each triangle must be corresponding
if (segTri1.Equals(tri1.OtherSide(angle1Tri1)) && segTri2.Equals(tri2.OtherSide(angle2Tri2))) return newGrounded;
if (segTri1.Equals(tri1.OtherSide(angle2Tri1)) && segTri2.Equals(tri2.OtherSide(angle1Tri2))) return newGrounded;
//
// Construct the corrsesponding points between the triangles
//
List<Point> triangleOne = new List<Point>();
List<Point> triangleTwo = new List<Point>();
triangleOne.Add(angle1Tri1.GetVertex());
triangleTwo.Add(angle1Tri2.GetVertex());
triangleOne.Add(angle2Tri1.GetVertex());
triangleTwo.Add(angle2Tri2.GetVertex());
// We know the segment endpoint mappings above, now acquire the opposite point
triangleOne.Add(tri1.OtherPoint(angle1Tri1.GetVertex(), angle2Tri1.GetVertex()));
triangleTwo.Add(tri2.OtherPoint(angle1Tri2.GetVertex(), angle2Tri2.GetVertex()));
//
// Construct the new clauses: congruent triangles and CPCTC
//
GeometricCongruentTriangles gcts = new GeometricCongruentTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(cas1);
antecedent.Add(cas2);
antecedent.Add(css);
newGrounded.Add(new EdgeAggregator(antecedent, gcts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(gcts, triangleOne, triangleTwo));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToKite(Quadrilateral quad, CongruentSegments cs1, CongruentSegments cs2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The congruences should not share a side.
if (cs1.SharedSegment(cs2) != null) return newGrounded;
// The congruent pairs should not also be congruent to each other
if (cs1.cs1.CoordinateCongruent(cs2.cs1)) return newGrounded;
// Does both set of congruent segments apply to the quadrilateral?
if (!quad.HasAdjacentCongruentSides(cs1)) return newGrounded;
if (!quad.HasAdjacentCongruentSides(cs2)) return newGrounded;
//
// Create the new Kite object
//
Strengthened newKite = new Strengthened(quad, new Kite(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs1);
antecedent.Add(cs2);
newGrounded.Add(new EdgeAggregator(antecedent, newKite, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToRhombus(Quadrilateral quad, CongruentSegments cs1, CongruentSegments cs2, CongruentSegments cs3)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// The 3 congruent segments pairs must relate; one pair must link the two others.
// Determine the link segments as well as the opposite sides.
//
CongruentSegments link = null;
CongruentSegments opp1 = null;
CongruentSegments opp2 = null;
if (cs1.SharedSegment(cs2) != null && cs1.SharedSegment(cs3) != null)
{
link = cs1;
opp1 = cs2;
opp2 = cs3;
}
else if (cs2.SharedSegment(cs1) != null && cs2.SharedSegment(cs3) != null)
{
link = cs2;
opp1 = cs1;
opp2 = cs3;
}
else if (cs3.SharedSegment(cs1) != null && cs3.SharedSegment(cs2) != null)
{
link = cs3;
opp1 = cs1;
opp2 = cs2;
}
else return newGrounded;
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentSides(opp1)) return newGrounded;
if (!quad.HasOppositeCongruentSides(opp2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newRhombus = new Strengthened(quad, new Rhombus(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs1);
antecedent.Add(cs2);
antecedent.Add(cs3);
newGrounded.Add(new EdgeAggregator(antecedent, newRhombus, annotation));
return newGrounded;
}
/// <summary>
/// Figure out what possible segment combinations are before showing the window.
/// </summary>
protected override void OnShow()
{
options = new Dictionary<GeometryTutorLib.ConcreteAST.Segment, List<GeometryTutorLib.ConcreteAST.Segment>>();
//Get a list of all congruent segment givens
List<GroundedClause> csegs = new List<GroundedClause>();
foreach (GroundedClause gc in currentGivens)
{
CongruentSegments cseg = gc as CongruentSegments;
if (cseg != null)
{
csegs.Add(cseg);
}
}
//Pick a first segment...
foreach (GeometryTutorLib.ConcreteAST.Segment s1 in parser.backendParser.implied.segments)
{
List<GeometryTutorLib.ConcreteAST.Segment> possible = new List<GeometryTutorLib.ConcreteAST.Segment>();
//... and see what other segments are viable second options.
foreach (GeometryTutorLib.ConcreteAST.Segment s2 in parser.backendParser.implied.segments)
{
if (s1.Length == s2.Length)
{
CongruentSegments cseg = new CongruentSegments(s1, s2);
if (!s1.StructurallyEquals(s2) && !StructurallyContains(csegs, cseg))
{
possible.Add(s2);
}
}
}
//If we found a possible list of combinations, add it to the dictionary
if (possible.Count > 0)
{
options.Add(s1, possible);
}
}
//Set the options of the segment1 combo box
segment1.ItemsSource = null; //Graphical refresh
segment1.ItemsSource = options.Keys;
}
//
// Checks for SSS given the 5 values
//
private static List<EdgeAggregator> InstantiateSSS(Triangle tri1, Triangle tri2, CongruentSegments css1, CongruentSegments css2, CongruentSegments css3)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// All congruence pairs must minimally relate the triangles
//
if (!css1.LinksTriangles(tri1, tri2)) return newGrounded;
if (!css2.LinksTriangles(tri1, tri2)) return newGrounded;
if (!css3.LinksTriangles(tri1, tri2)) return newGrounded;
Segment seg1Tri1 = tri1.GetSegment(css1);
Segment seg1Tri2 = tri2.GetSegment(css1);
Segment seg2Tri1 = tri1.GetSegment(css2);
Segment seg2Tri2 = tri2.GetSegment(css2);
Segment seg3Tri1 = tri1.GetSegment(css3);
Segment seg3Tri2 = tri2.GetSegment(css3);
//
// The vertices of both triangles must all be distinct and cover the triangle completely.
//
Point vertex1Tri1 = seg1Tri1.SharedVertex(seg2Tri1);
Point vertex2Tri1 = seg2Tri1.SharedVertex(seg3Tri1);
Point vertex3Tri1 = seg1Tri1.SharedVertex(seg3Tri1);
if (vertex1Tri1 == null || vertex2Tri1 == null || vertex3Tri1 == null) return newGrounded;
if (vertex1Tri1.StructurallyEquals(vertex2Tri1) ||
vertex1Tri1.StructurallyEquals(vertex3Tri1) ||
vertex2Tri1.StructurallyEquals(vertex3Tri1)) return newGrounded;
Point vertex1Tri2 = seg1Tri2.SharedVertex(seg2Tri2);
Point vertex2Tri2 = seg2Tri2.SharedVertex(seg3Tri2);
Point vertex3Tri2 = seg1Tri2.SharedVertex(seg3Tri2);
if (vertex1Tri2 == null || vertex2Tri2 == null || vertex3Tri2 == null) return newGrounded;
if (vertex1Tri2.StructurallyEquals(vertex2Tri2) ||
vertex1Tri2.StructurallyEquals(vertex3Tri2) ||
vertex2Tri2.StructurallyEquals(vertex3Tri2)) return newGrounded;
//
// Construct the corresponding points between the triangles
//
List<Point> triangleOne = new List<Point>();
List<Point> triangleTwo = new List<Point>();
triangleOne.Add(vertex1Tri1);
triangleTwo.Add(vertex1Tri2);
triangleOne.Add(vertex2Tri1);
triangleTwo.Add(vertex2Tri2);
triangleOne.Add(vertex3Tri1);
triangleTwo.Add(vertex3Tri2);
//
// Construct the new clauses: congruent triangles and CPCTC
//
GeometricCongruentTriangles gcts = new GeometricCongruentTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(css1);
antecedent.Add(css2);
antecedent.Add(css3);
newGrounded.Add(new EdgeAggregator(antecedent, gcts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(gcts, triangleOne, triangleTwo));
return newGrounded;
}
//
// DO NOT generate a new clause, instead, report the result and generate all applicable
// clauses attributed to this strengthening of a triangle from scalene to isosceles
//
private static EdgeAggregator StrengthenToIsosceles(Triangle tri, CongruentSegments ccss)
{
Strengthened newStrengthened = new Strengthened(tri, new IsoscelesTriangle(tri));
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(ccss);
antecedent.Add(tri);
return new EdgeAggregator(antecedent, newStrengthened, annotation);
}
private static List<EdgeAggregator> InstantiateToTheorem(Quadrilateral quad, CongruentSegments cs1, CongruentSegments cs2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentSides(cs1)) return newGrounded;
if (!quad.HasOppositeCongruentSides(cs2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs1);
antecedent.Add(cs2);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
