//
// Generate Proportional relationships only if those proportions may be used by a figure (in this case, only triangles)
//
// Triangle(A, B, C), Triangle(D, E, F),
//
// Congruent(Segment(A, B), Segment(B, C)), Congruent(Segment(D, E), Segment(E, F)) -> Similar(Triangle(A, B, C), Triangle(D, E, F)),
// Proportional(Segment(A, B), Segment(D, E)),
// Proportional(Segment(A, B), Segment(E, F)),
// Proportional(Segment(B, C), Segment(D, E)),
// Proportional(Segment(B, C), Segment(E, F)),
//
public static List <EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.CONGRUENT_SEGMENTS_IMPLY_PROPORTIONAL_SEGMENTS_DEFINITION;
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (!(c is Triangle) && !(c is CongruentSegments))
{
return(newGrounded);
}
// If this is a new triangle, check for triangles which may be Similar to this new triangle
if (c is Triangle)
{
Triangle candidateTri = c as Triangle;
foreach (Triangle oldTriangle in candidateTriangles)
{
for (int m = 0; m < candidateCongruentSegments.Count - 1; m++)
{
for (int n = m + 1; n < candidateCongruentSegments.Count; n++)
{
newGrounded.AddRange(IfCongruencesApplyToTrianglesGenerate(candidateTri, oldTriangle, candidateCongruentSegments[m], candidateCongruentSegments[n]));
}
}
}
// Add this triangle to the list of possible clauses to unify later
candidateTriangles.Add(candidateTri);
}
//
// Two sets of congruent segments can lead to proportionality
//
else if (c is CongruentSegments)
{
CongruentSegments newCss = c as CongruentSegments;
// Avoid reflexive relationships since they will not lead to interesting proportional relationships
if (newCss.IsReflexive())
{
return(newGrounded);
}
for (int i = 0; i < candidateTriangles.Count - 1; i++)
{
for (int j = i + 1; j < candidateTriangles.Count; j++)
{
foreach (CongruentSegments css in candidateCongruentSegments)
{
newGrounded.AddRange(IfCongruencesApplyToTrianglesGenerate(candidateTriangles[i], candidateTriangles[j], css, newCss));
}
}
}
candidateCongruentSegments.Add(newCss);
}
return(newGrounded);
}
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);
}
//
// 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> InstantiateToDefinition(GroundedClause clause)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is Triangle)
{
// Avoid strengthening an equilateral triangle to an equilateral triangle.
if (clause is EquilateralTriangle || (clause as Triangle).provenEquilateral)
{
return(newGrounded);
}
candTriangles.Add(clause as Triangle);
}
else if (clause is CongruentSegments)
{
CongruentSegments cs = clause as CongruentSegments;
foreach (Triangle tri in candTriangles)
{
for (int s1 = 0; s1 < candCongruent.Count - 1; s1++)
{
for (int s2 = s1 + 1; s2 < candCongruent.Count; s2++)
{
newGrounded.AddRange(InstantiateToDefinition(tri, candCongruent[s1], candCongruent[s2]));
}
}
}
candCongruent.Add(cs);
}
return(newGrounded);
}
// B ---------V---------A
// \
// \
// \
// C
//
// Congruent(Segment(B, V), Segment(V, A)), Intersection(V, Segment(B, A), Segment(V, C)) -> SegmentBisector(Segment(V, C), Segment(B, A))
//
public static List <EdgeAggregator> InstantiateToSegmentBisector(GroundedClause c)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (c is CongruentSegments)
{
CongruentSegments conSegs = c as CongruentSegments;
// We are not interested in a reflexive relationship
if (conSegs.IsReflexive())
{
return(newGrounded);
}
// The congruent segments need to share an endpoint (adjacent congruent segments)
Point shared = conSegs.cs1.SharedVertex(conSegs.cs2);
if (shared == null)
{
return(newGrounded);
}
// The segments need to be collinear
if (!conSegs.cs1.IsCollinearWith(conSegs.cs2))
{
return(newGrounded);
}
// Match the congruences with the intersection
foreach (Intersection inter in candidateIntersection)
{
newGrounded.AddRange(InstantiateToDef(shared, inter, conSegs));
}
// Did not unify so add to the candidate list
candidateCongruent.Add(conSegs);
}
else if (c is Intersection)
{
Intersection inter = c as Intersection;
// /
// /
// /____
// If we have a corner situation, we are not interested
if (inter.StandsOnEndpoint())
{
return(newGrounded);
}
foreach (CongruentSegments cs in candidateCongruent)
{
newGrounded.AddRange(InstantiateToDef(cs.cs1.SharedVertex(cs.cs2), inter, cs));
}
// Did not unify so add to the candidate list
candidateIntersection.Add(inter);
}
return(newGrounded);
}
private static List <EdgeAggregator> InstantiateToRhombus(GroundedClause clause)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is Quadrilateral)
{
Quadrilateral quad = clause as Quadrilateral;
if (!quad.IsStrictQuadrilateral())
{
return(newGrounded);
}
foreach (CongruentSegments oldCs in candidateCongruent)
{
foreach (Parallel parallel in candidateParallel)
{
newGrounded.AddRange(InstantiateToTheorem(quad, oldCs, parallel));
}
}
candidateQuadrilateral.Add(quad);
}
else if (clause is CongruentSegments)
{
CongruentSegments newCs = clause as CongruentSegments;
if (newCs.IsReflexive())
{
return(newGrounded);
}
foreach (Quadrilateral quad in candidateQuadrilateral)
{
foreach (Parallel parallel in candidateParallel)
{
newGrounded.AddRange(InstantiateToTheorem(quad, newCs, parallel));
}
}
candidateCongruent.Add(newCs);
}
else if (clause is Parallel)
{
Parallel newParallel = clause as Parallel;
foreach (Quadrilateral quad in candidateQuadrilateral)
{
foreach (CongruentSegments oldCs in candidateCongruent)
{
newGrounded.AddRange(InstantiateToTheorem(quad, oldCs, newParallel));
}
}
candidateParallel.Add(newParallel);
}
return(newGrounded);
}
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);
}
// A D
// /\ / \
// / \ / \
// / \ / \
// /______\ /_______\
// B C E F
//
// In order for two triangles to be congruent, we require the following:
// Triangle(A, B, C), Triangle(D, E, F),
// Congruent(Segment(A, B), Segment(D, E)),
// Congruent(Segment(A, C), Angle(D, F)),
// Congruent(Segment(B, C), Segment(E, F)) -> Congruent(Triangle(A, B, C), Triangle(D, E, F)),
// Congruent(Angle(A, B, C), Angle(D, E, F)),
// Congruent(Angle(C, A, B), Angle(F, D, E)),
// Congruent(Angle(B, C, A), Angle(E, F, D)),
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.SSS;
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is CongruentSegments)
{
CongruentSegments newCss = clause as CongruentSegments;
// Check all combinations of triangles to see if they are congruent
// This congruence must include the new segment congruence
for (int i = 0; i < candidateTriangles.Count - 1; i++)
{
for (int j = i + 1; j < candidateTriangles.Count; j++)
{
for (int m = 0; m < candidateSegments.Count - 1; m++)
{
for (int n = m + 1; n < candidateSegments.Count; n++)
{
newGrounded.AddRange(InstantiateSSS(candidateTriangles[i], candidateTriangles[j], candidateSegments[m], candidateSegments[n], newCss));
}
}
}
}
// Add this segment to the list of possible clauses to unify later
candidateSegments.Add(newCss);
}
// If this is a new triangle, check for triangles which may be congruent to this new triangle
else if (clause is Triangle)
{
Triangle newTriangle = clause as Triangle;
// Check all combinations of triangles to see if they are congruent
// This congruence must include the new segment congruence
foreach (Triangle oldTri in candidateTriangles)
{
for (int m = 0; m < candidateSegments.Count - 1; m++)
{
for (int n = m + 1; n < candidateSegments.Count - 1; n++)
{
for (int p = n + 1; p < candidateSegments.Count - 2; p++)
{
newGrounded.AddRange(InstantiateSSS(newTriangle, oldTri, candidateSegments[m], candidateSegments[n], candidateSegments[p]));
}
}
}
}
candidateTriangles.Add(newTriangle);
}
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> InstantiateToRhombus(GroundedClause clause)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is Quadrilateral)
{
Quadrilateral quad = clause as Quadrilateral;
if (!quad.IsStrictQuadrilateral())
{
return(newGrounded);
}
for (int i = 0; i < candidateCongruent.Count - 1; i++)
{
for (int j = i + 1; j < candidateCongruent.Count; j++)
{
for (int k = j + 1; k < candidateCongruent.Count; k++)
{
newGrounded.AddRange(InstantiateToRhombus(quad, candidateCongruent[i], candidateCongruent[j], candidateCongruent[k]));
}
}
}
candidateQuadrilateral.Add(quad);
}
else if (clause is CongruentSegments)
{
CongruentSegments newCs = clause as CongruentSegments;
if (newCs.IsReflexive())
{
return(newGrounded);
}
foreach (Quadrilateral quad in candidateQuadrilateral)
{
for (int i = 0; i < candidateCongruent.Count - 1; i++)
{
for (int j = i + 1; j < candidateCongruent.Count; j++)
{
newGrounded.AddRange(InstantiateToRhombus(quad, newCs, candidateCongruent[i], candidateCongruent[j]));
}
}
}
candidateCongruent.Add(newCs);
}
return(newGrounded);
}
private static List <EdgeAggregator> InstantiateToMidpoint(GroundedClause clause)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is InMiddle && !(clause is Midpoint))
{
InMiddle inMid = clause as InMiddle;
foreach (CongruentSegments css in candidateCongruent)
{
newGrounded.AddRange(InstantiateToMidpoint(inMid, css));
}
// No need to add this InMiddle object to the list since it was added previously in InstantiateFrom
}
else if (clause is CongruentSegments)
{
CongruentSegments css = clause as CongruentSegments;
// A reflexive relationship cannot possibly create a midpoint situation
if (css.IsReflexive())
{
return(newGrounded);
}
// The congruence must relate two collinear segments...
if (!css.cs1.IsCollinearWith(css.cs2))
{
return(newGrounded);
}
// ...that share a vertex
if (css.cs1.SharedVertex(css.cs2) == null)
{
return(newGrounded);
}
foreach (InMiddle im in candidateInMiddle)
{
newGrounded.AddRange(InstantiateToMidpoint(im, css));
}
candidateCongruent.Add(css);
}
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;
}
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);
}
//
// A
// / \
// B---C
//
// Triangle(A, B, C), Congruent(Segment(A, B), Segment(A, C)) -> Congruent(\angle ABC, \angle ACB)
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.CONGRUENT_SIDES_IN_TRIANGLE_IMPLY_CONGRUENT_ANGLES;
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is CongruentSegments)
{
CongruentSegments css = clause as CongruentSegments;
// Only generate or add to possible congruent pairs if this is a non-reflexive relation
if (css.IsReflexive())
{
return(newGrounded);
}
for (int t = 0; t < candTris.Count; t++)
{
newGrounded.AddRange(InstantiateToCongruence(candTris[t], css));
}
candSegs.Add(css);
}
else if (clause is Triangle)
{
Triangle newTriangle = clause as Triangle;
//
// Do any of the congruent segment pairs merit calling this new triangle isosceles?
//
foreach (CongruentSegments css in candSegs)
{
newGrounded.AddRange(InstantiateToCongruence(newTriangle, css));
}
// Add the the list of candidates if it was not determined isosceles now.
candTris.Add(newTriangle);
}
return(newGrounded);
}
//
// 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);
}
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));
}
//
// 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));
}
//
// 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);
}
//
// Checks for SAS given the 5 values
//
private static List <EdgeAggregator> InstantiateSAS(Triangle tri1, Triangle tri2, CongruentSegments css1, CongruentSegments css2, CongruentAngles cas)
{
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 (!cas.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 angleTri1 = tri1.NormalizeAngle(tri1.AngleBelongs(cas));
Angle angleTri2 = tri2.NormalizeAngle(tri2.AngleBelongs(cas));
Segment seg1Tri1 = tri1.GetSegment(css1);
Segment seg1Tri2 = tri2.GetSegment(css1);
Segment seg2Tri1 = tri1.GetSegment(css2);
Segment seg2Tri2 = tri2.GetSegment(css2);
if (!angleTri1.IsIncludedAngle(seg1Tri1, seg2Tri1) || !angleTri2.IsIncludedAngle(seg1Tri2, seg2Tri2))
{
return(newGrounded);
}
//
// Construct the corrsesponding points between the triangles
//
List <Point> triangleOne = new List <Point>();
List <Point> triangleTwo = new List <Point>();
triangleOne.Add(angleTri1.GetVertex());
triangleTwo.Add(angleTri2.GetVertex());
triangleOne.Add(seg1Tri1.OtherPoint(angleTri1.GetVertex()));
triangleTwo.Add(seg1Tri2.OtherPoint(angleTri2.GetVertex()));
triangleOne.Add(seg2Tri1.OtherPoint(angleTri1.GetVertex()));
triangleTwo.Add(seg2Tri2.OtherPoint(angleTri2.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(css1);
antecedent.Add(css2);
antecedent.Add(cas);
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);
}
//
// In order for two triangles to be isosceles, we require the following:
//
// Triangle(A, B, C), Congruent(Segment(A, B), Segment(B, C)) -> IsoscelesTriangle(A, B, C)
//
// This does not generate a new clause explicitly; it simply strengthens the existent object
//
public static List <EdgeAggregator> Instantiate(GroundedClause c)
{
annotation.active = EngineUIBridge.JustificationSwitch.ISOSCELES_TRIANGLE_DEFINITION;
if (c is IsoscelesTriangle || c is Strengthened)
{
return(InstantiateDefinition(c));
}
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (!(c is CongruentSegments) && !(c is Triangle))
{
return(newGrounded);
}
//
// Unify
//
if (c is CongruentSegments)
{
CongruentSegments css = c as CongruentSegments;
// Only generate or add to possible congruent pairs if this is a non-reflexive relation
if (css.IsReflexive())
{
return(newGrounded);
}
for (int t = 0; t < candTris.Count; t++)
{
if (candTris[t].HasSegment(css.cs1) && candTris[t].HasSegment(css.cs2))
{
newGrounded.Add(StrengthenToIsosceles(candTris[t], css));
// There should be only one possible Isosceles triangle from this congruent segments
// So we can remove this relationship and triangle from consideration
candTris.RemoveAt(t);
return(newGrounded);
}
}
candSegs.Add(css);
}
else if (c is Triangle)
{
Triangle newTriangle = c as Triangle;
//
// Do any of the congruent segment pairs merit calling this new triangle isosceles?
//
for (int cs = 0; cs < candSegs.Count; cs++)
{
if (newTriangle.HasSegment(candSegs[cs].cs1) && newTriangle.HasSegment(candSegs[cs].cs2))
{
newGrounded.Add(StrengthenToIsosceles(newTriangle, candSegs[cs]));
return(newGrounded);
}
}
// Add to the list of candidates if it was not determined isosceles now.
candTris.Add(newTriangle);
}
return(newGrounded);
}
// A
// /\
// / \
// / \
// /______\
// B C
//
// In order for two triangles to be congruent, we require the following:
// Triangle(A, B, C), Triangle(D, E, F),
// Congruent(Angle(A, B, C), Angle(D, E, F)),
// Congruent(Segment(B, C), Segment(E, F)),
// Congruent(Angle(A, C, B), Angle(D, F, E)) -> Congruent(Triangle(A, B, C), Triangle(D, E, F)),
// Congruent(Segment(A, B), Angle(D, E)),
// Congruent(Segment(A, C), Angle(D, F)),
// Congruent(Angle(B, A, C), Angle(E, D, F)),
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.ASA;
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is CongruentSegments)
{
CongruentSegments newCss = clause as CongruentSegments;
// Check all combinations of triangles to see if they are congruent
// This congruence must include the new segment congruence
for (int i = 0; i < candidateTriangles.Count - 1; i++)
{
for (int j = i + 1; j < candidateTriangles.Count; j++)
{
for (int m = 0; m < candidateAngles.Count - 1; m++)
{
for (int n = m + 1; n < candidateAngles.Count; n++)
{
newGrounded.AddRange(InstantiateASA(candidateTriangles[i], candidateTriangles[j], candidateAngles[m], candidateAngles[n], newCss));
}
}
}
}
// Add this segment to the list of possible clauses to unify later
candidateSegments.Add(newCss);
}
else if (clause is CongruentAngles)
{
CongruentAngles newCas = clause as CongruentAngles;
// Except for reflexive congruent triangle (a triangle and itself), reflexive angles cannot lead to congruency
if (newCas.IsReflexive())
{
return(newGrounded);
}
// Check all combinations of triangles to see if they are congruent
// This congruence must include the new segment congruence
for (int i = 0; i < candidateTriangles.Count - 1; i++)
{
for (int j = i + 1; j < candidateTriangles.Count; j++)
{
foreach (CongruentSegments css in candidateSegments)
{
foreach (CongruentAngles oldCas in candidateAngles)
{
newGrounded.AddRange(InstantiateASA(candidateTriangles[i], candidateTriangles[j], oldCas, newCas, css));
}
}
}
}
candidateAngles.Add(newCas);
}
// If this is a new triangle, check for triangles which may be congruent to this new triangle
else if (clause is Triangle)
{
Triangle newTriangle = clause as Triangle;
// Check all combinations of triangles to see if they are congruent
// This congruence must include the new segment congruence
foreach (Triangle oldTri in candidateTriangles)
{
for (int m = 0; m < candidateAngles.Count - 1; m++)
{
for (int n = m + 1; n < candidateAngles.Count; n++)
{
foreach (CongruentSegments css in candidateSegments)
{
newGrounded.AddRange(InstantiateASA(newTriangle, oldTri, candidateAngles[m], candidateAngles[n], css));
}
}
}
}
candidateTriangles.Add(newTriangle);
}
return(newGrounded);
}
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);
}
private static List <EdgeAggregator> InstantiateToIsoscelesTrapezoid(GroundedClause clause)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is Trapezoid)
{
Trapezoid trapezoid = clause as Trapezoid;
if (trapezoid is IsoscelesTrapezoid)
{
return(newGrounded);
}
foreach (CongruentSegments css in candidateCongruent)
{
newGrounded.AddRange(InstantiateToIsoscelesTrapezoid(trapezoid, css, trapezoid));
}
candidateTrapezoid.Add(trapezoid);
}
else if (clause is Strengthened)
{
Strengthened streng = clause as Strengthened;
if (!(streng.strengthened is Trapezoid))
{
return(newGrounded);
}
//Don't strengthen an isosceles trapezoid to an isosceles trapezoid
if (streng.strengthened is IsoscelesTrapezoid)
{
return(newGrounded);
}
foreach (CongruentSegments css in candidateCongruent)
{
newGrounded.AddRange(InstantiateToIsoscelesTrapezoid(streng.strengthened as Trapezoid, css, streng));
}
candidateStrengthened.Add(streng);
}
else if (clause is CongruentSegments)
{
CongruentSegments newCss = clause as CongruentSegments;
if (newCss.IsReflexive())
{
return(newGrounded);
}
foreach (Trapezoid trapezoid in candidateTrapezoid)
{
newGrounded.AddRange(InstantiateToIsoscelesTrapezoid(trapezoid, newCss, trapezoid));
}
foreach (Strengthened streng in candidateStrengthened)
{
newGrounded.AddRange(InstantiateToIsoscelesTrapezoid(streng.strengthened as Trapezoid, newCss, streng));
}
candidateCongruent.Add(newCss);
}
return(newGrounded);
}
//
// 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);
}
// A
// |\
// | \
// |_ \
// |_|_\
// B C
// In order for two right triangles to be congruent, we require the following:
// RightTriangle(A, B, C), RightTriangle(D, E, F),
// Congruent(Segment(A, B), Segment(D, E)),
// Congruent(Segment(A, C), Segment(D, F)) -> Congruent(Triangle(A, B, C), Triangle(D, E, F)),
// Congruent(Segment(A, C), Angle(D, F)),
// Congruent(Angle(C, A, B), Angle(F, D, E)),
// Congruent(Angle(B, C, A), Angle(E, F, D)),
//
// Note: we need to figure out the proper order of the sides to guarantee congruence
//
public static List <EdgeAggregator> Instantiate(GroundedClause clause)
{
annotation.active = EngineUIBridge.JustificationSwitch.HYPOTENUSE_LEG;
// The list of new grounded clauses if they are deduced
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
if (clause is CongruentSegments)
{
CongruentSegments newCs = clause as CongruentSegments;
// Check all combinations of strict right triangle objects
for (int i = 0; i < candidateRightTriangles.Count - 1; i++)
{
for (int j = i + 1; j < candidateRightTriangles.Count; j++)
{
foreach (CongruentSegments css in candidateSegments)
{
newGrounded.AddRange(ReconfigureAndCheck(candidateRightTriangles[i], candidateRightTriangles[j], newCs, css));
}
}
}
// Check all combinations of (1) strict right triangle and (2) a strengthened triangle
foreach (RightTriangle rt in candidateRightTriangles)
{
foreach (Strengthened streng in candidateStrengthened)
{
foreach (CongruentSegments css in candidateSegments)
{
newGrounded.AddRange(ReconfigureAndCheck(rt, streng, newCs, css));
}
}
}
// Check all combinations of strengthened triangles
for (int i = 0; i < candidateStrengthened.Count - 1; i++)
{
for (int j = i + 1; j < candidateStrengthened.Count; j++)
{
foreach (CongruentSegments css in candidateSegments)
{
newGrounded.AddRange(ReconfigureAndCheck(candidateStrengthened[i], candidateStrengthened[j], newCs, css));
}
}
}
// Add this segment to the list of possible clauses to unify later
candidateSegments.Add(newCs);
}
//
// A triangle is either strictly a right triangle object, or a triangle is strengthened to be a right triangle
//
else if (clause is RightTriangle)
{
RightTriangle newRt = clause as RightTriangle;
// Check all combinations of strict right triangle objects
foreach (RightTriangle oldRt in candidateRightTriangles)
{
for (int i = 0; i < candidateSegments.Count - 1; i++)
{
for (int j = i + 1; j < candidateSegments.Count; j++)
{
newGrounded.AddRange(ReconfigureAndCheck(newRt, oldRt, candidateSegments[i], candidateSegments[j]));
}
}
}
// Check all combinations of (1) strict right triangle and (2) a strengthened triangle
foreach (Strengthened streng in candidateStrengthened)
{
for (int i = 0; i < candidateSegments.Count - 1; i++)
{
for (int j = i + 1; j < candidateSegments.Count; j++)
{
newGrounded.AddRange(ReconfigureAndCheck(newRt, streng, candidateSegments[i], candidateSegments[j]));
}
}
}
candidateRightTriangles.Add(newRt);
}
else if (clause is Strengthened)
{
Strengthened newStreng = clause as Strengthened;
// Only interested in strengthened Right Triangles
if (!(newStreng.strengthened is RightTriangle))
{
return(newGrounded);
}
// Check all combinations of strict right triangle objects
foreach (RightTriangle oldRt in candidateRightTriangles)
{
for (int i = 0; i < candidateSegments.Count - 1; i++)
{
for (int j = i + 1; j < candidateSegments.Count; j++)
{
newGrounded.AddRange(ReconfigureAndCheck(oldRt, newStreng, candidateSegments[i], candidateSegments[j]));
}
}
}
// Check all combinations of (1) strict right triangle and (2) a strengthened triangle
foreach (Strengthened oldStreng in candidateStrengthened)
{
for (int i = 0; i < candidateSegments.Count - 1; i++)
{
for (int j = i + 1; j < candidateSegments.Count; j++)
{
newGrounded.AddRange(ReconfigureAndCheck(newStreng, oldStreng, candidateSegments[i], candidateSegments[j]));
}
}
}
candidateStrengthened.Add(newStreng);
}
return(newGrounded);
}
// 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);
}
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);
}
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);
}
//
// 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);
}
//
//
//
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);
}