//
// For generation of transitive SimilarTriangles Lines
//
private static List <EdgeAggregator> CreateTransitiveSimilarTriangles(SimilarTriangles simTris1, SimilarTriangles simTris2)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// If there is a deduction relationship between the given congruences, do not perform another substitution
// CTA: remove?
if (simTris1.HasGeneralPredecessor(simTris2))
{
return(newGrounded);
}
int numSharedExps = simTris1.SharesNumTriangles(simTris2);
switch (numSharedExps)
{
case 0:
// Nothing is shared: do nothing
break;
case 1:
// Expected case to create a new congruence relationship
return(SimilarTriangles.CreateTransitiveSimilarTriangles(simTris1, simTris2));
case 2:
// This is either reflexive or the exact same congruence relationship (which shouldn't happen)
break;
default:
throw new Exception("Similar Triangles may only have 0, 1, or 2 common expressions; not, " + numSharedExps);
}
return(newGrounded);
}
public static List <GenericInstantiator.EdgeAggregator> GenerateCorrespondingParts(List <KeyValuePair <Point, Point> > pairs, List <GroundedClause> antecedent, Hypergraph.EdgeAnnotation givenAnnotation)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// If pairs is populated, we have a Similiarity
if (!pairs.Any())
{
return(newGrounded);
}
// Create the similarity between the triangles
List <Point> triangleOne = new List <Point>();
List <Point> triangleTwo = new List <Point>();
foreach (KeyValuePair <Point, Point> pair in pairs)
{
triangleOne.Add(pair.Key);
triangleTwo.Add(pair.Value);
}
GeometricSimilarTriangles simTris = new GeometricSimilarTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
newGrounded.Add(new EdgeAggregator(antecedent, simTris, givenAnnotation));
// Add all the corresponding parts as new Similar clauses
newGrounded.AddRange(SimilarTriangles.GenerateComponents(simTris, triangleOne, triangleTwo));
return(newGrounded);
}
//
// Generate all new relationships from a Geoemetric, Congruent Pair of SimilarTriangles Segments
//
private static List <EdgeAggregator> HandleNewSimilarTrianglesRelation(SimilarTriangles simTris)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// New transitivity? G + G -> A
foreach (GeometricSimilarTriangles gsts in geoSimilarTriangles)
{
newGrounded.AddRange(CreateTransitiveSimilarTriangles(gsts, simTris));
}
if (simTris is GeometricSimilarTriangles)
{
// New transitivity? G + A -> A
foreach (AlgebraicSimilarTriangles asts in algSimilarTriangles)
{
newGrounded.AddRange(CreateTransitiveSimilarTriangles(asts, simTris));
}
}
return(newGrounded);
}
//
// Checks for AA given the 4 values
//
private static List <EdgeAggregator> InstantiateAASimilarity(Triangle tri1, Triangle tri2, CongruentAngles cas1, CongruentAngles cas2)
{
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);
}
// 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);
}
//
// 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(new Segment(angle1Tri1.GetVertex(), angle2Tri1.GetVertex())));
triangleTwo.Add(tri2.OtherPoint(new Segment(angle1Tri2.GetVertex(), angle2Tri2.GetVertex())));
//
// Construct the new clauses: similar triangles and resultant components
//
GeometricSimilarTriangles simTris = new GeometricSimilarTriangles(new Triangle(triangleOne), new Triangle(triangleTwo));
// Hypergraph edge
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(cas1);
antecedent.Add(cas2);
newGrounded.Add(new EdgeAggregator(antecedent, simTris, annotation));
// Add all the corresponding parts as new Similar clauses
newGrounded.AddRange(SimilarTriangles.GenerateComponents(simTris, triangleOne, triangleTwo));
return(newGrounded);
}
