//
// 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;
}
//
//
//
private static List<EdgeAggregator> CollectAndCheckSAS(Triangle ct1, Triangle ct2, CongruentAngles cas, SegmentRatioEquation sre)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Proportions must actually equate
//if (!pss1.ProportionallyEquals(pss2)) return newGrounded;
//// The smaller and larger segments of the proportionality must be distinct, respectively.
//if (!pss1.IsDistinctFrom(pss2)) return newGrounded;
// The proportional relationships need to link the given triangles
if (!cas.LinksTriangles(ct1, ct2)) return newGrounded;
if (!sre.LinksTriangles(ct1, ct2)) return newGrounded;
//if (!pss1.LinksTriangles(ct1, ct2)) return newGrounded;
//if (!pss2.LinksTriangles(ct1, ct2)) return newGrounded;
// The smaller segments must belong to one triangle, same for larger segments.
//if (!(ct1.HasSegment(pss1.smallerSegment) && ct1.HasSegment(pss2.smallerSegment) &&
// ct2.HasSegment(pss1.largerSegment) && ct2.HasSegment(pss2.largerSegment)) &&
// !(ct2.HasSegment(pss1.smallerSegment) && ct2.HasSegment(pss2.smallerSegment) &&
// ct1.HasSegment(pss1.largerSegment) && ct1.HasSegment(pss2.largerSegment)))
// return newGrounded;
KeyValuePair<Segment, Segment> segsTri1 = sre.GetSegments(ct1);
KeyValuePair<Segment, Segment> segsTri2 = sre.GetSegments(ct2);
//Segment seg1Tri1 = ct1.GetSegment(pss1);
//Segment seg2Tri1 = ct1.GetSegment(pss2);
//Segment seg1Tri2 = ct2.GetSegment(pss1);
//Segment seg2Tri2 = ct2.GetSegment(pss2);
// Avoid redundant segments, if they arise
if (segsTri1.Key.StructurallyEquals(segsTri1.Value)) return newGrounded;
if (segsTri2.Key.StructurallyEquals(segsTri2.Value)) return newGrounded;
//if (seg1Tri1.StructurallyEquals(seg2Tri1)) return newGrounded;
//if (seg1Tri2.StructurallyEquals(seg2Tri2)) return newGrounded;
Angle angleTri1 = ct1.AngleBelongs(cas);
Angle angleTri2 = ct2.AngleBelongs(cas);
// Check both triangles if this is the included angle; if it is, we have SAS
if (!angleTri1.IsIncludedAngle(segsTri1.Key, segsTri1.Value)) return newGrounded;
if (!angleTri2.IsIncludedAngle(segsTri2.Key, segsTri2.Value)) return newGrounded;
//
// Generate Similar Triangles
//
Point vertex1 = angleTri1.GetVertex();
Point vertex2 = angleTri2.GetVertex();
// Construct a list of pairs to return; this is the correspondence from triangle 1 to triangle 2
List<KeyValuePair<Point, Point>> pairs = new List<KeyValuePair<Point, Point>>();
// The vertices of the angles correspond
pairs.Add(new KeyValuePair<Point, Point>(vertex1, vertex2));
// For the segments, look at the congruences and select accordingly
pairs.Add(new KeyValuePair<Point, Point>(segsTri1.Key.OtherPoint(vertex1), segsTri2.Key.OtherPoint(vertex2)));
pairs.Add(new KeyValuePair<Point, Point>(segsTri1.Value.OtherPoint(vertex1), segsTri2.Value.OtherPoint(vertex2)));
List<GroundedClause> simTriAntecedent = new List<GroundedClause>();
simTriAntecedent.Add(ct1);
simTriAntecedent.Add(ct2);
simTriAntecedent.Add(cas);
simTriAntecedent.Add(sre);
newGrounded.AddRange(GenerateCorrespondingParts(pairs, simTriAntecedent, annotation));
return newGrounded;
}
//
// 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;
}
//
// Acquires all of the applicable congruent segments as well as congruent angles. Then checks for SAS
//
private static List<EdgeAggregator> CheckAndGenerateThirdCongruentPair(Triangle tri1, Triangle tri2, CongruentAngles cas1, CongruentAngles cas2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// We have eliminated all reflexive relationships at this point
// The congruent relations should not share any angles
if (cas1.AngleShared(cas2) != null) return newGrounded;
// Both congruent pairs of angles must relate both triangles
if (!cas1.LinksTriangles(tri1, tri2)) return newGrounded;
if (!cas2.LinksTriangles(tri1, tri2)) return newGrounded;
Angle firstAngleTri1 = tri1.AngleBelongs(cas1);
Angle secondAngleTri1 = tri1.AngleBelongs(cas2);
Angle firstAngleTri2 = tri2.AngleBelongs(cas1);
Angle secondAngleTri2 = tri2.AngleBelongs(cas2);
Angle thirdAngle1 = tri1.OtherAngle(firstAngleTri1, secondAngleTri1);
Angle thirdAngle2 = tri2.OtherAngle(firstAngleTri2, secondAngleTri2);
CongruentAngles newCas = new CongruentAngles(thirdAngle1, thirdAngle2);
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri1);
antecedent.Add(tri2);
antecedent.Add(cas1);
antecedent.Add(cas2);
newGrounded.Add(new EdgeAggregator(antecedent, newCas, annotation));
return newGrounded;
}
