//
// Take the angle congruence and bisector and create the AngleBisector relation
//
private static List<EdgeAggregator> InstantiateToMedian(Triangle tri, SegmentBisector sb, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The Bisector cannot be a side of the triangle.
if (tri.CoincidesWithASide(sb.bisector) != null) return newGrounded;
// Acquire the intersection segment that coincides with the base of the triangle
Segment triangleBaseCandidate = sb.bisected.OtherSegment(sb.bisector);
Segment triangleBase = tri.CoincidesWithASide(triangleBaseCandidate);
if (triangleBase == null) return newGrounded;
// The candidate base and the actual triangle side must equate exactly
if (!triangleBase.HasSubSegment(triangleBaseCandidate) || !triangleBaseCandidate.HasSubSegment(triangleBase)) return newGrounded;
// The point opposite the base of the triangle must be within the endpoints of the bisector
Point oppPoint = tri.OtherPoint(triangleBase);
if (!sb.bisector.PointLiesOnAndBetweenEndpoints(oppPoint)) return newGrounded;
// -> Median(Segment(V, C), Triangle(A, B, C))
Median newMedian = new Median(sb.bisector, tri);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(tri);
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, newMedian, 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;
}
//
// 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> InstantiateToAltitude(Triangle triangle, Perpendicular perp, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Acquire the side of the triangle containing the intersection point
// This point may or may not be directly on the triangle side
Segment baseSegment = triangle.GetSegmentWithPointOnOrExtends(perp.intersect);
if (baseSegment == null) return newGrounded;
// The altitude must pass through the intersection point as well as the opposing vertex
Point oppositeVertex = triangle.OtherPoint(baseSegment);
Segment altitude = new Segment(perp.intersect, oppositeVertex);
// The alitude must alig with the intersection
if (!perp.ImpliesRay(altitude)) return newGrounded;
// The opposing side must align with the intersection
if (!perp.OtherSegment(altitude).IsCollinearWith(baseSegment)) return newGrounded;
//
// Create the new Altitude object
//
Altitude newAltitude = new Altitude(triangle, altitude);
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(triangle);
antecedent.Add(original);
newGrounded.Add(new EdgeAggregator(antecedent, newAltitude, annotation));
//
// Check if this induces a second altitude for a right triangle (although we don't know this is a strengthened triangle)
// The intersection must be on the vertex of the triangle
if (triangle.HasPoint(perp.intersect))
{
Angle possRightAngle = new Angle(triangle.OtherPoint(new Segment(perp.intersect, oppositeVertex)), perp.intersect, oppositeVertex);
if (triangle.HasAngle(possRightAngle))
{
Altitude secondAltitude = new Altitude(triangle, new Segment(perp.intersect, oppositeVertex));
newGrounded.Add(new EdgeAggregator(antecedent, secondAltitude, annotation));
}
}
return newGrounded;
}
