// // 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; }