private static List <EdgeAggregator> CheckAndGenerateProportionality(Triangle tri, Intersection inter1,
Intersection inter2, Parallel parallel)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
// The two intersections should not be at the same vertex
if (inter1.intersect.Equals(inter2.intersect))
{
return(newGrounded);
}
//
// Do these intersections share a segment? That is, do they share the transversal?
//
Segment transversal = inter1.AcquireTransversal(inter2);
if (transversal == null)
{
return(newGrounded);
}
//
// Is the transversal a side of the triangle? It should not be.
//
if (tri.LiesOn(transversal))
{
return(newGrounded);
}
//
// Determine if one parallel segment is a side of the triangle (which must occur)
//
Segment coinciding = tri.DoesParallelCoincideWith(parallel);
if (coinciding == null)
{
return(newGrounded);
}
// The transversal and common segment must be distinct
if (coinciding.IsCollinearWith(transversal))
{
return(newGrounded);
}
//
// Determine if the simplified transversal is within the parallel relationship.
//
Segment parallelTransversal = parallel.OtherSegment(coinciding);
Segment simpleParallelTransversal = new Segment(inter1.intersect, inter2.intersect);
if (!parallelTransversal.IsCollinearWith(simpleParallelTransversal))
{
return(newGrounded);
}
// A
// /\
// / \
// / \
// off1 /------\ off2
// / \
// B /__________\ C
//
// Both intersections should create a T-shape.
//
Point off1 = inter1.CreatesTShape();
Point off2 = inter2.CreatesTShape();
if (off1 == null || off2 == null)
{
return(newGrounded);
}
// Get the intersection segments which should coincide with the triangle sides
KeyValuePair <Segment, Segment> otherSides = tri.OtherSides(coinciding);
// The intersections may be outside this triangle
if (otherSides.Key == null || otherSides.Value == null)
{
return(newGrounded);
}
Segment side1 = inter1.OtherSegment(transversal);
Segment side2 = inter2.OtherSegment(transversal);
// Get the actual sides of the triangle
Segment triangleSide1 = null;
Segment triangleSide2 = null;
if (side1.IsCollinearWith(otherSides.Key) && side2.IsCollinearWith(otherSides.Value))
{
triangleSide1 = otherSides.Key;
triangleSide2 = otherSides.Value;
}
else if (side1.IsCollinearWith(otherSides.Value) && side2.IsCollinearWith(otherSides.Key))
{
triangleSide1 = otherSides.Value;
triangleSide2 = otherSides.Key;
}
else
{
return(newGrounded);
}
// Verify the opposing parts of the T are on the opposite sides of the triangle
if (!triangleSide1.PointLiesOnAndExactlyBetweenEndpoints(off2))
{
return(newGrounded);
}
if (!triangleSide2.PointLiesOnAndExactlyBetweenEndpoints(off1))
{
return(newGrounded);
}
//
// Construct the new proprtional relationship and resultant equation
//
Point sharedVertex = triangleSide1.SharedVertex(triangleSide2);
SegmentRatio newProp1 = new SegmentRatio(new Segment(sharedVertex, off2), triangleSide1);
SegmentRatio newProp2 = new SegmentRatio(new Segment(sharedVertex, off1), triangleSide2);
GeometricSegmentRatioEquation newEq = new GeometricSegmentRatioEquation(newProp1, newProp2);
// Construct hyperedge
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(tri);
antecedent.Add(inter1);
antecedent.Add(inter2);
antecedent.Add(parallel);
newGrounded.Add(new EdgeAggregator(antecedent, newEq, 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);
}