//
// Creates an H-Shape
//
// | |
// |_____|
// | |
// | |
//
public bool CreatesHShape(Intersection thatInter)
{
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(false);
}
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn())
{
return(false);
}
if (this.StandsOnEndpoint() || this.StandsOnEndpoint())
{
return(false);
}
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
// The tips of the intersections must be within the transversal (at the endpoint) for an H
if (!transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT))
{
return(false);
}
if (!transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT))
{
return(false);
}
return(true);
}
//
// Creates an S-Shape
//
// |______
// |
// ______|
// |
//
// Order of non-collinear points is order of intersections: <this, that>
public KeyValuePair <Point, Point> CreatesStandardSShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
Point thisNonCollinear = this.CreatesTShape();
Point thatNonCollinear = thatInter.CreatesTShape();
if (thisNonCollinear == null || thatNonCollinear == null)
{
return(nullPair);
}
//
// Verify that the shape is PI and not an S-shape; look for the intersection point NOT between the endpoints of the transversal
//
// The transversal should be valid
Segment transversal = this.AcquireTransversal(thatInter);
Point intersection = transversal.FindIntersection(new Segment(thisNonCollinear, thatNonCollinear));
// PI-shape
if (!transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
return(nullPair);
}
// S-Shape
return(new KeyValuePair <Point, Point>(thisNonCollinear, thatNonCollinear));
}
//
// Chair Corresponding
//
// | | |
// |_____|____ leftInter |_________ tipOfT
// | | |
// | | |
// off tipOfT
//
// bottomInter
private static List<EdgeAggregator> InstantiateChairIntersection(Parallel parallel, Intersection inter1, Point off, Intersection inter2, Point bottomTip)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
Segment transversal = inter1.AcquireTransversal(inter2);
Point tipOfT1 = inter1.CreatesTShape();
Point tipOfT2 = inter2.CreatesTShape();
Point leftTip = null;
Intersection leftInter = null;
Intersection bottomInter = null;
if (transversal.PointLiesOn(tipOfT1))
{
leftInter = inter1;
bottomInter = inter2;
leftTip = tipOfT1;
}
// thatInter is leftInter
else if (transversal.PointLiesOn(tipOfT2))
{
leftInter = inter2;
bottomInter = inter1;
leftTip = tipOfT2;
}
//
// Generate the new congruence
//
List<CongruentAngles> newAngleRelations = new List<CongruentAngles>();
// CTA: Hack fix to alleviate exception thrown from improper congruent constructions.
GeometricCongruentAngles gca = null;
try
{
gca = new GeometricCongruentAngles(new Angle(leftTip, bottomInter.intersect, bottomTip),
new Angle(bottomInter.intersect, leftInter.intersect, off));
}
catch (Exception e)
{
if (Utilities.DEBUG) System.Diagnostics.Debug.WriteLine(e.ToString());
return newGrounded;
}
newAngleRelations.Add(gca);
return MakeRelations(newAngleRelations, parallel, inter1, inter2);
}
//
// Creates a shape like a crazy person flying
//
// | |
// |_____|___ off
// | |
// | |
//
// Similar to H-shape with an extended point
// Returns the 'larger' intersection that contains the point: off
public KeyValuePair <Intersection, Point> CreatesFlyingShape(Intersection thatInter)
{
KeyValuePair <Intersection, Point> nullPair = new KeyValuePair <Intersection, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn())
{
return(nullPair);
}
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint())
{
return(nullPair);
}
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
// We have an H-Shape if the tips of the intersections are at the endpoints of the transversal
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT) && transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT))
{
return(nullPair);
}
Intersection retInter = null;
Point off = null;
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT))
{
retInter = thatInter;
off = thatTipOfT;
}
else
{
retInter = this;
off = thisTipOfT;
}
return(new KeyValuePair <Intersection, Point>(retInter, off));
}
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;
}
//
// Creates an S-Shape
//
// |______
// |
// ______|
// |
//
// Order of non-collinear points is order of intersections: <this, that>
public KeyValuePair<Point, Point> CreatesStandardSShape(Intersection thatInter)
{
KeyValuePair<Point, Point> nullPair = new KeyValuePair<Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter)) return nullPair;
Point thisNonCollinear = this.CreatesTShape();
Point thatNonCollinear = thatInter.CreatesTShape();
if (thisNonCollinear == null || thatNonCollinear == null) return nullPair;
//
// Verify that the shape is PI and not an S-shape; look for the intersection point NOT between the endpoints of the transversal
//
// The transversal should be valid
Segment transversal = this.AcquireTransversal(thatInter);
Point intersection = transversal.FindIntersection(new Segment(thisNonCollinear, thatNonCollinear));
// PI-shape
if (!transversal.PointLiesOnAndBetweenEndpoints(intersection)) return nullPair;
// S-Shape
return new KeyValuePair<Point, Point>(thisNonCollinear, thatNonCollinear);
}
//
// Creates an H-Shape
//
// | |
// |_____|
// | |
// | |
//
public bool CreatesHShape(Intersection thatInter)
{
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter)) return false;
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn()) return false;
if (this.StandsOnEndpoint() || this.StandsOnEndpoint()) return false;
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
// The tips of the intersections must be within the transversal (at the endpoint) for an H
if (!transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT)) return false;
if (!transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT)) return false;
return true;
}
//
// Creates a shape like a crazy person flying
//
// | |
// |_____|___ off
// | |
// | |
//
// Similar to H-shape with an extended point
// Returns the 'larger' intersection that contains the point: off
public KeyValuePair<Intersection, Point> CreatesFlyingShape(Intersection thatInter)
{
KeyValuePair<Intersection, Point> nullPair = new KeyValuePair<Intersection,Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter)) return nullPair;
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn()) return nullPair;
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint()) return nullPair;
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
// We have an H-Shape if the tips of the intersections are at the endpoints of the transversal
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT) && transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT)) return nullPair;
Intersection retInter = null;
Point off = null;
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT))
{
retInter = thatInter;
off = thatTipOfT;
}
else
{
retInter = this;
off = thisTipOfT;
}
return new KeyValuePair<Intersection, Point>(retInter, off);
}
//
// Creates a Chair
//
// | | |
// |_____|____ leftInter |_________ tipOfT
// | | |
// | | |
// off tipOfT
//
// bottomInter
//
// <leftInter, bottomInter>
// Returns the legs of the chair in specific ordering: <off, bottomTip>
public KeyValuePair<Point, Point> CreatesChairShape(Intersection thatInter)
{
KeyValuePair<Point, Point> nullPair = new KeyValuePair<Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter)) return nullPair;
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn()) return nullPair;
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint()) return nullPair;
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
Intersection leftInter = null;
Intersection bottomInter = null;
// Avoid:
// |
// |______
// | |
// | |
// this is leftInter
Point bottomTip = null;
if (transversal.PointLiesOn(thisTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT)) return nullPair;
leftInter = this;
bottomInter = thatInter;
bottomTip = thisTipOfT;
}
// thatInter is leftInter
else if (transversal.PointLiesOn(thatTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT)) return nullPair;
leftInter = thatInter;
bottomInter = this;
bottomTip = thisTipOfT;
}
// Otherwise, this indicates a PI-shaped scenario
else return nullPair;
//
// Returns the bottom of the legs of the chair
//
Segment parallelLeft = leftInter.OtherSegment(transversal);
Segment crossingTester = new Segment(parallelLeft.Point1, bottomTip);
Point intersection = transversal.FindIntersection(crossingTester);
Point off = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelLeft.Point2 : parallelLeft.Point1;
return new KeyValuePair<Point, Point>(off, bottomTip);
}
//
// Creates a Chair
//
// | | |
// |_____|____ leftInter |_________ tipOfT
// | | |
// | | |
// off tipOfT
//
// bottomInter
//
// <leftInter, bottomInter>
// Returns the legs of the chair in specific ordering: <off, bottomTip>
public KeyValuePair <Point, Point> CreatesChairShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Both intersections must be standing on (and not endpoints)
if (!this.StandsOn() || !thatInter.StandsOn())
{
return(nullPair);
}
if (this.StandsOnEndpoint() || thatInter.StandsOnEndpoint())
{
return(nullPair);
}
Point thisTipOfT = this.CreatesTShape();
Point thatTipOfT = thatInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
Intersection leftInter = null;
Intersection bottomInter = null;
// Avoid:
// |
// |______
// | |
// | |
// this is leftInter
Point bottomTip = null;
if (transversal.PointLiesOn(thisTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thisTipOfT))
{
return(nullPair);
}
leftInter = this;
bottomInter = thatInter;
bottomTip = thisTipOfT;
}
// thatInter is leftInter
else if (transversal.PointLiesOn(thatTipOfT))
{
if (transversal.PointLiesOnAndBetweenEndpoints(thatTipOfT))
{
return(nullPair);
}
leftInter = thatInter;
bottomInter = this;
bottomTip = thisTipOfT;
}
// Otherwise, this indicates a PI-shaped scenario
else
{
return(nullPair);
}
//
// Returns the bottom of the legs of the chair
//
Segment parallelLeft = leftInter.OtherSegment(transversal);
Segment crossingTester = new Segment(parallelLeft.Point1, bottomTip);
Point intersection = transversal.FindIntersection(crossingTester);
Point off = transversal.PointLiesOnAndBetweenEndpoints(intersection) ? parallelLeft.Point2 : parallelLeft.Point1;
return(new KeyValuePair <Point, Point>(off, bottomTip));
}