//
// Is this triangle encased in the given, larger triangle.
// That is, two sides are defined by the larger triangle and one side by the altitude
//
public bool IsDefinedBy(RightTriangle rt, Altitude altitude)
{
// The opposite side of the smaller triangle has to be a side of the larger triangle.
if (!rt.HasSegment(this.GetOppositeSide(this.rightAngle)))
{
return(false);
}
// The smaller triangle's right angle must have a ray collinear with the altitude segment
Segment altSegment = null;
if (this.rightAngle.ray1.IsCollinearWith(altitude.segment))
{
altSegment = this.rightAngle.ray1;
}
else if (this.rightAngle.ray2.IsCollinearWith(altitude.segment))
{
altSegment = this.rightAngle.ray2;
}
if (altSegment == null)
{
return(false);
}
// The last segment needs to be collinear with a side of the larger triangle
return(rt.LiesOn(this.rightAngle.OtherRayEquates(altSegment)));
}
public override bool Equals(Object obj)
{
Altitude alt = obj as Altitude;
if (alt == null)
{
return(false);
}
return(triangle.Equals(alt.triangle) && segment.Equals(alt.segment) && base.Equals(obj));
}
public override bool StructurallyEquals(Object obj)
{
Altitude alt = obj as Altitude;
if (alt == null)
{
return(false);
}
return(triangle.StructurallyEquals(alt.triangle) && segment.StructurallyEquals(alt.segment));
}
//
// Is this triangle encased in the given, larger triangle.
// That is, two sides are defined by the larger triangle and one side by the altitude
//
public bool IsDefinedBy(RightTriangle rt, Altitude altitude)
{
// The opposite side of the smaller triangle has to be a side of the larger triangle.
if (!rt.HasSegment(this.GetOppositeSide(this.rightAngle))) return false;
// The smaller triangle's right angle must have a ray collinear with the altitude segment
Segment altSegment = null;
if (this.rightAngle.ray1.IsCollinearWith(altitude.segment))
{
altSegment = this.rightAngle.ray1;
}
else if (this.rightAngle.ray2.IsCollinearWith(altitude.segment))
{
altSegment = this.rightAngle.ray2;
}
if (altSegment == null) return false;
// The last segment needs to be collinear with a side of the larger triangle
return rt.LiesOn(this.rightAngle.OtherRayEquates(altSegment));
}
public static List<EdgeAggregator> InstantiateRight(RightTriangle rt, Altitude altitude, GroundedClause original)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The altitude must connect the vertex defining the right angle and the opposite side.
if (!altitude.segment.HasPoint(rt.rightAngle.GetVertex())) return newGrounded;
// The other point of the altitude must lie on the opposite side of the triangle
Point altPointOppRightAngle = altitude.segment.OtherPoint(rt.rightAngle.GetVertex());
Segment oppositeSide = rt.GetOppositeSide(rt.rightAngle);
if (!Segment.Between(altPointOppRightAngle, oppositeSide.Point1, oppositeSide.Point2)) return newGrounded;
//
// Find the two smaller right triangles in the candidate list (which should be in the list at this point)
//
RightTriangle first = null;
RightTriangle second = null;
foreach (RightTriangle smallerRT in candRightTriangles)
{
if (smallerRT.IsDefinedBy(rt, altitude))
{
if (first == null)
{
first = smallerRT;
}
else
{
second = smallerRT;
break;
}
}
}
// CTA: We did not check to see points aligned, but these are the original triangles from the figure
GeometricSimilarTriangles gsts1 = new GeometricSimilarTriangles(rt, first);
GeometricSimilarTriangles gsts2 = new GeometricSimilarTriangles(rt, second);
GeometricSimilarTriangles gsts3 = new GeometricSimilarTriangles(first, second);
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original);
antecedent.Add(altitude);
newGrounded.Add(new EdgeAggregator(antecedent, gsts1, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gsts2, annotation));
newGrounded.Add(new EdgeAggregator(antecedent, gsts3, annotation));
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;
}
private static List<EdgeAggregator> InstantiateFromAltitude(Intersection inter, Altitude altitude)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The intersection should contain the altitude segment
if (!inter.HasSegment(altitude.segment)) return newGrounded;
// The triangle should contain the other segment in the intersection
Segment triangleSide = altitude.triangle.CoincidesWithASide(inter.OtherSegment(altitude.segment));
if (triangleSide == null) return newGrounded;
if (!inter.OtherSegment(altitude.segment).HasSubSegment(triangleSide)) return newGrounded;
//
// Create the Perpendicular relationship
//
Strengthened streng = new Strengthened(inter, new Perpendicular(inter));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(inter);
antecedent.Add(altitude);
newGrounded.Add(new EdgeAggregator(antecedent, streng, annotation));
return newGrounded;
}
