/// <summary>
/// Figure out what possible triangle combinations are before showing the window.
/// </summary>
protected override void OnShow()
{
options = new Dictionary<Triangle, List<Triangle>>();
//Get a list of all congruent segment givens
List<GroundedClause> ctris = new List<GroundedClause>();
foreach (GroundedClause gc in currentGivens)
{
GeometricCongruentTriangles ctri = gc as GeometricCongruentTriangles;
if (ctri != null)
{
ctris.Add(ctri);
}
}
//Pick a first triangle...
foreach (Triangle t1 in parser.backendParser.implied.polygons[GeometryTutorLib.ConcreteAST.Polygon.TRIANGLE_INDEX])
{
List<Triangle> possible = new List<Triangle>();
//... and see what other triangles are viable second options.
foreach (Triangle t2 in parser.backendParser.implied.polygons[GeometryTutorLib.ConcreteAST.Polygon.TRIANGLE_INDEX])
{
if (isCongruent(t1, t2))
{
GeometricCongruentTriangles ctri = new GeometricCongruentTriangles(t1, t2);
if (!t1.StructurallyEquals(t2) && !StructurallyContains(ctris, ctri))
{
possible.Add(t2);
}
}
}
//If we found a possible list of combinations, add it to the dictionary
if (possible.Count > 0)
{
options.Add(t1, possible);
}
}
//Set the options of the segment1 combo box
triangle1.ItemsSource = null; //Graphical refresh
triangle1.ItemsSource = options.Keys;
}
//
// 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;
}
//
// Acquires all of the applicable congruent segments; then checks HL
//
private static List<EdgeAggregator> CollectAndCheckHL(RightTriangle rt1, RightTriangle rt2,
CongruentSegments css1, CongruentSegments css2,
GroundedClause original1, GroundedClause original2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The Congruence pairs must relate the two triangles
if (!css1.LinksTriangles(rt1, rt2) || !css2.LinksTriangles(rt1, rt2)) return newGrounded;
// One of the congruence pairs must relate the hypotenuses
Segment hypotenuse1 = rt1.OtherSide(rt1.rightAngle);
Segment hypotenuse2 = rt2.OtherSide(rt2.rightAngle);
// Determine the specific congruence pair that relates the hypotenuses
CongruentSegments hypotenuseCongruence = null;
CongruentSegments nonHypotenuseCongruence = null;
if (css1.HasSegment(hypotenuse1) && css1.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css1;
nonHypotenuseCongruence = css2;
}
else if (css2.HasSegment(hypotenuse1) && css2.HasSegment(hypotenuse2))
{
hypotenuseCongruence = css2;
nonHypotenuseCongruence = css1;
}
else return newGrounded;
// Sanity check that the non hypotenuse congruence pair does not contain hypotenuse
if (nonHypotenuseCongruence.HasSegment(hypotenuse1) || nonHypotenuseCongruence.HasSegment(hypotenuse2)) return newGrounded;
//
// We now have a hypotenuse leg situation; acquire the point-to-point congruence mapping
//
List<Point> triangleOne = new List<Point>();
List<Point> triangleTwo = new List<Point>();
// Right angle vertices correspond
triangleOne.Add(rt1.rightAngle.GetVertex());
triangleTwo.Add(rt2.rightAngle.GetVertex());
Point nonRightVertexRt1 = rt1.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse1);
Point nonRightVertexRt2 = rt2.GetSegment(nonHypotenuseCongruence).SharedVertex(hypotenuse2);
triangleOne.Add(nonRightVertexRt1);
triangleTwo.Add(nonRightVertexRt2);
triangleOne.Add(hypotenuse1.OtherPoint(nonRightVertexRt1));
triangleTwo.Add(hypotenuse2.OtherPoint(nonRightVertexRt2));
//
// Construct the new deduced relationships
//
GeometricCongruentTriangles ccts = new GeometricCongruentTriangles(new Triangle(triangleOne),
new Triangle(triangleTwo));
// Hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(original1);
antecedent.Add(original2);
antecedent.Add(css1);
antecedent.Add(css2);
newGrounded.Add(new EdgeAggregator(antecedent, ccts, annotation));
// Add all the corresponding parts as new congruent clauses
newGrounded.AddRange(CongruentTriangles.GenerateCPCTC(ccts, triangleOne, triangleTwo));
return newGrounded;
}
//
// Checks for SSS given the 5 values
//
private static List<EdgeAggregator> InstantiateSSS(Triangle tri1, Triangle tri2, CongruentSegments css1, CongruentSegments css2, CongruentSegments css3)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// All congruence pairs must minimally relate the triangles
//
if (!css1.LinksTriangles(tri1, tri2)) return newGrounded;
if (!css2.LinksTriangles(tri1, tri2)) return newGrounded;
if (!css3.LinksTriangles(tri1, tri2)) return newGrounded;
Segment seg1Tri1 = tri1.GetSegment(css1);
Segment seg1Tri2 = tri2.GetSegment(css1);
Segment seg2Tri1 = tri1.GetSegment(css2);
Segment seg2Tri2 = tri2.GetSegment(css2);
Segment seg3Tri1 = tri1.GetSegment(css3);
Segment seg3Tri2 = tri2.GetSegment(css3);
//
// The vertices of both triangles must all be distinct and cover the triangle completely.
//
Point vertex1Tri1 = seg1Tri1.SharedVertex(seg2Tri1);
Point vertex2Tri1 = seg2Tri1.SharedVertex(seg3Tri1);
Point vertex3Tri1 = seg1Tri1.SharedVertex(seg3Tri1);
if (vertex1Tri1 == null || vertex2Tri1 == null || vertex3Tri1 == null) return newGrounded;
if (vertex1Tri1.StructurallyEquals(vertex2Tri1) ||
vertex1Tri1.StructurallyEquals(vertex3Tri1) ||
vertex2Tri1.StructurallyEquals(vertex3Tri1)) return newGrounded;
Point vertex1Tri2 = seg1Tri2.SharedVertex(seg2Tri2);
Point vertex2Tri2 = seg2Tri2.SharedVertex(seg3Tri2);
Point vertex3Tri2 = seg1Tri2.SharedVertex(seg3Tri2);
if (vertex1Tri2 == null || vertex2Tri2 == null || vertex3Tri2 == null) return newGrounded;
if (vertex1Tri2.StructurallyEquals(vertex2Tri2) ||
vertex1Tri2.StructurallyEquals(vertex3Tri2) ||
vertex2Tri2.StructurallyEquals(vertex3Tri2)) return newGrounded;
//
// Construct the corresponding points between the triangles
//
List<Point> triangleOne = new List<Point>();
List<Point> triangleTwo = new List<Point>();
triangleOne.Add(vertex1Tri1);
triangleTwo.Add(vertex1Tri2);
triangleOne.Add(vertex2Tri1);
triangleTwo.Add(vertex2Tri2);
triangleOne.Add(vertex3Tri1);
triangleTwo.Add(vertex3Tri2);
//
// 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(css1);
antecedent.Add(css2);
antecedent.Add(css3);
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;
}