protected bool HasSamePoints(Quadrilateral quad)
{
foreach (Point p in quad.points)
{
if (!this.points.Contains(p))
{
return(false);
}
}
return(true);
}
private static Polygon ActuallyConstructThePolygonObject(List <Segment> orderedSides)
{
//
// Check for lines that are actually collinear (and can be compressed into a single segment).
//
bool change = true;
while (change)
{
change = false;
for (int s = 0; s < orderedSides.Count; s++)
{
Segment first = orderedSides[s];
Segment second = orderedSides[(s + 1) % orderedSides.Count];
Point shared = first.SharedVertex(second);
// We know these lines share an endpoint and that they are collinear.
if (first.IsCollinearWith(second))
{
Segment newSegment = new Segment(first.OtherPoint(shared), second.OtherPoint(shared));
// Replace the two original lines with the new line.
orderedSides.Insert(s, newSegment);
orderedSides.Remove(first);
orderedSides.Remove(second);
change = true;
}
}
}
KeyValuePair <List <Point>, List <Angle> > pair = MakePointsAngle(orderedSides);
// If the polygon is concave, make that object.
if (IsConcavePolygon(pair.Key))
{
return(new ConcavePolygon(orderedSides, pair.Key, pair.Value));
}
// Otherwise, make the other polygons
switch (orderedSides.Count)
{
case 3:
return(new Triangle(orderedSides));
case 4:
return(Quadrilateral.GenerateQuadrilateral(orderedSides));
default:
return(new Polygon(orderedSides, pair.Key, pair.Value));
}
//return null;
}
public static Quadrilateral GetFigureQuadrilateral(Quadrilateral q)
{
// Search for exact segment first
foreach (Quadrilateral quad in figureQuadrilaterals)
{
if (quad.StructurallyEquals(q))
{
return(quad);
}
}
return(null);
}
public Limitation(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 11, 0); points.Add(b);
Point c = new Point("C", 0, 5); points.Add(c);
Point d = new Point("D", 11, 5); points.Add(d);
Point e = new Point("E", 5, 5); points.Add(e);
Point f = new Point("F", 4, 0); points.Add(f);
Point g = new Point("G", 8, 5); points.Add(g);
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bd = new Segment(b, d); segments.Add(bd);
Segment ae = new Segment(a, e); segments.Add(ae);
Segment ef = new Segment(e, f); segments.Add(ef);
Segment fg = new Segment(f, g); segments.Add(fg);
Segment bg = new Segment(b, g); segments.Add(bg);
List<Point> pts = new List<Point>();
pts.Add(c);
pts.Add(e);
pts.Add(g);
pts.Add(d);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(f);
pts.Add(b);
collinear.Add(new Collinear(pts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = new Quadrilateral(ac, bd, (Segment)parser.Get(new Segment(c, d)), (Segment)parser.Get(new Segment(a, b)));
given.Add(new Strengthened(quad, new Rectangle(quad)));
known.AddSegmentLength(ac, 5);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 11);
List<Figure> tris = new List<Figure>();
tris.Add(new Triangle(a, e, f));
tris.Add(new Triangle(f, g, b));
goalRegions = parser.implied.GetAtomicRegionsNotByFigures(tris);
SetSolutionArea(27.5);
problemName = "Limiting Problem We Cannot Calculate";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public override bool Equals(Object obj)
{
Quadrilateral thatQuad = obj as Quadrilateral;
if (thatQuad == null)
{
return(false);
}
if (!thatQuad.IsStrictQuadrilateral())
{
return(false);
}
return(this.HasSamePoints(thatQuad));
}
public Page10Prob18(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 7); points.Add(b);
Point c = new Point("C", 7, 7); points.Add(c);
Point d = new Point("D", 7, 0); points.Add(d);
Point o = new Point("O", 0, 3.5); points.Add(o);
Point p = new Point("P", 3.5, 7); points.Add(p);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment da = new Segment(d, a); segments.Add(da);
List<Point> pts = new List<Point>();
pts.Add(b);
pts.Add(o);
pts.Add(a);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(b);
pts.Add(p);
pts.Add(c);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(o, 3.5));
circles.Add(new Circle(p, 3.5));
parser = new TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = new Quadrilateral((Segment)parser.Get(new Segment(a, b)), cd,
(Segment)parser.Get(new Segment(b, c)), da);
given.Add(new Strengthened(quad, new Square(quad)));
known.AddSegmentLength(cd, 7);
goalRegions = parser.implied.GetAllAtomicRegions();
SetSolutionArea(49 + (12.25 * System.Math.PI));
problemName = "Glencoe Page 10 Problem 18";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//
// Can this Quadrilateral be strengthened to any of the specific quadrilaterals (parallelogram, kite, square, etc)?
//
public static List <Strengthened> CanBeStrengthened(Quadrilateral thatQuad)
{
List <Strengthened> strengthened = new List <Strengthened>();
if (thatQuad.VerifyParallelogram())
{
strengthened.Add(new Strengthened(thatQuad, new Parallelogram(thatQuad)));
}
if (thatQuad.VerifyRectangle())
{
strengthened.Add(new Strengthened(thatQuad, new Rectangle(thatQuad)));
}
if (thatQuad.VerifySquare())
{
strengthened.Add(new Strengthened(thatQuad, new Square(thatQuad)));
}
if (thatQuad.VerifyRhombus())
{
strengthened.Add(new Strengthened(thatQuad, new Rhombus(thatQuad)));
}
if (thatQuad.VerifyKite())
{
strengthened.Add(new Strengthened(thatQuad, new Kite(thatQuad)));
}
if (thatQuad.VerifyTrapezoid())
{
Trapezoid newTrap = new Trapezoid(thatQuad);
strengthened.Add(new Strengthened(thatQuad, newTrap));
if (thatQuad.VerifyIsoscelesTrapezoid())
{
strengthened.Add(new Strengthened(newTrap, new IsoscelesTrapezoid(thatQuad)));
}
}
return(strengthened);
}
public Page9Prob33(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 2.5); points.Add(b);
Point c = new Point("C", 0, 5); points.Add(c);
Point d = new Point("D", 5, 5); points.Add(d);
Point e = new Point("E", 5, 0); points.Add(e);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment de = new Segment(d, e); segments.Add(de);
Segment ea = new Segment(e, a); segments.Add(ea);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
circles.Add(new Circle(b, 2.5));
parser = new TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Quadrilateral quad = new Quadrilateral((Segment)parser.Get(new Segment(a, c)), de, cd, ea);
given.Add(new Strengthened(quad, new Square(quad)));
known.AddSegmentLength(cd, 5);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 4, 4));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(25 - (2.5 * 2.5 * System.Math.PI / 2.0));
problemName = "Glencoe Page 9 Problem 33";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public new static List <FigSynthProblem> SubtractShape(Figure outerShape, List <Connection> conns, List <Point> points)
{
// Possible quadrilaterals.
List <Quadrilateral> quads = null;
if (outerShape is ConcavePolygon)
{
quads = Quadrilateral.GetQuadrilateralsFromPoints(outerShape as ConcavePolygon, points);
}
else
{
quads = Quadrilateral.GetQuadrilateralsFromPoints(points);
}
List <FigSynthProblem> composed = new List <FigSynthProblem>();
foreach (Quadrilateral quad in quads)
{
// Select only rhombi that don't match the outer shape.
if (quad.VerifyRhombus() && !quad.HasSamePoints(outerShape as Polygon))
{
Rhombus rhombus = new Rhombus(quad);
SubtractionSynth subSynth = new SubtractionSynth(outerShape, rhombus);
try
{
subSynth.SetOpenRegions(FigSynthProblem.AcquireOpenAtomicRegions(conns, rhombus.points, rhombus));
composed.Add(subSynth);
}
catch (Exception) { }
}
}
return(FigSynthProblem.RemoveSymmetric(composed));
}
private static List<EdgeAggregator> InstantiateToRhombus(Quadrilateral quad, CongruentSegments cs1, CongruentSegments cs2, CongruentSegments cs3)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// The 3 congruent segments pairs must relate; one pair must link the two others.
// Determine the link segments as well as the opposite sides.
//
CongruentSegments link = null;
CongruentSegments opp1 = null;
CongruentSegments opp2 = null;
if (cs1.SharedSegment(cs2) != null && cs1.SharedSegment(cs3) != null)
{
link = cs1;
opp1 = cs2;
opp2 = cs3;
}
else if (cs2.SharedSegment(cs1) != null && cs2.SharedSegment(cs3) != null)
{
link = cs2;
opp1 = cs1;
opp2 = cs3;
}
else if (cs3.SharedSegment(cs1) != null && cs3.SharedSegment(cs2) != null)
{
link = cs3;
opp1 = cs1;
opp2 = cs2;
}
else return newGrounded;
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentSides(opp1)) return newGrounded;
if (!quad.HasOppositeCongruentSides(opp2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newRhombus = new Strengthened(quad, new Rhombus(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs1);
antecedent.Add(cs2);
antecedent.Add(cs3);
newGrounded.Add(new EdgeAggregator(antecedent, newRhombus, annotation));
return newGrounded;
}
public Parallelogram(Quadrilateral quad) : this(quad.left, quad.right, quad.top, quad.bottom)
{
}
public IsoscelesTrapezoid(Quadrilateral quad)
: this(quad.left, quad.right, quad.top, quad.bottom)
{
}
//
// Are the parallel sides subsegments of sides of the quadrilateral?
// If so, instantiate.
//
private static List<EdgeAggregator> InstantiateToTrapezoidSubsegments(Quadrilateral quad, Parallel parallel)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Does this parallel set apply to this quadrilateral?
if (!quad.HasOppositeParallelSubsegmentSides(parallel)) return newGrounded;
//
// The other set of sides should NOT be parallel (that's a parallelogram)
//
List<Segment> otherSides = quad.GetOtherSubsegmentSides(parallel);
if (otherSides.Count != 2)
{
throw new ArgumentException("Expected TWO sides returned from a quadrilateral / parallel relationship: "
+ quad + " " + parallel + " returned " + otherSides.Count);
}
if (otherSides[0].IsParallelWith(otherSides[1])) return newGrounded;
return MakeTrapezoid(quad, parallel);
}
protected bool HasSamePoints(Quadrilateral quad)
{
foreach (Point p in quad.points)
{
if (!this.points.Contains(p)) return false;
}
return true;
}
private static List<EdgeAggregator> MakeTrapezoid(Quadrilateral quad, Parallel parallel)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
//
// Create the new Trapezoid object
//
Strengthened newTrapezoid = new Strengthened(quad, new Trapezoid(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(parallel);
newGrounded.Add(new EdgeAggregator(antecedent, newTrapezoid, annotation));
return newGrounded;
}
public static Quadrilateral GetFigureQuadrilateral(Quadrilateral q)
{
// Search for exact segment first
foreach (Quadrilateral quad in figureQuadrilaterals)
{
if (quad.StructurallyEquals(q)) return quad;
}
return null;
}
private static List<EdgeAggregator> InstantiateToParallelogram(Quadrilateral quad, Parallel parallel1, Parallel parallel2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Does this paralle set apply to this triangle?
if (!quad.HasOppositeParallelSides(parallel1)) return newGrounded;
if (!quad.HasOppositeParallelSides(parallel2)) return newGrounded;
//
// Create the new Parallelogram object
//
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(parallel1);
antecedent.Add(parallel2);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToTheorem(Quadrilateral quad, CongruentSegments cs, Parallel parallel)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentSides(cs)) return newGrounded;
if (!quad.HasOppositeParallelSides(parallel)) return newGrounded;
// Do the congruent segments coincide with these parallel segments?
if (!parallel.segment1.HasSubSegment(cs.cs1) && !parallel.segment2.HasSubSegment(cs.cs1)) return newGrounded;
if (!parallel.segment1.HasSubSegment(cs.cs2) && !parallel.segment2.HasSubSegment(cs.cs2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs);
antecedent.Add(parallel);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
//
// Can this Quadrilateral be strengthened to any of the specific quadrilaterals (parallelogram, kite, square, etc)?
//
public static List<Strengthened> CanBeStrengthened(Quadrilateral thatQuad)
{
List<Strengthened> strengthened = new List<Strengthened>();
if (thatQuad.VerifyParallelogram())
{
strengthened.Add(new Strengthened(thatQuad, new Parallelogram(thatQuad)));
}
if (thatQuad.VerifyRectangle())
{
strengthened.Add(new Strengthened(thatQuad, new Rectangle(thatQuad)));
}
if (thatQuad.VerifySquare())
{
strengthened.Add(new Strengthened(thatQuad, new Square(thatQuad)));
}
if (thatQuad.VerifyRhombus())
{
strengthened.Add(new Strengthened(thatQuad, new Rhombus(thatQuad)));
}
if (thatQuad.VerifyKite())
{
strengthened.Add(new Strengthened(thatQuad, new Kite(thatQuad)));
}
if (thatQuad.VerifyTrapezoid())
{
Trapezoid newTrap = new Trapezoid(thatQuad);
strengthened.Add(new Strengthened(thatQuad, newTrap));
if (thatQuad.VerifyIsoscelesTrapezoid())
{
strengthened.Add(new Strengthened(newTrap, new IsoscelesTrapezoid(thatQuad)));
}
}
return strengthened;
}
private static List<EdgeAggregator> InstantiateToKite(Quadrilateral quad, CongruentSegments cs1, CongruentSegments cs2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The congruences should not share a side.
if (cs1.SharedSegment(cs2) != null) return newGrounded;
// The congruent pairs should not also be congruent to each other
if (cs1.cs1.CoordinateCongruent(cs2.cs1)) return newGrounded;
// Does both set of congruent segments apply to the quadrilateral?
if (!quad.HasAdjacentCongruentSides(cs1)) return newGrounded;
if (!quad.HasAdjacentCongruentSides(cs2)) return newGrounded;
//
// Create the new Kite object
//
Strengthened newKite = new Strengthened(quad, new Kite(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cs1);
antecedent.Add(cs2);
newGrounded.Add(new EdgeAggregator(antecedent, newKite, annotation));
return newGrounded;
}
public Rhombus(Quadrilateral quad)
: this(quad.left, quad.right, quad.top, quad.bottom,
quad.TopLeftDiagonalIsValid(), quad.BottomRightDiagonalIsValid(), quad.diagonalIntersection)
{
}
// A _________________ B
// / /
// / \/ /
// / /\ /
// D /________________/ C
//
// Quadrilateral(A, B, C, D), SegmentBisector(Segment(A, C), Segment(B, D)),
// SegmentBisector(Segment(B, D), Segment(A, C)) -> Parallelogram(A, B, C, D)
//
private static List<EdgeAggregator> InstantiateToTheorem(Quadrilateral quad, SegmentBisector sb1, SegmentBisector sb2, GroundedClause originalSB1, GroundedClause originalSB2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// The two segment bisectors must intersect at the same point
if (!sb1.bisected.intersect.StructurallyEquals(sb2.bisected.intersect)) return newGrounded;
// The bisectors must be part of the other segment bisector.
if (!sb1.bisected.HasSegment(sb2.bisector)) return newGrounded;
if (!sb2.bisected.HasSegment(sb1.bisector)) return newGrounded;
// Do these segment bisectors define the diagonals of the quadrilateral?
if (!sb1.bisector.HasSubSegment(quad.topLeftBottomRightDiagonal) && !sb2.bisector.HasSubSegment(quad.topLeftBottomRightDiagonal)) return newGrounded;
if (!sb1.bisector.HasSubSegment(quad.bottomLeftTopRightDiagonal) && !sb2.bisector.HasSubSegment(quad.bottomLeftTopRightDiagonal)) return newGrounded;
// Determine the CongruentSegments opposing sides and output that.
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(originalSB1);
antecedent.Add(originalSB2);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
private static List<EdgeAggregator> InstantiateToTheorem(Quadrilateral quad, CongruentAngles cas1, CongruentAngles cas2)
{
List<EdgeAggregator> newGrounded = new List<EdgeAggregator>();
// Are the pairs on the opposite side of this quadrilateral?
if (!quad.HasOppositeCongruentAngles(cas1)) return newGrounded;
if (!quad.HasOppositeCongruentAngles(cas2)) return newGrounded;
//
// Create the new Rhombus object
//
Strengthened newParallelogram = new Strengthened(quad, new Parallelogram(quad));
// For hypergraph
List<GroundedClause> antecedent = new List<GroundedClause>();
antecedent.Add(quad);
antecedent.Add(cas1);
antecedent.Add(cas2);
newGrounded.Add(new EdgeAggregator(antecedent, newParallelogram, annotation));
return newGrounded;
}
public static Quadrilateral MakeQuadrilateral(Point a, Point b, Point c, Point d)
{
Segment left = new Segment(a, d);
Segment right = new Segment(b, c);
Segment top = new Segment(a, b);
Segment bottom = new Segment(c, d);
Quadrilateral quad = null;
try
{
quad = new Quadrilateral(left, right, top, bottom);
}
catch (Exception)
{
left = new Segment(a, d);
right = new Segment(b, c);
top = new Segment(a, c);
bottom = new Segment(b, d);
quad = new Quadrilateral(left, right, top, bottom);
}
return quad;
}
public Parallelogram(Quadrilateral quad)
: this(quad.left, quad.right, quad.top, quad.bottom)
{
}
public IsoscelesTrapezoid(Quadrilateral quad) : this(quad.left, quad.right, quad.top, quad.bottom)
{
}
public Rectangle(Quadrilateral quad) : this(quad.left, quad.right, quad.top, quad.bottom,
quad.TopLeftDiagonalIsValid(), quad.BottomRightDiagonalIsValid(), quad.diagonalIntersection)
{
}
public override List<GroundedClause> GetGivens()
{
Polygon thisPoly = figure as Polygon;
if (thisPoly == null) return new List<GroundedClause>();
//
// Create the simple version of the figure; we already have the strengthened version.
//
Polygon simple = null;
if (thisPoly.points.Count == 3) simple = new Triangle(thisPoly.points);
if (thisPoly.points.Count == 4) simple = new Quadrilateral(thisPoly.orderedSides[0], thisPoly.orderedSides[2],
thisPoly.orderedSides[1], thisPoly.orderedSides[3]);
return Utilities.MakeList<GroundedClause>(new Strengthened(simple, this.figure));
}