public static Triangle ConstructDefaultTriangle()
{
Point other1 = PointFactory.GeneratePoint(Figure.GenerateIntValue(), 0);
Point other2 = PointFactory.GeneratePoint(Figure.GenerateIntValue(), Figure.GenerateIntValue());
return(new Triangle(origin, other1, other2));
}
public static Trapezoid ConstructDefaultTrapezoid()
{
int smallBase = Figure.DefaultSideLength();
int largeBase = Figure.DefaultSideLength();
int height = Figure.DefaultSideLength();
int offset = Figure.SmallIntegerValue();
// Acquire a non-equal side.
while (smallBase >= largeBase)
{
smallBase = Figure.DefaultSideLength();
largeBase = Figure.DefaultSideLength();
}
Point topLeft = PointFactory.GeneratePoint(offset, height);
Point topRight = PointFactory.GeneratePoint(offset + smallBase, height);
Point bottomRight = PointFactory.GeneratePoint(largeBase, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new Trapezoid(left, right, top, bottom));
}
public static IsoscelesTrapezoid ConstructDefaultIsoscelesTrapezoid()
{
int base1 = Figure.DefaultSideLength();
int side = Figure.DefaultSideLength();
// Ensure a smaller side then base for a 'normal' look.
while (base1 <= side)
{
base1 = Figure.DefaultSideLength();
side = Figure.DefaultSideLength();
}
int baseAngle = Figure.DefaultFirstQuadrantNonRightAngle();
Point topLeft = Figure.GetPointByLengthAndAngleInStandardPosition(side, baseAngle);
topLeft = PointFactory.GeneratePoint(topLeft.X, topLeft.Y);
Point topRight = Figure.GetPointByLengthAndAngleInThirdQuadrant(side, baseAngle);
topRight = PointFactory.GeneratePoint(base1 + topRight.X, topRight.Y);
Point bottomRight = PointFactory.GeneratePoint(base1, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new IsoscelesTrapezoid(left, right, top, bottom));
}
private List <Point> ConstructMidpoints(Point end1, Point end2, int level)
{
List <Point> middlePoints = new List <Point>();
// Recursive Base Case
if (level == NUM_MID_SEGMENT_POINTS)
{
return(middlePoints);
}
Point midpoint = PointFactory.GeneratePoint(end1.Midpoint(end2));
//
// Recursively construct all points between
//
middlePoints.AddRange(ConstructMidpoints(end1, midpoint, level + 1));
middlePoints.Add(midpoint);
// Add to the list of midpoints clauses (for instantiation during figure synthesis).
midpoints.Add(new Midpoint(new InMiddle(midpoint, new Segment(end1, end2))));
middlePoints.AddRange(ConstructMidpoints(midpoint, end2, level + 1));
return(middlePoints);
}
public static IsoscelesTriangle ConstructDefaultIsoscelesTriangle()
{
int baseLength = Figure.DefaultSideLength();
int height = Figure.DefaultSideLength();
Point top = PointFactory.GeneratePoint(baseLength / 2.0, height);
Point bottomRight = PointFactory.GeneratePoint(baseLength, 0);
Segment left = new Segment(origin, top);
Segment right = new Segment(top, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new IsoscelesTriangle(left, right, bottom));
}
public static RightTriangle ConstructDefaultRightTriangle()
{
int length = Figure.DefaultSideLength();
int width = Figure.DefaultSideLength();
Point topLeft = PointFactory.GeneratePoint(0, width);
Point bottomRight = PointFactory.GeneratePoint(length, 0);
Segment left = new Segment(origin, topLeft);
Segment hypotenuse = new Segment(topLeft, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new RightTriangle(left, bottom, hypotenuse));
}
public static Square ConstructDefaultSquare()
{
int length = Figure.DefaultSideLength();
Point topLeft = PointFactory.GeneratePoint(0, length);
Point topRight = PointFactory.GeneratePoint(length, length);
Point bottomRight = PointFactory.GeneratePoint(length, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new Square(left, right, top, bottom));
}
public static EquilateralTriangle ConstructDefaultEquilateralTriangle()
{
int sideLength = Figure.DefaultSideLength();
Point top = Figure.GetPointByLengthAndAngleInStandardPosition(sideLength, 60);
top = PointFactory.GeneratePoint(top.X, top.Y);
Point bottomRight = PointFactory.GeneratePoint(sideLength, 0);
Segment left = new Segment(origin, top);
Segment right = new Segment(top, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new EquilateralTriangle(left, right, bottom));
}
public static Parallelogram ConstructDefaultParallelogram()
{
int baseLength = Figure.DefaultSideLength();
int height = Figure.DefaultSideLength();
int offset = Figure.SmallIntegerValue();
Point topLeft = PointFactory.GeneratePoint(offset, height);
Point topRight = PointFactory.GeneratePoint(offset + baseLength, height);
Point bottomRight = PointFactory.GeneratePoint(baseLength, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new Parallelogram(left, right, top, bottom));
}
public static Kite ConstructDefaultKite()
{
int height = Figure.DefaultSideLength() / 2;
int width1 = Figure.DefaultSideLength() / 2;
int width2 = Figure.DefaultSideLength() / 2;
Point top = PointFactory.GeneratePoint(width1, height);
Point right = PointFactory.GeneratePoint(width1 + width2, 0);
Point bottom = PointFactory.GeneratePoint(width1, -height);
Segment leftTop = new Segment(origin, top);
Segment rightTop = new Segment(top, right);
Segment rightBottom = new Segment(right, bottom);
Segment leftBottom = new Segment(bottom, origin);
return(new Kite(leftTop, rightBottom, rightTop, leftBottom));
}
public static Rhombus ConstructDefaultRhombus()
{
int sideLength = Figure.DefaultSideLength();
int baseAngle = Figure.DefaultFirstQuadrantNonRightAngle();
Point topLeft = Figure.GetPointByLengthAndAngleInStandardPosition(sideLength, baseAngle);
double offsetX = topLeft.X;
double offsetY = topLeft.Y;
topLeft = PointFactory.GeneratePoint(topLeft.X, topLeft.Y);
Point topRight = PointFactory.GeneratePoint(offsetX + sideLength, offsetY);
Point bottomRight = PointFactory.GeneratePoint(sideLength, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new Rhombus(left, right, top, bottom));
}
public static Quadrilateral ConstructDefaultRectangle()
{
int length = Figure.DefaultSideLength();
int width = Figure.DefaultSideLength();
// Ensure we don't have a square.
while (width == length)
{
length = Figure.DefaultSideLength();
width = Figure.DefaultSideLength();
}
Point topLeft = PointFactory.GeneratePoint(0, width);
Point topRight = PointFactory.GeneratePoint(length, width);
Point bottomRight = PointFactory.GeneratePoint(length, 0);
Segment left = new Segment(origin, topLeft);
Segment top = new Segment(topLeft, topRight);
Segment right = new Segment(topRight, bottomRight);
Segment bottom = new Segment(bottomRight, origin);
return(new Rectangle(left, right, top, bottom));
}
//
// C
// /)
// / )
// / )
// / )
// A /)_________ B
//
// Tangent(Circle(O), Segment(AB)), Intersection(Segment(AC), Segment(AB)) -> 2 * Angle(CAB) = Arc(C, B)
//
public static List <EdgeAggregator> InstantiateTheorem(Intersection inter, Tangent tangent, GroundedClause original)
{
List <EdgeAggregator> newGrounded = new List <EdgeAggregator>();
CircleSegmentIntersection tan = tangent.intersection as CircleSegmentIntersection;
//
// Does this tangent apply to this intersection?
//
if (!inter.intersect.StructurallyEquals(tangent.intersection.intersect))
{
return(newGrounded);
}
Segment secant = null;
Segment tanSegment = null;
if (tan.HasSegment(inter.lhs))
{
secant = inter.rhs;
tanSegment = inter.lhs;
}
else if (tan.HasSegment(inter.rhs))
{
secant = inter.lhs;
tanSegment = inter.rhs;
}
else
{
return(newGrounded);
}
//
// Acquire the angle and intercepted arc.
//
Segment chord = tan.theCircle.GetChord(secant);
if (chord == null)
{
return(newGrounded);
}
//Segment chord = tan.theCircle.ContainsChord(secant);
// Arc
// We want the MINOR ARC only!
if (tan.theCircle.DefinesDiameter(chord))
{
Arc theArc = null;
Point midpt = PointFactory.GeneratePoint(tan.theCircle.Midpoint(chord.Point1, chord.Point2));
Point opp = PointFactory.GeneratePoint(tan.theCircle.OppositePoint(midpt));
Point tanPoint = tanSegment.OtherPoint(inter.intersect);
if (tanPoint != null)
{
// Angle; the smaller angle is always the chosen angle
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanPoint);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
}
else
{
// Angle; the smaller angle is always the chosen angle
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point1);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
// Angle; the smaller angle is always the chosen angle
theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point2);
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, midpt, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
theArc = new Semicircle(tan.theCircle, chord.Point1, chord.Point2, opp, chord);
newGrounded.Add(CreateClause(inter, original, theAngle, theArc));
}
}
else
{
Arc theArc = new MinorArc(tan.theCircle, chord.Point1, chord.Point2);
// Angle; the smaller angle is always the chosen angle
Point endPnt = (inter.intersect.StructurallyEquals(tanSegment.Point1)) ? tanSegment.Point2 : tanSegment.Point1;
Angle theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, endPnt);
if (theAngle.measure > 90)
{
//If the angle endpoint was already set to Point2, or if the intersect equals Point2, then the smaller angle does not exist
//In this case, should we create a major arc or return nothing?
if (endPnt.StructurallyEquals(tanSegment.Point2) || inter.intersect.StructurallyEquals(tanSegment.Point2))
{
return(newGrounded);
}
theAngle = new Angle(chord.OtherPoint(inter.intersect), inter.intersect, tanSegment.Point2);
}
Multiplication product = new Multiplication(new NumericValue(2), theAngle);
GeometricAngleArcEquation angArcEq = new GeometricAngleArcEquation(product, theArc);
// For hypergraph
List <GroundedClause> antecedent = new List <GroundedClause>();
antecedent.Add(original);
antecedent.Add(inter);
antecedent.Add(theArc);
antecedent.Add(theAngle);
newGrounded.Add(new EdgeAggregator(antecedent, angArcEq, annotation));
}
return(newGrounded);
}