//Demonstrates: Tangents are perpendicular to radii
public Page296Theorem7_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Segment ot = new Segment(o, t); segments.Add(ot);
List<Point> pnts = new List<Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
Intersection inter = parser.GetIntersection(ot, rs);
goals.Add(new Strengthened(inter, new Perpendicular(inter)));
}
//Demonstrates: Use of AngleArc equation, Central angle equal to intercepted arc
public Test01(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", -5, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 0, 5); points.Add(c);
Segment oc = new Segment(o, c); segments.Add(oc);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(o);
pnts.Add(b);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc m1 = (MinorArc)parser.Get(new MinorArc(circle, a, c));
MinorArc m2 = (MinorArc)parser.Get(new MinorArc(circle, b, c));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, o, c)), (Angle)parser.Get(new Angle(b, o, c))));
goals.Add(new GeometricCongruentArcs(m1, m2));
}
public Circle OtherCircle(Circle thatCircle)
{
if (cc1.StructurallyEquals(thatCircle)) return cc2;
if (cc2.StructurallyEquals(thatCircle)) return cc1;
return null;
}
public Page4prob17(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", -System.Math.Sqrt(27), 3); points.Add(a);
Point b = new Point("B", System.Math.Sqrt(27), 3); points.Add(b);
Point o = new Point("O", 0, 0); points.Add(o);
Point p = new Point("P", 0, -6); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment op = new Segment(o, p); segments.Add(op);
Segment ao = new Segment(a, o); segments.Add(ao);
Segment bo = new Segment(b, o); segments.Add(bo);
Circle circle = new Circle(o, 6.0);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength(op, 6);
given.Add(new GeometricArcEquation((MinorArc)parser.Get(new MinorArc(circle, a, b)), new NumericValue(120)));
List<Point> unwanted = new List<Point>();
unwanted.Add(new Point("", 5, 3.3));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea(24 * System.Math.PI + (9 * System.Math.Sqrt(3)));
problemName = "Jurgensen Page 4 Problem 17";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//Demonstrates: Minor Arcs Congruent if central angles congruent
public Test10(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle center
Point o = new Point("O", 0, 0); points.Add(o);
//Vertices for angle TOV, a central angle of circle O, with one endpoint at 90 degrees and another at 30 degrees
Point t = new Point("T", -3, 4); points.Add(t);
Point v = new Point("V", 0, 5); points.Add(v);
//Vertices for angle VOA, a central angle of circle C, with one endpoint at 90 degrees and another at 30 degrees
Point a = new Point("A", 3, 4); points.Add(a);
Segment ot = new Segment(o, t); segments.Add(ot);
Segment ov = new Segment(o, v); segments.Add(ov);
Segment oa = new Segment(o, a); segments.Add(oa);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentArcs((MinorArc)parser.Get(new MinorArc(circleO, t, v)), (MinorArc)parser.Get(new MinorArc(circleO, v, a))));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(t, o, v)), (Angle)parser.Get(new Angle(v, o, a))));
}
//Demonstrates: congruent chords have congruent arcs
public Page306Theorem7_4_1(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, 4); points.Add(r);
Point s = new Point("S", 2, Math.Sqrt(21)); points.Add(s);
Point t = new Point("T", 2, -Math.Sqrt(21)); points.Add(t);
Point u = new Point("U", -3, -4); points.Add(u);
Segment rt = new Segment(r, t);
Segment su = new Segment(s, u);
Point v = rt.FindIntersection(su); points.Add(v);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment ut = new Segment(u, t); segments.Add(ut);
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(rs, ut));
MinorArc a1 = (MinorArc)parser.Get(new MinorArc(c, r, s));
MinorArc a2 = (MinorArc)parser.Get(new MinorArc(c, t, u));
MajorArc ma1 = (MajorArc)parser.Get(new MajorArc(c, r, s));
MajorArc ma2 = (MajorArc)parser.Get(new MajorArc(c, t, u));
goals.Add(new GeometricCongruentArcs(a1, a2));
goals.Add(new GeometricCongruentArcs(ma1, ma2));
}
public Page4Prob15(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 8); points.Add(a);
Point b = new Point("B", 8, 0); points.Add(b);
Point o = new Point("O", 0, 0); points.Add(o);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ao = new Segment(a, o); segments.Add(ao);
Segment bo = new Segment(b, o); segments.Add(bo);
Circle circle = new Circle(o, 8.0);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle aob = (Angle)parser.Get(new Angle(a, o, b));
given.Add(new Strengthened(aob, new RightAngle(aob)));
known.AddAngleMeasureDegree(aob, 90);
known.AddSegmentLength(bo, 8);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 7.5, 2.5));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(16 * System.Math.PI - 32);
problemName = "Jurgensen Page 4 Problem 15";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//Demonstrates: ChordTangentAngleHalfInterceptedArc
public Test02(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point r = new Point("R", -3, -5); points.Add(r);
Point s = new Point("S", 8, -5); points.Add(s);
Point t = new Point("T", 0, -5); points.Add(t);
Point u = new Point("U", -3, 4); points.Add(u);
Point v = new Point("V", 3, 4); points.Add(v);
Segment tu = new Segment(t, u); segments.Add(tu);
Segment tv = new Segment(t, v); segments.Add(tv);
List<Point> pnts = new List<Point>();
pnts.Add(r);
pnts.Add(t);
pnts.Add(s);
collinear.Add(new Collinear(pnts));
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc m1 = (MinorArc)parser.Get(new MinorArc(c, t, u));
MinorArc m2 = (MinorArc)parser.Get(new MinorArc(c, t, v));
Segment rs = (Segment)parser.Get(new Segment(r, s));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(t, c, rs));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
given.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(r, t, u)), (Angle)parser.Get(new Angle(s, t, v))));
goals.Add(new GeometricCongruentArcs(m1, m2));
}
//Demonstrates: congruent chords have congruent arcs
public Page306Theorem7_4_1_Semicircle(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point c = new Point("C", 15, 0); points.Add(c);
Point s = new Point("S", -3, -4); points.Add(s);
Point t = new Point("T", 3, 4); points.Add(t);
Point u = new Point("U", 2, Math.Sqrt(21)); points.Add(u);
Point a = new Point("A", 12, 4); points.Add(a);
Point b = new Point("B", 18, -4); points.Add(b);
Point d = new Point("D", 16, -Math.Sqrt(24)); points.Add(d);
Segment st = new Segment(s, t); segments.Add(st);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ou = new Segment(o, u); segments.Add(ou);
Segment cd = new Segment(c, d); segments.Add(cd);
Circle c1 = new Circle(o, 5.0);
Circle c2 = new Circle(c, 5.0);
circles.Add(c1);
circles.Add(c2);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
given.Add(new GeometricCongruentSegments(st, ab));
Semicircle semi1 = (Semicircle)parser.Get(new Semicircle(c1, s, t, u, st));
Semicircle semi2 = (Semicircle)parser.Get(new Semicircle(c2, a, b, d,ab));
goals.Add(new GeometricCongruentArcs(semi1, semi2));
}
//
// If no radii are drawn, construct them as well as the chords connecting them.
//
private void AddImpliedSegments(GeometryTutorLib.ConcreteAST.Circle circle)
{
List <GeometryTutorLib.ConcreteAST.Segment> constructedChords = new List <GeometryTutorLib.ConcreteAST.Segment>();
List <GeometryTutorLib.ConcreteAST.Segment> constructedRadii = new List <GeometryTutorLib.ConcreteAST.Segment>();
List <Point> imagPoints = new List <Point>();
List <GeometryTutorLib.ConcreteAST.Point> interPts = circle.GetIntersectingPoints();
// If there are no points of interest, the circle is the atomic region.
if (!interPts.Any())
{
return;
}
// Construct the radii
foreach (Point interPt in interPts)
{
GeometryTutorLib.Utilities.AddStructurallyUnique <GeometryTutorLib.ConcreteAST.Segment>(implied.segments,
new GeometryTutorLib.ConcreteAST.Segment(circle.center, interPt));
}
// Construct the chords
for (int p1 = 0; p1 < interPts.Count - 1; p1++)
{
for (int p2 = p1 + 1; p2 < interPts.Count; p2++)
{
GeometryTutorLib.Utilities.AddStructurallyUnique <GeometryTutorLib.ConcreteAST.Segment>(implied.segments,
new GeometryTutorLib.ConcreteAST.Segment(interPts[p1], interPts[p2]));
}
}
}
//Demonstrates: A segment perpendicular to a radius is a tangent, tangents from point are congruent
public Page296Theorem7_1_Test3(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//Intersection point for two tangents
Point c = new Point("C", 0, 6.25); points.Add(c);
//Points for two tangents
Point a = new Point("A", 3, 4); points.Add(a);
Point b = new Point("B", -3, 4); points.Add(b);
//Tangent and Radii segments
Segment ac = new Segment(a, c); segments.Add(ac);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment oa = new Segment(o, a); segments.Add(oa);
Segment ob = new Segment(o, b); segments.Add(ob);
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Intersection inter1 = parser.GetIntersection(ac, oa);
Intersection inter2 = parser.GetIntersection(bc, ob);
given.Add(new Strengthened(inter1, new Perpendicular(inter1)));
given.Add(new Strengthened(inter2, new Perpendicular(inter2)));
//CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circle, ap));
//given.Add(new Strengthened(cInter, new Tangent(cInter)));
goals.Add(new GeometricCongruentSegments(ac, bc));
}
//Demonstrates: If a quad is inscribed in a circle, then its opposite angles are supplementary
public Page312Corollary2(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//Points and segments for an inscribed rectangle
Point r = new Point("R", -3, 4); points.Add(r);
Point s = new Point("S", 3, 4); points.Add(s);
Point t = new Point("T", 3, -4); points.Add(t);
Point u = new Point("U", -3, -4); points.Add(u);
Segment rs = new Segment(r, s); segments.Add(rs);
Segment st = new Segment(s, t); segments.Add(st);
Segment tu = new Segment(t, u); segments.Add(tu);
Segment ur = new Segment(u, r); segments.Add(ur);
Circle c = new Circle(o, 5.0);
circles.Add(c);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle angle1 = (Angle)parser.Get(new Angle(r, s, t));
Angle angle2 = (Angle)parser.Get(new Angle(u, r, s));
Angle angle3 = (Angle)parser.Get(new Angle(s, t, u));
given.Add(new Strengthened(angle1, new RightAngle(angle1)));
given.Add(new GeometricCongruentAngles(angle2, angle3));
Quadrilateral quad = (Quadrilateral)parser.Get(new Quadrilateral(ur, st, rs, tu));
goals.Add(new Strengthened(quad, new Rectangle(quad)));
}
//Demonstrates: A diameter perpendicular to a chord bisects the chord
public Page307Theorem7_5(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", -3, -4); points.Add(a);
Point b = new Point("B", 3, -4); points.Add(b);
Point x = new Point("X", 0, 5); points.Add(x);
Point y = new Point("Y", 0, -4); points.Add(y);
Point z = new Point("Z", 0, -5); points.Add(z);
List<Point> pnts = new List<Point>();
pnts.Add(x);
pnts.Add(o);
pnts.Add(y);
pnts.Add(z);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(a);
pnts.Add(y);
pnts.Add(b);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 5.0);
circles.Add(circle);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Intersection inter = (Intersection)parser.Get(new Intersection(y, (Segment)parser.Get(new Segment(x, z)), (Segment)parser.Get(new Segment(a, b))));
given.Add(new Strengthened(inter, new Perpendicular(inter)));
goals.Add(new GeometricCongruentSegments((Segment)parser.Get(new Segment(a, y)), (Segment)parser.Get(new Segment(b, y))));
}
public Page8Row6Prob43(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 15); points.Add(a);
Point b = new Point("B", 0, 10); points.Add(b);
Point c = new Point("C", 0, 5); points.Add(c);
Point d = new Point("D", 0, 0); points.Add(d);
Point e = new Point("E", 0, -5); points.Add(e);
Point f = new Point("F", 0, -10); points.Add(f);
Point g = new Point("G", 0, -15); points.Add(g);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
pts.Add(d);
pts.Add(e);
pts.Add(f);
pts.Add(g);
collinear.Add(new Collinear(pts));
Circle outer = new Circle(c, 15);
Circle top = new Circle(b, 5);
Circle mid1 = new Circle(c, 10);
Circle mid2 = new Circle(e, 10);
Circle bottom = new Circle(f, 5);
circles.Add(outer);
circles.Add(top);
circles.Add(mid1);
circles.Add(mid2);
circles.Add(bottom);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ag = (Segment)parser.Get(new Segment(a, g));
known.AddSegmentLength(ag, 30);
//Problem is slightly ambiguous as written, appears to be reliant on assumption:
//The three 'stacked' segments of the diameter each make up 1/3 of the total length
Segment ac = (Segment)parser.Get(new Segment(a, c));
ac.multiplier = 3;
Segment ae = (Segment)parser.Get(new Segment(a, e));
ae.multiplier = 2;
given.Add(new GeometricSegmentEquation(ac, ag));
given.Add(new GeometricSegmentEquation(ae, ag));
given.Add(new GeometricCongruentCircles(top, bottom));
given.Add(new GeometricCongruentCircles(mid1, mid2));
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 1, 5));
wanted.Add(new Point("", 7.5, 5));
wanted.Add(new Point("", 12.5, 5));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(150 * System.Math.PI);
problemName = "Glencoe Page 8 Row 6 Problem 43";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page2Prob18(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point a = new Point("A", 0, 4); points.Add(a);
Point b = new Point("B", 4, 0); points.Add(b);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ao = new Segment(a, o); segments.Add(ao);
Segment bo = new Segment(b, o); segments.Add(bo);
Circle theCircle = new Circle(o, 4);
circles.Add(theCircle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc arcAB = (MinorArc)parser.Get(new MinorArc(theCircle, a, b));
given.Add(new GeometricArcEquation(arcAB, new NumericValue(90.0)));
known.AddArcMeasureDegree(arcAB, 90.0);
known.AddSegmentLength(ao, 4.0);
known.AddSegmentLength(bo, 4.0);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0, -1));
wanted.Add(new Point("", 1, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(45.69911184);
problemName = "Jurgensen Page 2 Problem 18";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
//Demonstrates: An angle inscribed in a semi circle is a right angle
public Page312Theorem7_7_Semicircle(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
//diameter points plus extra point to define semicircle
Point a = new Point("A", -5, 0); points.Add(a);
Point b = new Point("B", 5, 0); points.Add(b);
Point c = new Point("C", 1, -Math.Sqrt(24)); points.Add(c);
//vertex point
Point x = new Point("X", -2, -Math.Sqrt(21)); points.Add(x);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment ax = new Segment(a, x); segments.Add(ax);
Segment bx = new Segment(b, x); segments.Add(bx);
Circle c1 = new Circle(o, 5.0);
circles.Add(c1);
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Angle angle = (Angle)parser.Get(new Angle(a, x, b));
goals.Add(new Strengthened(angle, new RightAngle(angle)));
}
public Page7Prob26(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 4); points.Add(b);
Point c = new Point("C", 4, 4); points.Add(c);
Point d = new Point("D", 4, 0); points.Add(d);
Point o = new Point("O", 2, 2); points.Add(o);
Point p = new Point("P", 0, 2); points.Add(p);
Point q = new Point("Q", 4, 2); points.Add(q);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
List<Point> pts = new List<Point>();
pts.Add(a); pts.Add(p); pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(p); pts.Add(o); pts.Add(q);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(c); pts.Add(q); pts.Add(d);
collinear.Add(new Collinear(pts));
Circle circle = new Circle(o, 2);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment cd = (Segment)parser.Get(new Segment(c, d));
Angle a1 = (Angle)parser.Get(new Angle(a, b, c));
Angle a2 = (Angle)parser.Get(new Angle(b, c, d));
Angle a3 = (Angle)parser.Get(new Angle(c, d, a));
Angle a4 = (Angle)parser.Get(new Angle(d, a, b));
CircleSegmentIntersection cInter = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(q, circle, cd));
known.AddSegmentLength(da, 4);
known.AddSegmentLength(cd, 4);
given.Add(new Strengthened(a1, new RightAngle(a1)));
given.Add(new Strengthened(a2, new RightAngle(a2)));
given.Add(new Strengthened(a3, new RightAngle(a3)));
given.Add(new Strengthened(a4, new RightAngle(a4)));
given.Add(new GeometricSegmentEquation(da, new NumericValue(4)));
given.Add(new GeometricSegmentEquation(cd, new NumericValue(4)));
given.Add(new Strengthened(cInter, new Tangent(cInter)));
List<Point> unwanted = new List<Point>();
unwanted.Add(new Point("", 0.1, 3.8));
unwanted.Add(new Point("", 3.9, 3.8));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea(8 + 2 * System.Math.PI);
problemName = "McDougall Page 7 Problem 24";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page5Row5Prob17(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 6); points.Add(b);
Point c = new Point("C", 6, 6); points.Add(c);
Point d = new Point("D", 6, 0); points.Add(d);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
Point x = new Point("X", 0, 3.0); points.Add(x);
Point y = new Point("Y", 6, 3.0); points.Add(y);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(x);
pts.Add(b);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(c);
pts.Add(y);
pts.Add(d);
collinear.Add(new Collinear(pts));
Circle circleX = new Circle(x, 3.0);
Circle circleY = new Circle(y, 3.0);
circles.Add(circleX);
circles.Add(circleY);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(b, circleX, bc));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(c, circleY, bc));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, circleX, da));
CircleSegmentIntersection cInter4 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, circleY, da));
given.Add(new GeometricCongruentSegments(da, (Segment)parser.Get(new Segment(a, b))));
given.Add(new GeometricCongruentSegments(da, (Segment)parser.Get(new Segment(c, d))));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
given.Add(new Strengthened(cInter3, new Tangent(cInter3)));
given.Add(new Strengthened(cInter4, new Tangent(cInter4)));
known.AddSegmentLength(da, 6);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, b)), 6);
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 6);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 3, .5));
wanted.Add(new Point("", 3, 5.5));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(36 - System.Math.PI * 3 * 3);
problemName = "Jurgensen Page 5 Problem 17";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page2Prob20(bool onoff, bool complete)
: base(onoff, complete)
{
double x = System.Math.Sqrt(3);
double y = 1;
Point a = new Point("A", -x, y); points.Add(a);
Point b = new Point("B", x, y); points.Add(b);
Point c = new Point("C", -x, -y); points.Add(c);
Point d = new Point("D", x, -y); points.Add(d);
Point o = new Point("O", 0, 0); points.Add(o);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment ac = new Segment(a, c); segments.Add(ac);
//Segment bd = new Segment(b, d); segments.Add(bd);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(o);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(b);
pnts.Add(o);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 2);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc arcAB = (MinorArc)parser.Get(new MinorArc(circle, a, b));
MinorArc arcBD = (MinorArc)parser.Get(new MinorArc(circle, b, d));
MinorArc arcDC = (MinorArc)parser.Get(new MinorArc(circle, d, c));
MinorArc arcAC = (MinorArc)parser.Get(new MinorArc(circle, a, c));
known.AddSegmentLength(ac, 2);
known.AddArcMeasureDegree(arcAB, 120);
known.AddArcMeasureDegree(arcBD, 60);
known.AddArcMeasureDegree(arcDC, 120);
known.AddArcMeasureDegree(arcAC, 60);
given.Add(new GeometricArcEquation(arcAB, new NumericValue(120)));
given.Add(new GeometricArcEquation(arcBD, new NumericValue(60)));
given.Add(new GeometricArcEquation(arcDC, new NumericValue(120)));
given.Add(new GeometricArcEquation(arcAC, new NumericValue(60)));
List<Point> unwanted = new List<Point>();
unwanted.Add(new Point("", 0, y+0.2));
unwanted.Add(new Point("", 0, -y-0.2));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea((4.0 / 3.0) * System.Math.PI + 2.0 * System.Math.Sqrt(3.0));
problemName = "Jurgensen Page 2 Problem 20";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public MajorArc(Circle circle, Point e1, Point e2, List<Point> minorPts, List<Point> majorPts)
: base(circle, e1, e2, minorPts, majorPts)
{
if (circle.DefinesDiameter(new Segment(e1, e2)))
{
System.Diagnostics.Debug.WriteLine("Major Arc should not be constructed when a semicircle is appropriate.");
}
}
//Demonstrates: ExteriorAngleHalfDifferenceInterceptedArcs : two secants
public Test04(bool onoff, bool complete)
: base(onoff, complete)
{
//Circle
Point o = new Point("O", 0, 0); points.Add(o);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
//Intersection point for two secants
Point x = new Point("X", 0, 6); points.Add(x);
//Secant intersection points for circle O
Point a = new Point("A", -3, -4); points.Add(a);
Point b = new Point("B", 3, -4); points.Add(b);
Point c, d, trash;
circleO.FindIntersection(new Segment(b, x), out c, out trash);
if (b.StructurallyEquals(c)) c = trash;
c = new Point("C", c.X, c.Y);
points.Add(c);
circleO.FindIntersection(new Segment(a, x), out d, out trash);
if (a.StructurallyEquals(d)) d = trash;
d = new Point("D", d.X, d.Y);
points.Add(d);
//Create point for another arc (Arc(CE)) of equal measure to (1/2)*(Arc(AB)-Arc(CD))
Point e = new Point("E", 3, 4); points.Add(e);
//Should now be able to form segments for a central angle of equal measure to (1/2)*(Arc(AB)-Arc(CD))
Segment oc = new Segment(o, c); segments.Add(oc);
Segment oe = new Segment(o, e); segments.Add(oe);
//Label the intersection betweeen OE and BX
Point i = oe.FindIntersection(new Segment(b, x));
i = new Point("I", i.X, i.Y); points.Add(i);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(d);
pnts.Add(x);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(b);
pnts.Add(i);
pnts.Add(c);
pnts.Add(x);
collinear.Add(new Collinear(pnts));
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
MinorArc farMinor1 = (MinorArc)parser.Get(new MinorArc(circleO, a, b));
MinorArc closeMinor1 = (MinorArc)parser.Get(new MinorArc(circleO, c, d));
MinorArc centralAngleArc = (MinorArc)parser.Get(new MinorArc(circleO, c, e));
given.Add(new GeometricArcEquation(new Multiplication(new NumericValue(2), centralAngleArc), new Subtraction(farMinor1, closeMinor1)));
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(a, x, b)), (Angle)parser.Get(new Angle(c, o, e))));
}
public OsProb8(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 40); points.Add(b);
Point c = new Point("C", 40, 0); points.Add(c);
Point n = new Point("N", 20, 20); points.Add(n);
Point o = new Point("O", 0, 20); points.Add(o);
Point p = new Point("P", 20, 0); points.Add(p);
//Needed until triangles are sent for processing
Segment on = new Segment(o, n); segments.Add(on);
Segment pn = new Segment(p, n); segments.Add(pn);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(o);
pnts.Add(b);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(a);
pnts.Add(p);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(b);
pnts.Add(n);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
Circle circle1 = new Circle(o, 20);
Circle circle2 = new Circle(p, 20);
circles.Add(circle1);
circles.Add(circle2);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Triangle tri = (Triangle)parser.Get(new Triangle(a, b, c));
given.Add(new Strengthened(tri, new RightTriangle(tri)));
known.AddSegmentLength((Segment)parser.Get(new Segment(o, a)), 20);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, p)), 20);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 15, 14.8));
wanted.Add(new Point("", 15, 15.2));
wanted.Add(new Point("", 21, 19.1));
wanted.Add(new Point("", 18, 22.2));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(400 * System.Math.PI - 800);
problemName = "Old School Problem 8";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public TvPage1Prob6(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 8); points.Add(b);
Point c = new Point("C", 10, 8); points.Add(c);
Point d = new Point("D", 10, 0); points.Add(d);
Point o = new Point("O", 0, 2); points.Add(o);
Point p = new Point("P", 10, 4); points.Add(p);
Point q = new Point("Q", 0, 4); points.Add(q);
Segment bc = new Segment(b, c); segments.Add(bc);
Segment da = new Segment(d, a); segments.Add(da);
List<Point> pnts = new List<Point>();
pnts.Add(b);
pnts.Add(q);
pnts.Add(o);
pnts.Add(a);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(c);
pnts.Add(p);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Circle small = new Circle(o, 2);
Circle big = new Circle(p, 4);
circles.Add(small);
circles.Add(big);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(c, big, bc));
CircleSegmentIntersection cInter2 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(d, big, da));
CircleSegmentIntersection cInter3 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(a, small, da));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
given.Add(new Strengthened(cInter2, new Tangent(cInter2)));
given.Add(new Strengthened(cInter3, new Tangent(cInter3)));
known.AddSegmentLength((Segment)parser.Get(new Segment(b, q)), 4);
known.AddSegmentLength((Segment)parser.Get(new Segment(c, d)), 8);
known.AddSegmentLength(bc, 10);
List<Point> unwanted = new List<Point>();
unwanted.Add(new Point("", -0.5, 2));
unwanted.Add(new Point("", 0.5, 2));
goalRegions = parser.implied.GetAllAtomicRegionsWithoutPoints(unwanted);
SetSolutionArea(80 + 6 * System.Math.PI);
problemName = "Tutor Vista Page 1 Problem 6";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public MgProb7(bool onoff, bool complete)
: base(onoff, complete)
{
double y = 4 * System.Math.Sqrt(3);
Point m = new Point("M", 0, 0); points.Add(m);
Point j = new Point("J", -4, 0); points.Add(j);
Point k = new Point("K", 0, y); points.Add(k);
Point l = new Point("L", 4, 0); points.Add(l);
Point n = new Point("N", -2, y / 2); points.Add(n);
Point o = new Point("O", 2, y / 2); points.Add(o);
Segment mk = new Segment(m, k); segments.Add(mk);
Segment mn = new Segment(m, n); segments.Add(mn);
Segment mo = new Segment(m, o); segments.Add(mo);
List<Point> pnts = new List<Point>();
pnts.Add(j);
pnts.Add(n);
pnts.Add(k);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(k);
pnts.Add(o);
pnts.Add(l);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(j);
pnts.Add(m);
pnts.Add(l);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(m, 4);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Triangle tri = (Triangle)parser.Get(new Triangle(j, k, l));
given.Add(new Strengthened(tri, new EquilateralTriangle(tri)));
known.AddSegmentLength((Segment)parser.Get(new Segment(m, j)), 4);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 0, -1));
wanted.Add(new Point("", -3.9, 0.2));
wanted.Add(new Point("", 3.9, 0.2));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea((40/3.0) * System.Math.PI - 4 * y);
problemName = "Magoosh Problem 7";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public CongruentCircles(Circle c1, Circle c2)
: base()
{
cc1 = c1;
cc2 = c2;
if (!Utilities.CompareValues(c1.radius, c2.radius))
{
throw new ArgumentException("Circles deduced congruent when radii differ " + this);
}
}
public CircleCircleIntersection(Point p, Circle c1, Circle c2)
: base(p, c1)
{
otherCircle = c2;
// Find the intersection points
Point pt1, pt2;
theCircle.FindIntersection(otherCircle, out pt1, out pt2);
intersection1 = pt1;
intersection2 = pt2;
}
public CircleSegmentIntersection(Point p, Circle circ, Segment thatSegment)
: base(p, circ)
{
segment = thatSegment;
isTangent = CalcTangency();
// Find the intersection points
Point pt1, pt2;
theCircle.FindIntersection(segment, out pt1, out pt2);
intersection1 = pt1;
intersection2 = pt2;
}
public Page4Prob19(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 0, 3); points.Add(b);
Point c = new Point("C", 0, 6); points.Add(c);
Point d = new Point("D", 4, 3); points.Add(d);
Point e = new Point("E", 8, 0); points.Add(e);
Point f = new Point("F", 4, 0); points.Add(f);
Point x = new Point("X", -3, 3); points.Add(x);
Point y = new Point("Y", 8, 6); points.Add(y);
Point z = new Point("Z", 4, -4); points.Add(z);
List<Point> pts = new List<Point>();
pts.Add(a);
pts.Add(b);
pts.Add(c);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(c);
pts.Add(d);
pts.Add(e);
collinear.Add(new Collinear(pts));
pts = new List<Point>();
pts.Add(a);
pts.Add(f);
pts.Add(e);
collinear.Add(new Collinear(pts));
Circle circleI = new Circle(b, 3);
Circle circleII = new Circle(f, 4);
Circle circleIII = new Circle(d, 5);
semicircles.Add(new Semicircle(circleI, a, c, x, new Segment(a, c)));
semicircles.Add(new Semicircle(circleII, a, e, z, new Segment(a, e)));
semicircles.Add(new Semicircle(circleIII, c, e, y, new Segment(c, e)));
parser = new LiveGeometry.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, c)), 6);
known.AddSegmentLength((Segment)parser.Get(new Segment(a, e)), 8);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 4, -3));
wanted.Add(new Point("", 7, 5));
wanted.Add(new Point("", -1, 3));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(42.25 * System.Math.PI - 30);
}
//Demonstrates: If two inscribed angles intercept the same arc, the angles are congruent
public Test11(bool onoff, bool complete)
: base(onoff, complete)
{
//Circles
Point o = new Point("O", 0, 0); points.Add(o);
Circle circleO = new Circle(o, 5.0);
circles.Add(circleO);
Point r = new Point("R", 0, 5); points.Add(r);
Circle circleR = new Circle(r, 10.0);
circles.Add(circleR);
//Chords
Point a = new Point("A", 0, -5); points.Add(a);
Point d = new Point("D", -5, Math.Sqrt(75) + 5); points.Add(d);
Point e = new Point("E", 5, Math.Sqrt(75) + 5); points.Add(e);
Point f = new Point("F", 6, 13); points.Add(f);
Point b, c, trash;
circleO.FindIntersection(new Segment(a, d), out b, out trash);
if (b.StructurallyEquals(a)) b = trash;
circleO.FindIntersection(new Segment(a, e), out c, out trash);
if (c.StructurallyEquals(a)) c = trash;
b = new Point("B", b.X, b.Y); points.Add(b);
c = new Point("C", c.X, c.Y); points.Add(c);
Point g = (new Segment(a, e)).FindIntersection(new Segment(f, d));
g = new Point("G", g.X, g.Y); points.Add(g);
List<Point> pnts = new List<Point>();
pnts.Add(a);
pnts.Add(b);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(a);
pnts.Add(c);
pnts.Add(g);
pnts.Add(e);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(f);
pnts.Add(g);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Segment fe = new Segment(f, e); segments.Add(fe);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
goals.Add(new GeometricCongruentAngles((Angle)parser.Get(new Angle(d, a, e)), (Angle)parser.Get(new Angle(d, f, e))));
}
public Page64(bool onoff, bool complete)
: base(onoff, complete)
{
Point a = new Point("A", 0, 0); points.Add(a);
Point b = new Point("B", 6, 4); points.Add(b);
Point c = new Point("C", 14, 4); points.Add(c);
Point d = new Point("D", 20, 0); points.Add(d);
Point o = new Point("O", 10, 4); points.Add(o);
Point p = new Point("P", 10, 0); points.Add(p);
Segment ab = new Segment(a, b); segments.Add(ab);
Segment cd = new Segment(c, d); segments.Add(cd);
Segment op = new Segment(o, p); segments.Add(op);
List<Point> pnts = new List<Point>();
pnts.Add(b);
pnts.Add(o);
pnts.Add(c);
collinear.Add(new Collinear(pnts));
pnts = new List<Point>();
pnts.Add(a);
pnts.Add(p);
pnts.Add(d);
collinear.Add(new Collinear(pnts));
Circle circle = new Circle(o, 4);
circles.Add(circle);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
Segment ad = (Segment)parser.Get(new Segment(a, d));
Angle a1 = (Angle)parser.Get(new Angle(b, o, p));
CircleSegmentIntersection cInter1 = (CircleSegmentIntersection)parser.Get(new CircleSegmentIntersection(p, circle, ad));
given.Add(new Strengthened(a1, new RightAngle(a1)));
given.Add(new Strengthened(cInter1, new Tangent(cInter1)));
known.AddSegmentLength(ad, 20);
known.AddSegmentLength((Segment)parser.Get(new Segment(b, c)), 8);
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 5, 1));
wanted.Add(new Point("", 15, 1));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(56 - 8 * System.Math.PI);
problemName = "Collected Learning Page 64";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
public Page8Row6Prob44(bool onoff, bool complete)
: base(onoff, complete)
{
Point o = new Point("O", 0, 0); points.Add(o);
Point p = new Point("P", 2.5, 0); points.Add(p);
Point q = new Point("Q", 5, 0); points.Add(q);
Point r = new Point("R", 7.5, 0); points.Add(r);
Point s = new Point("S", 10, 0); points.Add(s);
Point t = new Point("T", 12.5, 0); points.Add(t);
Point u = new Point("U", 15, 0); points.Add(u);
List<Point> pts = new List<Point>();
pts.Add(o);
pts.Add(p);
pts.Add(q);
pts.Add(r);
pts.Add(s);
pts.Add(t);
pts.Add(u);
collinear.Add(new Collinear(pts));
Circle outer = new Circle(r, 7.5);
Circle left = new Circle(p, 2.5);
Circle middle = new Circle(r, 2.5);
Circle right = new Circle(t, 2.5);
circles.Add(outer);
circles.Add(left);
circles.Add(middle);
circles.Add(right);
parser = new GeometryTutorLib.TutorParser.HardCodedParserMain(points, collinear, segments, circles, onoff);
known.AddSegmentLength((Segment)parser.Get(new Segment(o, u)), 15);
//Problem is slightly ambiguous as written, appears to be reliant on assumption that the diameter of each inner circle is 1/3 the total diameter
Segment oq = (Segment)parser.Get(new Segment(o, q));
oq.multiplier = 3;
given.Add(new GeometricSegmentEquation(oq, (Segment)parser.Get(new Segment(o, u))));
given.Add(new GeometricCongruentCircles(left, middle));
given.Add(new GeometricCongruentCircles(middle, right));
List<Point> wanted = new List<Point>();
wanted.Add(new Point("", 7, 7));
goalRegions = parser.implied.GetAtomicRegionsByPoints(wanted);
SetSolutionArea(18.75 * System.Math.PI);
problemName = "Glencoe Page 8 Row 6 Problem 44";
GeometryTutorLib.EngineUIBridge.HardCodedProblemsToUI.AddProblem(problemName, points, circles, segments);
}
/// <summary>
/// Parse a CircleBase.
/// </summary>
/// <param name="c"> The circle to parse.</param>
private void ParseCircle(CircleBase cb)
{
// Acquire the defining characteristics from the UI
IPoint center = cb.Dependencies.FindPoint(cb.Center, 0);
double radius = cb.Radius;
// Parse the center of the circle.
Parse(center as IFigure);
// Create the Tutor version of the point
GeometryTutorLib.ConcreteAST.Circle tutorCircle = new GeometryTutorLib.ConcreteAST.Circle(uiToEngineMap[center] as Point, radius);
// Add to the list of known circles from the UI
circles.Add(tutorCircle);
uiToEngineMap.Add(cb, tutorCircle);
}
//
// Atomize the circle by creating:
// (1) all radii connecting to other known polygon / circle intersection points.
// (2) all chords connecting the radii
//
// All constructed segments may intersect at imaginary points; these need to be calculated
//
public static List <GeometryTutorLib.Area_Based_Analyses.Atomizer.AtomicRegion> Atomize(GeometryTutorLib.ConcreteAST.Circle circle)
{
List <GeometryTutorLib.Area_Based_Analyses.Atomizer.AtomicRegion> atoms = new List <GeometryTutorLib.Area_Based_Analyses.Atomizer.AtomicRegion>();
List <GeometryTutorLib.ConcreteAST.Point> interPts = circle.GetIntersectingPoints();
//
// Construct the radii
//
List <GeometryTutorLib.ConcreteAST.Segment> radii = new List <GeometryTutorLib.ConcreteAST.Segment>();
foreach (GeometryTutorLib.ConcreteAST.Point interPt in interPts)
{
radii.Add(new GeometryTutorLib.ConcreteAST.Segment(circle.center, interPt));
}
//
// Construct the chords
//
List <GeometryTutorLib.ConcreteAST.Segment> chords = new List <GeometryTutorLib.ConcreteAST.Segment>();
for (int p1 = 0; p1 < interPts.Count - 1; p1++)
{
for (int p2 = p1 + 1; p2 < interPts.Count; p2++)
{
chords.Add(new GeometryTutorLib.ConcreteAST.Segment(interPts[p1], interPts[p2]));
}
}
//
// Do any of the chords intersect the radii?
//
//
// Do the chords intersect each other?
//
return(new List <GeometryTutorLib.Area_Based_Analyses.Atomizer.AtomicRegion>());
}
