// Does this angle lie between the two lines? This is mainly for a parallelism check
public bool OnInteriorOf(Intersection inter1, Intersection inter2)
{
Intersection angleBelongs = null;
Intersection angleDoesNotBelong = null;
// Determine the intersection to which the angle belongs
if (inter1.InducesNonStraightAngle(this))
{
angleBelongs = inter1;
angleDoesNotBelong = inter2;
}
else if (inter2.InducesNonStraightAngle(this))
{
angleBelongs = inter2;
angleDoesNotBelong = inter1;
}
if (angleBelongs == null || angleDoesNotBelong == null)
{
return(false);
}
// Make the transversal out of the points of intersection
Segment transversal = new Segment(angleBelongs.intersect, angleDoesNotBelong.intersect);
Segment angleRayOnTraversal = this.ray1.IsCollinearWith(transversal) ? ray1 : ray2;
// Is the endpoint of the angle (on the transversal) between the two intersection points?
// Or, is that same endpoint on the far end beyond the other line: the other intersection point lies between the other points
return(Segment.Between(angleRayOnTraversal.OtherPoint(this.GetVertex()), angleBelongs.intersect, angleDoesNotBelong.intersect) ||
Segment.Between(angleDoesNotBelong.intersect, angleBelongs.intersect, angleRayOnTraversal.OtherPoint(this.GetVertex())));
}
public static void MakeTriangles(Segment side, int length, int angle, out List <Triangle> tris)
{
tris = new List <Triangle>();
// 1
Segment newSide1 = side.ConstructSegmentByAngle(side.Point1, angle, length);
Point newPoint1 = newSide1.OtherPoint(side.Point1);
tris.Add(new Triangle(side.Point1, side.Point2, newPoint1));
// 2
Segment newSide2 = side.ConstructSegmentByAngle(side.Point2, angle, length);
Point newPoint2 = newSide2.OtherPoint(side.Point2);
tris.Add(new Triangle(side.Point1, side.Point2, newPoint2));
// 3
Point oppNewPoint1 = side.GetReflectionPoint(newPoint1);
tris.Add(new Triangle(side.Point1, side.Point2, oppNewPoint1));
// 4
Point oppNewPoint2 = side.GetReflectionPoint(newPoint1);
tris.Add(new Triangle(side.Point1, side.Point2, oppNewPoint2));
}
//
// Do these segments overlay this angle?
//
public bool IsIncludedAngle(Segment seg1, Segment seg2)
{
// Do not allow the same segment.
if (seg1.StructurallyEquals(seg2))
{
return(false);
}
// Check direct inclusion
if (seg1.Equals(ray1) && seg2.Equals(ray2) || seg1.Equals(ray2) && seg2.Equals(ray1))
{
return(true);
}
// Check overlaying angle
Point shared = seg1.SharedVertex(seg2);
if (shared == null)
{
return(false);
}
Angle thatAngle = new Angle(seg1.OtherPoint(shared), shared, seg2.OtherPoint(shared));
return(this.Equates(thatAngle));
}
//
// Creates a Leaner-Shape (a bench you can sit on)
//
// top
// |______ tipStands
// |
// tipEndpt ______|
//
// Returns <tipEndpoint, tipStands>
public KeyValuePair <Point, Point> CreatesLeanerShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
//
// Determine which is the stands and which is the endpoint
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else if (thatInter.StandsOnEndpoint() && this.StandsOn())
{
endpointInter = thatInter;
standsInter = this;
}
else
{
return(nullPair);
}
//
// Acquire Points
//
Point tipStands = standsInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
Segment parallelEndpoint = endpointInter.OtherSegment(transversal);
Point tipEndpoint = parallelEndpoint.OtherPoint(endpointInter.intersect);
// Determine sides
Segment crossingTester = new Segment(tipEndpoint, tipStands);
Point intersection = transversal.FindIntersection(crossingTester);
// F-Shape
if (!transversal.PointLiesOnAndBetweenEndpoints(intersection))
{
return(nullPair);
}
// Desired Leaner shape
return(new KeyValuePair <Point, Point>(tipEndpoint, tipStands));
}
// Corresponding angles if:
// offRightEnd
// standsOn (o) o e
// o e standsOnEndpoint (e)
// offLeftEnd eeeoeeeeeeee
// o
// o
//
// Returns <offLeftEnd, offRightEnd>
//
public KeyValuePair <Point, Point> CreatesSimpleTShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
//
// Determine which is the crossing intersection and which stands on the endpoints
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else if (thatInter.Crossing() && this.StandsOnEndpoint())
{
endpointInter = thatInter;
standsInter = this;
}
else
{
return(nullPair);
}
//
// Determine if the endpoint intersection extends beyond the stands parallel line
//
Segment transversal = this.AcquireTransversal(thatInter);
Segment transversalEndpoint = endpointInter.GetCollinearSegment(transversal);
if (transversal.PointLiesOnAndBetweenEndpoints(transversalEndpoint.Point1) &&
transversal.PointLiesOnAndBetweenEndpoints(transversalEndpoint.Point2))
{
return(nullPair);
}
//
// Acquire the returning points
//
Segment parallelEndpoint = endpointInter.OtherSegment(transversal);
Point offLeftEnd = transversalEndpoint.OtherPoint(endpointInter.intersect);
Point offRightEnd = parallelEndpoint.OtherPoint(endpointInter.intersect);
return(new KeyValuePair <Point, Point>(offLeftEnd, offRightEnd));
}
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 void MakeRightTriangles(Segment side, int length, out List <RightTriangle> tris)
{
tris = new List <RightTriangle>();
//
// 1
//
Segment perp = side.GetPerpendicularByLength(side.Point1, length);
tris.Add(new RightTriangle(new Triangle(side.Point1, side.Point2, perp.OtherPoint(side.Point1))));
// 2
Segment oppPerp = perp.GetOppositeSegment(side.Point1);
tris.Add(new RightTriangle(new Triangle(side.Point1, side.Point2, oppPerp.OtherPoint(side.Point1))));
// 3
perp = side.GetPerpendicularByLength(side.Point2, length);
tris.Add(new RightTriangle(new Triangle(side.Point1, side.Point2, perp.OtherPoint(side.Point2))));
// 4
oppPerp = perp.GetOppositeSegment(side.Point2);
tris.Add(new RightTriangle(new Triangle(side.Point1, side.Point2, oppPerp.OtherPoint(side.Point2))));
}
//
// o
// eoooooooo offStands
// e
//offEndpoint eeeeeee
// o
// Returns: <offEndpoint, offStands>
public KeyValuePair <Point, Point> CreatesSimpleSShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Restrict to desired combination
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
//
// Determine which is the stands and which is the endpoint
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else if (thatInter.StandsOnEndpoint() && this.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else
{
return(nullPair);
}
// Determine S shape
Point offStands = standsInter.CreatesTShape();
Segment transversal = this.AcquireTransversal(thatInter);
Segment parallelEndpoint = endpointInter.OtherSegment(transversal);
Point offEndpoint = parallelEndpoint.OtherPoint(endpointInter.intersect);
Segment crossingTester = new Segment(offStands, offEndpoint);
Point intersection = transversal.FindIntersection(crossingTester);
return(transversal.PointLiesOnAndBetweenEndpoints(intersection) ? new KeyValuePair <Point, Point>(offEndpoint, offStands) : nullPair);
}
public Angle(Segment ray1, Segment ray2)
: base()
{
Point vertex = ray1.SharedVertex(ray2);
if (vertex == null) throw new ArgumentException("Rays do not share a vertex: " + ray1 + " " + ray2);
this.A = ray1.OtherPoint(vertex);
this.B = vertex;
this.C = ray2.OtherPoint(vertex);
this.ray1 = ray1;
this.ray2 = ray2;
this.measure = toDegrees(findAngle(A, B, C));
if (measure <= 0)
{
//System.Diagnostics.Debug.WriteLine("NO-OP");
// throw new ArgumentException("Measure of " + this.ToString() + " is ZERO");
}
}
public Angle(Segment ray1, Segment ray2) : base()
{
Point vertex = ray1.SharedVertex(ray2);
if (vertex == null)
{
throw new ArgumentException("Rays do not share a vertex: " + ray1 + " " + ray2);
}
this.A = ray1.OtherPoint(vertex);
this.B = vertex;
this.C = ray2.OtherPoint(vertex);
this.ray1 = ray1;
this.ray2 = ray2;
this.measure = toDegrees(findAngle(A, B, C));
if (measure <= 0)
{
//System.Diagnostics.Debug.WriteLine("NO-OP");
// throw new ArgumentException("Measure of " + this.ToString() + " is ZERO");
}
}
public static void MakeRectangles(Segment side, double length, out Rectangle rect1, out Rectangle rect2)
{
//
// First rectangle
//
Segment adj1 = side.GetPerpendicularByLength(side.Point1, length);
Segment adj2 = side.GetPerpendicularByLength(side.Point2, length);
Segment oppSide = new Segment(adj1.OtherPoint(side.Point1), adj2.OtherPoint(side.Point2));
rect1 = new Rectangle(side, oppSide, adj1, adj2);
//
// Second rectangle
//
Segment otherAdj1 = adj1.GetOppositeSegment(side.Point1);
Segment otherAdj2 = adj2.GetOppositeSegment(side.Point2);
oppSide = new Segment(otherAdj1.OtherPoint(side.Point1), otherAdj2.OtherPoint(side.Point2));
rect2 = new Rectangle(side, oppSide, otherAdj1, otherAdj2);
}
// Parallel arrays of (1) vertices and (2) segments that share that given vertex.
public static Polygon ConstructPolygon(List <Point> vertices, List <KeyValuePair <Segment, Segment> > pairs)
{
List <Segment> orderedSides = new List <Segment>();
// Follow the trail of sides starting at one of the first sides
Segment currentSide = pairs[0].Key;
orderedSides.Add(currentSide);
Point currentVertex = currentSide.Point1;
for (int v = 1; v < vertices.Count; v++)
{
// Where is the current vertex located?
int nextVertexIndex = vertices.IndexOf(currentVertex);
// Find the next side to follow.
if (pairs[nextVertexIndex].Key.StructurallyEquals(currentSide))
{
currentSide = pairs[nextVertexIndex].Value;
}
else
{
currentSide = pairs[nextVertexIndex].Key;
}
orderedSides.Add(currentSide);
// Find the next vertex (moving along the next side)
currentVertex = currentSide.OtherPoint(currentVertex);
}
if (orderedSides.Count != vertices.Count)
{
throw new Exception("Construction of new polygon failed.");
}
return(ActuallyConstructThePolygonObject(orderedSides));
}
// Does the given segment overlay this segment; we are looking at both as a RAY only.
// We assume both rays share the same start vertex
public bool RayOverlays(Segment thatRay)
{
if (this.Equals(thatRay))
{
return(true);
}
if (!this.IsCollinearWith(thatRay))
{
return(false);
}
// Do they share a vertex?
Point shared = this.SharedVertex(thatRay);
if (shared == null)
{
return(false);
}
Point thatOtherPoint = thatRay.OtherPoint(shared);
Point thisOtherPoint = this.OtherPoint(shared);
// Is thatRay smaller than the this ray
if (Between(thatOtherPoint, shared, thisOtherPoint))
{
return(true);
}
// Or if that Ray extends this Ray
if (Between(thisOtherPoint, shared, thatOtherPoint))
{
return(true);
}
return(false);
}
//
// Determine if the segment passes through the circle (we know it is not a chord since they have been filtered).
//
private bool IsSecant(Segment segment, List<Point> figPoints, out Segment chord)
{
// Make it null and overwrite when necessary.
chord = null;
// Is the segment exterior to the circle, but intersects at an endpoint (and wasn't tangent).
if (this.PointIsExterior(segment.Point1) && this.PointLiesOn(segment.Point2)) return false;
if (this.PointIsExterior(segment.Point2) && this.PointLiesOn(segment.Point1)) return false;
// Is one endpoint of the segment simply on the interior of the circle (so we have nothing)?
if (this.PointIsInterior(segment.Point1) || this.PointIsInterior(segment.Point2)) return false;
if (ContainsDiameter(segment))
{
chord = ConstructChord(segment, this.center, this.radius, figPoints);
// Add radii to the list.
radii.Add(new Segment(this.center, chord.Point1));
radii.Add(new Segment(this.center, chord.Point2));
return true;
}
// Acquire the line perpendicular to the segment that passes through the center of the circle.
Segment perpendicular = segment.GetPerpendicular(this.center);
// Is this perpendicular segment a radius? If so, it's tangent, not a secant
//if (Utilities.CompareValues(perpendicular.Length, this.radius)) return false;
// Is the perpendicular a radius? Check if the intersection of the segment and the perpendicular is on the circle. If so, it's tangent
Point intersection = segment.FindIntersection(perpendicular);
if (this.PointLiesOn(intersection)) return false;
//Adjust perpendicular segment to include intersection with segment
perpendicular = new Segment(intersection, this.center);
// Filter the fact that there are no intersections
if (perpendicular.Length > this.radius) return false;
// 1/2 chord length
// _____ circPoint
// | /
// | /
// perp.Length | / radius
// | /
// |/
// Determine the half-chord length via Pyhtagorean Theorem.
double halfChordLength = Math.Sqrt(Math.Pow(this.radius, 2) - Math.Pow(perpendicular.Length, 2));
chord = ConstructChord(segment, perpendicular.OtherPoint(this.center), halfChordLength, figPoints);
return true;
}
//
// Is this a direct radius segment where one endpoint originates at the origin and extends outward?
// Return the exact radius.
private Segment IsRadius(Segment segment, List<Point> figPoints)
{
// The segment must originate from the circle center.
if (!segment.HasPoint(this.center)) return null;
// The segment must be at least as long as a radius.
if (!Utilities.CompareValues(segment.Length, this.radius)) return null;
Point nonCenterPt = segment.OtherPoint(this.center);
// Check for a direct radius.
if (this.PointLiesOn(nonCenterPt)) return segment;
//
// Check for an extended segment.
//
// radius
// center _____ circPt
//
// Find the exact coordinates of the 'circ' points.
//
Point inter1 = null;
Point inter2 = null;
this.FindIntersection(segment, out inter1, out inter2);
Point figPoint = Utilities.GetStructurally<Point>(figPoints, inter1);
if (figPoint == null) figPoint = Utilities.GetStructurally<Point>(figPoints, inter2);
return new Segment(center, figPoint);
}
// Does the given segment overlay this segment; we are looking at both as a RAY only.
// We assume both rays share the same start vertex
public bool RayOverlays(Segment thatRay)
{
if (this.Equals(thatRay)) return true;
if (!this.IsCollinearWith(thatRay)) return false;
// Do they share a vertex?
Point shared = this.SharedVertex(thatRay);
if (shared == null) return false;
Point thatOtherPoint = thatRay.OtherPoint(shared);
Point thisOtherPoint = this.OtherPoint(shared);
// Is thatRay smaller than the this ray
if (Between(thatOtherPoint, shared, thisOtherPoint)) return true;
// Or if that Ray extends this Ray
if (Between(thisOtherPoint, shared, thatOtherPoint)) return true;
return false;
}
//
// Do these segments overlay this angle?
//
public bool IsIncludedAngle(Segment seg1, Segment seg2)
{
// Do not allow the same segment.
if (seg1.StructurallyEquals(seg2)) return false;
// Check direct inclusion
if (seg1.Equals(ray1) && seg2.Equals(ray2) || seg1.Equals(ray2) && seg2.Equals(ray1)) return true;
// Check overlaying angle
Point shared = seg1.SharedVertex(seg2);
if (shared == null) return false;
Angle thatAngle = new Angle(seg1.OtherPoint(shared), shared, seg2.OtherPoint(shared));
return this.Equates(thatAngle);
}
// top
// o
// offStands oooooooe
// e
//offEndpoint eeeeeee
// o
// bottom
// Returns: <offEndpoint, offStands>
public KeyValuePair <Point, Point> CreatesSimplePIShape(Intersection thatInter)
{
KeyValuePair <Point, Point> nullPair = new KeyValuePair <Point, Point>(null, null);
// A valid transversal is required for this shape
if (!this.CreatesAValidTransversalWith(thatInter))
{
return(nullPair);
}
// Restrict to desired combination
if (this.StandsOnEndpoint() && thatInter.StandsOnEndpoint())
{
return(nullPair);
}
//
// Determine which is the stands and which is the endpoint
//
Intersection endpointInter = null;
Intersection standsInter = null;
if (this.StandsOnEndpoint() && thatInter.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else if (thatInter.StandsOnEndpoint() && this.StandsOn())
{
endpointInter = this;
standsInter = thatInter;
}
else
{
return(nullPair);
}
//
// Avoid Some shapes
//
Segment transversal = this.AcquireTransversal(thatInter);
Segment transversalStands = standsInter.GetCollinearSegment(transversal);
Point top = null;
Point bottom = null;
if (Segment.Between(standsInter.intersect, transversalStands.Point1, endpointInter.intersect))
{
top = transversalStands.Point1;
bottom = transversalStands.Point2;
}
else
{
top = transversalStands.Point2;
bottom = transversalStands.Point1;
}
// Avoid: ____ Although this shouldn't happen since both intersections do not stand on endpoints
// ____|
//
// Also avoid Simple F-Shape
//
if (transversal.HasPoint(top) || transversal.HasPoint(bottom))
{
return(nullPair);
}
// Determine S shape
Point offStands = standsInter.CreatesTShape();
Segment parallelEndpoint = endpointInter.OtherSegment(transversal);
Point offEndpoint = parallelEndpoint.OtherPoint(endpointInter.intersect);
Segment crossingTester = new Segment(offStands, offEndpoint);
Point intersection = transversal.FindIntersection(crossingTester);
// S-shape // PI-Shape
return(transversal.PointLiesOnAndBetweenEndpoints(intersection) ? nullPair : new KeyValuePair <Point, Point>(offEndpoint, offStands));
}
