//
// Orthogonal
//
//
// Orthogonal arcs intersect at 90^0: radii connecting to intersection point are perpendicular.
//
public bool AreOrthognal(Arc thatArc)
{
if (!this.theCircle.AreOrthognal(thatArc.theCircle))
{
return(false);
}
// Find the intersection points
Point inter1;
Point inter2;
this.theCircle.FindIntersection(thatArc.theCircle, out inter1, out inter2);
// Is the intersection between the endpoints of both arcs? Check both.
if (Arc.BetweenMinor(inter1, this) && Arc.BetweenMinor(inter1, thatArc))
{
return(true);
}
if (Arc.BetweenMinor(inter2, this) && Arc.BetweenMinor(inter2, thatArc))
{
return(true);
}
return(false);
}
public override void FindIntersection(Arc that, out Point inter1, out Point inter2)
{
// Find the points of intersection
this.theCircle.FindIntersection(that.theCircle, out inter1, out inter2);
// The points must be on this minor arc.
if (this is MinorArc)
{
if (!Arc.BetweenMinor(inter1, this))
{
inter1 = null;
}
if (!Arc.BetweenMinor(inter2, this))
{
inter2 = null;
}
}
else
{
if (!Arc.BetweenMajor(inter1, this))
{
inter1 = null;
}
if (!Arc.BetweenMajor(inter2, this))
{
inter2 = null;
}
}
// The points must be on thatArc
if (that is MinorArc)
{
if (!Arc.BetweenMinor(inter1, that))
{
inter1 = null;
}
if (!Arc.BetweenMinor(inter2, that))
{
inter2 = null;
}
}
else
{
if (!Arc.BetweenMajor(inter1, that))
{
inter1 = null;
}
if (!Arc.BetweenMajor(inter2, that))
{
inter2 = null;
}
}
if (inter1 == null && inter2 != null)
{
inter1 = inter2;
inter2 = null;
}
}
public override void FindIntersection(Segment that, out Point inter1, out Point inter2)
{
// Find the points of intersection
this.theCircle.FindIntersection(that, out inter1, out inter2);
// The points must be on this minor arc.
if (this is MinorArc)
{
if (!Arc.BetweenMinor(inter1, this))
{
inter1 = null;
}
if (!Arc.BetweenMinor(inter2, this))
{
inter2 = null;
}
}
else if (this is MajorArc)
{
if (!Arc.BetweenMajor(inter1, this))
{
inter1 = null;
}
if (!Arc.BetweenMajor(inter2, this))
{
inter2 = null;
}
}
else if (this is Semicircle)
{
if (!(this as Semicircle).PointLiesOn(inter1))
{
inter1 = null;
}
if (!(this as Semicircle).PointLiesOn(inter2))
{
inter2 = null;
}
}
if (!that.PointLiesOnAndBetweenEndpoints(inter1))
{
inter1 = null;
}
if (!that.PointLiesOnAndBetweenEndpoints(inter2))
{
inter2 = null;
}
if (inter1 == null && inter2 != null)
{
inter1 = inter2;
inter2 = null;
}
}
//
// Tangent circle have 1 intersection point
//
public Point AreTangent(Arc thatArc)
{
Point intersection = this.theCircle.AreTangent(thatArc.theCircle);
// Is the intersection between the endpoints of both arcs? Check both.
if (Arc.BetweenMinor(intersection, this) && Arc.BetweenMinor(intersection, thatArc))
{
return(intersection);
}
if (Arc.BetweenMinor(intersection, this) && Arc.BetweenMinor(intersection, thatArc))
{
return(intersection);
}
return(null);
}
//
// Point is on the perimeter?
//
public override bool PointLiesOn(Point pt)
{
if (pt == null)
{
return(false);
}
// Radii
KeyValuePair <Segment, Segment> radii = theArc.GetRadii();
if (radii.Key.PointLiesOnAndBetweenEndpoints(pt) || radii.Value.PointLiesOnAndBetweenEndpoints(pt))
{
return(true);
}
// This point must lie on the circle in question, minimally.
if (!theArc.theCircle.PointLiesOn(pt))
{
return(false);
}
// Arc
if (theArc is MajorArc)
{
return(Arc.BetweenMajor(pt, theArc as MajorArc));
}
else if (theArc is MinorArc)
{
return(Arc.BetweenMinor(pt, theArc as MinorArc));
}
else if (theArc is Semicircle)
{
Semicircle semi = theArc as Semicircle;
// The point in question must lie on the same side of the diameter as the middle point
Segment candSeg = new Segment(pt, semi.middlePoint);
Point intersection = semi.diameter.FindIntersection(candSeg);
return(!candSeg.PointLiesOnAndBetweenEndpoints(intersection));
}
return(false);
}
private static Arc GetInscribedInterceptedArc(Circle circle, Angle angle)
{
Point endpt1, endpt2;
Point pt1, pt2;
circle.FindIntersection(angle.ray1, out pt1, out pt2);
endpt1 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
circle.FindIntersection(angle.ray2, out pt1, out pt2);
endpt2 = pt1.StructurallyEquals(angle.GetVertex()) ? pt2 : pt1;
// Need to check if the angle is a diameter and create a semicircle
Segment chord = new Segment(endpt1, endpt2);
if (circle.DefinesDiameter(chord))
{
Point opp = circle.Midpoint(endpt1, endpt2, angle.GetVertex());
Semicircle semi = new Semicircle(circle, endpt1, endpt2, circle.OppositePoint(opp), chord);
//Find a defined semicircle of the figure that lies on the same side
Semicircle sameSideSemi = figureSemicircles.Where(s => semi.SameSideSemicircle(s)).FirstOrDefault();
//If none were found, should we throw an exception or just return the original semi?
if (sameSideSemi == null)
{
return(semi);
}
else
{
return(sameSideSemi);
}
}
//Initially assume intercepted arc is the minor arc
Arc intercepted = null;
intercepted = new MinorArc(circle, endpt1, endpt2);
//Verify assumption, create major arc if necessary
if (Arc.BetweenMinor(angle.GetVertex(), intercepted))
{
intercepted = new MajorArc(circle, endpt1, endpt2);
}
return(intercepted);
}
public bool SameSideSemicircle(Semicircle thatSemi)
{
// First, the endpoints and the diameter must match
if (!(this.diameter.StructurallyEquals(thatSemi.diameter) && base.StructurallyEquals(thatSemi)))
{
return(false);
}
// if either of the 2 minor arcs formed by this semicircle's middlepoint contain the middlepoint of thatSemi,
// then the two semicircles form the same 'side' of the circle
MinorArc m = new MinorArc(this.theCircle, this.endpoint1, this.middlePoint);
MinorArc m2 = new MinorArc(this.theCircle, this.middlePoint, this.endpoint2);
if (Arc.BetweenMinor(thatSemi.middlePoint, m) || Arc.BetweenMinor(thatSemi.middlePoint, m2))
{
return(true);
}
else
{
return(false);
}
}
// Does this arc contain a sub-arc:
// A-------B-------C------D
// A subarc is: AB, AC, AD, BC, BD, CD
public bool HasMinorSubArc(Arc arc)
{
return(Arc.BetweenMinor(arc.endpoint1, this) && Arc.BetweenMinor(arc.endpoint2, this));
}
public override bool PointLiesOn(Point pt)
{
return(Arc.BetweenMinor(pt, this));
}
public override bool PointLiesOn(Point pt)
{
return(Arc.BetweenMinor(pt, new MinorArc(theCircle, endpoint1, middlePoint)) ||
Arc.BetweenMinor(pt, new MinorArc(theCircle, endpoint2, middlePoint)));
}