public static Circle ConstructCircle(Point p1, Point p2, Point p3)
{
//
// Find the center of the circle.
//
Segment chord1 = new Segment(p1, p2);
Segment chord2 = new Segment(p2, p3);
Segment perpBis1 = chord1.GetPerpendicular(chord1.Midpoint());
Segment perpBis2 = chord2.GetPerpendicular(chord2.Midpoint());
Point center = perpBis1.FindIntersection(perpBis2);
//
// Radius is the distance between the circle and any of the original points.
//
return new Circle(center, Point.calcDistance(center, p1));
}
public static Circle ConstructCircle(Point p1, Point p2, Point p3)
{
//
// Find the center of the circle.
//
Segment chord1 = new Segment(p1, p2);
Segment chord2 = new Segment(p2, p3);
Segment perpBis1 = chord1.GetPerpendicular(chord1.Midpoint());
Segment perpBis2 = chord2.GetPerpendicular(chord2.Midpoint());
Point center = perpBis1.FindIntersection(perpBis2);
//
// Radius is the distance between the circle and any of the original points.
//
return(new Circle(center, Point.calcDistance(center, p1)));
}
//
// 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;
}
// return the midpoint between these two on the circle.
public Point Midpoint(Point a, Point b)
{
if (!this.PointLiesOn(a)) return null;
if (!this.PointLiesOn(b)) return null;
// Make the chord.
Segment chord = new Segment(a, b);
Point pt1 = null;
Point pt2 = null;
// Is this a diameter? If so, quickly return a point perpendicular to the diameter
if (DefinesDiameter(chord))
{
Segment perp = chord.GetPerpendicular(center);
this.FindIntersection(perp, out pt1, out pt2);
// Arbitrarily choose one of the points.
return pt1 != null ? pt1 : pt2;
}
// Make radius through the midpoint of the chord.
Segment radius = new Segment(center, chord.Midpoint());
this.FindIntersection(radius, out pt1, out pt2);
if (pt2 == null) return pt1;
Point theMidpoint = Arc.StrictlyBetweenMinor(pt1, new MinorArc(this, a, b)) ? pt1 : pt2;
double angle1 = new Angle(a, center, theMidpoint).measure;
double angle2 = new Angle(b, center, theMidpoint).measure;
if (!Utilities.CompareValues(angle1, angle2))
{
throw new ArgumentException("Midpoint is incorrect; angles do not equate: " + angle1 + " " + angle2);
}
return theMidpoint;
}
//
// Determine tangency of the given segment.
// Indicate tangency by returning the segment which creates the 90^0 angle.
//
public Segment IsTangent(Segment segment)
{
// If the center and the segment points are collinear, this will not be a tangent.
if (segment.PointLiesOn(this.center)) return null;
// Acquire the line perpendicular to the segment that passes through the center of the circle.
Segment perpendicular = segment.GetPerpendicular(this.center);
// If the segment was found to pass through the center, it is not a tangent
if (perpendicular.Equals(segment)) return null;
// Is this perpendicular segment a radius? Check length
//if (!Utilities.CompareValues(perpendicular.Length, this.radius)) return null;
// Is the perpendicular a radius? Check that the intersection of the segment and the perpendicular is on the circle
Point intersection = segment.FindIntersection(perpendicular);
if (!this.PointLiesOn(intersection)) return null;
// The intersection between the perpendicular and the segment must be within the endpoints of the segment.
return segment.PointLiesOnAndBetweenEndpoints(intersection) ? perpendicular : null;
}