/// <summary>
/// Create a circle from three points.
/// </summary>
/// <param name="pt1">A point.</param>
/// <param name="pt2">A point.</param>
/// <param name="pt3">A point.</param>
public Circle2D(Point2D pt1, Point2D pt2, Point2D pt3)
: this(pt1.X, pt1.Y, pt2.X, pt2.Y, pt3.X, pt3.Y)
{
}
/// <summary>
/// Creates a new instance with the center at the given point and a radius of r.
/// </summary>
/// <param name="center">The center of the circle.</param>
/// <param name="radius">The radius of the circle.</param>
public Circle2D(Point2D center, decimal radius)
{
_center = center;
_radius = 0m; // to satisfy compiler
this.Radius = radius;
}
/// <summary>
/// Gets the points of intersection between this circle and the line which
/// contains the given line segment.
/// </summary>
/// <param name="l">Line segment used to determine line equation.</param>
public Point2D[] GetIntersectFast(ref LineSeg2D l)
{
decimal[] x = new decimal[2];
decimal m = 0m;
decimal b = 0m;
decimal aCoeff = 0m;
decimal bCoeff = 0m;
decimal cCoeff = 0m;
decimal lineX = 0m;
decimal t = 0m;
decimal p = 0m;
decimal q = 0m;
Point2D[] pts = null;
if (!l.IsVertical)
{
// Circle (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2
// Center: (h, k)
// Radius: r
// Line y = m * x + b
// (x - h) ^ 2 + (m * x + b - k) ^ 2 = r ^ 2
// (x - h) * (x - h) + (m * x + b - k) * (m * x + b - k) = r^2
// (x^2 - 2 * h * x + h^2) + (m^2 * x^2 + 2 * (b - k) * m * x + (b - k)^2 = r^2
// (m^2 + 1) * x^2 + (2 * (b - k) * m - 2 * h) * x + (h^2 + (b - k)^2 - r^2) = 0
m = l.Slope;
b = l.YIntersect;
aCoeff = DecimalEx.Pow(m, 2) + 1;
bCoeff = 2 * (b - _center.Y) * m - 2 * _center.X;
cCoeff = DecimalEx.Pow(_center.X, 2) + DecimalEx.Pow(b - _center.Y, 2) - DecimalEx.Pow(_radius, 2);
x = DecimalEx.SolveQuadratic(aCoeff, bCoeff, cCoeff);
if (x.Length == 0)
{
return new Point2D[] { }
}
;
pts = new Point2D[x.Length];
for (var i = 0; i <= x.Length - 1; i++)
{
pts[i] = new Point2D(x[i], m * x[i] + b);
}
}
else
{
// Circle (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2
// Center: (h, k)
// Radius: r
// Line x = lineX
// Got the following from
// http://www.sonoma.edu/users/w/wilsonst/Papers/Geometry/circles/T1--2/T1-3-2.html
// http://www.sonoma.edu/users/w/wilsonst/Papers/Geometry/circles/default.html
lineX = l.Pt1.X;
t = _radius * _radius - (lineX - _center.X) * (lineX - _center.X);
if (t < 0)
{
return(new Point2D[] { });
}
else
{
p = _center.Y + DecimalEx.Sqrt(t);
q = _center.Y - DecimalEx.Sqrt(t);
pts = new Point2D[1];
pts[0] = new Point2D(lineX, p);
// NOTE that P=Q when t=0
if (p != q)
{
Array.Resize(ref pts, 2);
pts[1] = new Point2D(lineX, q);
}
}
}
return(pts);
}
/// <summary>
/// Returns distance to the given point from the circle. If the
/// point is on the circle, distance is 0. If the point is inside
/// the circle, the distance is expressed as a negative number
/// whose absolute value is the distance from the outside of the circle.
/// </summary>
/// <param name="pt">The point to get distance to.</param>
public decimal DistanceTo(Point2D pt)
{
return(Center.DistanceTo(pt) - Radius);
}
/// <summary>
/// Creates a new instance with the center at (x, y) and a radius of r.
/// </summary>
/// <param name="x">The X component of the center.</param>
/// <param name="y">The Y component of the center.</param>
/// <param name="radius">The radius of the circle.</param>
public Circle2D(decimal x, decimal y, decimal radius)
{
_center = new Point2D(x, y);
_radius = 0m; // to satisfy compiler
this.Radius = radius;
}
public static Circle2D[] FromTwoPointsAndRadius(Point2D pt1, Point2D pt2, decimal radius)
{
return(FromTwoPointsAndRadius(pt1.X, pt1.Y, pt2.X, pt2.Y, radius));
}
/// <summary>
/// Creates a new instance with the center at the origin with the provided radius.
/// </summary>
/// <param name="radius">The radius of the circle.</param>
public Circle2D(decimal radius)
{
_center = Point2D.Origin;
_radius = 0m; // to satisfy compiler
this.Radius = radius;
}
/// <summary>
/// Gets the points of intersection between this circle and another circle.
/// </summary>
/// <param name="other">The other circle.</param>
/// <param name="decimals">Determines rounding that should be performed when determining
/// if line intersection happens on zero, one, or two points. Default is -1 for
/// no rounding.</param>
/// <param name="impreciseResult">Which value to return for an imprecise result,
/// i.e. tangency determined by rounding. If positive, returns the point on the larger circle. If
/// negative, returns the point on the smaller circle. If 0, returns the midpoint between these
/// two points.</param>
public Point2D[] GetIntersect(Circle2D other, int decimals = -1, int impreciseResult = 0)
{
Vector2D meToOtherVector = default(Vector2D);
meToOtherVector = this.Center.GetVectorTo(other.Center);
if (decimals >= 0)
{
// The only intersection decision that can be made to a given precision is whether
// the two circles are tangent to each other, either internally or externally.
if (this.IsTangentTo(other, decimals))
{
// If the smaller circle is inside the other, then the smaller is
// considered internally tangent to the larger.
if ((this.Radius < other.Radius && this.IsInside(other, decimals)) || (other.Radius < this.Radius && other.IsInside(this, decimals)))
{
// Internal tangent
Point2D pointOnLargeCircle = default(Point2D);
Point2D pointOnSmallCircle = default(Point2D);
// Vectors to the two tangent points are both pointing in the same
// direction--from the center of the larger circle towards the
// center of the smaller circle. Their magnitude is the same as the
// radius of the circle whose center they start from.
if (this.Radius > other.Radius)
{
// Go from center of larger circle, Me, to smaller circle, other.
pointOnLargeCircle = this.Center + new Vector2D(meToOtherVector, this.Radius);
pointOnSmallCircle = other.Center + new Vector2D(meToOtherVector, other.Radius);
}
else
{
// Go from center of larger circle, other, to smaller circle, Me.
pointOnLargeCircle = other.Center - new Vector2D(meToOtherVector, other.Radius);
pointOnSmallCircle = this.Center - new Vector2D(meToOtherVector, this.Radius);
}
if (impreciseResult > 0)
{
// Point on larger
return(new Point2D[] { pointOnLargeCircle });
}
else if (impreciseResult < 0)
{
// Point on smaller
return(new Point2D[] { pointOnSmallCircle });
}
else
{
// Split difference
LineSeg2D l = new LineSeg2D(pointOnLargeCircle, pointOnSmallCircle);
return(new Point2D[] { l.MidPoint });
}
}
else
{
// External tangent
Point2D pointOnMe = default(Point2D);
Point2D pointOnOther = default(Point2D);
// Vectors to the two tangent points are simply pointing at the other
// circle's center with a magnitude of the radius of the circle whose
// center it originates in.
pointOnMe = this.Center + new Vector2D(meToOtherVector, this.Radius);
pointOnOther = other.Center - new Vector2D(meToOtherVector, other.Radius);
if (impreciseResult > 0)
{
// Point on larger
return(new Point2D[] { (this.Radius > other.Radius ? pointOnMe : pointOnOther) });
}
else if (impreciseResult < 0)
{
// Point on smaller
return(new Point2D[] { (this.Radius < other.Radius ? pointOnMe : pointOnOther) });
}
else
{
if (pointOnMe == pointOnOther)
{
return(new Point2D[] { pointOnMe });
}
else
{
// Split difference
return(new Point2D[] { new LineSeg2D(pointOnMe, pointOnOther).MidPoint });
}
}
}
}
}
// Detect situations where two points touch
decimal a = 0m;
decimal h = 0m;
decimal r2mina2 = 0m;
Vector2D vToIntersectMidPt = default(Vector2D);
Vector2D vToIntersect1 = default(Vector2D);
// The following two equations are from:
// http://paulbourke.net/geometry/2circle/
a = (DecimalEx.Pow(meToOtherVector.Magnitude, 2) - DecimalEx.Pow(other.Radius, 2) + DecimalEx.Pow(this.Radius, 2)) / (2 * meToOtherVector.Magnitude);
r2mina2 = DecimalEx.Pow(this.Radius, 2) - DecimalEx.Pow(a, 2);
// No intersection points -- one circle is inside or outside the other
if (r2mina2 < 0)
{
return new Point2D[] { }
}
;
vToIntersectMidPt = new Vector2D(this.Center, other.Center);
vToIntersectMidPt.Magnitude = a;
if (r2mina2 == 0)
{
// Only one intersection point
return(new Point2D[] { this.Center + vToIntersectMidPt });
}
h = DecimalEx.Sqrt(r2mina2);
vToIntersect1 = vToIntersectMidPt.GetPerpendicular();
vToIntersect1.Magnitude = h;
return(new Point2D[] {
this.Center + vToIntersectMidPt + vToIntersect1,
this.Center + vToIntersectMidPt - vToIntersect1
});
}
