/// <summary>
/// Gets the two line segments that start at the given point and terminate
/// on the circle and are tangent to the circle.
/// </summary>
/// <param name="point">The point for the tangent segments to go through.</param>
/// <remarks>
/// Got strategy from Wikipedia's description involving Thale's theorem.
/// http://en.wikipedia.org/wiki/Tangent_lines_to_circles
/// </remarks>
public LineSeg2D[] TangentsThroughPoint(Point2D point)
{
Circle2D intersectingCircle = default(Circle2D);
Point2D[] intersects = null;
if (point.DistanceTo(this.Center) <= this.Radius)
{
return(null);
}
intersectingCircle = new Circle2D(this.Center, point);
intersects = this.GetIntersect(intersectingCircle);
if (intersects.Length != 2)
{
throw new Exception("Unexpected number of intersects when getting tangents through a point.");
}
return(new LineSeg2D[] {
new LineSeg2D(point, intersects[0]),
new LineSeg2D(point, intersects[1])
});
}
/// <summary>
/// Creates an arc based on another arc, but with a different radius.
/// </summary>
/// <param name="a">An arc from which to take the center and start/end angles.</param>
/// <param name="radius">A radius for the new arc.</param>
public Arc2D(Arc2D a, decimal radius)
{
Circle = new Circle2D(a.Center, radius);
_startAngle = a._startAngle;
_endAngle = a._endAngle;
}
/// <summary>
/// Creates an arc on the given circle with the start angle projected through
/// the start point and the end angle projected through the end point.
/// </summary>
/// <param name="c">Circle that the arc lies on.</param>
/// <param name="startPoint">Point that start angle is projected through.</param>
/// <param name="endPoint">Point that end angle is projected through.</param>
public Arc2D(Circle2D c, Point2D startPoint, Point2D endPoint)
{
this.Circle = c;
_startAngle = c.AngleThroughPoint(startPoint);
_endAngle = c.AngleThroughPoint(endPoint);
}
/// <summary>
/// Creates an arc centered on the given point with the specified radius and start/end angle.
/// </summary>
/// <param name="center">Center of the arc.</param>
/// <param name="radius">Radius of the arc.</param>
/// <param name="startAngle">Start angle.</param>
/// <param name="endAngle">End angle.</param>
public Arc2D(Point2D center, decimal radius, decimal startAngle, decimal endAngle)
{
this.Circle = new Circle2D(center, radius);
_startAngle = startAngle;
_endAngle = endAngle;
}
/// <summary>
/// Creates an arc centered at (0,0) with the given radius and start/end angle.
/// </summary>
/// <param name="radius">Radius of the arc.</param>
/// <param name="startAngle">Start angle.</param>
/// <param name="endAngle">End angle.</param>
public Arc2D(decimal radius, decimal startAngle, decimal endAngle)
{
this.Circle = new Circle2D(0, 0, radius);
_startAngle = startAngle;
_endAngle = endAngle;
}
/// <summary>
/// Creates and arc with the given circle and start/end angle.
/// </summary>
/// <param name="c">The circle that the arc lies on.</param>
/// <param name="startAngle">Start angle.</param>
/// <param name="endAngle">End angle.</param>
public Arc2D(Circle2D c, decimal startAngle, decimal endAngle)
{
this.Circle = c;
_startAngle = startAngle;
_endAngle = endAngle;
}
public decimal DistanceTo(Circle2D c)
{
return(c.DistanceTo(this));
}
public Point2D[] GetIntersect(Circle2D c, int decimals = -1)
{
_CheckIsValid();
return(c.GetIntersect(this, decimals));
}
/// <summary>
/// Returns circles that are tangent to another circle and line.
/// </summary>
/// <param name="line">Line that returned circles should be tangent to.</param>
/// <param name="circle">Circle that returned circles should be tangent to.</param>
/// <param name="radius">Radius of new circles.</param>
/// <returns>External tangent circles are listed first.</returns>
public static Circle2D[] FromTangentTangentRadius(LineSeg2D line, Circle2D circle, decimal radius)
{
return(FromTangentTangentRadius(circle, line, 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
});
}
