/// <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>
/// <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>
public Point2D[] GetIntersect(LineSeg2D l, int decimals = -1)
{
LineSeg2D centToLine = default(LineSeg2D);
decimal centToLineLength = 0m;
decimal centToLineLengthForComp = 0m;
decimal radiusForComp = 0m;
if (l.IsHorizontal)
{
// The center to any horizontal line is a vertical line through
// the center of the circle.
centToLine = new LineSeg2D(this.Center, this.Center + new Vector2D(0, 1));
}
else
{
centToLine = LineSeg2D.FromPointSlope(this.Center, l.PerpendicularSlope);
}
centToLine.Pt2 = l.GetIntersect(centToLine, true).Value;
centToLineLength = centToLine.Length;
// Get numbers for comparison, rounding if necessary
centToLineLengthForComp = centToLineLength;
radiusForComp = _radius;
if (decimals >= 0)
{
centToLineLengthForComp = centToLineLengthForComp.RoundFromZero(decimals);
radiusForComp = radiusForComp.RoundFromZero(decimals);
}
// See if line is outside of circle
if (centToLineLengthForComp > radiusForComp)
{
return(new Point2D[] { });
}
// See if line is tangent to circle
if (centToLineLengthForComp == radiusForComp)
{
return(new Point2D[] { centToLine.Pt2 });
}
// Line must intersect in two places
Vector2D vCentToChord = default(Vector2D);
decimal halfChord = 0m;
// Get a vector from the center to the intersecting chord
vCentToChord = centToLine.GetVectorP1toP2();
if (vCentToChord.Magnitude == 0)
{
Vector2D offsetVector = default(Vector2D);
// Line goes through circle center
if (l.IsVertical)
{
// Slope undefined so just go up the length of the radius
offsetVector = new Vector2D(0, _radius);
}
else
{
offsetVector = new Vector2D(_radius * DecimalEx.Cos(DecimalEx.ATan(l.Slope)), _radius * DecimalEx.Sin(DecimalEx.ATan(l.Slope)));
}
return(new Point2D[] {
this.Center + offsetVector,
this.Center - offsetVector
});
}
else
{
Vector2D vChord = default(Vector2D);
// Get a vector along the chord
vChord = vCentToChord.GetPerpendicular();
// Determine the length of half the chord
halfChord = RightTriangle.GetSideFromSideHyp(centToLineLength, _radius);
// Set the magnitude of the vector along the chord
// to be half the chord length
vChord.Magnitude = halfChord;
// The two intersecting points are points translated
// from the center of the circle to the chord (+vCentToChord)
// and then translated to the ends of the chord (+-vChord)
return(new Point2D[] {
this.Center + vCentToChord + vChord,
this.Center + vCentToChord - vChord
});
}
}
/// <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
});
}
