/// <summary>Finds the intersection points between the edge of this circle and circle <paramref name='b'/>.</summary>
/// <returns>Null (no intersection), an array of length 1, or an array of length 2.</returns>
public WPoint[] GetIntersectionPoints(WCircle b)
{
//following the method in math/intersectionCircleCircle.png
WCircle a = this;
double d = a.Center.Distance(b.Center); //distance between centers
if (d > a.Radius + b.Radius)
{
return(null); //circles too far apart to intersect
}
if (a.ContainsOrIsContained(b))
{
return(null); //one circle is wholly inside the other
}
//the radical line is the line between the two intersecting points of the circles
//Point c is the center of the radical line, which is also on the line between the centers
double dA = (Math.Pow(a.Radius, 2) - Math.Pow(b.Radius, 2) + Math.Pow(d, 2)) / (2 * d); //distance from centerA to pointC
if (dA == a.Radius)
{
return(new WPoint[] { Geometry.PointOnLine(a.Center, b.Center, a.Radius) }); //circles intersect at single point
}
WPoint c = a.Center + dA * (b.Center - a.Center) / d;
//h is the distance from pointC to either intersection point (the hypotenus of triangle centerA-C-intersection)
double h = Math.Sqrt(Math.Pow(a.Radius, 2) - Math.Pow(dA, 2));
return(new WPoint[] {
new WPoint(c.X + (h * (b.Y - a.Y) / d), c.Y - h * (b.X - a.X) / d),
new WPoint(c.X - (h * (b.Y - a.Y) / d), c.Y + h * (b.X - a.X) / d)
});
}
/// <summary>
/// Returns true if this circle entirely contains circle <paramref name='b'/>, or <paramref name='b'/> entirely contains this circle, or they exactly overlap.
/// </summary>
public bool ContainsOrIsContained(WCircle b)
{
if (this.Radius > b.Radius)
{
return(this.Contains(b));
}
return(b.Contains(this));
}
/// <summary>
/// Returns true if any part of this circle overlaps any part of circle <paramref name='b'/>.
/// </summary>
public bool Overlaps(WCircle b)
{
WPoint[] intersections = this.GetIntersectionPoints(b);
if (intersections != null)
{
return(true);
}
return(this.ContainsOrIsContained(b));
}
/// <summary>
/// Find the two tangent points on the circle that form lines to point <paramref name='b'/>.
/// </summary>
/// <returns>Array of length 2.</returns>
public WPoint[] GetTangentPoints(WPoint b)
{
//point C and D are the tangents
WCircle a = this;
double distanceAB = a.Center.Distance(b);
double degreesAB = DegreesAtPoint(b);
double degreesAB_AC = Math.Cos(Radius / distanceAB);
WPoint c = PointAtDegrees(degreesAB + degreesAB_AC);
WPoint d = PointAtDegrees(degreesAB - degreesAB_AC);
return(new WPoint[] { c, d });
}
/// <summary>
/// Returns true if this wedge fully contains circle <paramref name='b'/>.
/// </summary>
public bool Contains(WCircle b)
{
WPoint[] tangentPoints = b.GetTangentPoints(this.Circle.Center);
foreach (WPoint point in tangentPoints)
{
if (!Contains(point))
{
return(false);
}
}
return(true);
}
/// <summary>
/// Returns true if this circle entirely contains circle <paramref name='b'/>, or they exactly overlap.
/// </summary>
public bool Contains(WCircle b)
{
if (b.Radius > this.Radius)
{
return(false);
}
if (b.Radius == this.Radius)
{
return(b.Center == this.Center);
}
double d = this.Center.Distance(b.Center);
return(this.Radius >= d + b.Radius);
}
/// <summary>
/// Returns true if any part of this wedge overlaps any part of circle <paramref name='b'/>.
/// </summary>
public bool Overlaps(WCircle b)
{
WWedge a = this;
WPoint[] intersections = a.Circle.GetIntersectionPoints(b);
if (intersections == null)
{
if (!a.Circle.ContainsOrIsContained(b))
{
return(false);
}
}
//line edge overlaps circle
foreach (WLineSegment lineA in this.LineEdges)
{
if (b.Overlaps(lineA))
{
return(true);
}
}
//arc overlaps circle
if (a.ArcOverlapsArc(new WWedge(b, 0, WCircle.DEGREES_IN_CIRCLE)))
{
return(true);
}
//wedge entirely contains circle or circle entirely contains wedge
if (a.Contains(b))
{
return(true);
}
if (b.Contains(a))
{
return(true);
}
return(false);
}
/// <param name="circle">The full circle this wedge is a part of.</param>
/// <param name="degreeRange">The range of degrees this wedge covers.</param>
public WWedge(WCircle circle, WRangeCircular degreeRange) : base(circle.Center, degreeRange)
{
Radius = circle.Radius;
}
/// <param name="circle">The full circle this wedge is a part of.</param>
/// <param name="degreeStart">The starting degree the wedge covers.</param>
/// <param name="degreeEnd">The ending degree the wedge covers.</param>
public WWedge(WCircle circle, double degreeStart, double degreeEnd) : base(circle.Center, degreeStart, degreeEnd)
{
Radius = circle.Radius;
}
