public override List <Intersection> Intersect(CircLine other)
{
List <Intersection> intersections = new List <Intersection>();
if (other is Circle)
{
Circle otherC = (Circle)other;
Complex p0 = this.Center;
Complex p1 = otherC.Center;
double d = (p1 - p0).Modulus;
double r0 = this.Radius;
double r1 = otherC.Radius;
if (d > (r0 + r1)) // outside
{
return(null);
}
if (d < Math.Abs(r0 - r1))
{
return(intersections);
}
if (d == 0)
{
return(intersections);
}
double a = (r0 * r0 - r1 * r1 + d * d) / (2 * d);
double h = Math.Sqrt(r0 * r0 - a * a);
Complex p2 = p0 + a * (p1 - p0) / d;
Complex intersect;
intersect = new Complex(
p2.Re + h * (p1.Im - p0.Im) / d,
p2.Im - h * (p1.Re - p0.Re) / d
);
intersections.Add(new Intersection(
intersect,
Math.Atan2(p0.Im - intersect.Im, p0.Re - intersect.Re),
Math.Atan2(p1.Im - intersect.Im, p1.Re - intersect.Re)
));
intersect = new Complex(
p2.Re - h * (p1.Im - p0.Im) / d,
p2.Im + h * (p1.Re - p0.Re) / d
);
intersections.Add(new Intersection(
intersect,
Math.Atan2(p0.Im - intersect.Im, p0.Re - intersect.Re),
Math.Atan2(p1.Im - intersect.Im, p1.Re - intersect.Re)
));
return(intersections);
}
Line line = (Line)other;
Complex nearPoint = line.Project(Center).Point - line.Origin;
double dist = (Center - nearPoint).Modulus;
if (dist - Radius > 0)
{
return(null);
}
Complex p;
p = Line.Create(nearPoint, line.Angle).Evaluate(Math.Sqrt(RadiusSquared - dist * dist));
intersections.Add(new Intersection(
p,
line.Angle - Math.Asin(dist / Radius),
line.Project(p).Param
));
p = Line.Create(nearPoint, line.Angle).Evaluate(-Math.Sqrt(RadiusSquared - dist * dist));
intersections.Add(new Intersection(
p,
line.Angle + Math.Asin(dist / Radius) + Math.PI,
line.Project(p).Param
));
return(intersections);
}
public static Circle CreateFromRadiusSquared(Complex center, double radiusSquared)
{
return(new Circle(-center, center.ModulusSquared - radiusSquared));
}
public override CircLine Scale(Complex scale)
{
return(Create(Center * scale, Radius * scale.Modulus));
}
public override CircLine Translate(Complex translation)
{
return(CreateFromRadiusSquared(Center + translation, RadiusSquared));
}
public override Complex Evaluate(double t)
{
return(Center + Complex.CreatePolar(Radius, t));
}
public Circle(Complex b, double c)
: base(1, b, c)
{
Debug.Assert(RadiusSquared > -Accuracy.LinearToleranceSquared);
}