public static Point2d[] HyperbolaHyperbola(Hyperbola2d hyp1, Hyperbola2d hyp2)
{
Transform2d tr = hyp1.ToStandardPosition;
hyp2 = new Hyperbola2d(hyp2); //copy for modification
hyp2.Transform(tr);
Point2dSet res = StdHyperbolaConic(hyp1.Ratio, hyp2);
res.InverseTransform(tr);
return(res.ToArray());
}
public static Point2d[] ParabolaHyperbola(Parabola2d pab, Hyperbola2d hyp) //tested ok
{
Transform2d tr = pab.ToStandardPosition; //y=x^2
hyp = new Hyperbola2d(hyp); //copy for transformation
hyp.Transform(tr); //to standard space of parabola for stabillity
GeneralConic2d gencon = hyp.ToGeneralConic();
var ptset = StandardPosParabolaGeneralConic(gencon);
ptset.Transform(tr.Inversed);
return(ptset.ToArray());
}
public static Point2d[] HyperbolaEllipse(Hyperbola2d hyp, Ellipse2d elp)
{
//TODO: this is probably more stable intersecting hyperbola with unitcircle. Rewrite.
Transform2d tr = hyp.ToStandardPosition;
hyp = new Hyperbola2d(hyp);
elp = new Ellipse2d(elp);
hyp.Transform(tr);
elp.Transform(tr);
GeneralConic2d hcon = new GeneralConic2d(1, 0.0, -1 / (hyp.B * hyp.B), 0.0, 0.0, -1);
Point2dSet pset = new Point2dSet();
pset.AddRange(ConicConic(hcon, elp.ToGeneralConic()));
pset.Transform(tr.Inversed);
return(pset.ToArray());
}
public static Circle2d[] CirclePointPoint(Circle2d ci, Point2d pt1, Point2d pt2)
{
// Solution by Robert.P. 2013-02-10
// solved by intersecting the line which has equal distance to pt1 and pt2 at every point,
// with the hyperbola that has equal distance to ci and pt1 at every point.
List <Circle2d> res = null;
//get squared constants of hyperbola
double c2 = ci.Center.SquaredDistance(pt1) / 4.0; //center->focus distance squared
double a = 0.5 * ci.Radius;
double b = Math.Sqrt(c2 - a * a);
if (double.IsNaN(b))
{
return(null); //negative square root, no such hyperbola
}
// this hyperbola has equal distance to ci and pt1 at every point.
// it also has focus at ci.Center and pt1
Hyperbola2d hyper = new Hyperbola2d(new Point2d((ci.X + pt1.X) * 0.5, (ci.Y + pt1.Y) * 0.5), a, b, ci.Center.Angle(pt1));
//get constants of line dx+ey+f=0, which is equal distance from p1,p2 on every point
double dx = pt2.X - pt1.X, dy = pt2.Y - pt1.Y;
double mx = pt1.X + dx * 0.5;
double my = pt1.Y + dy * 0.5;
Line2d perp = new Line2d(mx, my, mx - dy, my + dx); //starts from mipoint pt1-pt2 and is perpendicular to that line
var intpts = Intersect2d.HyperbolaLine(hyper, perp);
if (intpts == null)
{
return(null);
}
foreach (Point2d intpt in intpts)
{
AddResult(ref res, intpt.X, intpt.Y, intpt.Distance(pt1));
}
return(MakeResult(res));
}
public override bool Transform(Transform2d t)
{
//transform hyperbola centered at origin, because it's more stable general conic
Hyperbola2d hyp = new Hyperbola2d(this);
hyp.center = Point2d.Origo;
var gencon = hyp.ToGeneralConic();
if (!gencon.Transform(new Transform2d(t.AX, t.AY, t.BX, t.BY, 0.0, 0.0)))
{
return(false);
}
hyp = gencon.Reduce() as Hyperbola2d;
if (hyp == null)
{
return(false);
}
//now transform centerpoint separately,
//and write bac to this
center = center.GetTransformed(t);
ratio = hyp.ratio;
majoraxis = hyp.majoraxis;
return(true);
/* double majax = majoraxis.Length;
* double minax = -majax * ratio;
* double rot = Rotation;
* bool reverse;
* Hyperbola_Transform(ref majax, ref minax, ref rot, ref center, t, out reverse);
*
* majoraxis = Vector2d.FromAngleAndLength(rot, majax);
* ratio = minax / majax;
*
* return true;*/
}
public static double[] HyperbolaLineParametric(Hyperbola2d hyp, Line2d lin)
{
// Computes intersection points with a hyperbola and a line
// solved and created by Robert.P. 2013-02-11
//
// solution is created by transforming system to hyperbola standard position,
// and then solving the system x^2/a^2-y^2/b^2-1=0 , x=x0+t*dx and y=y0+t*dy (note that a is 1 in std. pos.)
Transform2d tr = hyp.ToStandardPosition;
//extract standard spaced line
double x0, y0, x1, y1, dx, dy, b = hyp.Ratio;
tr.Apply(lin.X1, lin.Y1, out x0, out y0, true);
tr.Apply(lin.X2, lin.Y2, out x1, out y1, true);
dx = x1 - x0; dy = y1 - y0;
double t2 = -dy * dy + b * b * dx * dx;
double t1 = -2 * dy * y0 + 2 * b * b * dx * x0;
double t0 = -y0 * y0 + b * b * x0 * x0 - b * b;
return(RealPolynomial.SolveQuadric(t2, t1, t0, 0.0));
}
public static Point2d[] HyperbolaRay(Hyperbola2d hyp, Line2d ray)
{
return(LineParamsToPoints(HyperbolaLineParametric(hyp, ray), ray, seg_minparam, double.PositiveInfinity));
}
public static Point2d[] HyperbolaLine(Hyperbola2d hyp, Line2d lin)
{
return(LineParamsToPoints(HyperbolaLineParametric(hyp, lin), lin, double.NegativeInfinity, double.PositiveInfinity));
}
public static Point2d[] HyperbolaSeg(Hyperbola2d hyp, Line2d seg)
{
return(LineParamsToPoints(HyperbolaLineParametric(hyp, seg), seg, seg_minparam, seg_maxparam));
}
public Hyperbola2d(Hyperbola2d tocopy)
{
center = tocopy.center;
majoraxis = tocopy.majoraxis;
ratio = tocopy.Ratio;
}