public static Point2d[] ParabolaParabola(Parabola2d pab1, Parabola2d pab2) //tested ok
{
Transform2d tr = pab1.ToStandardPosition;
pab2 = new Parabola2d(pab2); //copy for transformation
pab2.Transform(tr);
var ptset = StandardPosParabolaGeneralConic(pab2.ToGeneralConic());
ptset.Transform(tr.Inversed);
return(ptset.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 double[] ParabolaLineParamteric(Parabola2d pab, Line2d lin) //tested ok
{
double x1, y1, x2, y2; //line points in parabola standard position
Transform2d tr = pab.ToStandardPosition; //intersect line with y=x^2 => easier
tr.Apply(lin.X1, lin.Y1, out x1, out y1, true);
tr.Apply(lin.X2, lin.Y2, out x2, out y2, true);
double dx = x2 - x1;
double dy = y2 - y1;
double c2 = -dx * dx;
double c1 = dy - 2 * dx * x1;
double c0 = y1 - x1 * x1;
//y1-x1^2+t*(dy-2*dx*x1)-dx^2*t^2=0
double[] ts = RealPolynomial.SolveQuadric(c2, c1, c0);
return(ts);
}
public static Point2d[] ParabolaLine(Parabola2d pab, Line2d lin)
{
return(LineParamsToPoints(ParabolaLineParamteric(pab, lin), lin, double.NegativeInfinity, double.PositiveInfinity));
}
public Parabola2d(Parabola2d tocopy)
{
vertex = tocopy.vertex;
rotation = tocopy.rotation;
a = tocopy.a;
}
