public override GeneralConic2d ToGeneralConic()
{
Transform2d tr = Transform2d.Scale(MajorRadius) * Transform2d.Rotate(Rotation) * Transform2d.Translate(center.X, center.Y);
GeneralConic2d elcon = new GeneralConic2d(1, 0, 1.0 / (sigratio * sigratio), 0, 0, -1); //x^2+(1/b)^2-1=0 => unit ellipse
elcon.Transform(tr); //transform conic to position of ellipse
return(elcon); //TODO: optimize this function
}
public override GeneralConic2d ToGeneralConic()
{
Transform2d tr = Transform2d.Rotate(rotation) * Transform2d.Translate(vertex.X, vertex.Y);
GeneralConic2d res = new GeneralConic2d(a, 0, 0, 0, -1, 0); //y=ax^2
res.Transform(tr);
return(res); //TODO: optimize this function
}
public override GeneralConic2d ToGeneralConic()
{
//TODO: test this function
Transform2d tr = Transform2d.Scale(majoraxis.Length) * Transform2d.Rotate(Rotation) * Transform2d.Translate(center.X, center.Y);
GeneralConic2d hypcon = new GeneralConic2d(1, 0, -1.0 / (ratio * ratio), 0, 0, -1); //x^2-(y/b)^2-1=0 => unit
hypcon.Transform(tr);
return(hypcon); //TODO: optimize this function
}
/// <summary>
/// Intersects a line with a conic that is in standard position, that is, not rotated and
/// centered at 0,0
/// </summary>
/// <param name="con"></param>
/// <param name="lin"></param>
/// <returns>A list of parameters on line that is intersection points, or null if no intersections</returns>
private static double[] ConicLineParametric(GeneralConic2d con, Line2d lin)
{
//We construct a matrix so that: conic is unrotated (B term=0) and line starts at origo and has length=1.0
//This is to improve stabillity of the equation
double invlen = 1.0 / lin.Length;
if (double.IsInfinity(invlen))
{
return(null); //zero length line does not intersect
}
Transform2d tr = Transform2d.Translate(-lin.X1, -lin.Y1) * Transform2d.Rotate(-con.Rotation) * Transform2d.Scale(invlen);
GeneralConic2d c = new GeneralConic2d(con); //copy for modification
double x1 = lin.X2, y1 = lin.Y2;
c.Transform(tr);
tr.Apply(x1, y1, out x1, out y1, true); //transformed line end
double t2 = y1 * y1 * c.C + x1 * x1 * c.A;
double t1 = y1 * c.E + x1 * c.D;
double t0 = c.F;
double[] ts = RealPolynomial.SolveQuadric(t2, t1, t0);
return(ts);
/*double dx=lin.DX;
* double dy=lin.DY;
* double x0=lin.X1;
* double y0=lin.Y1;
*
* double t2=con.C*dy*dy+con.A*dx*dx;
* double t1=2*con.C*dy*y0+2*con.A*dx*x0+dy*con.E+con.D*dx;
* double t0=con.C*y0*y0+con.E*y0+con.A*x0*x0+con.D*x0+con.F;
*
* return RealPolynomial.SolveQuadric(t2, t1, t0, 1e-9);*/
}
/// <summary>
/// Gets the line geometries, one or two lines. The type of the conic has to be
/// Intersecting lines (2 results), Paralell lines (2 results) or Coincident lienes (1 result),
/// otherwise the result is null.
/// </summary>
/// <returns></returns>
public Line2d[] ToLines()
{
// Inspired by line extraction conmat.c from book Graphics Gems V
double xx, yy;
ConicType type = Type;
Line2d tmplin;
Transform2d tr;
GeneralConic2d cpy;
List <Line2d> res = null;
double de = B * B * 0.25 - A * C;
if (MathUtil.IsZero(A) && MathUtil.IsZero(B) && MathUtil.IsZero(C))
{ //single line
// compute endpoints of the line, avoiding division by zero
res = new List <Line2d>();
if (Math.Abs(d) > Math.Abs(e))
{
res.Add(new Line2d(-f / (d), 0.0, -(e + f) / (d), 1.0));
}
else
{
res.Add(new Line2d(0.0, -f / (e), 1.0, -(d + f) / (e)));
}
}
else
{ // two lines
cpy = new GeneralConic2d(this);
double a = cpy.a, b = cpy.b * 0.5, c = cpy.c, d = cpy.d * 0.5, e = cpy.e * 0.5, f = cpy.f; //get matrix coefficient
// use the expression for phi that takes atan of the smallest argument
double phi = (Math.Abs(b + b) < Math.Abs(a - c) ?
Math.Atan((b + b) / (a - c)) :
MathUtil.Deg360 - Math.Atan((a - c) / (b + b))) / 2.0;
//phi = cpy.Rotation;
if (MathUtil.IsZero(de))
{ //parallel lines
tr = Transform2d.Rotate(-phi);
cpy.Transform(tr);
a = cpy.A; b = cpy.B * 0.5; c = cpy.c; d = cpy.d * 0.5; e = cpy.e * 0.5; f = cpy.f; //get matrix coefficient
if (Math.Abs(c) < Math.Abs(a)) // vertical
{
double[] xs = RealPolynomial.SolveQuadric(a, d, f);
if (xs != null)
{
res = new List <Line2d>();
foreach (double x in xs)
{
tmplin = new Line2d(x, -1, x, 1);
tmplin.Transform(tr.Inversed); //back to original spacxe
res.Add(tmplin);
}
}
}
else //horizontal
{
double[] ys = RealPolynomial.SolveQuadric(c, e, f, 0.0);
if (ys != null)
{
res = new List <Line2d>();
foreach (double y in ys)
{
tmplin = new Line2d(-1, y, 1, y);
tmplin.Transform(tr.Inversed);
res.Add(tmplin);
}
}
}
} //end parallel lines case
else
{ //crossing lines
Point2d center = Center;
double rot = this.Rotation;
tr = Transform2d.Translate(-center.X, -center.Y) * Transform2d.Rotate(-rot);
cpy.Transform(tr);
a = cpy.A; b = cpy.B * 0.5; c = cpy.c; d = cpy.c * 0.5; e = cpy.e * 0.5; f = cpy.f;
res = new List <Line2d>();
xx = Math.Sqrt(Math.Abs(1.0 / a));
yy = Math.Sqrt(Math.Abs(1.0 / c));
tr = tr.Inversed;
tmplin = new Line2d(-xx, -yy, xx, yy);
tmplin.Transform(tr);
res.Add(tmplin);
tmplin = new Line2d(new Line2d(-xx, yy, xx, -yy));
tmplin.Transform(tr);
res.Add(tmplin);
} //end crossing lines case
} //end two lines
if (res == null || res.Count == 0)
{
return(null);
}
return(res.ToArray());
}
