/// <summary>
/// Retrieve an elipse in its center-radius form using parameters from the SVG specification
/// </summary>
/// <param name="cur">Current point</param>
/// <param name="radii">The ellipse radius</param>
/// <param name="xRotation">The rotation of the ellipse in relation to the x-axis</param>
/// <param name="largeArc">Wheter the large arc should be selected or not</param>
/// <param name="sweep">Sweep direction (false for clockwise, true for counterclockwise)</param>
/// <param name="target">The target point</param>
/// <returns></returns>
public static Curve EllipticArc(Double2 cur, Double2 radii, double xRotation, bool largeArc, bool sweep, Double2 target)
{
// The algorithm used here is presented on this link: https://svgwg.org/svg2-draft/implnote.html
var xpun = (cur - target) / 2;
var xpr = xpun.Rotate(-xRotation);
// Guarantee that the radii are positive
radii.X = Math.Abs(radii.X); radii.Y = Math.Abs(radii.Y);
// Guarantee that the radius are large enough
var rr = radii.X * radii.X * xpr.Y * xpr.Y + radii.Y * radii.Y * xpr.X * xpr.X;
var r2 = radii.X * radii.X * radii.Y * radii.Y;
double skr;
if (rr > r2)
{
radii *= Math.Sqrt(rr / r2);
skr = 0;
}
else
{
skr = Math.Sqrt((r2 - rr) / rr);
}
var cpr = new Double2(skr * radii.X * xpr.Y / radii.Y, -skr * radii.Y * xpr.X / radii.X);
if (largeArc == sweep)
{
cpr = -cpr;
}
// Calculate the center
var cpun = cpr.Rotate(xRotation) + (target + cur) / 2;
// Calculate the angle
var t1 = Math.Atan2(radii.X * (xpr.Y - cpr.Y), radii.Y * (xpr.X - cpr.X));
var t2 = Math.Atan2(radii.X * (-xpr.Y - cpr.Y), radii.Y * (-xpr.X - cpr.X));
var dt = t2 - t1;
if (!sweep && dt > 0)
{
dt -= TwoPi;
}
else if (sweep && dt < 0)
{
dt += TwoPi;
}
return(EllipticArcInternal(cpun, radii, Double2.FromAngle(xRotation), t1, dt));
}
