main/src/georegression/geometry/UtilEllipse_F64.java
public static EllipseQuadratic_F64 convert( EllipseRotated_F64 input , EllipseQuadratic_F64 output ) {
		if( output == null )
			output = new EllipseQuadratic_F64();

		double x0 = input.center.x;
		double y0 = input.center.y;
		double a = input.a;
		double b = input.b;
		double phi = input.phi;

		double cphi = Math.cos(phi);
		double sphi = Math.sin(phi);
		double cphi2 = cphi*cphi;
		double sphi2 = sphi*sphi;

		double a2 = a*a;
		double b2 = b*b;
		double x02 = x0*x0;
		double y02 = y0*y0;

		// TODO simplfy using more trig identities
		output.A = cphi2/a2 + sphi2/b2;
		output.B = sphi*cphi/a2 - sphi*cphi/b2;
		output.C = sphi2/a2 + cphi2/b2;
		output.D = -x0*cphi2/a2 - y0*sphi*cphi/a2 - x0*sphi2/b2 + y0*sphi*cphi/b2;
		output.E = -x0*sphi*cphi/a2 - y0*sphi2/a2 + x0*sphi*cphi/b2 - y0*cphi2/b2;
		output.F = x02*cphi2/a2 + 2*x0*y0*sphi*cphi/a2 + y02*sphi2/a2 +
				x02*sphi2/b2 - 2*x0*y0*sphi*cphi/b2 + y02*cphi2/b2 - 1;

		return output;
	}
public static EllipseQuadratic_F64 convert( EllipseRotated_F64 input , EllipseQuadratic_F64 output ) {
		if( output == null )
			output = new EllipseQuadratic_F64();

		double x0 = input.center.x;
		double y0 = input.center.y;
		double a = input.a;
		double b = input.b;
		double phi = input.phi;

		double cphi = Math.cos(phi);
		double sphi = Math.sin(phi);
		double cphi2 = cphi*cphi;
		double sphi2 = sphi*sphi;

		double a2 = a*a;
		double b2 = b*b;
		double x02 = x0*x0;
		double y02 = y0*y0;

		// TODO simplfy using more trig identities
		output.A = cphi2/a2 + sphi2/b2;
		output.B = sphi*cphi/a2 - sphi*cphi/b2;
		output.C = sphi2/a2 + cphi2/b2;
		output.D = -x0*cphi2/a2 - y0*sphi*cphi/a2 - x0*sphi2/b2 + y0*sphi*cphi/b2;
		output.E = -x0*sphi*cphi/a2 - y0*sphi2/a2 + x0*sphi*cphi/b2 - y0*cphi2/b2;
		output.F = x02*cphi2/a2 + 2*x0*y0*sphi*cphi/a2 + y02*sphi2/a2 +
				x02*sphi2/b2 - 2*x0*y0*sphi*cphi/b2 + y02*cphi2/b2 - 1;

		return output;
	}
Convert from rotated to quadratic.

@param input Input rotated format.
@param output (Optional) Storage for quadratic format.  Can be null.
@return Ellipse in quadratic format.