Shap2d06.dat, 6th 'shape' file for CPO2D
General conic section, defined by users equations.
See also shap2d07.
The form of the general formula for a conic section that we use gives a radius of curvature R at (r,z) = (0,0), namely
r*r = (e*e - 1)*z*z + 2*R*z,
where e is the ellipticity, and where the correspondence between the values of e and the type of conic section is:
e = 0, circle,
e = 0 to 1, ellipse,
e = 1, parabola,
e > 1, hyperbola.
In the data above the parameter a is used for convenience instead of e, where a = e*e - 1.
It is also convenient to express z in terms of r:
z = (sqrt(R*R+a*r*r+1.e-10)-R)/a,
and where the small constant is added to help prevent failures if the argument of the square root becomes zero.
In the data above, a = 1, corresponding to e = 1.414, a hyperbola.
The range of r is given as 0.1 to 1, giving an aperture of radius 0.1.