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.