The Fresnel Integrals are two functions
$$S(x)=\int_0^x \sin(t^2),dt$$
and
$$C(x)=\int_0^x \cos(t^2),dt$$
which come up a lot in optics and stuff. It'd be nice if we could provide these functions to users, but there's no material on them in Numerical Recipes. I've experimented with a few different approximations, but I think the nicest is probably the one due to J. Boersma in this paper (doi↗).
The only trouble is, it uses $i$ in the calculations, so I would need to use the num_complex crate. I know this was discussed in #6 a few months ago. I'm happy to draft a PR if this sounds like a useful contribution...
The Fresnel Integrals are two functions
$$S(x)=\int_0^x \sin(t^2),dt$$
$$C(x)=\int_0^x \cos(t^2),dt$$
and
which come up a lot in optics and stuff. It'd be nice if we could provide these functions to users, but there's no material on them in Numerical Recipes. I've experimented with a few different approximations, but I think the nicest is probably the one due to J. Boersma in this paper (doi↗).
The only trouble is, it uses$i$ in the calculations, so I would need to use the
num_complexcrate. I know this was discussed in #6 a few months ago. I'm happy to draft a PR if this sounds like a useful contribution...