geometry icon indicating copy to clipboard operation
geometry copied to clipboard

Inconsistent formulas for meridian distances

Open cffk opened this issue 4 years ago • 0 comments

It would be nice if quarter_meridian, meridian_direct, and meridian_inverse all used consistent approximations. Instead:

  • quarter_meridian is accurate to n^16 with the coefficient given to full precision.
  • meridian_direct is accurate to n^4 with the coefficients given approximately, e.g., 1.572916667 instead of CT(151)/CT(96).
  • meridian_inverse is supposed to be accurate to n^5, however the n^4 contribution to C0 and the n^5 contribution to C2 are omitted and the coefficients are given approximately, e.g. -0.729166667 instead of CT(-35)/CT(48).

I recommend that both median_inverse and meridian_direct include terms up to n^6 which is needed to full double precision accuracy for the earth. If these routines used Horner and Clenshaw summation then there would be little cost in making n^6 the minimum order provided.

cffk avatar Mar 24 '21 18:03 cffk