While trying to convert ecliptic coordinates from mean
equinox of date to true equinox of date, I ran into excessive
overhead from the IAU2000B nutation model. The fact that it
uses 77 trigonometric terms made the calculations a lot slower.
https://apps.dtic.mil/sti/pdfs/AD1112517.pdf
Page 4 in the above document mentions a shorter series
“NOD version 2” that has 13 terms instead of 77 as used in IAU2000B.
I had not noticed NOD2 before, because it appears only in
the FORTRAN version of NOVAS 3.x, not the C version.
After reading the FORTRAN code, I realized NOD2 is the same
as IAU2000B, only it keeps the first 13 of 77 terms.
The terms are already arranged in descending order of
significance, so it is easy to truncate the series.
Based on this discovery, I realized I could achieve all of
the required accuracy needed for Astronomy Engine by
keeping only the first 5 terms of the nutation series.
This tremendously speeds up nutation calculations while
sacrificing only a couple of arcseconds of accuracy.
It also makes the minified JavaScript code smaller:
Before: 119500 bytes.
After: 116653 bytes.
So that's what I did here. Most of the work was updating
unit tests for accepting slightly different calculation
results.
The nutation formula change did trigger detection of a
lurking bug in the inverse_terra functions, which convert
a geocentric vector into latitude, longitude, and elevation
(i.e. an Observer object). The Newton's Method loop in
this function was not always converging, resulting in
an infinite loop. I fixed that by increasing the
convergence threshold and throwing an exception
if the loop iterates more than 10 times.
I also fixed a couple of bugs in the `demotest` scripts.
The demo worldmap.cpp now also prints out the
geographic locations where the Sun/Moon appear
to be straight up (at the zenith) for the given time.
This illustrates that Astronomy_VectorObserver can
turn a geocentric vector into a location on the
Earth that is in the same direction from the Earth's
center that a given celestial body lies.
The worldmap.cpp demo was calculating each pixel's
observer location twice. Now it does so only once.
Added verification that the output PNG file is
exactly as expected, using a sha256 checksum.
The new demo worldmap.cpp generates a PNG image of
a Mercator projection of the Earth, showing color-coded
intensity of sunlight (yellow) and moonlight (blue).
This sample program shows how to efficiently calculate
horizontal altitudes of the Sun and Moon across many
different geographic locations, for a given observation time.
