# UFO Alert Tool needs special math for Earth accuracy.

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### Skybuck Flying

Dec 8, 2022, 3:58:14 PM12/8/22
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The following math is required to make UFO Alert Tool really accurate:

1. Ray-tracing a spheroid.

2. Great Ellipse distance between two points.

3. Shortest Distance from a point to a Great Ellipse.

These math problems are due to the Earth being flattened by gravity.

For now I will try to proceed with an spherical Earth but this will be less accurate.

The preferred math is with vectors so it can handle x,y,z positions returned by the ray-tracer.

This special math is needed for visualization of arcs across the Earth.

Bye for now,
Skybuck.

### Skybuck Flying

Dec 8, 2022, 8:34:14 PM12/8/22
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I would prefer to use the latest and greatest solution to not waste energy/effort.

The best I have found so far seems to be:

https://proj.org/geodesic.html

which came from:

https://geographiclib.sourceforge.io/doc/library.html#languages

and

https://github.com/geographiclib/geographiclib-c

which leads to apperently the latest and greatest solution:

https://proj.org/zreferences.html#id25

Which referes to the latest and greatest algorithms:

[Karney2013]
Karney, C. F. F. Algorithms for geodesics. Journal of Geodesy, 87(1):43–55, 2013. doi:10.1007/s00190-012-0578-z.

Reading it now, lot's of math to investigate ! =D

Nanometer accuracy ! LOL.

Bye,
Skybuck =D

### Skybuck Flying

Dec 9, 2022, 1:22:59 AM12/9/22
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OK, I read it quickly, the math seems to be quite heavy.

I also came across an interesting solution for a simpler spherical model:

https://www.movable-type.co.uk/scripts/latlong-vectors.html

It would be less accurate, I fear it will cause problems with geodesic data sets.

But it is worthy of a mention !

One possibility could be to scale the geodesic data sets of earth to a sphere, but then I worry the distances will be inaccurate, not sure if this can be solved...

And if it would be a problem at all, but I like to keep it real if possible ! ;)

Bye for now,
Skybuck.