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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.
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
to
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
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
to
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.
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.
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