The local projection - and its matehamtics

[Pål_Herman_Sund]

A client is about to specify a wish/need for a local reference-/coordinate system type of "BIM/CAD" like. I have played a little with the Local projection which seems to do the trick. But are there any resources to provide the mathemathics for this projection? 

best

pH 

[NeilAyres]

If you want to see the maths behind projections this is it :

Map projections: A working manual 

[Pål_HermanSund2]

Thanks Neil, the "working manual" is (as always) one of the sources. But I am not skilled enough.. In the help sections it is stated (for the Local projection) "...This map projection is the same as the Orthographic projection, but supported on spheroids and spheres. The Orthographic projection is supported on spheres only..." In Snyder the details on Orthographic is found at page 145 but then still some details on the Local is "missing" to me. Maybe I can work it out.

The usecase is a local reference system for an airport with grid north being along a defined centreline of one of the runways. 

[NeilAyres]

Wiki page on coordinate rotation :

Rotation of axes - Wikipedia 

[MelitaKennedy]

EPSG is planning to add the Local projection to its registry. I've been slowly, very slowly writing up the mathematics so that it can be published in the 7-2 Guidance Note. I'm hoping to finish it up over the holidays.

Melita

[Pål_HermanSund2]

Thanks Melita Kennedy‌, definitively looking forward to see it there! Happy holidays!

best

Pål Herman

[Pål_Herman_Sund]

Hi Melita Kennedy‌ - sorry to bother again on this matter 😕

I have tried a little more and I am close to be happy. The case is to make local reference systems on smaller airports (one runway). So I use the ARP (Airport Reference Point) as my origo and wish to use the centreline (CL) of the runway as my North/Y. Grabbing lon/lat for the start and end-points to calculate the azimuth needed. A perfect result would be to have a constant Y for the CL in the new reference system - but for the 2 tests I have done I always end up with a difference in Y coordinates between start- and stop of the runway CL in the range 5-12 cm over a runway typically 1 - 2 km long.

I guess this would be related to the azimuth being a little off. So my question would be which of the possible azimuths should be calculated and (as a bonus) if You have a preferred formula. 

best

pH