feat: localiser backbeam approaches

[tracernz]

Fixes #[issue_no]

Summary of Changes

• fix: remove erroneous MathUtils.round Number.prototype.toFixed` already does the rounding itself, and I'm about to change MathUtils.round...
• fix: make fbw MathUtils.round quantise like msfssdk This is much more powerful and paves the way to avoiding importing both.
• feat: add angle normalise to MathUtils Add functions to normalise angles to the common +/- 180, 0-360, and radian equivalents.
• fix(fms): back course approach names Fixes the naming of LOC back-course approaches in the FMS (BACnn)
• fix(fms): back course related bugs, and add output vars Fixed some issues relating to tuning of back courses, and add the output data for the FG to consume (and other systems directly in the meanwhile until the FG knows how).
• fix(isis): loc deviation on back beam We never showed the correct deviations when on the backbeam, as the SimVar we use gives deviations close to -180 or 180 depending which side you're on and that is always off-scale. Other places are fixed in a different commit with new features as well.
• feat: port angle function to C++ Port the angle related functions to C++ utils in preparation for AP..
• feat(nd): backbeam loc Implement backbeam localiser support on the ND ROSE LS page. When a backbeam is tuned the glideslope scale is hidden, a B/C reminder is shown on the left of the localiser scale, and the localiser deviations are inverted. The B/C reminder is replaced by a LOC reminder for LOC/F-GS approaches so prepare for that too when I complete the MMR. Note that the B/C reminder positioning may be a little off as I did not yet have a photograph of a real ND to check. I will fix this in future as needed.
• feat(pfd): loc backbeam, refactor to modern framework Implement backbeam localiser support on the PFD. When a backbeam is tuned the glideslope scale is hidden, a B/C reminder is shown on the left of the localiser scale, and the localiser deviations are inverted. The B/C reminder is replaced by a LOC reminder for LOC/F-GS approaches so prepare for that too when I complete the MMR. I refactored some of the parts I touched to modern framework style, fixing a couple of bugs with missing subs in the process and turning the mapping functions into pure functions.
• fix(pfd): heading tape ls indications Fixed a bug where the heading tape was listening for the LS button H event directly, rather than using the bus data. This caused it to become out of sync with the actual state in some cases.
• feat(ap): loc backbeam Add some workarounds in the FBW interface to allow the AP to fly localiser back courses.

Screenshots (if necessary)

Note ISIS LOC deviation is uncorrected:

References

Additional context

Discord username (if different from GitHub):

Testing instructions

• Fly a couple of back-course approaches and ensure the AP can capture and fly the LOC in LOC B/C mode. There is a list below, but they are not filtered by runway length aircraft category so some may be no good for the A320. Check that the deviations on the PFD LS scale and ND ROSE LS page show a B/C reminder flag and invert the deviation so the indicator shows the correct direction to capture the localiser. The ISIS should not have the corrected deviation, and instead be inverted, as it does not have an FMGC input bus to know when a backbeam is tuned. Note: the AP will not be able to track the LOC when you get too close to the runway/localiser, as the localiser transmitter is not at the far end of the runway like a normal LOC approach; it should remain stable until the published minima.
• Fly a regular front-course ILS approach with AP and ensure it works fine and the LOC deviations are on the correct side as normal.

Airport	Approach
CYOD	BAC13L
CYYR	BAC26-Y
CYYR	BAC26-Z
KALO	BAC30
KBMI	BAC11
KBRO	BAC31
KCGI	BAC28
KCLL	BAC17
KCMX	BAC14
KDEC	BAC24
KEAU	BAC04
KESC	BAC28
KEWB	BAC23
KFAY	BAC22
KGFK	BAC17R
KGRB	BAC24
KGRI	BAC17
KHON	BAC30
KHRL	BAC35L
KHUT	BAC31
KIDA	BAC03
KIMT	BAC19
KJMS	BAC13
KLBB	BAC35L
KLRD	BAC36L
KMCE	BAC12
KMLB	BAC27L
KMOT	BAC13
KOSH	BAC18
KOTM	BAC13
KPTK	BAC27L
KRDD	BAC16
KRFD	BAC19
KROW	BAC03
KSLE	BAC13
KSNA	BAC02L
KSQI	BAC07
KSTJ	BAC17
KTOP	BAC31
KUIN	BAC22
PABR	BAC26
PACD	BAC33
PAHO	BAC22
PAKN	BAC30
PAOM	BAC10
PASC	BAC24
PASN	BAC18
PAYA	BAC29
PHKO	BAC35

How to download the PR for QA

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4. Click on either flybywire-aircraft-a320-neo or flybywire-aircraft-a380-842 download link at the bottom of the page

[tracernz]

Rebased, and fixed a couple of fms-v2 bugs while at it in LandingSystemSelectionManager, and FlightPlan.

[tracernz]

Rescued a commit from the reflog that I somehow dropped in an interactive rebase 😬 . Thanks to saschl for noticing!

[Saschl]

QA Report

Tester: saschl

Testing Process:

Tested several programmed Backcourse approaches, ND and PFD show proper indications and AP follows the B/C LOC properly. Tested manually entered LOC Backcourse (LOWI OEJ), Flags were shown properly and AP was tracking as expected. Tested "normal" ILS/LOC approaches, are shown and tracked as before.

Media:

Testing Results: Passed