# azimuth and distance from various functions in qgis

I am comparing the various ways of calculating distance and azimuth between two points with Qgis. I am struggling with the various results and their interpretation.

I need to calculate a loxodromic bearing (rhumb line, i.e. a path beetween two points with constant bearing) : which function should I use ? According to my partial conclusions from the data below, none of them returns loxodromic bearing !

• the bearing and measureLine functions compute orthodromic route and distance (both from the function computeDistanceBearing that uses a Vincenty algorithm which indeed aims to calculate a great circle distance and bearing, according to Wikipedia page)
• the azimuth function computes a calculation with a "flat" formula according to api documentation (note that the computeDistanceFlat function returns the square root of the distance when the coordinates are in degrees and the distance when the coordinates are in meters and Mercator system, cf. numeric example below)
• since my loxodromic calculation seems to be wrong, I don't know if one is close to loxodromic figures

Below are some results of functions and my partial conclusions with the example of New-York (-74,40.73) and Paris (2.34,48.86) - coordinates in long/lat or EPSG 4326.

The results of the various functions are :

``````tool                                  distance ParistoNY   NYtoParis
tool.bearing(p1,p2)                       -       292        54
tool.measureLine(p1,p2)                 5850       -         -
tool.computeDistanceFlat(p1,p2)           76       -         -
pow(tool.computeDistanceFlat(p1,p2),2)  5893       -         -
p1.azimuth(p2), p2.azimuth(p1)            -       264        84
``````

after conversion of coordinates into Mercator system:

``````tool                          distance   ParistoNY   NYtoParis
p1.azimuth(p2), p2.azimuth(p1)    -         261          81
tool.computeDistanceFlat(p1,p2)  8593130
``````

Manual calculation from wikipedia formulas for a sphere :

``````tool                                    distance   ParistoNY   NYtoParis
orthodromic distance and initial route    5830         54          292
loxodromic distance and route          344017235       89           89
manual flat azimuth on epsg4326             -         264           84
``````