Angle Conversions¶

The hera.utils.angle module provides functions to convert between the three angle conventions commonly used in meteorology, mathematics, and navigation.

Importing¶

from hera.utils import toMeteorologicalAngle, toMathematicalAngle, toAzimuthAngle

Angle Convention Reference¶

Convention	0 degrees	Direction of increase	Typical use
Mathematical	East	Counter-clockwise	Trigonometry, polar coordinates
Meteorological	North	Clockwise (wind from)	Wind direction reporting
Azimuth	North	Clockwise	Navigation, compass bearing

toMeteorologicalAngle and toAzimuthAngle take a mathematical angle; toMathematicalAngle takes a meteorological angle. All values are in degrees.

Functions¶

toMeteorologicalAngle¶

Convert a mathematical angle to meteorological convention. The result indicates the direction wind is coming from.

from hera.utils import toMeteorologicalAngle

# East wind in math convention (0 deg) -> coming from the West in meteo (270 deg)
toMeteorologicalAngle(0)    # 270
toMeteorologicalAngle(90)   # 180
toMeteorologicalAngle(180)  # 90
toMeteorologicalAngle(270)  # 0

toMathematicalAngle¶

Convert a meteorological angle back to mathematical convention. This is the same transformation as toMeteorologicalAngle (the conversion is its own inverse):

from hera.utils import toMathematicalAngle

toMathematicalAngle(270)  # 0  (East)
toMathematicalAngle(0)    # 270

toAzimuthAngle¶

Convert a mathematical angle to an azimuth (compass) bearing (0 = North, increasing clockwise):

from hera.utils import toAzimuthAngle

toAzimuthAngle(0)    # 90   (East -> 90 deg azimuth)
toAzimuthAngle(90)   # 0    (North -> 0 deg azimuth)
toAzimuthAngle(180)  # 270  (West -> 270 deg azimuth)
toAzimuthAngle(270)  # 180  (South -> 180 deg azimuth)

Note

Unlike the other two functions, toAzimuthAngle does not wrap with % 360, so it only returns a value in [0, 360) for inputs in (-270, 450]. It also uses a Python if, so it accepts scalars only; toMeteorologicalAngle / toMathematicalAngle also work element-wise on NumPy arrays and pandas Series.

Quick Reference Table¶

Math angle	Compass direction	Meteorological	Azimuth
0	East	270	90
90	North	180	0
180	West	90	270
270	South	0	180