Altitude or height (sometimes known as' depth') is specify based on the context in which it is used (aviation, geometry, geographical survey, sport, atmospheric pressure, and many more).Although the term altitude is normally used to mean the height above sea degree of a location, in geography the term elevation is often preferred for this usage.

COMING SOON!

```
from math import atan, cos, radians, sin, tan
from haversine_distance import haversine_distance
def lamberts_ellipsoidal_distance(
lat1: float, lon1: float, lat2: float, lon2: float
) -> float:
"""
Calculate the shortest distance along the surface of an ellipsoid between
two points on the surface of earth given longitudes and latitudes
https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle, sigma
Representing the earth as an ellipsoid allows us to approximate distances between points
on the surface much better than a sphere. Ellipsoidal formulas treat the Earth as an
oblate ellipsoid which means accounting for the flattening that happens at the North
and South poles. Lambert's formulae provide accuracy on the order of 10 meteres over
thousands of kilometeres. Other methods can provide millimeter-level accuracy but this
is a simpler method to calculate long range distances without increasing computational
intensity.
Args:
lat1, lon1: latitude and longitude of coordinate 1
lat2, lon2: latitude and longitude of coordinate 2
Returns:
geographical distance between two points in metres
>>> from collections import namedtuple
>>> point_2d = namedtuple("point_2d", "lat lon")
>>> SAN_FRANCISCO = point_2d(37.774856, -122.424227)
>>> YOSEMITE = point_2d(37.864742, -119.537521)
>>> NEW_YORK = point_2d(40.713019, -74.012647)
>>> VENICE = point_2d(45.443012, 12.313071)
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters"
'254,351 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters"
'4,138,992 meters'
>>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters"
'9,737,326 meters'
"""
# CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System
# Distance in metres(m)
AXIS_A = 6378137.0
AXIS_B = 6356752.314245
EQUATORIAL_RADIUS = 6378137
# Equation Parameters
# https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines
flattening = (AXIS_A - AXIS_B) / AXIS_A
# Parametric latitudes https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
b_lat1 = atan((1 - flattening) * tan(radians(lat1)))
b_lat2 = atan((1 - flattening) * tan(radians(lat2)))
# Compute central angle between two points
# using haversine theta. sigma = haversine_distance / equatorial radius
sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS
# Intermediate P and Q values
P_value = (b_lat1 + b_lat2) / 2
Q_value = (b_lat2 - b_lat1) / 2
# Intermediate X value
# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
X_numerator = (sin(P_value) ** 2) * (cos(Q_value) ** 2)
X_demonimator = cos(sigma / 2) ** 2
X_value = (sigma - sin(sigma)) * (X_numerator / X_demonimator)
# Intermediate Y value
# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
Y_numerator = (cos(P_value) ** 2) * (sin(Q_value) ** 2)
Y_denominator = sin(sigma / 2) ** 2
Y_value = (sigma + sin(sigma)) * (Y_numerator / Y_denominator)
return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (X_value + Y_value)))
if __name__ == "__main__":
import doctest
doctest.testmod()
```