transforms84 1.0.0

Geographic system transformations with helper functions

transforms84

Python library for geographic system transformations with additional helper functions.

This package focuses on:

1. Performance
2. Support for different matrix shapes:
   • Ideal point shape of (3,1), (nPoints,3,1) (as well as (3,) and (nPoints,3))
   • Separate input array for each axis in the coordinate system of size (nPoints,)
3. Functions that adapt to differing input matrices shapes: one-to-one, many-to-many and one-to-many points. See below for an example.

Installation

pip install transforms84

Operations

Coordinate Transformations

The following coordinate transformations have been implemented:

• geodetic → ECEF 🔗
• ECEF → geodetic 🔗
• ECEF → ENU 🔗
• ENU → ECEF 🔗
• ENU → AER 🔗
• AER → ENU 🔗
• ECEF → NED 🔗 🔗
• NED → ECEF 🔗 🔗
• NED → AER 🔗 🔗
• AER → NED 🔗 🔗
• geodetic → UTM 🔗
• UTM → geodetic 🔗

Velocity Transformations

The following velocity transformations have been implemented:

• ECEF → NED
• NED → ECEF
• ENU → ECEF
• ECEF → ENU

Distances

The following distance formulae have been implemented:

• Haversine 🔗

Additional Functions

The following functions have been implemented:

• Angular difference (smallest and largest)
• [rad, rad, X] → [deg, deg, X]
• [deg, deg, X] → [rad, rad, X]

Examples

See the Jupyter notebooks in examples to see how to use the transform84. Run pip install transforms84[examples] to run the examples locally.

Many-to-many & one-to-many

The transforms.ECEF2ENU transformation accepts same and differing matrix shape sizes. Below showcases the many-to-many method where three target points, rrm_target, in the geodetic coordinate system are transformed to the local ENU coordinate system about the point rrm_local, where both matrices are of shape (3, 3, 1):

>> import numpy as np
>> from transforms84.systems import WGS84
>> from transforms84.helpers import DDM2RRM
>> from transforms84.transforms import ECEF2ENU, geodetic2ECEF
>>
>> rrm_local = DDM2RRM(
>>     np.array(
>>         [[[30], [31], [0]], [[30], [31], [0]], [[30], [31], [0]]], dtype=np.float64
>>     )
>> )  # convert each point from [deg, deg, X] to [rad, rad, X]
>> rrm_target = DDM2RRM(
>>     np.array(
>>         [[[31], [32], [0]], [[31], [32], [0]], [[31], [32], [0]]], dtype=np.float64
>>     )
>> )
>> ECEF2ENU(
>>     rrm_local, geodetic2ECEF(rrm_target, WGS84.a, WGS84.b), WGS84.a, WGS84.b
>> )  # geodetic2ECEF -> ECEF2ENU
array(
    [
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
    ]
)

We can achieve the same result using the one-to-many method with a single local point of shape (3, 1):

>> rrm_local_one_point = DDM2RRM(np.array([[30], [31], [0]], dtype=np.float64))
>> ECEF2ENU(rrm_local_one_point, geodetic2ECEF(rrm_target, WGS84.a, WGS84.b), WGS84.a, WGS84.b)
array(
    [
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
        [[95499.41373564], [111272.00245298], [-1689.19916788]],
    ]
)

Again, we can achieve the same result by splitting the arrays over each coordiante system axis:

>> rad_lat_target = np.deg2rad(np.array([31, 31, 31], dtype=np.float64))
>> rad_lon_target = np.deg2rad(np.array([32, 32, 32], dtype=np.float64))
>> m_alt_target = np.array([0, 0, 0], dtype=np.float64)
>> rad_lat_origin = np.deg2rad(np.array([30, 30, 30], dtype=np.float64))
>> rad_lon_origin = np.deg2rad(np.array([31, 31, 31], dtype=np.float64))
>> m_alt_origin = np.array([0, 0, 0], dtype=np.float64)
>> ECEF2ENU(
      rad_lat_origin,
      rad_lon_origin,
      m_alt_origin,
      *geodetic2ECEF(rad_lat_target, rad_lon_target, m_alt_target, WGS84.a, WGS84.b),
      WGS84.a,
      WGS84.b,
  )
(
    array([95499.41373564, 95499.41373564, 95499.41373564]),
    array([111272.00245298, 111272.00245298, 111272.00245298]),
    array([-1689.19916788, -1689.19916788, -1689.19916788]),
)

World Geodetic Systems Standards

transforms84.systems includes the WGS84 class, which is the WGS 84 version of the standard. Other standards can be created:

>> from transforms84.systems import WGS, WGS72
>> WGS72 == WGS(6378135.0, 6356750.520016094)
True

Helpful Resources

...in no particular order:

• Geographic coordinate conversion
• Local tangent plane coordinates
• Coordinate systems for navigation
• Fundamental coordinate system concepts
• Coordinate systems for modeling
• Coordinate systems for display

Contributing

PRs are always welcome and appreciated!

After forking the repo install the dev requirements: pip install -e .[dev].