transforms84

Python library for geographic system transformations with additional helper functions.

This package focuses on:

1. Performance
2. Ideal mathematical shapes of (NumPy) matrices: (3,1) or (nPoints,3,1). Shapes (3,) and (nPoints,3) are also supported.
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 🔗 🔗

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(
    [
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
    ]
)

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

>> rrm_local = DDM2RRM(np.array([[30], [31], [0]], dtype=np.float64))
>> ECEF2ENU(rrm_local, geodetic2ECEF(rrm_target, WGS84.a, WGS84.b), WGS84.a, WGS84.b)
array(
    [
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
        [[4.06379074e01], [-6.60007585e-01], [1.46643956e05]],
    ]
)

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].

Pre-commit hooks may be installed: pre-commit install --hook-type pre-commit --hook-type pre-push. This isn't required as pull requests are checked with tox and apply lint automatically.