Update readme

README.md

@@ -6,19 +6,14 @@
 
 Small geographic coordinate systems Python library with a few additional helper functions.
 
-This package focuses on performance, correct matrix shapes, single to many point functions and many to many point functions
-
 This package focuses on:
 1. Performance
 2. Input and output coordinates of ideal mathematical shapes. Ideally, all coordinates should be of shapes (3,1) or (nPoints,3,1), but shapes (3,) and (nPoints,3) are supported too.
-3. Functions that adapt to differing input matrices shapes: one-to-one, many-to-many and one-to-many points. See [here](examples/example1.ipynb) for an example.
+3. Functions that adapt to differing input matrices shapes: one-to-one, many-to-many and one-to-many points. See [below](#many-to-many--one-to-many) for an example.
 
 ## Installation
 `pip install transforms84`
 
-## Examples
-See the Jupyter notebooks in [examples](examples) to see how to use the transform84. Run `pip install transforms84[examples]` to run the examples locally.
-
 ## Operations
 ### Transformations
 The following transformations have been implemented:
@@ -39,5 +34,49 @@ The following functions have been implemented:
 - [rad, rad, X] → [deg, deg, X]
 - [deg, deg, X] → [rad, rad, X]
 
+## Examples
+See the Jupyter notebooks in [examples](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 ([WGS84](https://en.wikipedia.org/wiki/World_Geodetic_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([[[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]],
+
+       [[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]],
+
+       [[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]]])
+```
+
+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([[[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]],
+
+       [[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]],
+
+       [[ 4.06379074e+01],
+        [-6.60007585e-01],
+        [ 1.46643956e+05]]])
+```
+
 ## Contributing
-PRs are always welcome and appreciated!
+PRs are always welcome and appreciated! Please install the pre-commit hooks before making commits.