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cwhanse merged 2 commits into from
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edit the transformations page, add geographic to pvcollada example #77

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edit the transformations, add geo to pvc example
cwhanse Jun 16, 2026
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Update docs/pvcollada_coordinate_transformation_with_diagram.md
cwhanse Jun 16, 2026
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121 changes: 84 additions & 37 deletions docs/pvcollada_coordinate_transformation_with_diagram.md
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@

# PVCollada Coordinate Transformation Guide
# Guide to Coordinates and Coordinate Transformations

## ENU Coordinate Frame

Expand All @@ -14,44 +14,31 @@ latitude, longitude and altitude stored in the COLLADA document.

## Example Geometry

Cube definition in local coordinates:
We'll illustrate coordinates and transformations using a cube defined in PVCollada's local coordinates:

- lower corner `(1,1,1)`
- size `(3,2,1)`

Assume that the topocentric coordinate origin is at the this geolocation:
![PVCollada cube](pvcollada_cube_diagram.png)


## From Local ENU to Geographic Coordinates

Assume that the topocentric coordinate origin is at this geolocation in the WGS84 datum:

- Albuquerque, NM, USA
- Latitude `35.0845`
- Longitude `-106.651`
- Altitude `1619`
- Projection `EPSG:32613`

## Diagram

![PVCollada cube](pvcollada_cube_diagram.png)

The diagram shows the cube in the local coordinate system along with the ENU axes.
- Projection `EPSG:4326`

## Computed Geographic Coordinates
EPSG:4326 is the identifier for the WGS-84 geographic coordinate system.

The geocoordinate of the cube are computed using the python library pymap3d.
The WGS-84 geocoordinates of the cube can be computed using either the pymap3d or pyproj.

| x | y | z | latitude | longitude | altitude |
|-----------:|-----------:|-----------:|------------:|--------------:|--------------:|
| 1.00000000 | 1.00000000 | 1.00000000 | 35.08450901 | -106.65098904 | 1620.00000016 |
| 4.00000000 | 1.00000000 | 1.00000000 | 35.08453605 | -106.65098904 | 1620.00000134 |
| 1.00000000 | 3.00000000 | 1.00000000 | 35.08450901 | -106.65096711 | 1620.00000078 |
| 4.00000000 | 3.00000000 | 1.00000000 | 35.08453605 | -106.65096711 | 1620.00000196 |
| 1.00000000 | 1.00000000 | 2.00000000 | 35.08450901 | -106.65098904 | 1621.00000016 |
| 4.00000000 | 1.00000000 | 2.00000000 | 35.08453605 | -106.65098904 | 1621.00000134 |
| 1.00000000 | 3.00000000 | 2.00000000 | 35.08450901 | -106.65096711 | 1621.00000078 |
| 4.00000000 | 3.00000000 | 2.00000000 | 35.08453605 | -106.65096711 | 1621.00000196 |

## Python Examples
### Using pymap3d

```python
# Using pymap3d

import pandas as pd
import pymap3d as pm
Expand All @@ -61,7 +48,7 @@ lon0 = -106.651
alt0 = 1619.0

# Local coordinates of corners of the cube
coords = pd.DataFrame(
topocentric_coords = pd.DataFrame(
columns=['x', 'y', 'z'],
data=[[1., 1., 1.],
[4., 1., 1.],
Expand All @@ -74,21 +61,35 @@ coords = pd.DataFrame(
)

# Translate the cube to geocoordinates
# pymap3d.enu2geodetic uses WGS-84 by default. We'll specify a datum to show how
# it is done.

datum = pm.Ellipsoid.from_name('wgs84')

lat, lon, alt = pm.enu2geodetic(coords['y'], coords['x'], coords['z'],
lat0, lon0, alt0)
lat0, lon0, alt0, ell=datum)

coords['lat'] = lat
coords['lon'] = lon
coords['alt'] = alt
geodetic_coords = pd.DataFrame({'lat': lat, 'lon': lon, 'alt': alt})

print('Topocentric to Geodetic coordinates')
print(coords.to_markdown(index=False))
print('Topocentric to Geodetic coordinates using pymap3d')
print(geodetic_coords.to_markdown(index=False, floatfmt=".8f"))

```
Topocentric to Geodetic coordinates using pymap3d
| lat | lon | alt |
|------------:|--------------:|--------------:|
| 35.08450901 | -106.65098904 | 1620.00000016 |
| 35.08453605 | -106.65098904 | 1620.00000134 |
| 35.08450901 | -106.65096711 | 1620.00000078 |
| 35.08453605 | -106.65096711 | 1620.00000196 |
| 35.08450901 | -106.65098904 | 1621.00000016 |
| 35.08453605 | -106.65098904 | 1621.00000134 |
| 35.08450901 | -106.65096711 | 1621.00000078 |
| 35.08453605 | -106.65096711 | 1621.00000196 |

### Using pyproj

```python
# Using pyproj

import pandas as pd
import pyproj
Expand Down Expand Up @@ -132,11 +133,57 @@ coords = pd.DataFrame(
lon, lat, alt = transformer.transform(
coords['x'], coords['y'], coords['z'])

coords['latitude'] = lat
coords['longitude'] = lon
coords['altitude'] = alt
geodetic_coords = pd.DataFrame({'lat': lat, 'lon': lon, 'alt': alt})

print('Topocentric to Geodetic coordinates using pymap3d')
print(geodetic_coords.to_markdown(index=False, floatfmt=".8f"))

```

## From Geographic or Projected Coordinates to PVCollada ENU

We'll show how we can reverse the above transformation, from WGS-84 geographic coordinates to PVCollada's ENU coordinates,
using either pymap3d or pyproj.

### Using pymap3d

print('Topocentric to Geodetic coordinates')
```python

import numpy as np
import pandas as pd
import pymap3d as pm


geocoords = pd.DataFrame(
columns=['lat', 'lon', 'alt'],
data = np.array(
[[35.08450901, -106.65098904, 1620.00000016],
[35.08453605, -106.65098904, 1620.00000134],
[35.08450901, -106.65096711, 1620.00000078],
[35.08453605, -106.65096711, 1620.00000196],
[35.08450901, -106.65098904, 1621.00000016],
[35.08453605, -106.65098904, 1621.00000134],
[35.08450901, -106.65096711, 1621.00000078],
[35.08453605, -106.65096711, 1621.00000196]]
)
)

# origin of ENU coordinates
lat0 = 35.0845
lon0 = -106.651
alt0 = 1619.0
datum = pm.Ellipsoid.from_name('wgs84')

x, y, z = pm.geodetic2enu(
geocoords['lat'], geocoords['lon'], geocoords['alt'],
lat0, lon0, alt0, ell=datum
)

# put x, y, z into a DataFrame for convenient printing
enucoords = pd.DataFrame({'x': x, 'y': y, 'z': z})

print('Geodetic to Topocentric coordinates using pymap3d')
print(coords.to_markdown(index=False, floatfmt=".8f"))

```