Datum Transformation¶

GeodePy has the ability to tranform between datums. Here we will discuss how to change between datums without changing the reference epoch while in the time dependant tutorial we will discuss changing epochs. To learn more about transformation refer to the GDA2020 technical manual.

Common Example¶

The most common example for datum transformation is converting from MGA94 to MGA2020. This is handled by a function in the transformation module that converts the grid input to a caresian coordinate (xyz), and then runs a 7 paramter helmert transformation using the gda94_to_gda2020 transformation constant. This process will be explored more in the latter part of this tutorial but first lets use this function.

Begin by importing GeodePy.

import geodepy.transform

Next, define some coordinate values in MGA94.

zone_94 = 55
east_94 = 696053.3373
north_94 = 6086610.1338

Now, transform this coordinate to MGA2020.

(zone_20, east_20, north_20, _, _) = geodepy.transform.transform_mga94_to_mga2020(
    zone_94,
    east_94,
    north_94
)

print(zone_20, east_20, north_20)

>>55 696053.872 6086611.549

This it the MGA2020 coordinates.

To complete this transformation a function from the transformation module was used. This will not always be the case. In the next section transformations where a function is not already present will be explored.

Constructing a new Transformation Function¶

Here we will explore how to complete a transformation between datums without a dedicated function. We will then create a new function for this new transformation. Here we are going to transform from AGD84 to GDA2020.

First import GeodePy.

import geodepy.transform
import geodepy.constants
import geodepy.angles

Now we need some starting coordinates.

lat = geodepy.angles.DMSAngle(-23,33,25.21)
long = geodepy.angles.DMSAngle(133,49,13.87)
height = 427.863

print(f"The AGD84 position is {lat}, {long}, {height}"

>>The AGD84 position is -23 33 25.21, 133 49 13.87, 427.863

All transformations in GeodePy need to be completed with corrdinates in cartesian (xyz) form. Lets transform to xyz.

x, y, z = geodepy.transform.llh2xyz(lat, long, height)
print(x, y, z)

>>-4050634.051819 4220935.13646 -2533555.369303

Now we need some transformation parameters. Within Geodepy there are many transformaton parameters already present within the constants module. A table of these can be seen here. If the transformation needed isn’t currently in Geodepy, new transformations can be added using the transformation class. Here the agd66_to_gda94 transformation will be used.

print(geodepy.constants.agd84_to_gda94)

>>Transformation: From 'AGD84' to 'GDA94'
>>Reference Epoch: 0
>>tx: -117.763m + 0.0m/yr
>>ty: -51.51m + 0.0m/yr
>>tz: 139.061m + 0.0m/yr
>>sc: -0.191ppm + 0.0ppm/yr
>>rx: -0.292" + 0.0"/yr
>>ry: -0.443" + 0.0"/yr
>>rz: -0.277" + 0.0"/yr

These transformation parameters will be used to complete a 7 paramter helmert transformation.

x_94, y_94, z_94, _ = geodepy.transform.conform7(
    x,
    y,
    z,
    geodepy.constants.agd84_to_gda94 #transformation parameters
)
print(x_94, y_94, z_94)

>>-4050762.150962 4220880.96717 -2533401.14935

Tip

The “_” in the conform7 variables is for a vcv matrix. If you dont input a vcv matrix then the resulting variable will be None. However as the variable needs to be assigned for the function to work using “_” meets to requirement but doesn’t store the variable in a meaningful way.

Now we need to transform from GDA94 to GDA2020 using the same method but with the gda94_to_gda2020 transformation class.

x_20, y_20, z_20, _ = geodepy.transform.conform7(
    x_94,
    y_94,
    z_94,
    geodepy.constants.gda94_to_gda2020 #transformation parameters
)

print(x_20, y_20, z_20)

>>-4050763.124034 4220880.75310 -2533399.713463

Now the cartesian coordinates can be converted back to geographic coordinates (lat, long)

lat_20, long_20, height_20 = geodepy.transform.xyz2llh(x_20, y_20, z_20)

print(f"The GDA2020 position is
{geodepy.angles.dec2dms(lat_20)},
{geodepy.angles.dec2dms(long_20)},
{height_20}")

>>The GDA2020 position is -23 33 19.921108332, 133 49 18.481110119, 411.61055134

All of this can now be combined into one function.

def transform_agd84_to_gda2020(lat, long, height):

    x, y, z = geodepy.transform.llh2xyz(lat, long, height)
    x_94, y_94, z_94, _ = geodepy.transform.conform7(
        x, y, z,
        geodepy.constants.agd84_to_gda94
    )
    x_20, y_20, z_20, _ = geodepy.transform.conform7(
        x_94, y_94, z_94,
        geodepy.constants.gda94_to_gda2020
    )

    return geodepy.transform.xyz2llh(x_20, y_20, z_20)

lat_new, long_new, height_new = transform_agd84_to_gda2020(lat, long, height)

print(f"The GDA2020 position is
    {geodepy.angles.dec2dms(lat_new)},
    {geodepy.angles.dec2dms(long_new)},
    {height_new}")

>>The GDA2020 position is -23 33 19.921108332, 133 49 18.481110119, 411.61055134