Debugging Quaternions

This workflow demonstrates how to debug quaternion orientations by moving a satellite, adding points of interest, and calculating angles to verify the orientation. The process involves positioning the satellite, creating a reference point, and analyzing the angle between a line and the satellite's local axis.

Here is the full code for the workflow which you can copy/paste directly into the integrated editor and click on excute.

let satellitePosition = [62.0, 34.0, 500.0];
mov("sat", satellitePosition, true);

let pointOfInterestCoords = geo2xyz([60.186, 24.828, 0]);
addPoint("KS", pointOfInterestCoords);

createLine("sat2KS", "sat", "KS");

let rotationQuaternion = [-0.6313439, -0.1346824, -0.6313439, -0.4297329];
rot("sat", rotationQuaternion);

let angle_between_pointing_and_target = angle(
     "sat2KS", point("sat").frame.z
);

log(angle_between_pointing_and_target);

Let’s break that down with additional details about what happens under the hood.

By default, an OrientedPoint named sat is created for convenience. This represents a satellite and is initialized with a default position and orientation. This saves time for workflows that require a satellite as a starting point.

1. Position the Satellite

Move the default point (sat) near Helsinki using the mov command. The latitude is 62°, the longitude is 34°, and the altitude is 500 km. The true parameter specifies that the provided coordinates are geographic (latitude, longitude, altitude) instead of Earth-Centered, Earth-Fixed (ECEF) coordinates provided in xyz form.

let satellitePosition = [62.0, 34.0, 500.0];
mov("sat", satellitePosition, true);

2. Define a Point of Interest

Convert the geographic coordinates (60.186°N, 24.828°E, 0 m altitude) to ECEF coordinates using geo2xyz. Add a point (KS) at the calculated location. When a point is added using the addPoint function, it is registered with the provided name (in this case, KS), so it can be referred to later.

let pointOfInterestCoords = geo2xyz([60.186, 24.828, 0]);
addPoint("KS", pointOfInterestCoords);

3. Connect the Satellite and Point

Create a line (sat2KS) between the satellite and the point of interest to visualize their connection. The createLine function can take either:

• The names of registered points (e.g., "sat" and "KS")
• Raw ECEF coordinates (tuples of three numbers)

Here, we use the registered points for simplicity and clarity.

createLine("sat2KS", "sat", "KS");

4. Rotate the Satellite and Analyze Orientation

1. Apply a quaternion rotation (rotationQuaternion) to simulate an incorrect satellite orientation using the rot function.
2. Calculate the angle between the satellite's z-axis and the line sat2KS. The point function retrieves the OrientedPoint registered as sat. This object provides access to the frame property, which describes the local axes of the satellite.
3. Log it to the integrated console using the log function.

let rotationQuaternion = [-0.6313439, -0.1346824, -0.6313439, -0.4297329];
rot("sat", rotationQuaternion);

let angle_between_pointing_and_target = angle(
     "sat2KS", point("sat").frame.z
);

log(angle_between_pointing_and_target);

Alternatively, we could have defined the first argument of angle using the special notation point_name_start->point_name_end, which in this case would've resulted on sat->ks. Like this we would have defined the vector for the angle calculation without having to explicitly create a line. We did the latter so that an actual line would be drawn on the scene.