Sensor Projection

In this tutorial, we will demonstrate how to define a sensor geometry and project its trace onto the Earth.

Setup

Let's import the necessary dependencies:

import numpy as np
import pandas as pd

import plotly.graph_objs as go

from ostk.mathematics.geometry.d2 import Object as Object2d
from ostk.mathematics.geometry.d2.object import Point as Point2d
from ostk.mathematics.geometry.d2.object import Polygon as Polygon2d
from ostk.mathematics.geometry.d3.object import Point as Point3d
from ostk.mathematics.geometry.d3.object import Polygon as Polygon3d
from ostk.mathematics.geometry.d3.object import Pyramid

from ostk.physics.coordinate.spherical import LLA
from ostk.physics.coordinate import Frame
from ostk.physics import Environment
from ostk.physics.environment.object import Geometry

<frozen importlib._bootstrap>:241: FutureWarning: pybind11-bound class 'ostk.physics.coordinate.frame.provider.Dynamic' is using an old-style placement-new '__init__' which has been deprecated. See the upgrade guide in pybind11's docs. This message is only visible when compiled in debug mode.

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Computation

Scene

We first set up a simple scene, with the Earth only (the default Environment will suffice here):

environment = Environment.default();

Then, we access the Earth object (managed by the Environment):

earth = environment.access_object_with_name("Earth")

Once the Earth has been obtained, we can also get its geometry (an Ellipsoid, defined in ITRF in this case):

earth_geometry = earth.get_geometry_in(Frame.ITRF(), environment.get_instant())

Sensor

Let's define a pyramidal geometry:

apex = Point3d(7000e3, 0.0, 0.0)
base = Polygon3d(
    Polygon2d(
        [
            Point2d(-1.0, -1.0),
            Point2d(+1.0, -1.0),
            Point2d(+1.0, +1.0),
            Point2d(-1.0, +1.0),
        ]
    ),
    apex - np.array((0.8, 0.0, 0.0)),
    np.array((0.0, 1.0, 0.0)),
    np.array((0.0, 0.0, 1.0)),
)

pyramid = Pyramid(base, apex)

That we express in ITRF:

sensor_geometry = Geometry(pyramid, Frame.ITRF())

Intersection

Now that we have both Earth and sensor geometries clearly defined, we can compute their intersection:

intersection_ITRF = sensor_geometry.intersection_with(earth_geometry)

And convert this 3D intersection into a 2D set of geodetic points:

intersection_points = [
    Point2d(lla.get_longitude().in_degrees(), lla.get_latitude().in_degrees())
    for lla in [
        LLA.cartesian(
            point_ITRF.as_vector(),
            earth.get_equatorial_radius(),
            earth.get_flattening(),
        )
        for point_ITRF in intersection_ITRF.access_composite()
        .access_object_at(0)
        .as_line_string()
    ]
]

We further convert this set into a Pandas Dataframe, as a very convenient way for storing / managing data in Python:

intersection_df = pd.DataFrame(
    [
        [float(intersection_point.x()), float(intersection_point.y())]
        for intersection_point in intersection_points
    ],
    columns=["Longitude", "Latitude"],
);

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Visualization

Table:

intersection_df.head()

	Longitude	Latitude
0	-8.768110	-8.724722
1	-8.152081	-5.915811
2	-7.861134	-3.893096
3	-7.713082	-2.226165
4	-7.649110	-0.725557

Now, we're ready to visualize the intersection on a map!

figure = go.Figure(
    data=go.Scattergeo(
        lon=intersection_df["Longitude"],
        lat=intersection_df["Latitude"],
        mode="lines",
        line=dict(
            width=1,
            color="red",
        ),
    ),
    layout=go.Layout(
        title=None,
        showlegend=False,
        geo=dict(
            showland=True,
            landcolor="rgb(243, 243, 243)",
            countrycolor="rgb(204, 204, 204)",
        ),
        height=600,
        width=1200,
    ),
)

figure.show("svg")

It is also possible to obtain the WKT representation of the intersection polygon:

Polygon2d(intersection_points).to_string(Object2d.Format.WKT)

POLYGON((-8.76811 -8.72472,-8.15208 -5.91581,-7.86113 -3.8931,-7.71308 -2.22617,-7.64911 -0.725557,-7.64911 0.725557,-7.71308 2.22617,-7.86113 3.8931,-8.15208 5.91581,-8.76811 8.72472,-8.76811 8.72472,-5.93863 8.16636,-3.90611 7.90015,-2.23303 7.76406,-0.727714 7.70513,0.727714 7.70513,2.23303 7.76406,3.90611 7.90015,5.93863 8.16636,8.76811 8.72472,8.76811 8.72472,8.15208 5.91581,7.86113 3.8931,7.71308 2.22617,7.64911 0.725557,7.64911 -0.725557,7.71308 -2.22617,7.86113 -3.8931,8.15208 -5.91581,8.76811 -8.72472,8.76811 -8.72472,5.93863 -8.16636,3.90611 -7.90015,2.23303 -7.76406,0.727714 -7.70513,-0.727714 -7.70513,-2.23303 -7.76406,-3.90611 -7.90015,-5.93863 -8.16636,-8.76811 -8.72472,-8.76811 -8.72472))

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