Inverse Location

The aim of this tutorial is to compute the inverse location of a point on Earth in order to give the sensor pixel, with the associated line, seeing this point.

We will also explain how to find the date at which sensor sees a ground point, which is a kind of inverse location only focusing on date.

Inverse location of a point on Earth

The initialization of Rugged is similar as in the Direct location tutorial up to rugged initialization..

Point defined by its latitude, longitude and altitude

Once Rugged initialized, one can compute the line number and the pixel number of a point defined by its Geodetic coordinates:

```import org.orekit.bodies.GeodeticPoint;
import org.orekit.rugged.linesensor.SensorPixel;
GeodeticPoint gp = new GeodeticPoint(latitude, longitude, altitude);
SensorPixel sensorPixel = rugged.inverseLocation(sensorName, gp, minLine, maxLine);
```

where minLine (maxLine, respectively) is the minimum line number for the search interval (maximum line number, respectively).

The inverse location will give the sensor pixel number and the associated line number seeing the point on ground. In case the point cannot be seen between the prescribed line numbers, the return result is null. No exception will be thrown in this particular case.

Point defined by its latitude and longitude (no altitude)

Similarly, one can compute the line number and the pixel number of a point defined solely by its latitude en longitude. The altitude will be determined automatically with the DEM.

``` SensorPixel sensorPixel = rugged.inverseLocation(sensorName, latitude, longitude, minLine, maxLine);
```

Date location

Once Rugged initialized, one can compute the date at which sensor sees a point on Earth.

Point defined by its latitude, longitude and altitude

For a point defined by its Geodetic coordinates:

``` AbsoluteDate dateLine = rugged.dateLocation(sensorName, gp, minLine, maxLine);
```

Point defined by its latitude and longitude (no altitude)

Similarly, for a point defined solely by its latitude en longitude (altitude determined automatically with the DEM):

``` AbsoluteDate dateLine = rugged.dateLocation(sensorName, latitude, longitude, minLine, maxLine);
```

Determine the min/max lines interval

Rugged provides a way to determine a very rough estimation of the line using only the position-velocities of the satellite. It assumes the position-velocities are regular enough and without holes.

``` OneAxisEllipsoid oneAxisEllipsoid = ruggedBuilder.getEllipsoid();
Frame pvFrame = ruggedBuilder.getInertialFrame();
RoughVisibilityEstimator roughVisibilityEstimator= new RoughVisibilityEstimator(oneAxisEllipsoid, pvFrame, satellitePVList);
```

One can compute the approximated line with the rough visibility estimator:

``` AbsoluteDate roughLineDate = roughVisibilityEstimator.estimateVisibility(gp);
double roughLine = lineSensor.getLine(roughLineDate);
```

The result will never be null, but may be really far from reality if ground point is away from trajectory. With this rough line, taken some margin around (for instance 100), one can initialize the min/max lines as search boundaries for inverse location, taken into account sensor min and max lines:

``` int minLineRough = (int) FastMath.max(FastMath.floor(roughLine - margin), sensorMinLine);
int maxLineRough = (int) FastMath.min(FastMath.floor(roughLine + margin), sensorMaxLine);
```

then one can compute the inverse location:

``` SensorPixel sensorPixel = rugged.inverseLocation(sensorName, gp, minLineRough, maxLineRough);
```

Source code

The source code is available in InverseLocation.java (package fr.cs.examples under src/tutorials)

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