Class SatelliteTracking

All Implemented Interfaces:
Serializable, Parameterized, LenientComparable, org.opengis.referencing.operation.MathTransform, org.opengis.referencing.operation.MathTransform2D

public class SatelliteTracking extends NormalizedProjection
Satellite-Tracking projection. This projection has been developed in 1977 by Snyder and has no associated EPSG code. This projection is neither conformal or equal-area, but has the property that ground tracks for satellites orbiting the Earth with the same orbital parameters are shown as straight lines on the map. Other properties are (Snyder 1987):
  • All meridians are equally spaced straight lines. They are parallel on cylindrical form and converging to a common point on conical form.
  • All parallels are straight but unequally spaced. They are parallel on cylindrical form and are concentric circular arcs on conical form.
  • Conformality occurs along two chosen parallels. Scale is correct along one of these parameters on the conical form and along both on the cylindrical form.

Limitations

This map projection supports only circular orbits. The Earth is assumed spherical. Areas close to poles cannot be mapped.

References

John P. Snyder., 1987. Map Projections - A Working Manual chapter 28: Satellite-tracking projections.
Since:
1.1
Version:
1.3
See Also:
  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      For cross-version compatibility.
      See Also:
    • cos_i

      private final double cos_i
      Sines and cosines of inclination between the plane of the Earth's Equator and the plane of the satellite orbit. The angle variable name is i in Snyder's book.
      See Also:
    • sin_i

      private final double sin_i
      Sines and cosines of inclination between the plane of the Earth's Equator and the plane of the satellite orbit. The angle variable name is i in Snyder's book.
      See Also:
    • cos2_i

      private final double cos2_i
      Sines and cosines of inclination between the plane of the Earth's Equator and the plane of the satellite orbit. The angle variable name is i in Snyder's book.
      See Also:
    • p2_on_p1

      private final double p2_on_p1
      Ratio of satellite orbital period (P₂) over ascending node period (P₁).
      See Also:
    • n

      private final double n
      Coefficients for the Conic Satellite-Tracking Projection. Those values are Double.NaN in the cylindrical case.
    • s0

      private final double s0
      Coefficients for the Conic Satellite-Tracking Projection. Those values are Double.NaN in the cylindrical case.
    • isConic

      private final boolean isConic
      true if this projection is conic, or false if cylindrical or unknown.
  • Constructor Details

    • SatelliteTracking

      public SatelliteTracking(org.opengis.referencing.operation.OperationMethod method, Parameters parameters)
      Creates a Satellite Tracking projection from the given parameters.
      Parameters:
      method - description of the projection parameters.
      parameters - the parameter values of the projection to create.
      Throws:
      org.opengis.parameter.InvalidParameterValueException - if some parameters have incompatible values.
    • SatelliteTracking

      private SatelliteTracking(Initializer initializer)
      Work around for RFE #4093999 in Sun's bug database ("Relax constraint on placement of this()/super() call in constructors").
  • Method Details

    • initializer

      @Workaround(library="JDK", version="1.8") static Initializer initializer(org.opengis.referencing.operation.OperationMethod method, Parameters parameters)
      Work around for RFE #4093999 in Sun's bug database ("Relax constraint on placement of this()/super() call in constructors").
    • createMapProjection

      public org.opengis.referencing.operation.MathTransform createMapProjection(org.opengis.referencing.operation.MathTransformFactory factory) throws org.opengis.util.FactoryException
      Returns the sequence of normalizationthisdenormalization transforms as a whole. The transform returned by this method expects (longitude, latitude) coordinates in degrees and returns (x,y) coordinates in metres.
      Overrides:
      createMapProjection in class NormalizedProjection
      Parameters:
      factory - The factory to use for creating the transform.
      Returns:
      the map projection from (λ,φ) to (x,y) coordinates.
      Throws:
      org.opengis.util.FactoryException - if an error occurred while creating a transform.
      See Also:
    • getInternalParameterNames

      final String[] getInternalParameterNames()
      Returns the names of additional internal parameters which need to be taken in account when comparing two SatelliteTracking projections or formatting them in debug mode.
      Overrides:
      getInternalParameterNames in class NormalizedProjection
    • getInternalParameterValues

      final double[] getInternalParameterValues()
      Returns the values of additional internal parameters which need to be taken in account when comparing two SatelliteTracking projections or formatting them in debug mode.
      Overrides:
      getInternalParameterValues in class NormalizedProjection
    • F

      private double F(double cos2_φ, org.opengis.parameter.ParameterDescriptor<Double> source)
      Computes the F₁ or F₂ coefficient using Snyder equation 28-9. Note that this is the same equation than F₁′ in above cylindrical case, but with the addition of arc-tangent. This value is constant after construction time.
      Parameters:
      cos2_φ - square of cosine of φ₁ or φ₂.
      source - description of φ argument. Used for error message only.
      Returns:
      F coefficient for the given φ latitude.
    • L

      private double L(double sinφ, org.opengis.parameter.ParameterDescriptor<Double> source)
      Computes the L₀, L₁ or L₂ coefficient using Snyder equation 28-2a to 28-4a. This value is constant after construction time.
      Parameters:
      sinφ - sine of φ₀, φ₁ or φ₂.
      source - description of φ argument. Used for error message only.
      Returns:
      L coefficient for the given φ latitude.
    • invalid

      private org.opengis.parameter.InvalidParameterValueException invalid(org.opengis.parameter.ParameterDescriptor<Double> source)
      Returns an exception for a latitude parameter out of range. The range is assumed given by satellite orbit inclination.
      Parameters:
      source - description of invalid φ argument.
    • transform

      public org.opengis.referencing.operation.Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws ProjectionException
      Projects the specified (λ,φ) coordinates and stores the result in dstPts. In addition, opportunistically computes the projection derivative if derivate is true. The units of measurement are implementation-specific (see super-class javadoc). The results must be multiplied by the denormalization matrix before to get linear distances.

      The y axis lies along the central meridian λ₀, y increasing northerly, and x axis intersects perpendicularly at latitude of origin φ₀, x increasing easterly.

      Specified by:
      transform in class NormalizedProjection
      Parameters:
      srcPts - the array containing the source point coordinates, as (longitude, latitude) angles in radians.
      srcOff - the offset of the single coordinate tuple to be converted in the source array.
      dstPts - the array into which the converted coordinates is returned (may be the same than srcPts). Coordinates will be expressed in a dimensionless unit, as a linear distance on a unit sphere or ellipse.
      dstOff - the offset of the location of the converted coordinates that is stored in the destination array.
      derivate - true for computing the derivative, or false if not needed.
      Returns:
      the matrix of the projection derivative at the given source position, or null if the derivate argument is false.
      Throws:
      ProjectionException - if the coordinates cannot be converted.
      See Also:
    • inverseTransform

      protected void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) throws ProjectionException
      Transforms the specified (x,y) coordinates and stores the result in dstPts (angles in radians).
      Specified by:
      inverseTransform in class NormalizedProjection
      Parameters:
      srcPts - the array containing the source point coordinates, as linear distance on a unit sphere or ellipse.
      srcOff - the offset of the point to be converted in the source array.
      dstPts - the array into which the converted point coordinates is returned (may be the same than srcPts). Coordinates will be (longitude, latitude) angles in radians.
      dstOff - the offset of the location of the converted point that is stored in the destination array.
      Throws:
      ProjectionException - if the coordinates cannot be converted.