Package org.apache.sis.referencing.operation.projection

Class ObliqueStereographic

java.lang.Object
org.apache.sis.io.wkt.FormattableObject
org.apache.sis.referencing.operation.transform.AbstractMathTransform
org.apache.sis.referencing.operation.transform.AbstractMathTransform2D
org.apache.sis.referencing.operation.projection.NormalizedProjection
org.apache.sis.referencing.operation.projection.ObliqueStereographic
All Implemented Interfaces:
Serializable, Parameterized, LenientComparable, org.opengis.referencing.operation.MathTransform, org.opengis.referencing.operation.MathTransform2D
Direct Known Subclasses:
ObliqueStereographic.Spherical
public class ObliqueStereographic extends NormalizedProjection
Oblique Stereographic projection (EPSG code 9809). See the following references for an overview:

Description

The directions starting from the central point are true, but the areas and the lengths become increasingly deformed as one moves away from the center. This projection is frequently used for mapping polar areas, but can also be used for other limited areas centered on a point.

This projection involves two steps: first a conversion of geodetic coordinates to conformal coordinates (i.e. latitudes and longitudes on a conformal sphere), then a spherical stereographic projection. For this reason this projection method is sometimes known as "Double Stereographic".

Note: there is another method known as "Oblique Stereographic Alternative" or sometimes just "Stereographic". That alternative uses a simplified conversion computing the conformal latitude of each point on the ellipsoid. Both methods are considered valid but produce slightly different results. For this reason EPSG considers them as different projection methods.
Since:
0.7
Version:
1.3
See Also:

  • Field Details

    • serialVersionUID

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

    • χ0

      final double χ0
      Conformal latitude of origin (χ₀), together with its sine and cosine. In the spherical case, χ₀ = φ₀ (the geodetic latitude of origin).

    • sinχ0

      final double sinχ0
      Conformal latitude of origin (χ₀), together with its sine and cosine. In the spherical case, χ₀ = φ₀ (the geodetic latitude of origin).

    • cosχ0

      final double cosχ0
      Conformal latitude of origin (χ₀), together with its sine and cosine. In the spherical case, χ₀ = φ₀ (the geodetic latitude of origin).

    • c

      private final double c
      Parameters used in the conformal sphere definition. Those parameters are used in both the forward and inverse projection. If the user supplied ellipsoid is already a sphere, then those parameters are equal to 1.

    • n

      private final double n
      Parameters used in the conformal sphere definition. Those parameters are used in both the forward and inverse projection. If the user supplied ellipsoid is already a sphere, then those parameters are equal to 1.

    • g

      private final double g
      Parameters used in the inverse projection. More precisely g and h are used to compute intermediate parameters i and j, which are themselves used to compute conformal latitude and longitude.

    • h

      private final double h
      Parameters used in the inverse projection. More precisely g and h are used to compute intermediate parameters i and j, which are themselves used to compute conformal latitude and longitude.

  • Constructor Details

    • ObliqueStereographic

      public ObliqueStereographic(org.opengis.referencing.operation.OperationMethod method, Parameters parameters)
      Creates an Oblique Stereographic projection from the given parameters. The method argument can be the description of one of the following:
      • "Oblique Stereographic", also known as "Roussilhe".
      Parameters:
      method - description of the projection parameters.
      parameters - the parameter values of the projection to create.

    • ObliqueStereographic

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

    • ObliqueStereographic

      ObliqueStereographic(ObliqueStereographic other)
      Creates a new projection initialized to the same parameters than the given one.

  • Method Details

    • initializer

      @Workaround(library="JDK", version="1.7") private 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").

    • getInternalParameterNames

      final String[] getInternalParameterNames()
      Returns the names of additional internal parameters which need to be taken in account when comparing two ObliqueStereographic projections or formatting them in debug mode.

      We could report any of the internal parameters. But since they are all derived from φ₀ and the eccentricity and since the eccentricity is already reported by the super-class, we report only χ₀ as a representative of the internal parameters.

      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 ObliqueStereographic projections or formatting them in debug mode.
      Overrides:
      getInternalParameterValues in class NormalizedProjection

    • createMapProjection

      public org.opengis.referencing.operation.MathTransform createMapProjection(org.opengis.referencing.operation.MathTransformFactory factory) throws org.opengis.util.FactoryException
      Returns the sequence of normalization → this → denormalization transforms as a whole. The transform returned by this method expects (longitude, latitude) coordinates in degrees and returns (x,y) coordinates in metres.

      The non-linear part of the returned transform will be this transform, except if the ellipsoid is spherical. In the latter case, this transform may be replaced by a simplified implementation.

      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:

    • 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.
      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
      Converts 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 point cannot be converted.