org.geotools.referencing.operation.projection
Class Stereographic

java.lang.Object
  org.geotools.referencing.wkt.Formattable
      org.geotools.referencing.operation.transform.AbstractMathTransform
          org.geotools.referencing.operation.projection.MapProjection
              org.geotools.referencing.operation.projection.Stereographic

All Implemented Interfaces:

org.opengis.referencing.operation.MathTransform, org.opengis.referencing.operation.MathTransform2D, java.io.Serializable

Direct Known Subclasses:

StereographicOblique, StereographicPolar

public abstract class Stereographic

extends MapProjection

Stereographic Projection. 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 used to represent polar areas. It can be adapted for other areas having a circular form.

This implementation, and its subclasses, provides transforms for six cases of the stereographic projection:

• "Oblique_Stereographic" (EPSG code 9809), alias "Double_Stereographic" in ESRI software
• "Stereographic" in ESRI software (NOT EPSG code 9809)
• "Polar_Stereographic" (EPSG code 9810, uses a series calculation for the inverse)
• "Polar Stereographic (variant B)" (EPSG code 9829, uses a series calculation for the inverse)
• "Stereographic_North_Pole" in ESRI software (uses itteration for the inverse)
• "Stereographic_South_Pole" in ESRI software (uses itteration for the inverse)

Both the "Oblique_Stereographic" and "Stereographic" projections are "double" projections involving two parts: 1) a conformal transformation of the geographic coordinates to a sphere and 2) a spherical Stereographic projection. The EPSG considers both methods to be valid, but considers them to be a different coordinate operation methods.

The "Stereographic" case uses the USGS equations of Snyder. This employs a simplified conversion to the conformal sphere that computes the conformal latitude of each point on the sphere.

The "Oblique_Stereographic" case uses equations from the EPSG. This uses a more generalized form of the conversion to the conformal sphere; using only a single conformal sphere at the origin point. Since this is a "double" projection, it is sometimes called the "Double Stereographic". The "Oblique_Stereographic" is used in New Brunswick (Canada) and the Netherlands.

The "Stereographic" and "Double Stereographic" names are used in ESRI's ArcGIS 8.x product. The "Oblique_Stereographic" name is the EPSG name for the later only.

WARNING: Tests points calculated with ArcGIS's "Double Stereographic" are not always equal to points calculated with the "Oblique_Stereographic". However, where there are differences, two different implementations of these equations (EPSG guidence note 7 and libproj) calculate the same values as we do. Until these differences are resolved, please be careful when using this projection.

If a "latitude_of_origin" parameter is supplied and is not consistent with the projection classification (for example a latitude different from ±90? for the polar case), then the oblique or polar case will be automatically inferred from the latitude. In other words, the latitude of origin has precedence on the projection classification. If ommited, then the default value is 90?N for "Polar_Stereographic" and 0? for "Oblique_Stereographic".

Polar projections that use the series equations for the inverse calculation will be little bit faster, but may be a little bit less accurate. If a polar "latitude_of_origin" is used for the "Oblique_Stereographic" or "Stereographic", the itterative equations will be used for inverse polar calculations.

The "Polar Stereographic (variant B)", "Stereographic_North_Pole", and "Stereographic_South_Pole" cases include a "standard_parallel_1" parameter. This parameter sets the latitude with a scale factor equal to the supplied scale factor. The "Polar Stereographic (variant B)" recieves its "latitude_of_origin" paramater value from the hemisphere of the "standard_parallel_1" value.

References:

• John P. Snyder (Map Projections - A Working Manual,
  U.S. Geological Survey Professional Paper 1395, 1987)
• "Coordinate Conversions and Transformations including Formulas",
  EPSG Guidence Note Number 7, Version 19.
• Gerald Evenden. "Supplementary PROJ.4 Notes - Oblique Stereographic Alternative"
• Krakiwsky, E.J., D.B. Thomson, and R.R. Steeves. 1977. A Manual For Geodetic Coordinate Transformations in the Maritimes. Geodesy and Geomatics Engineering, UNB. Technical Report No. 48.
• Thomson, D.B., M.P. Mepham and R.R. Steeves. 1977. The Stereographic Double Projection. Geodesy and Geomatics Engineereng, UNB. Technical Report No. 46.

Since:

2.1

Version:

$Id: Stereographic.java 17672 2006-01-19 00:25:55Z desruisseaux $

Author:

Andr? Gosselin, Martin Desruisseaux, Rueben Schulz

See Also:

Stereographic projection on MathWorld, Polar_Stereographic, Oblique_Stereographic, Stereographic, Some Random Stereographic Issues, Serialized Form

Nested Class Summary

static class	Stereographic.Provider_North_Pole The MathTransformProvider for a Stereographic North Polar projection.
static class	Stereographic.Provider_Oblique The MathTransformProvider for a Stereographic Oblique projection.
static class	Stereographic.Provider_Polar_A The MathTransformProvider for a Stereographic Polar projection.
static class	Stereographic.Provider_Polar_B The MathTransformProvider for a Stereographic Polar (Variant B) projection.
static class	Stereographic.Provider_South_Pole The MathTransformProvider for a Stereographic North Polar projection.
static class	Stereographic.Provider_USGS The MathTransformProvider for a Stereographic (USGS equations) projection.

Nested classes inherited from class org.geotools.referencing.operation.projection.MapProjection

MapProjection.AbstractProvider

Field Summary

protected static short	EPSG Projection mode for switch statement.
protected static short	POLAR_A Projection mode for switch statement.
protected static short	POLAR_B Projection mode for switch statement.
protected static short	POLAR_NORTH Projection mode for switch statement.
protected static short	POLAR_SOUTH Projection mode for switch statement.
protected short	stereoType The type of stereographic projection, used for wkt parameters.
protected static short	USGS Projection mode for switch statement.

Fields inherited from class org.geotools.referencing.operation.projection.MapProjection

centralMeridian, excentricity, excentricitySquared, falseEasting, falseNorthing, globalScale, isSpherical, latitudeOfOrigin, scaleFactor, semiMajor, semiMinor

Method Summary

org.opengis.parameter.ParameterDescriptorGroup

getParameterDescriptors() Returns the parameter descriptors for this map projection. This is used for a providing a default implementation of MapProjection.getParameterValues(), as well as arguments checking.

Methods inherited from class org.geotools.referencing.operation.projection.MapProjection

equals, getParameterValues, getSourceDimensions, getTargetDimensions, getToleranceForAssertions, hashCode, inverse, inverseTransformNormalized, transform, transform, transform, transformNormalized

Methods inherited from class org.geotools.referencing.operation.transform.AbstractMathTransform

createTransformedShape, derivative, derivative, ensureNonNull, formatWKT, getDimSource, getDimTarget, isIdentity, needCopy, rollLongitude, transform

Methods inherited from class org.geotools.referencing.wkt.Formattable

toString, toWKT, toWKT, toWKT

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.opengis.referencing.operation.MathTransform2D

createTransformedShape, derivative

Methods inherited from interface org.opengis.referencing.operation.MathTransform

derivative, isIdentity, toWKT, transform

Field Detail

EPSG

protected static final short EPSG

Projection mode for switch statement.

See Also:

Constant Field Values

USGS

protected static final short USGS

Projection mode for switch statement.

See Also:

Constant Field Values

POLAR_A

protected static final short POLAR_A

Projection mode for switch statement.

See Also:

Constant Field Values

POLAR_B

protected static final short POLAR_B

Projection mode for switch statement.

See Also:

Constant Field Values

POLAR_NORTH

protected static final short POLAR_NORTH

Projection mode for switch statement.

See Also:

Constant Field Values

POLAR_SOUTH

protected static final short POLAR_SOUTH

Projection mode for switch statement.

See Also:

Constant Field Values

stereoType

protected short stereoType

The type of stereographic projection, used for wkt parameters.

Method Detail

getParameterDescriptors

public org.opengis.parameter.ParameterDescriptorGroup getParameterDescriptors()

Returns the parameter descriptors for this map projection. This is used for a providing a default implementation of MapProjection.getParameterValues(), as well as arguments checking.

Specified by:

getParameterDescriptors in class MapProjection