org.geotools.referencing.operation.projection

Class IdrObliqueMercator

java.lang.Object

MapProjection

org.geotools.referencing.operation.projection.IdrObliqueMercator

public class IdrObliqueMercator
extends MapProjection

Oblique Mercator Projection. A conformal, oblique, cylindrical projection with the cylinder touching the ellipsoid (or sphere) along a great circle path (the central line). The Mercator and Transverse Mercator projections can be thought of as special cases of the oblique mercator, where the central line is along the equator or a meridian, respectively. The Oblique Mercator projection has been used in Switzerland, Hungary, Madagascar, Malaysia, Borneo and the panhandle of Alaska.

The Oblique Mercator projection uses a (U,V) coordinate system, with the U axis along the central line. During the forward projection, coordinates from the ellipsoid are projected conformally to a sphere of constant total curvature, called the 'aposphere', before being projected onto the plane. The projection coordinates are further convented to a (X,Y) coordinate system by rotating the calculated (u,v) coordinates to give output (x,y) coordinates. The rotation value is usually the same as the projection azimuth (the angle, east of north, of the central line), but some cases allow a separate rotation parameter.

There are two forms of the oblique mercator, differing in the origin of their grid coordinates. The Hotine_Oblique_Mercator (EPSG code 9812) has grid coordinates start at the intersection of the central line and the equator of the aposphere. The Oblique_Mercator (EPSG code 9815) is the same, except the grid coordinates begin at the central point (where the latitude of center and central line intersect). ESRI separates these two case by appending "Natural_Origin" (for the Hotine_Oblique_Mercator) and "Center" (for the Obique_Mercator) to the projection names.

Two different methods are used to specify the central line for the oblique mercator: 1) a central point and an azimuth, east of north, describing the central line and 2) two points on the central line. The EPSG does not use the two point method, while ESRI separates the two cases by putting "Azimuth" and "Two_Point" in their projection names. Both cases use the point where the "latitude_of_center" parameter crosses the central line as the projection's central point. The central meridian is not a projection parameter, and is instead calculated as the intersection between the central line and the equator of the aposphere.

For the azimuth method, the central latitude cannot be +- 90.0 degrees and the central line cannot be at a maximum or minimum latitude at the central point. In the two point method, the latitude of the first and second points cannot be equal. Also, the latitude of the first point and central point cannot be +- 90.0 degrees. Furthermore, the latitude of the first point cannot be 0.0 and the latitude of the second point cannot be - 90.0 degrees. A change of 10^-7 radians can allow calculation at these special cases. Snyder's restriction of the central latitude being 0.0 has been removed, since the equaitons appear to work correctly in this case.

Azimuth values of 0.0 and +- 90.0 degrees are allowed (and used in Hungary and Switzerland), though these cases would usually use a Mercator or Transverse Mercator projection instead. Azimuth values > 90 degrees cause errors in the equations.

The oblique mercator is also called the "Rectified Skew Orthomorphic" (RSO). It appears is that the only difference from the oblique mercator is that the RSO allows the rotation from the (U,V) to (X,Y) coordinate system to be different from the azimuth. This separate parameter is called "rectified_grid_angle" (or "XY_Plane_Rotation" by ESRI) and is also included in the EPSG's parameters for the Oblique Mercator and Hotine Oblique Mercator. The rotation parameter is optional in all the non-two point projections and will be set to the azimuth if not specified.

Projection cases and aliases implemented by the IdrObliqueMercator are:

• Oblique_Mercator (EPSG code 9815) - grid coordinates begin at the central point, has "rectified_grid_angle" parameter.
• Hotine_Oblique_Mercator_Azimuth_Center (ESRI) - grid coordinates begin at the central point.
• Rectified_Skew_Orthomorphic_Center (ESRI) - grid coordinates begin at the central point, has "rectified_grid_angle" parameter.
• Hotine_Oblique_Mercator (EPSG code 9812) - grid coordinates begin at the interseciton of the central line and aposphere equator, has "rectified_grid_angle" parameter.
• Hotine_Oblique_Mercator_Azimuth_Natural_Origin (ESRI) - grid coordinates begin at the interseciton of the central line and aposphere equator.
• Rectified_Skew_Orthomorphic_Natural_Origin (ESRI) - grid coordinates begin at the interseciton of the central line and aposphere equator, has "rectified_grid_angle" parameter.
• Hotine_Oblique_Mercator_Two_Point_Center (ESRI) - grid coordinates begin at the central point.
• Hotine_Oblique_Mercator_Two_Point_Natural_Origin (ESRI) - grid coordinates begin at the interseciton of the central line and aposphere equator.

References:

• libproj4 is available at libproj4 Miscellanea
  Relevent files are: PJ_omerc.c, pj_tsfn.c, pj_fwd.c, pj_inv.c and lib_proj.h
• 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 part 2, Version 24.
• Gerald Evenden, 2004, Documentation of revised Oblique Mercator

See Also:

Oblique Mercator projection on MathWorld, hotine_oblique_mercator on Remote Sensing, oblique_mercator on Remote Sensing

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	IdrObliqueMercator.Provider The org.geotools.referencing.operation.MathTransformProvider for an IdrObliqueMercator projection.
static class	IdrObliqueMercator.Provider_Hotine The org.geotools.referencing.operation.MathTransformProvider for a Hotine IdrObliqueMercator projection.
static class	IdrObliqueMercator.Provider_Hotine_TwoPoint The org.geotools.referencing.operation.MathTransformProvider for a Hotine IdrObliqueMercator projection, specified with two points on the central line (instead of a central point and azimuth).
static class	IdrObliqueMercator.Provider_TwoPoint The org.geotools.referencing.operation.MathTransformProvider for a IdrObliqueMercator projection, specified with two points on the central line (instead of a central point and azimuth).

Method Summary

Modifier and Type	Method and Description
boolean	equals(java.lang.Object object) Compares the specified object with this map projection for equality.
ParameterDescriptorGroup	getParameterDescriptors()
ParameterValueGroup	getParameterValues()
protected double	getToleranceForAssertions(double longitude, double latitude) Maximal error (in metres) tolerated for assertion, if enabled.
int	hashCode() Returns a hash value for this projection.
protected java.awt.geom.Point2D	inverseTransformNormalized(double x, double y, java.awt.geom.Point2D ptDst)
protected java.awt.geom.Point2D	transformNormalized(double x, double y, java.awt.geom.Point2D ptDst)

Methods inherited from class java.lang.Object

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

Method Detail

getParameterDescriptors

public ParameterDescriptorGroup getParameterDescriptors()

getParameterValues

public ParameterValueGroup getParameterValues()

transformNormalized

protected java.awt.geom.Point2D transformNormalized(double x,
                                                    double y,
                                                    java.awt.geom.Point2D ptDst)
                                             throws ProjectionException

Throws:

ProjectionException

inverseTransformNormalized

protected java.awt.geom.Point2D inverseTransformNormalized(double x,
                                                           double y,
                                                           java.awt.geom.Point2D ptDst)
                                                    throws ProjectionException

Throws:

ProjectionException

getToleranceForAssertions

protected double getToleranceForAssertions(double longitude,
                                           double latitude)

Maximal error (in metres) tolerated for assertion, if enabled.

Parameters:

longitude - The longitude in degrees.

latitude - The latitude in degrees.

Returns:

The tolerance level for assertions, in meters.

hashCode

public int hashCode()

Returns a hash value for this projection.

equals

public boolean equals(java.lang.Object object)

Compares the specified object with this map projection for equality.