public class ObliqueMercator extends MapProjection
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 "Oblique_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 equations 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 nontwo point
projections and will be set to the azimuth if not specified.
Projection cases and aliases implemented by the ObliqueMercator
are:
Oblique_Mercator
(EPSG code 9815)"rectified_grid_angle"
parameter.
Hotine_Oblique_Mercator_Azimuth_Center
(ESRI)Rectified_Skew_Orthomorphic_Center
(ESRI)"rectified_grid_angle"
parameter.
Hotine_Oblique_Mercator
(EPSG code 9812)"rectified_grid_angle"
parameter.
Hotine_Oblique_Mercator_Azimuth_Natural_Origin
(ESRI)Rectified_Skew_Orthomorphic_Natural_Origin
(ESRI)"rectified_grid_angle"
parameter.
Hotine_Oblique_Mercator_Two_Point_Center
(ESRI)Hotine_Oblique_Mercator_Two_Point_Natural_Origin
(ESRI)References:
libproj4
is available at libproj4 MiscellaneaPJ_omerc.c
, pj_tsfn.c
, pj_fwd.c
, pj_inv.c
and lib_proj.h
Modifier and Type  Class and Description 

static class 
ObliqueMercator.Provider
The math transform
provider for an Oblique Mercator projection (EPSG code 9815).

static class 
ObliqueMercator.Provider_TwoPoint
The math transform
provider for a Oblique Mercator projection, specified with two
points on the central line (instead of a central point and azimuth).

MapProjection.AbstractProvider
Modifier and Type  Field and Description 

protected double 
azimuth
The azimuth of the central line passing throught the centre of the projection, in radians.

protected double 
latitudeOfCentre
Latitude of the projection centre.

protected double 
longitudeOfCentre
Longitude of the projection centre.

protected double 
rectifiedGridAngle
The rectified bearing of the central line, in radians.

centralMeridian, en0, en1, en2, en3, en4, excentricity, excentricitySquared, falseEasting, falseNorthing, globalScale, invertible, isSpherical, latitudeOfOrigin, LOGGER, scaleFactor, semiMajor, semiMinor, SKIP_SANITY_CHECKS
SINGLE_LINE
Modifier  Constructor and Description 

protected 
ObliqueMercator(ParameterValueGroup parameters)
Constructs a new map projection from the supplied parameters.

Modifier and Type  Method and Description 

boolean 
equals(Object object)
Compares the specified object with this map projection for equality.

ParameterDescriptorGroup 
getParameterDescriptors()
Returns the parameter descriptors for this map projection.

ParameterValueGroup 
getParameterValues()
Returns the parameter values for this map projection.

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 Point2D 
inverseTransformNormalized(double x,
double y,
Point2D ptDst)
Transforms the specified coordinate and stores the result in
ptDst . 
protected Point2D 
transformNormalized(double x,
double y,
Point2D ptDst)
Transforms the specified coordinate and stores the result in
ptDst . 
checkReciprocal, getSourceDimensions, getTargetDimensions, inv_mlfn, inverse, mlfn, orthodromicDistance, resetWarnings, transform, transform, transform
createTransformedShape, derivative, derivative, ensureNonNull, formatWKT, getName, isIdentity, needCopy, normalizeAngle, rollLongitude, transform, transform, transform
cleanupThreadLocals, toString, toWKT, toWKT, toWKT, toWKT
createTransformedShape, derivative
derivative, isIdentity, toWKT, transform, transform, transform
protected final double latitudeOfCentre
MapProjection.latitudeOfOrigin
, but the
latitude of origin is the Earth equator on aposphere for the oblique mercator.protected final double longitudeOfCentre
MapProjection.centralMeridian
, which is the meridian where the central line intersects the Earth equator
on aposphere.
This parameter applies to the "azimuth" case only. It is set to NaN
for
the "two points" case.
protected final double azimuth
protected final double rectifiedGridAngle
"rectified_grid_angle"
parameter value
is not set.protected ObliqueMercator(ParameterValueGroup parameters) throws ParameterNotFoundException
parameters
 The parameter values in standard units.ParameterNotFoundException
 if a mandatory parameter is missing.public ParameterDescriptorGroup getParameterDescriptors()
MapProjection.getParameterValues()
, as well as arguments checking.getParameterDescriptors
in class MapProjection
null
.OperationMethod.getParameters()
public ParameterValueGroup getParameterValues()
getParameterValues
in class MapProjection
Operation.getParameterValues()
protected Point2D transformNormalized(double x, double y, Point2D ptDst) throws ProjectionException
ptDst
. This method is
usually (but not guaranteed) to be invoked with values of x in
the range [PI..PI]
and values of y in the range [PI/2..PI/2]
.
Values outside those ranges are accepted (sometime with a warning logged) on the assumption
that most implementations use those values only in trigonometric functions like sin and cos.
Coordinates have the MapProjection.centralMeridian
removed from lambda before this
method is invoked. After this method is invoked, the results in ptDst
are multiplied
by MapProjection.globalScale
, and the MapProjection.falseEasting
and MapProjection.falseNorthing
are added.
This means that projections that implement this method are performed on an ellipse (or
sphere) with a semimajor axis of 1.
In PROJ.4, the same standardization,
described above, is handled by pj_fwd.c
. Therefore when porting projections from
PROJ.4, the forward transform equations can be used directly here with minimal change. In the
equations of Snyder, MapProjection.falseEasting
, MapProjection.falseNorthing
and MapProjection.scaleFactor
are usually not given. When implementing these equations here, you will not need to remove
the MapProjection.centralMeridian
from lambda or apply the MapProjection.semiMajor
(a or R).
transformNormalized
in class MapProjection
x
 The longitude of the coordinate, in radians.y
 The latitude of the coordinate, in radians.ptDst
 the specified coordinate point that stores the result of transforming ptSrc
, or null
. Ordinates will be in a dimensionless unit, as a linear distance
on a unit sphere or ellipse.lambda
, phi
) and storing the
result in ptDst
.ProjectionException
 if the point can't be transformed.protected Point2D inverseTransformNormalized(double x, double y, Point2D ptDst) throws ProjectionException
ptDst
. This method
returns longitude as x values in the range [PI..PI]
and latitude as
y values in the range [PI/2..PI/2]
. It will be checked by the caller, so
this method doesn't need to performs this check.
Input coordinates have the MapProjection.falseEasting
and MapProjection.falseNorthing
removed and
are divided by MapProjection.globalScale
before this method is invoked. After this method is
invoked, the MapProjection.centralMeridian
is added to the x
results in ptDst
.
This means that projections that implement this method are performed on an ellipse (or
sphere) with a semimajor axis of 1.
In PROJ.4, the same standardization,
described above, is handled by pj_inv.c
. Therefore when porting projections from
PROJ.4, the inverse transform equations can be used directly here with minimal change. In the
equations of Snyder, MapProjection.falseEasting
, MapProjection.falseNorthing
and MapProjection.scaleFactor
are usually not given. When implementing these equations here, you will not need to add the
MapProjection.centralMeridian
to the output longitude or remove the MapProjection.semiMajor
(a or R).
inverseTransformNormalized
in class MapProjection
x
 The easting of the coordinate, linear distance on a unit sphere or ellipse.y
 The northing of the coordinate, linear distance on a unit sphere or ellipse.ptDst
 the specified coordinate point that stores the result of transforming ptSrc
, or null
. Ordinates will be in radians.x
, y
and storing the result
in ptDst
.ProjectionException
 if the point can't be transformed.protected double getToleranceForAssertions(double longitude, double latitude)
getToleranceForAssertions
in class MapProjection
longitude
 The longitude in decimal degrees.latitude
 The latitude in decimal degrees.public int hashCode()
hashCode
in class MapProjection
public boolean equals(Object object)
equals
in class MapProjection
object
 The object to compare with this transform.true
if the given object is a transform of the same class and if, given
identical source position, the transformed position would be the equals.Copyright © 1996–2018 Geotools. All rights reserved.