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java.lang.Objectorg.geotools.referencing.wkt.Formattable
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 ObliqueMercator are:
| Nested Class Summary | |
static class |
ObliqueMercator.Provider
The MathTransformProvider
for an ObliqueMercator projection. |
static class |
ObliqueMercator.Provider_Hotine
The MathTransformProvider
for a Hotine ObliqueMercator projection. |
static class |
ObliqueMercator.Provider_Hotine_TwoPoint
The MathTransformProvider
for a Hotine ObliqueMercator projection, specified with
two points on the central line (instead of a central point and azimuth). |
static class |
ObliqueMercator.Provider_TwoPoint
The MathTransformProvider
for a ObliqueMercator projection, specified with
two points on the central line (instead of a central point and azimuth). |
| Nested classes inherited from class org.geotools.referencing.operation.projection.MapProjection |
MapProjection.AbstractProvider |
| Field Summary |
| Fields inherited from class org.geotools.referencing.operation.projection.MapProjection |
centralMeridian, excentricity, excentricitySquared, falseEasting, falseNorthing, globalScale, isSpherical, latitudeOfOrigin, scaleFactor, semiMajor, semiMinor |
| Method Summary | |
boolean |
equals(java.lang.Object object)
Compares the specified object with this map projection for equality. |
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. |
org.opengis.parameter.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 java.awt.geom.Point2D |
inverseTransformNormalized(double x,
double y,
java.awt.geom.Point2D ptDst)
Transforms the specified coordinate and stores the result in . This method returns longitude as x values in the range and latitude as y values in the range . It will be checked by the caller, so this method doesn't need to performs this check.
Input coordinates are also guarenteed to have the
In PROJ.4, the same
standardization, described above, is handled by .
Therefore when porting projections from PROJ.4, the inverse transform
equations can be used directly here with minimal change.
In the equations of Snyder, |
protected java.awt.geom.Point2D |
transformNormalized(double x,
double y,
java.awt.geom.Point2D ptDst)
Transforms the specified coordinate and stores the result in . This method is guaranteed to be invoked with values of x in the range and values of y in the range .
Coordinates are also guaranteed to have the
In PROJ.4, the same
standardization, described above, is handled by .
Therefore when porting projections from PROJ.4, the forward transform equations can
be used directly here with minimal change. In the equations of Snyder,
|
| Methods inherited from class org.geotools.referencing.operation.projection.MapProjection |
getSourceDimensions, getTargetDimensions, inverse, transform, transform, transform |
| 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 |
| Method Detail |
public org.opengis.parameter.ParameterDescriptorGroup getParameterDescriptors()
MapProjection.getParameterValues(), as well as arguments checking.
getParameterDescriptors in class MapProjectionpublic org.opengis.parameter.ParameterValueGroup getParameterValues()
getParameterValues in class MapProjection
protected java.awt.geom.Point2D transformNormalized(double x,
double y,
java.awt.geom.Point2D ptDst)
throws ProjectionException
Coordinates are also guaranteed to have the MapProjection.centralMeridian
removed from x before this method is invoked. After this method
is invoked, the results in 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 1.0.
In PROJ.4, the same
standardization, described above, is handled by .
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 x or apply the
MapProjection.semiMajor ('a' or 'R').
transformNormalized in class MapProjectionx - 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
, or . Ordinates will be in a
dimensionless unit, as a linear distance on a unit sphere or ellipse.
ProjectionException - if the point can't be transformed.
protected java.awt.geom.Point2D inverseTransformNormalized(double x,
double y,
java.awt.geom.Point2D ptDst)
throws ProjectionException
Input coordinates are also guarenteed to have the MapProjection.falseEasting
and MapProjection.falseNorthing removed and be divided by MapProjection.globalScale
before this method is invoked. After this method is invoked, the
MapProjection.centralMeridian is added to the results
in . This means that projections that implement this method
are performed on an ellipse (or sphere) with a semiMajor axis of 1.0.
In PROJ.4, the same
standardization, described above, is handled by .
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 MapProjectionx - 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
, or . Ordinates will be in
radians.
ProjectionException - if the point can't be transformed.
protected double getToleranceForAssertions(double longitude,
double latitude)
getToleranceForAssertions in class MapProjectionlongitude - The longitude in degrees.latitude - The latitude in degrees.
public int hashCode()
hashCode in class MapProjectionpublic boolean equals(java.lang.Object object)
equals in class MapProjection
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