Class TransverseMercator
 All Implemented Interfaces:
Serializable
,Parameterized
,LenientComparable
,MathTransform
,MathTransform2D
Description
This is a cylindrical projection, in which the cylinder has been rotated 90°. Instead of being tangent to the equator (or to an other standard latitude), it is tangent to a central meridian. Deformation are more important as we are going further from the central meridian. The Transverse Mercator projection is appropriate for region which have a greater extent northsouth than eastwest.There are a number of versions of the Transverse Mercator projection including the Universal (UTM) and Modified (MTM) Transverses Mercator projections. In these cases the earth is divided into zones. For the UTM the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from 180 degrees longitude, and between latitude 84 degrees North and 80 degrees South. The central meridian is taken as the center of the zone and the latitude of origin is the equator. A scale factor of 0.9996 and false easting of 500000 metres is used for all zones and a false northing of 10000000 metres is used for zones in the southern hemisphere.
Domain of validity
The difference between longitude values λ and the central meridian λ₀ should be less than 60°. Differences larger than 90° of longitude cause aProjectionException
to be thrown.
Differences between 60° and 90° are not rejected by Apache SIS but should be avoided.
See the projection method
for more information. Since:
 0.6
 See Also:
Defined in the sisreferencing
module

Nested Class Summary
Nested classes/interfaces inherited from class NormalizedProjection
NormalizedProjection.ParameterRole

Field Summary
Fields inherited from class NormalizedProjection
eccentricity, eccentricitySquared

Constructor Summary
ConstructorDescriptionTransverseMercator
(OperationMethod method, Parameters parameters) Creates a Transverse Mercator projection from the given parameters. 
Method Summary
Modifier and TypeMethodDescriptionReturns the sequence of normalization →this
→ denormalization transforms as a whole.protected void
inverseTransform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Transforms the specified (η, ξ) coordinates and stores the result indstPts
(angles in radians).transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) Converts the specified (λ,φ) coordinate (units in radians) and stores the result indstPts
.Methods inherited from class NormalizedProjection
computeHashCode, equals, getContextualParameters, getParameterDescriptors, getParameterValues, inverse, tryConcatenate
Methods inherited from class AbstractMathTransform2D
createTransformedShape, derivative, getSourceDimensions, getTargetDimensions, transform
Methods inherited from class AbstractMathTransform
derivative, equals, formatTo, hashCode, isIdentity, transform, transform, transform, transform, transform
Methods inherited from class FormattableObject
print, toString, toString, toWKT
Methods inherited from class Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface MathTransform
derivative, isIdentity, toWKT, transform, transform, transform, transform, transform

Constructor Details

TransverseMercator
Creates a Transverse Mercator projection from the given parameters. Themethod
argument can be the description of one of the following: "Transverse Mercator".
 "Transverse Mercator (South Orientated)".
 Parameters:
method
 description of the projection parameters.parameters
 the parameter values of the projection to create.


Method Details

createMapProjection
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 nonlinear part of the returned transform will be
this
transform, except if the ellipsoid is spherical. In the later case,this
transform will be replaced by a simplified implementation. Overrides:
createMapProjection
in classNormalizedProjection
 Parameters:
factory
 the factory to use for creating the transform. Returns:
 the map projection from (λ,φ) to (x,y) coordinates.
 Throws:
FactoryException
 if an error occurred while creating a transform. See Also:

transform
public Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws ProjectionException Converts the specified (λ,φ) coordinate (units in radians) and stores the result indstPts
. In addition, opportunistically computes the projection derivative ifderivate
istrue
.Accuracy and domain of validity
Projection errors depend on the difference ∆λ between longitude λ and the central meridian λ₀. All Universal Transverse Mercator (UTM) projections aim for ∆λ ≤ 3°, but this implementation can nevertheless handle larger values. Results have been compared with values provided by Karney, C.F.F. (2009). Test data for the transverse Mercator projection [Data set]. Zenodo. On the WGS84 ellipsoid we observed the following errors compared to Karney's data: Errors less than 1 centimetre for ∆λ < 60° at all latitudes.
 At latitudes far enough from equator (φ ≥ 20°), the domain can be extended up to ∆λ < (1 − ℯ)⋅90° (≈ 82.63627282416406551° on WGS84) with errors less than 70 centimetres.
Case of 82.6…° < ∆λ ≤ 90°
Karney (2009) uses an “extended” domain of transverse Mercator projection for ∆λ ≥ (1 − ℯ)⋅90°, but Apache SIS does not support such extension. Consequently ∆λ values between (1 − ℯ)⋅90° and 90° should be considered invalid but are not rejected by Apache SIS. Note that those invalid values are consistent with the inverse projection (i.e. applying a projection followed by an inverse projection gives approximately the original values).Rational: those coordinates are accepted despite the low accuracy of projection results because they are sometime needed for expressing bounding boxes. A bounding box may have corners located in invalid projection area even if all features inside the box have valid coordinates. For "contains" and "intersects" tests between envelopes, we do not need accurate coordinates; a monotonic behavior of x = f(λ) can be sufficient.Case of ∆λ > 90°
Longitude values at a distance greater than 90° from the central meridian are rejected. AProjectionException
is thrown in that case. This limit exists because the Transverse Mercator projection is conceptually a Mercator projection rotated by 90°. Consequently x values tend toward infinity for ∆λ close to ±90° Specified by:
transform
in classNormalizedProjection
 Parameters:
srcPts
 the array containing the source point coordinate, as (longitude, latitude) angles in radians.srcOff
 the offset of the single coordinate to be converted in the source array.dstPts
 the array into which the converted coordinate is returned (may be the same thansrcPts
). 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 coordinate that is stored in the destination array.derivate
true
for computing the derivative, orfalse
if not needed. Returns:
 the matrix of the projection derivative at the given source position,
or
null
if thederivate
argument isfalse
.  Throws:
ProjectionException
 if the coordinate can not be converted. See Also:

inverseTransform
protected void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) throws ProjectionException Transforms the specified (η, ξ) coordinates and stores the result indstPts
(angles in radians). Specified by:
inverseTransform
in classNormalizedProjection
 Parameters:
srcPts
 the array containing the source point coordinate, 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 coordinate is returned (may be the same thansrcPts
). 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 can not be converted.
