- All Implemented Interfaces:
DescriptionThis 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 north-south than east-west.
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 validityThe difference between longitude values λ and the central meridian λ₀ should be less than 60°. Differences larger than 90° of longitude cause a
ProjectionExceptionto be thrown. Differences between 60° and 90° are not rejected by Apache SIS but should be avoided. See the projection method for more information.
Nested Class Summary
Method SummaryModifier and TypeMethodDescriptionReturns the sequence of normalization →
this→ denormalization transforms as a whole.
(double srcPts, int srcOff, double dstPts, int dstOff)Transforms the specified (η, ξ) coordinates and stores the result in
dstPts(angles in radians).
(double srcPts, int srcOff, double dstPts, int dstOff, boolean derivate)Converts the specified (λ,φ) coordinate (units in radians) and stores the result in
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 Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
TransverseMercatorCreates a Transverse Mercator projection from the given parameters. The
methodargument can be the description of one of the following:
- "Transverse Mercator".
- "Transverse Mercator (South Orientated)".
method- description of the projection parameters.
parameters- the parameter values of the projection to create.
createMapProjectionReturns 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 non-linear part of the returned transform will be
thistransform, except if the ellipsoid is spherical. In the latter case,
thistransform may be replaced by a simplified implementation.
factory- the factory to use for creating the transform.
- the map projection from (λ,φ) to (x,y) coordinates.
FactoryException- if an error occurred while creating a transform.
- See Also:
transformpublic Matrix transform
(double srcPts, int srcOff, double dstPts, int dstOff, boolean derivate) throws ProjectionExceptionConverts the specified (λ,φ) coordinate (units in radians) and stores the result in
dstPts. In addition, opportunistically computes the projection derivative if
Accuracy and domain of validityProjection 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. A
ProjectionExceptionis 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:
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 than
srcPts). 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.
truefor computing the derivative, or
falseif not needed.
- the matrix of the projection derivative at the given source position,
ProjectionException- if the coordinate can not be converted.
- See Also:
inverseTransformprotected void inverseTransform
(double srcPts, int srcOff, double dstPts, int dstOff) throws ProjectionExceptionTransforms the specified (η, ξ) coordinates and stores the result in
dstPts(angles in radians).
- Specified by:
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 than
srcPts). 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.
ProjectionException- if the point can not be converted.