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 another 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 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 sis-referencing
module
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Nested Class Summary
Nested classes/interfaces inherited from class NormalizedProjection
NormalizedProjection.ParameterRole
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Field Summary
Fields inherited from class NormalizedProjection
eccentricity, eccentricitySquared
Fields inherited from class AbstractMathTransform2D
DIMENSION
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Constructor Summary
ConstructorsConstructorDescriptionTransverseMercator
(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.getDomain
(DomainDefinition criteria) Returns the domain of input coordinates.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) Projects the specified (λ,φ) coordinates (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
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Constructor Details
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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.
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Method Details
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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 non-linear part of the returned transform will be
this
transform, except if the ellipsoid is spherical. In the latter case,this
transform may 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:
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getDomain
Returns the domain of input coordinates. The limits defined by this method are arbitrary and may change in any future implementation. Current implementation sets a limit at 40° of longitude on each side of the central meridian (this limit is mentioned in EPSG guidance notes) and a limit at 84° of latitude (same asMercator
projection).- Overrides:
getDomain
in classAbstractMathTransform
- Parameters:
criteria
- controls the definition of transform domain.- Returns:
- estimation of a domain where this transform is considered numerically applicable.
- Since:
- 1.3
- See Also:
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transform
public Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws ProjectionException Projects the specified (λ,φ) coordinates (units in radians) and stores the result indstPts
. In addition, opportunistically computes the projection derivative ifderivate
istrue
. The results must be multiplied by the denormalization matrix before to get linear distances.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 reverse projection (i.e. applying a projection followed by a reverse projection gives approximately the original values).Rational: those coordinates are accepted despite the low accuracy of projection results because they are sometimes 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 coordinates, as (longitude, latitude) angles in radians.srcOff
- the offset of the single coordinate tuple to be converted in the source array.dstPts
- the array into which the converted coordinates 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 coordinates 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 coordinates cannot be converted.- See Also:
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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 coordinates, 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 coordinates 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 cannot be converted.
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