Class TransverseMercator
- All Implemented Interfaces:
Serializable
,Parameterized
,LenientComparable
,org.opengis.referencing.operation.MathTransform
,org.opengis.referencing.operation.MathTransform2D
- Direct Known Subclasses:
TransverseMercator.Spherical
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
- Version:
- 1.3
- See Also:
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionprivate static final class
Provides the transform equations for the spherical case of the Transverse Mercator projection.private static enum
Variants of the map projection.Nested classes/interfaces inherited from class org.apache.sis.referencing.operation.projection.NormalizedProjection
NormalizedProjection.ParameterRole
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
false
for using the original formulas as published by EPSG, ortrue
for using formulas modified using trigonometric identities.private final double
Coefficients in the series expansion of the forward projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the forward projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the forward projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the forward projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the reverse projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the reverse projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the reverse projection, depending only on eccentricity value.private final double
Coefficients in the series expansion of the reverse projection, depending only on eccentricity value.private static final long
For cross-version compatibility.Fields inherited from class org.apache.sis.referencing.operation.projection.NormalizedProjection
ANGULAR_TOLERANCE, context, eccentricity, eccentricitySquared, ITERATION_TOLERANCE, LARGE_LONGITUDE_LIMIT, MAXIMUM_ITERATIONS, POLAR_AREA_LIMIT
Fields inherited from class org.apache.sis.referencing.operation.transform.AbstractMathTransform2D
DIMENSION
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Constructor Summary
ConstructorsConstructorDescriptionTransverseMercator
(Initializer initializer) Creates a new Transverse Mercator projection from the given initializer.Creates a new projection initialized to the same parameters than the given one.TransverseMercator
(org.opengis.referencing.operation.OperationMethod method, Parameters parameters) Creates a Transverse Mercator projection from the given parameters. -
Method Summary
Modifier and TypeMethodDescriptionorg.opengis.referencing.operation.MathTransform
createMapProjection
(org.opengis.referencing.operation.MathTransformFactory factory) Returns the sequence of normalization →this
→ denormalization transforms as a whole.Optional
<org.opengis.geometry.Envelope> getDomain
(DomainDefinition criteria) Returns the domain of input coordinates.private static boolean
identityEquals
(double actual, double expected) Verifies if a trigonometric identity produced the expected value.private static Initializer
initializer
(org.opengis.referencing.operation.OperationMethod method, Parameters parameters) Work around for RFE #4093999 in Sun's bug database ("Relax constraint on placement of this()/super() call in constructors").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).private static org.opengis.referencing.operation.Matrix
outsideDomainOfValidity
(double[] dstPts, int dstOff, boolean derivate) Implementation oftransform(double[], int, double[], int, boolean)
for points outside domain of validity.org.opengis.referencing.operation.Matrix
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 org.apache.sis.referencing.operation.projection.NormalizedProjection
completeWithWraparound, computeHashCode, delegate, equals, getContextualParameters, getInternalParameterNames, getInternalParameterValues, getParameterDescriptors, getParameterValues, getWraparoundLongitude, inverse, tryConcatenate, tryConcatenate, variant
Methods inherited from class org.apache.sis.referencing.operation.transform.AbstractMathTransform2D
createTransformedShape, derivative, getSourceDimensions, getTargetDimensions, transform
Methods inherited from class org.apache.sis.referencing.operation.transform.AbstractMathTransform
derivative, equals, formatTo, hashCode, isIdentity, transform, transform, transform, transform, transform
Methods inherited from class org.apache.sis.io.wkt.FormattableObject
print, toString, toString, toWKT
Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface org.opengis.referencing.operation.MathTransform
derivative, isIdentity, toWKT, transform, transform, transform, transform, transform
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Field Details
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serialVersionUID
private static final long serialVersionUIDFor cross-version compatibility.- See Also:
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ALLOW_TRIGONOMETRIC_IDENTITIES
private static final boolean ALLOW_TRIGONOMETRIC_IDENTITIESfalse
for using the original formulas as published by EPSG, ortrue
for using formulas modified using trigonometric identities. The use of trigonometric identities is for reducing the amount of calls to theMath.sin(double)
and similar methods. Some identities used are:- sin(2θ) = 2⋅sinθ⋅cosθ
- cos(2θ) = cos²θ - sin²θ
- sin(3θ) = (3 - 4⋅sin²θ)⋅sinθ
- cos(3θ) = (4⋅cos³θ) - 3⋅cosθ
- sin(4θ) = (4 - 8⋅sin²θ)⋅sinθ⋅cosθ
- cos(4θ) = (8⋅cos⁴θ) - (8⋅cos²θ) + 1
- sinh(2θ) = 2⋅sinhθ⋅coshθ
- cosh(2θ) = cosh²θ + sinh²θ = 2⋅cosh²θ - 1 = 1 + 2⋅sinh²θ
- sinh(3θ) = (3 + 4⋅sinh²θ)⋅sinhθ
- cosh(3θ) = ((4⋅cosh²θ) - 3)⋅coshθ
- sinh(4θ) = (1 + 2⋅sinh²θ)⋅4.sinhθ⋅coshθ = 4.cosh(2θ).sinhθ⋅coshθ
- cosh(4θ) = (8⋅cosh⁴θ) - (8⋅cosh²θ) + 1 = 8⋅cosh²(θ) ⋅ (cosh²θ - 1) + 1 = 8⋅cosh²(θ) ⋅ sinh²(θ) + 1 = 2⋅sinh²(2θ) + 1
- See Also:
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cf2
private final double cf2Coefficients in the series expansion of the forward projection, depending only on eccentricity value. The series expansion is of the following form:cf₂⋅f(2θ) + cf₄⋅f(4θ) + cf₆⋅f(6θ) + cf₈⋅f(8θ)
Those coefficients are named h₁, h₂, h₃ and h₄ in §1.3.5.1 of IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – April 2015.Serialization note: we do not strictly need to serialize those fields since they could be computed after deserialization. Bu we serialize them anyway in order to simplify a little bit this class (it allows us to keep those fields final) and because values computed after deserialization could be slightly different than the ones computed after construction since the constructor uses the double-double values provided byInitializer
. -
cf4
private final double cf4Coefficients in the series expansion of the forward projection, depending only on eccentricity value. The series expansion is of the following form:cf₂⋅f(2θ) + cf₄⋅f(4θ) + cf₆⋅f(6θ) + cf₈⋅f(8θ)
Those coefficients are named h₁, h₂, h₃ and h₄ in §1.3.5.1 of IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – April 2015.Serialization note: we do not strictly need to serialize those fields since they could be computed after deserialization. Bu we serialize them anyway in order to simplify a little bit this class (it allows us to keep those fields final) and because values computed after deserialization could be slightly different than the ones computed after construction since the constructor uses the double-double values provided byInitializer
. -
cf6
private final double cf6Coefficients in the series expansion of the forward projection, depending only on eccentricity value. The series expansion is of the following form:cf₂⋅f(2θ) + cf₄⋅f(4θ) + cf₆⋅f(6θ) + cf₈⋅f(8θ)
Those coefficients are named h₁, h₂, h₃ and h₄ in §1.3.5.1 of IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – April 2015.Serialization note: we do not strictly need to serialize those fields since they could be computed after deserialization. Bu we serialize them anyway in order to simplify a little bit this class (it allows us to keep those fields final) and because values computed after deserialization could be slightly different than the ones computed after construction since the constructor uses the double-double values provided byInitializer
. -
cf8
private final double cf8Coefficients in the series expansion of the forward projection, depending only on eccentricity value. The series expansion is of the following form:cf₂⋅f(2θ) + cf₄⋅f(4θ) + cf₆⋅f(6θ) + cf₈⋅f(8θ)
Those coefficients are named h₁, h₂, h₃ and h₄ in §1.3.5.1 of IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2 – April 2015.Serialization note: we do not strictly need to serialize those fields since they could be computed after deserialization. Bu we serialize them anyway in order to simplify a little bit this class (it allows us to keep those fields final) and because values computed after deserialization could be slightly different than the ones computed after construction since the constructor uses the double-double values provided byInitializer
. -
ci2
private final double ci2Coefficients in the series expansion of the reverse projection, depending only on eccentricity value. -
ci4
private final double ci4Coefficients in the series expansion of the reverse projection, depending only on eccentricity value. -
ci6
private final double ci6Coefficients in the series expansion of the reverse projection, depending only on eccentricity value. -
ci8
private final double ci8Coefficients in the series expansion of the reverse projection, depending only on eccentricity value.
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Constructor Details
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TransverseMercator
public TransverseMercator(org.opengis.referencing.operation.OperationMethod method, Parameters parameters) 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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TransverseMercator
TransverseMercator(Initializer initializer) Creates a new Transverse Mercator projection from the given initializer. This constructor is used also byZonedGridSystem
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TransverseMercator
TransverseMercator(TransverseMercator other) Creates a new projection initialized to the same parameters than the given one.
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Method Details
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identityEquals
private static boolean identityEquals(double actual, double expected) Verifies if a trigonometric identity produced the expected value. This method is used in assertions only, for values close to the [-1 … +1] range. The tolerance threshold is approximately 1.5E-12 (note that it still about 7000 time greater thanMath.ulp(1.0)
).- See Also:
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initializer
@Workaround(library="JDK", version="1.7") private static Initializer initializer(org.opengis.referencing.operation.OperationMethod method, Parameters parameters) Work around for RFE #4093999 in Sun's bug database ("Relax constraint on placement of this()/super() call in constructors"). -
createMapProjection
public org.opengis.referencing.operation.MathTransform createMapProjection(org.opengis.referencing.operation.MathTransformFactory factory) throws org.opengis.util.FactoryException 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:
org.opengis.util.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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outsideDomainOfValidity
private static org.opengis.referencing.operation.Matrix outsideDomainOfValidity(double[] dstPts, int dstOff, boolean derivate) Implementation oftransform(double[], int, double[], int, boolean)
for points outside domain of validity. Should be invoked only when the longitude is at more than 90° from central meridian, in which case result does not exist. This method should not be invoked for points at Δλ ≤ 90° that we fail to compute, because in such cases aProjectionException
should be thrown instead. -
transform
public org.opengis.referencing.operation.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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