Class NormalizedProjection
- All Implemented Interfaces:
Serializable,Parameterized,LenientComparable,MathTransform,MathTransform2D
- Direct Known Subclasses:
AlbersEqualArea,AzimuthalEquidistant,CassiniSoldner,CylindricalEqualArea,LambertAzimuthalEqualArea,LambertConicConformal,Mercator,Mollweide,ObliqueMercator,ObliqueStereographic,Orthographic,PolarStereographic,Polyconic,SatelliteTracking,Sinusoidal,TransverseMercator
- On input, the
transform(…)method expects (longitude, latitude) angles in radians, sometimes pre-multiplied by other projection-specific factors (see point #3 below). Longitudes have the central meridian (λ₀) removed before the transform method is invoked. The conversion from degrees to radians and the longitude rotation are applied by the normalization affine transform. - On output, the
transform(…)method returns (x, y) values on a sphere or ellipse having a semi-major axis length (a) of 1, sometimes divided by other projection-specific factors (see point #3 below). The multiplication by the scale factor (k₀) and the translation by false easting (FE) and false northing (FN) are applied by the denormalization affine transform. - In addition to above-cited conversions, subclasses may opportunistically concatenate other linear operations
(scales and translations). They do that by changing the normalization and denormalization matrices shown below.
When such changes are applied, the
transform(…)inputs are no longer angles in radians but some other derived values.
NormalizedProjection respectively. Those matrices show only the basic parameters common to most projections.
Some projections will put more elements in those matrices.
NormalizedProjectionNormalizedProjection does not store the above cited parameters (central meridian, scale factor, etc.)
on intent (except indirectly), in order to make clear that those parameters are not used by subclasses.
The ability to recognize two NormalizedProjections as equivalent
without consideration for the scale factor (among other) allow more efficient concatenation in some cases
(typically some combinations of reverse projection followed by a direct projection).
All angles (either fields, method parameters or return values) in this class and subclasses are
in radians. This is the opposite of Parameters where all angles are in CRS-dependent units,
typically decimal degrees.
Serialization
Serialization of this class is appropriate for short-term storage or RMI use, but may not be compatible with future versions. For long term storage, WKT (Well Know Text) or XML are more appropriate.- Since:
- 0.6
- See Also:
Defined in the sis-referencing module
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionprotected static enumMaps the parameters to be used for initializingNormalizedProjectionand its normalization / denormalization matrices. -
Field Summary
FieldsModifier and TypeFieldDescriptionprotected final doubleEllipsoid eccentricity, equals tosqrt(eccentricitySquared).protected final doubleThe square of eccentricity: ℯ² = (a²-b²)/a² where ℯ is the eccentricity, a is the semi-major axis length and b is the semi-minor axis length.Fields inherited from class AbstractMathTransform2D
DIMENSION -
Constructor Summary
ConstructorsModifierConstructorDescriptionprotectedNormalizedProjection(OperationMethod method, Parameters parameters, Map<NormalizedProjection.ParameterRole, ? extends ParameterDescriptor<? extends Number>> roles) Constructs a new map projection from the supplied parameters. -
Method Summary
Modifier and TypeMethodDescriptionprotected intComputes a hash code value for thisNormalizedProjection.Returns the sequence of normalization →this→ denormalization transforms as a whole.booleanequals(Object object, ComparisonMode mode) Compares the given object with this transform for equivalence.protected final ContextualParametersReturns the parameters used for creating the complete map projection.Returns a description of the non-linear internal parameters of thisNormalizedProjection.Returns a copy of non-linear internal parameter values of thisNormalizedProjection.inverse()Returns the inverse of this map projection.protected abstract voidinverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Inverse converts the single coordinate tuple insrcPtsat the given offset and stores the result inptDstat the given offset.abstract Matrixtransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) Projects a single coordinate tuple insrcPtsat the given offset and stores the result indstPtsat the given offset.protected MathTransformtryConcatenate(boolean applyOtherFirst, MathTransform other, MathTransformFactory factory) Concatenates or pre-concatenates in an optimized way this projection with the given transform, if possible.Methods inherited from class AbstractMathTransform2D
createTransformedShape, derivative, getSourceDimensions, getTargetDimensions, transformMethods inherited from class AbstractMathTransform
derivative, equals, formatTo, getDomain, hashCode, isIdentity, transform, transform, transform, transform, transformMethods inherited from class FormattableObject
print, toString, toString, toWKTMethods inherited from class Object
clone, finalize, getClass, notify, notifyAll, wait, wait, waitMethods inherited from interface MathTransform
derivative, isIdentity, toWKT, transform, transform, transform, transform, transform
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Field Details
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eccentricity
protected final double eccentricityEllipsoid eccentricity, equals tosqrt(eccentricitySquared). Value 0 means that the ellipsoid is spherical. -
eccentricitySquared
protected final double eccentricitySquaredThe square of eccentricity: ℯ² = (a²-b²)/a² where ℯ is the eccentricity, a is the semi-major axis length and b is the semi-minor axis length.
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Constructor Details
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NormalizedProjection
protected NormalizedProjection(OperationMethod method, Parameters parameters, Map<NormalizedProjection.ParameterRole, ? extends ParameterDescriptor<? extends Number>> roles) Constructs a new map projection from the supplied parameters. This constructor applies the following operations on the contextual parameters:- On the normalization matrix (to be applied before
thistransform):- Subtract the central meridian value.
- Convert from degrees to radians.
- On the denormalization matrix (to be applied after
thistransform):- Scale by the semi-major axis length.
- If a scale factor is present (not all map projections have a scale factor), apply that scale.
- Translate by the false easting and false northing (after the scale).
- On the contextual parameters (not the parameters of
thistransform):- Store the values for semi-major axis length, semi-minor axis length, scale factor (if present), central meridian, false easting and false northing values.
Initial matrix coefficients after construction Normalization Denormalization Which parameters are considered
Therolesmap specifies which parameters to look for central meridian, scale factor, false easting, false northing and other values. All entries in therolesmap are optional. All descriptors in the map shall comply to the following constraints:- Descriptors associated to
NormalizedProjection.ParameterRole.SEMI_MAJOR,SEMI_MINOR,FALSE_EASTINGandFALSE_NORTHINGshall have the same linear unit of measurement (usually metre). - Descriptors associated to angular measures (
NormalizedProjection.ParameterRole.CENTRAL_MERIDIANandLATITUDE_OF_CONFORMAL_SPHERE_RADIUS) shall use degrees.
Parametersobject given in argument to this constructor. But those values will be converted to the units of measurement specified by the parameter descriptors in therolesmap, which must be the above-cited units.- Parameters:
method- description of the map projection parameters.parameters- the parameters of the projection to be created.roles- parameters to look for central meridian, scale factor, false easting, false northing and other values.
- On the normalization matrix (to be applied before
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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. Conversion to other units and changes in axis order are not managed by the returned transform.The default implementation is as below:
Subclasses can override this method if they wish to use alternative implementations under some circumstances. For example, many subclasses will replacereturn getContextualParameters().completeTransform(factory, this);
thisby a specialized implementation if they detect that the ellipsoid is actually spherical.- 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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getContextualParameters
Returns the parameters used for creating the complete map projection. Those parameters describe a sequence of normalize →this→ denormalize transforms, not including axis swapping. Those parameters are used for formatting Well Known Text (WKT) and error messages. Subclasses shall not use the values defined in the returned object for computation purpose, except at construction time.- Overrides:
getContextualParametersin classAbstractMathTransform- Returns:
- the parameter values for the sequence of normalize →
this→ denormalize transforms, ornullif unspecified.
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getParameterValues
Returns a copy of non-linear internal parameter values of thisNormalizedProjection. The returned group contains at least theeccentricityparameter value. Some subclasses add more non-linear parameters, but most of them do not because many parameters like the scale factor or the false easting/northing are handled by the (de)normalization affine transforms instead.Note: This method is mostly for debugging purposes since the isolation of non-linear parameters in this class is highly implementation dependent. Most GIS applications will instead be interested in the contextual parameters.- Specified by:
getParameterValuesin interfaceParameterized- Overrides:
getParameterValuesin classAbstractMathTransform- Returns:
- a copy of the internal parameter values for this normalized projection.
- See Also:
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getParameterDescriptors
Returns a description of the non-linear internal parameters of thisNormalizedProjection. The returned group contains at least a descriptor for theeccentricityparameter. Subclasses may add more parameters.This method is for inspecting the parameter values of this non-linear kernel only, not for inspecting the contextual parameters. Inspecting the kernel parameter values is usually for debugging purpose only.
- Specified by:
getParameterDescriptorsin interfaceParameterized- Overrides:
getParameterDescriptorsin classAbstractMathTransform- Returns:
- a description of the internal parameters.
- See Also:
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transform
public abstract Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws ProjectionException Projects a single coordinate tuple insrcPtsat the given offset and stores the result indstPtsat the given offset. In addition, opportunistically computes the transform derivative if requested.Normalization
The input coordinates are (λ,φ) (the variable names for longitude and latitude respectively) angles in radians, eventually pre-multiplied by projection-specific factors. Input coordinates shall have the central meridian removed from the longitude by the caller before this method is invoked. After this method is invoked, the caller will need to multiply the output coordinates by the global scale factor, apply the (false easting, false northing) offset and eventually other projection-specific factors. This means that projections that implement this method are performed on a sphere or ellipse having a semi-major axis length of 1.Note 1: it is generally not necessary to know the projection-specific additional factors applied by subclasses on the input and output values, becauseNormalizedProjectionshould never be used directly.NormalizedProjectioninstances are used only indirectly as a step in a concatenated transform that include the normalization and denormalization matrices documented in this class javadoc.Note 2: in the PROJ library, the same standardization, described above, is handled bypj_fwd.c, except for the projection-specific additional factors.Argument checks
The input longitude and latitude are usually (but not always) in the range [-π … π] and [-π/2 … π/2] respectively. However, values outside those ranges are accepted on the assumption that most implementations use those values only in trigonometric functions like sine and cosine. If this assumption is not applicable to a particular subclass, then it is implementer responsibility to check the range.- Specified by:
transformin classAbstractMathTransform- 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-truefor computing the derivative, orfalseif not needed.- Returns:
- the matrix of the projection derivative at the given source position,
or
nullif thederivateargument isfalse. - Throws:
ProjectionException- if the coordinates cannot be converted.- See Also:
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inverseTransform
protected abstract void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) throws ProjectionException Inverse converts the single coordinate tuple insrcPtsat the given offset and stores the result inptDstat the given offset. The output coordinates are (longitude, latitude) angles in radians, usually (but not necessarily) in the range [-π … π] and [-π/2 … π/2] respectively.Normalization
Input coordinates shall have the (false easting, false northing) removed by the caller and the result divided by the global scale factor before this method is invoked. After this method is invoked, the caller will need to add the central meridian to the longitude in the output coordinates. This means that projections that implement this method are performed on a sphere or ellipse having a semi-major axis of 1. Additional projection-specific factors may also need to be applied (see class javadoc).Note: in the PROJ library, the same standardization, described above, is handled bypj_inv.c, except for the projection-specific additional factors.- 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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inverse
Returns the inverse of this map projection. Subclasses do not need to override this method, as they should overrideinverseTransform(…)instead.- Specified by:
inversein interfaceMathTransform- Specified by:
inversein interfaceMathTransform2D- Overrides:
inversein classAbstractMathTransform2D- Returns:
- the inverse of this map projection.
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tryConcatenate
protected MathTransform tryConcatenate(boolean applyOtherFirst, MathTransform other, MathTransformFactory factory) throws FactoryException Concatenates or pre-concatenates in an optimized way this projection with the given transform, if possible. If transforms are concatenated in a (reverse projection) → (affine) → (projection) sequence where the (projection) and (reverse projection) steps are the inverse of each other, then in some particular case the sequence can be replaced by a single affine transform. If no such simplification is possible, this method returnsnull.- Overrides:
tryConcatenatein classAbstractMathTransform- Parameters:
applyOtherFirst-trueif the transformation order isotherfollowed bythis, orfalseif the transformation order isthisfollowed byother.other- the other math transform to (pre-)concatenate with this transform.factory- the factory which is (indirectly) invoking this method, ornullif none.- Returns:
- the simplified (usually affine) transform, or
nullif no such optimization is available. - Throws:
FactoryException- if an error occurred while combining the transforms.- Since:
- 0.8
- See Also:
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computeHashCode
protected int computeHashCode()Computes a hash code value for thisNormalizedProjection.- Overrides:
computeHashCodein classAbstractMathTransform- Returns:
- the hash code value.
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equals
Compares the given object with this transform for equivalence. The default implementation checks ifobjectis an instance of the same class thanthis, then compares the eccentricity.If this method returns
true, then for any given identical source position, the two compared map projections shall compute the same target position. Many of the contextual parameters used for creating the map projections are irrelevant and do not need to be known. Those projection parameters will be compared only if the comparison mode isComparisonMode.STRICTorBY_CONTRACT.Example: a Mercator projection can be created in the 2SP case with a standard parallel value of 60°. The same projection can also be created in the 1SP case with a scale factor of 0.5. Nevertheless those two map projections applied on a sphere gives identical results. Considering them as equivalent allows the referencing module to transform coordinates between those two projections more efficiently.- Specified by:
equalsin interfaceLenientComparable- Overrides:
equalsin classAbstractMathTransform- Parameters:
object- the object to compare with this map projection for equivalence.mode- the strictness level of the comparison. Default toComparisonMode.STRICT.- Returns:
trueif the given object is equivalent to this map projection.- See Also:
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