Class EllipsoidToCentricTransform
- All Implemented Interfaces:
Serializable
,Parameterized
,LenientComparable
,org.opengis.referencing.operation.MathTransform
- longitude (λ) relative to the prime meridian (usually Greenwich),
- latitude (φ),
- optionally height above the ellipsoid (h).
- In the Cartesian case:
- distance from Earth center on the X axis (toward the intersection of prime meridian and equator),
- distance from Earth center on the Y axis (toward the intersection of 90°E meridian and equator),
- distance from Earth center on the Z axis (toward North pole).
MathTransform
has been created:
EllipsoidToCentricTransform
instances created directly by the constructor expect (λ,φ) values in radians and compute (X,Y,Z) values in units of an ellipsoid having a semi-major axis length of 1.- Transforms created by the
createGeodeticConversion(…)
static method expect (λ,φ) values in degrees and compute (X,Y,Z) values in units of the ellipsoid axes (usually metres).
- Since:
- 0.7
- Version:
- 1.3
- See Also:
-
Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionprivate static final class
Converts Cartesian coordinates (X,Y,Z) to ellipsoidal coordinates (λ,φ) or (λ,φ,h).static enum
Whether the output coordinate system is Cartesian or Spherical. -
Field Summary
FieldsModifier and TypeFieldDescriptionprivate double
The b/a ratio where a is the semi-major axis length and b is the semi-minor axis length.(package private) final ContextualParameters
The parameters used for creating this conversion.private static org.opengis.parameter.ParameterDescriptorGroup
Internal parameter descriptor, used only for debugging purpose.private static final double
Minimal eccentricity value before to consider that the approximated φ value should be made more accurate by the use of an iterative method.protected final double
The square of eccentricity: ℯ² = (a²-b²)/a² where a is the semi-major axis length and b is the semi-minor axis length.private final AbstractMathTransform
The inverse of this transform.private static final long
Serial number for inter-operability with different versions.private boolean
Whether calculation of φ should use an iterative method after the first φ approximation.(package private) final boolean
true
if ellipsoidal coordinates include an ellipsoidal height (i.e.Fields inherited from class org.apache.sis.referencing.operation.transform.AbstractMathTransform
MAXIMUM_BUFFER_SIZE, MAXIMUM_FAILURES
-
Constructor Summary
ConstructorsConstructorDescriptionEllipsoidToCentricTransform
(double semiMajor, double semiMinor, javax.measure.Unit<javax.measure.quantity.Length> unit, boolean withHeight, EllipsoidToCentricTransform.TargetType target) Creates a transform from angles in radians on ellipsoid having a semi-major axis length of 1. -
Method Summary
Modifier and TypeMethodDescription(package private) final int
beforeFormat
(List<Object> transforms, int index, boolean inverse) Given a transformation chain to format in WKT, inserts a "Geographic 2D to 3D" pseudo-conversion before this transform (normallytransforms.get(index)
) if this conversion expects no height.protected int
Computes a hash value for this transform.(package private) final EllipsoidToCentricTransform
create2D()
Creates a transform with the same parameters than this transform, but expecting two-dimensional inputs instead of three-dimensional.static org.opengis.referencing.operation.MathTransform
createGeodeticConversion
(org.opengis.referencing.operation.MathTransformFactory factory, double semiMajor, double semiMinor, javax.measure.Unit<javax.measure.quantity.Length> unit, boolean withHeight, EllipsoidToCentricTransform.TargetType target) Creates a transform from geographic to geocentric coordinates.static org.opengis.referencing.operation.MathTransform
createGeodeticConversion
(org.opengis.referencing.operation.MathTransformFactory factory, org.opengis.referencing.datum.Ellipsoid ellipsoid, boolean withHeight) Creates a transform from geographic to Cartesian geocentric coordinates (convenience method).org.opengis.referencing.operation.Matrix
derivative
(org.opengis.geometry.DirectPosition point) Computes the derivative at the given location.boolean
equals
(Object object, ComparisonMode mode) Compares the specified object with this math transform for equality.protected ContextualParameters
Returns the parameters used for creating the complete conversion.org.opengis.parameter.ParameterDescriptorGroup
Returns a description of the internal parameters of thisEllipsoidToCentricTransform
transform.org.opengis.parameter.ParameterValueGroup
Returns a copy of internal parameter values of thisEllipsoidToCentricTransform
transform.final int
Gets the dimension of input points, which is 2 or 3.final int
Gets the dimension of output points, which is 3.Returns whether the target coordinate system is Cartesian or Spherical.org.opengis.referencing.operation.MathTransform
inverse()
Returns the inverse of this transform.protected void
inverseTransform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Converts Cartesian coordinates (X,Y,Z) to ellipsoidal coordinates (λ,φ) or (λ,φ,h).private void
Restores transient fields after deserialization.org.opengis.referencing.operation.Matrix
transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) Converts the (λ,φ) or (λ,φ,h) geodetic coordinates to to (X,Y,Z) geocentric coordinates, and optionally returns the derivative at that location.void
transform
(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) Converts the (λ,φ) or (λ,φ,h) geodetic coordinates to to (X,Y,Z) geocentric coordinates.private org.opengis.referencing.operation.Matrix
transform
(double λ, double φ, double h, double[] dstPts, int dstOff, boolean derivate, boolean wh) Implementation oftransform(double[], int, double[], int, boolean)
with possibility to override thewithHeight
value.protected org.opengis.referencing.operation.MathTransform
tryConcatenate
(boolean applyOtherFirst, org.opengis.referencing.operation.MathTransform other, org.opengis.referencing.operation.MathTransformFactory factory) If this transform expects three-dimensional inputs, and if the transform just before this one unconditionally sets the height to zero, then replaces this transform by a two-dimensional one.Methods inherited from class org.apache.sis.referencing.operation.transform.AbstractMathTransform
equals, formatTo, getDomain, hashCode, isIdentity, isInverseEquals, mismatchedDimension, 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
toWKT
-
Field Details
-
serialVersionUID
private static final long serialVersionUIDSerial number for inter-operability with different versions.- See Also:
-
DESCRIPTOR
Internal parameter descriptor, used only for debugging purpose. Created only when first needed.- See Also:
-
ECCENTRICITY_THRESHOLD
private static final double ECCENTRICITY_THRESHOLDMinimal eccentricity value before to consider that the approximated φ value should be made more accurate by the use of an iterative method. The iterative method is not needed for a planet of Earth eccentricity, but become useful for planets of higher eccentricity.Actually the need for iteration is not just a matter of eccentricity. It is also a matter of h values. But empirical tests suggest that with Earth's eccentricity (about 0.082), the limit for h is quite high (close to 2000 km for a point at 30°N). This limit is reduced to about 200 km for an eccentricity of 0.16. It may be possible to find a formula for the limit of h as a function of ℯ and φ, but this has not been explored yet.
-
eccentricitySquared
protected final double eccentricitySquaredThe square of eccentricity: ℯ² = (a²-b²)/a² where a is the semi-major axis length and b is the semi-minor axis length. -
axisRatio
private transient double axisRatioThe b/a ratio where a is the semi-major axis length and b is the semi-minor axis length. Since theEllipsoidToCentricTransform
class works on an ellipsoid where a = 1 (because of the work performed by the normalization matrices), we just drop a in the formulas - so this field could be written as just b.This value is related to
eccentricitySquared
and to the ε value used in EPSG guide by (assuming a=1):- ℯ² = 1 - b²
- ε = ℯ²/b²
Consider this field as final! It is not final only for the purpose of
readObject(ObjectInputStream)
. This field is recomputed fromeccentricitySquared
on deserialization. -
useIterations
private transient boolean useIterationsWhether calculation of φ should use an iterative method after the first φ approximation. The current implementation sets this field totrue
at construction time when the eccentricity value is greater than or equals toECCENTRICITY_THRESHOLD
, but this policy may change in any future SIS version (for example we do not take the h values in account yet).Consider this field as final! It is not final only for the purpose of
readObject(ObjectInputStream)
. This field is not serialized because its value may depend on the version of thisEllipsoidToCentricTransform
class. -
withHeight
final boolean withHeighttrue
if ellipsoidal coordinates include an ellipsoidal height (i.e. are 3-D). Iffalse
, then the input coordinates are expected to be two-dimensional and the ellipsoidal height is assumed to be 0. -
context
The parameters used for creating this conversion. They are used for formatting Well Known Text (WKT) and error messages.- See Also:
-
inverse
The inverse of this transform.Note: creation of this object is not deferred to the first call to theinverse()
method because this object is lightweight and typically needed soon anyway (may be as soon asConcatenatedTransform
construction time). In addition this field is part of serialization form in order to preserve the references graph.
-
-
Constructor Details
-
EllipsoidToCentricTransform
public EllipsoidToCentricTransform(double semiMajor, double semiMinor, javax.measure.Unit<javax.measure.quantity.Length> unit, boolean withHeight, EllipsoidToCentricTransform.TargetType target) Creates a transform from angles in radians on ellipsoid having a semi-major axis length of 1. More specificallyEllipsoidToCentricTransform
instances expect input coordinates as below:- longitudes in radians relative to the prime meridian (usually Greenwich),
- latitudes in radians,
- optionally heights above the ellipsoid, in units of an ellipsoid having a semi-major axis length of 1.
- distance from Earth center on the X axis (toward the intersection of prime meridian and equator),
- distance from Earth center on the Y axis (toward the intersection of 90°E meridian and equator),
- distance from Earth center on the Z axis (toward North pole).
Geographic to geocentric conversions
For converting geographic coordinates to geocentric coordinates,EllipsoidToCentricTransform
instances need to be concatenated with the following affine transforms:- Normalization before
EllipsoidToCentricTransform
:- Conversion of (λ,φ) from degrees to radians
- Division of (h) by the semi-major axis length
- Denormalization after
EllipsoidToCentricTransform
:- Multiplication of (X,Y,Z) by the semi-major axis length
EllipsoidToCentricTransform
construction, the full conversion chain including the above affine transforms can be created bygetContextualParameters().completeTransform(factory, this)}
.- Parameters:
semiMajor
- the semi-major axis length.semiMinor
- the semi-minor axis length.unit
- the unit of measurement for the semi-axes and the ellipsoidal height.withHeight
-true
if source geographic coordinates include an ellipsoidal height (i.e. are 3-D), orfalse
if they are only 2-D.target
- whether the target coordinate shall be Cartesian or Spherical.- See Also:
-
-
Method Details
-
readObject
Restores transient fields after deserialization.- Parameters:
in
- the input stream from which to deserialize the transform.- Throws:
IOException
- if an I/O error occurred while reading or if the stream contains invalid data.ClassNotFoundException
- if the class serialized on the stream is not on the classpath.
-
createGeodeticConversion
public static org.opengis.referencing.operation.MathTransform createGeodeticConversion(org.opengis.referencing.operation.MathTransformFactory factory, double semiMajor, double semiMinor, javax.measure.Unit<javax.measure.quantity.Length> unit, boolean withHeight, EllipsoidToCentricTransform.TargetType target) throws org.opengis.util.FactoryException Creates a transform from geographic to geocentric coordinates. This factory method combines theEllipsoidToCentricTransform
instance with the steps needed for converting degrees to radians and expressing the results in units of the given ellipsoid.Input coordinates are expected to contain:
- longitudes in degrees relative to the prime meridian (usually Greenwich),
- latitudes in degrees,
- optionally heights above the ellipsoid, in units of the ellipsoid axis (usually metres).
- distance from Earth center on the X axis (toward the intersection of prime meridian and equator),
- distance from Earth center on the Y axis (toward the intersection of 90°E meridian and equator),
- distance from Earth center on the Z axis (toward North pole).
- Parameters:
factory
- the factory to use for creating and concatenating the affine transforms.semiMajor
- the semi-major axis length.semiMinor
- the semi-minor axis length.unit
- the unit of measurement for the semi-axes and the ellipsoidal height.withHeight
-true
if source geographic coordinates include an ellipsoidal height (i.e. are 3-D), orfalse
if they are only 2-D.target
- whether the target coordinate shall be Cartesian or Spherical.- Returns:
- the conversion from geographic to geocentric coordinates.
- Throws:
org.opengis.util.FactoryException
- if an error occurred while creating a transform.
-
createGeodeticConversion
public static org.opengis.referencing.operation.MathTransform createGeodeticConversion(org.opengis.referencing.operation.MathTransformFactory factory, org.opengis.referencing.datum.Ellipsoid ellipsoid, boolean withHeight) throws org.opengis.util.FactoryException Creates a transform from geographic to Cartesian geocentric coordinates (convenience method). Invoking this method is equivalent to the following: The target type is assumed Cartesian because this is the most frequently used target.- Parameters:
factory
- the factory to use for creating and concatenating the affine transforms.ellipsoid
- the semi-major and semi-minor axis lengths with their unit of measurement.withHeight
-true
if source geographic coordinates include an ellipsoidal height (i.e. are 3-D), orfalse
if they are only 2-D.- Returns:
- the conversion from geographic to Cartesian geocentric coordinates.
- Throws:
org.opengis.util.FactoryException
- if an error occurred while creating a transform.
-
getContextualParameters
Returns the parameters used for creating the complete conversion. 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.- Overrides:
getContextualParameters
in classAbstractMathTransform
- Returns:
- the parameter values for the sequence of
normalize →
this
→ denormalize transforms.
-
getParameterValues
Returns a copy of internal parameter values of thisEllipsoidToCentricTransform
transform. The returned group contains parameter values for the number of dimensions and the eccentricity.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:
getParameterValues
in interfaceParameterized
- Overrides:
getParameterValues
in classAbstractMathTransform
- Returns:
- a copy of the internal parameter values for this transform.
- See Also:
-
getParameterDescriptors
Returns a description of the internal parameters of thisEllipsoidToCentricTransform
transform. The returned group contains parameter descriptors for the number of dimensions and the eccentricity.- Specified by:
getParameterDescriptors
in interfaceParameterized
- Overrides:
getParameterDescriptors
in classAbstractMathTransform
- Returns:
- a description of the internal parameters.
- See Also:
-
getSourceDimensions
public final int getSourceDimensions()Gets the dimension of input points, which is 2 or 3.- Specified by:
getSourceDimensions
in interfaceorg.opengis.referencing.operation.MathTransform
- Specified by:
getSourceDimensions
in classAbstractMathTransform
- Returns:
- 2 or 3.
- See Also:
-
getTargetDimensions
public final int getTargetDimensions()Gets the dimension of output points, which is 3.- Specified by:
getTargetDimensions
in interfaceorg.opengis.referencing.operation.MathTransform
- Specified by:
getTargetDimensions
in classAbstractMathTransform
- Returns:
- always 3.
- See Also:
-
getTargetType
Returns whether the target coordinate system is Cartesian or Spherical.- Returns:
- whether the target coordinate system is Cartesian or Spherical.
-
derivative
public org.opengis.referencing.operation.Matrix derivative(org.opengis.geometry.DirectPosition point) throws org.opengis.referencing.operation.TransformException Computes the derivative at the given location. This method relaxes a little bit theMathTransform
contract by accepting two- or three-dimensional points even if the number of dimensions does not match thegetSourceDimensions()
value.Rational: that flexibility on the number of dimensions is required for calculation of inverse transform derivative, because that calculation needs to inverse a square matrix with all terms in it before to drop the last row in the two-dimensional case.- Specified by:
derivative
in interfaceorg.opengis.referencing.operation.MathTransform
- Overrides:
derivative
in classAbstractMathTransform
- Parameters:
point
- the position where to evaluate the derivative.- Returns:
- the derivative at the specified point (never
null
). - Throws:
org.opengis.referencing.operation.TransformException
- if the derivative cannot be evaluated at the specified point.
-
transform
public org.opengis.referencing.operation.Matrix transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, boolean derivate) throws org.opengis.referencing.operation.TransformException Converts the (λ,φ) or (λ,φ,h) geodetic coordinates to to (X,Y,Z) geocentric coordinates, and optionally returns the derivative at that location.- Specified by:
transform
in classAbstractMathTransform
- Parameters:
srcPts
- the array containing the source coordinates (cannot benull
).srcOff
- the offset to the point to be transformed in the source array.dstPts
- the array into which the transformed coordinates is returned. May be the same thansrcPts
. May benull
if only the derivative matrix is desired.dstOff
- the offset to the location of the transformed point that is stored in the destination array.derivate
-true
for computing the derivative, orfalse
if not needed.- Returns:
- the matrix of the transform derivative at the given source position,
or
null
if thederivate
argument isfalse
. - Throws:
org.opengis.referencing.operation.TransformException
- if the point cannot be transformed or if a problem occurred while calculating the derivative.- See Also:
-
transform
private org.opengis.referencing.operation.Matrix transform(double λ, double φ, double h, double[] dstPts, int dstOff, boolean derivate, boolean wh) Implementation oftransform(double[], int, double[], int, boolean)
with possibility to override thewithHeight
value.- Parameters:
\u03bb
- longitude (radians).\u03c6
- latitude (radians).h
- height above the ellipsoid divided by the length of semi-major axis.dstPts
- the array into which the transformed coordinate is returned. May benull
if only the derivative matrix is desired.dstOff
- the offset to the location of the transformed point that is stored in the destination array.derivate
-true
for computing the derivative, orfalse
if not needed.wh
-true
for a 3×3 matrix, orfalse
for a 3×2 matrix excluding the height elements.
-
transform
public void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws org.opengis.referencing.operation.TransformException Converts the (λ,φ) or (λ,φ,h) geodetic coordinates to to (X,Y,Z) geocentric coordinates. This method performs the same conversion thantransform(double[], int, double[], int, boolean)
, but the formulas are repeated here for performance reasons.- Specified by:
transform
in interfaceorg.opengis.referencing.operation.MathTransform
- Overrides:
transform
in classAbstractMathTransform
- Parameters:
srcPts
- the array containing the source point coordinates.srcOff
- the offset to the first point to be transformed in the source array.dstPts
- the array into which the transformed point coordinates are returned. May be the same thansrcPts
.dstOff
- the offset to the location of the first transformed point that is stored in the destination array.numPts
- the number of point objects to be transformed.- Throws:
org.opengis.referencing.operation.TransformException
- if a point cannot be transformed.
-
inverseTransform
protected void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws org.opengis.referencing.operation.TransformException Converts Cartesian coordinates (X,Y,Z) to ellipsoidal coordinates (λ,φ) or (λ,φ,h). This method is invoked by the transform returned byinverse()
.- Parameters:
srcPts
- the array containing the source point coordinates.srcOff
- the offset to the first point to be transformed in the source array.dstPts
- the array into which the transformed point coordinates are returned. May be the same thansrcPts
.dstOff
- the offset to the location of the first transformed point that is stored in the destination array.numPts
- the number of point objects to be transformed.- Throws:
org.opengis.referencing.operation.TransformException
- if the calculation does not converge.
-
inverse
public org.opengis.referencing.operation.MathTransform inverse()Returns the inverse of this transform. The default implementation returns a transform that will delegate its work toinverseTransform(double[], int, double[], int, int)
.- Specified by:
inverse
in interfaceorg.opengis.referencing.operation.MathTransform
- Overrides:
inverse
in classAbstractMathTransform
- Returns:
- the conversion from (geo)centric to ellipsoidal coordinates.
-
computeHashCode
protected int computeHashCode()Computes a hash value for this transform. This method is invoked byAbstractMathTransform.hashCode()
when first needed.- Overrides:
computeHashCode
in classAbstractMathTransform
- Returns:
- the hash code value. This value may change between different execution of the Apache SIS library.
-
equals
Compares the specified object with this math transform for equality.- Specified by:
equals
in interfaceLenientComparable
- Overrides:
equals
in classAbstractMathTransform
- Parameters:
object
- the object to compare with this transform.mode
- the strictness level of the comparison. Default toSTRICT
.- Returns:
true
if the given object is considered equals to this math transform.- See Also:
-
beforeFormat
Given a transformation chain to format in WKT, inserts a "Geographic 2D to 3D" pseudo-conversion before this transform (normallytransforms.get(index)
) if this conversion expects no height.- Overrides:
beforeFormat
in classAbstractMathTransform
- Parameters:
transforms
- the full chain of concatenated transforms.index
- the index of this transform in thetransforms
chain.inverse
- alwaysfalse
, except if we are formatting the inverse transform.- Returns:
- index of this transform in the
transforms
chain after processing. - See Also:
-
tryConcatenate
protected org.opengis.referencing.operation.MathTransform tryConcatenate(boolean applyOtherFirst, org.opengis.referencing.operation.MathTransform other, org.opengis.referencing.operation.MathTransformFactory factory) throws org.opengis.util.FactoryException If this transform expects three-dimensional inputs, and if the transform just before this one unconditionally sets the height to zero, then replaces this transform by a two-dimensional one. The intent is to handle the following sequence of operations defined in the EPSG database:- Inverse of Geographic 3D to 2D conversion (EPSG:9659)
- Geographic/geocentric conversions (EPSG:9602)
EllipsoidToCentricTransform
instance allow the following optimizations:- Avoid computation of h value.
- Allow use of the more efficient
AffineTransform
before this transform instead of a transform based on a matrix of size 4×3.
- Overrides:
tryConcatenate
in classAbstractMathTransform
- Parameters:
applyOtherFirst
-true
if the transformation order isother
followed bythis
, orfalse
if the transformation order isthis
followed byother
.other
- the other math transform to (pre-)concatenate with this transform.factory
- the factory which is (indirectly) invoking this method, ornull
if none.- Returns:
- the combined math transform, or
null
if no optimized combined transform is available. - Throws:
org.opengis.util.FactoryException
- if an error occurred while combining the transforms.- See Also:
-
create2D
Creates a transform with the same parameters than this transform, but expecting two-dimensional inputs instead of three-dimensional.
-