BursaWolfParameters

All Implemented Interfaces:: Serializable, Cloneable

Direct Known Subclasses:: TimeDependentBWP

public class BursaWolfParameters extends FormattableObject implements Cloneable, Serializable

Parameters for a geographic transformation between two datum having the same prime meridian. Bursa-Wolf parameters are also known as Helmert transformation parameters. For an explanation of their purpose, see the Bursa-Wolf parameters section of DefaultGeodeticDatum class javadoc.

The Bursa-Wolf parameters shall be applied to geocentric coordinates, where the X axis points towards the Prime Meridian (usually Greenwich), the Y axis points East, and the Z axis points North.

Note: The upper case letters are intentional. By convention, (X, Y, Z) stand for geocentric coordinates while (x, y, z) stand for projected coordinates.

The "Bursa-Wolf" formula is expressed with 7 parameters, listed in the table below. The code, name and abbreviation columns list EPSG identifiers, while the legacy column lists the identifiers used in the legacy OGC 01-009 specification (still used in some Well Known Texts).

Parameters defined by EPSG
Code	Name	Abbr.	Legacy
8605	X-axis translation	`tX`	`dx`
8606	Y-axis translation	`tY`	`dy`
8607	Z-axis translation	`tZ`	`dz`
8608	X-axis rotation	`rX`	`ex`
8609	Y-axis rotation	`rY`	`ey`
8610	Z-axis rotation	`rZ`	`ez`
8611	Scale difference	`dS`	`ppm`

Geocentric coordinates transformation

from (X_s, Y_s, Z_s) to (X_t, Y_t, Z_t)
(ignoring unit conversions)

$[\begin{matrix} X_{t} \\ Y_{t} \\ Z_{t} \end{matrix}] = (1 + dS) \cdot [\begin{matrix} 1 & - r_{z} & + r_{y} \\ + r_{z} & 1 & - r_{x} \\ - r_{y} & + r_{x} & 1 \end{matrix}] \times [\begin{matrix} X_{s} \\ Y_{s} \\ Z_{s} \end{matrix}] + [\begin{matrix} t_{x} \\ t_{y} \\ t_{z} \end{matrix}]$

The numerical fields in this BursaWolfParameters class use the EPSG abbreviations with 4 additional constraints compared to the EPSG definitions:

Unit of scale difference (dS) is fixed to parts per million.
Unit of translation terms (tX, tY, tZ) is fixed to metres.
Unit of rotation terms (rX, rY, rZ) is fixed to arc-seconds.
Sign of rotation terms is fixed to the Position Vector convention (EPSG operation method 9606). This is the opposite sign than the Coordinate Frame Rotation (EPSG operation method 9607). The Position Vector convention is used by IAG and recommended by ISO 19111.

Source and target geodetic datum

The source datum in above coordinates transformation is the DefaultGeodeticDatum instance that contain this BursaWolfParameters. It can be any datum, including datum that are valid only locally. The target datum is specified at construction time and is often, but not necessarily, the World Geodetic System 1984 (WGS 84) datum.

If the source and target datum does not have the same prime meridian, then it is user's responsibility to apply longitude rotation before to use the Bursa-Wolf parameters.

When Bursa-Wolf parameters are used

BursaWolfParameters are used in three contexts:

Created as a step while creating a coordinate operation from the EPSG database.
Associated to a DefaultGeodeticDatum with the WGS 84 target datum for providing the parameter values to display in the TOWGS84[…] element of Well Known Text (WKT) version 1. Note that WKT version 2 does not have TOWGS84[…] element anymore.
Specified at DefaultGeodeticDatum construction time for arbitrary target datum. Apache SIS will ignore those Bursa-Wolf parameters, except as a fallback if no parameters can be found in the EPSG database for a given pair of source and target CRS.

In EPSG terminology, Apache SIS gives precedence to the late-binding approach (case 1 above) over the early-binding approach (case 3 above).

Since:

0.4

See Also:

Field Summary

Fields

Modifier and Type

Field

Description

double

dS

The scale difference in parts per million (EPSG:8611).

double

rX

X-axis rotation in arc-seconds (EPSG:8608), sign following the Position Vector convention.

double

rY

Y-axis rotation in arc-seconds (EPSG:8609), sign following the Position Vector convention.

double

rZ

Z-axis rotation in arc-seconds (EPSG:8610), sign following the Position Vector convention.

double

tX

X-axis translation in metres (EPSG:8605).

double

tY

Y-axis translation in metres (EPSG:8606).

double

tZ

Z-axis translation in metres (EPSG:8607).
Constructor Summary

Constructors

Constructor

Description

BursaWolfParameters(GeodeticDatum targetDatum, Extent domainOfValidity)

Creates a new instance for the given target datum and domain of validity.
Method Summary

Modifier and Type

Method

Description

BursaWolfParameters

clone()

Returns a copy of this object.

boolean

equals(Object object)

Compares the specified object with this object for equality.

protected String

formatTo(Formatter formatter)

Formats this object as a Well Known Text ToWGS84[…] element.

Extent

getDomainOfValidity()

Returns the region or timeframe in which a coordinate transformation based on those Bursa-Wolf parameters is valid, or null if unspecified.

Matrix

getPositionVectorTransformation(Date time)

Returns the position vector transformation (geocentric domain) as an affine transform.

GeodeticDatum

getTargetDatum()

Returns the target datum for this set of parameters, or null if unknown.

double[]

getValues()

Returns the parameter values.

int

hashCode()

Returns a hash value for this object.

void

invert()

Inverts in-place the transformation by inverting the sign of all numerical parameters.

boolean

isIdentity()

Returns true if a transformation built from this set of parameters would perform no operation.

boolean

isTranslation()

Returns true if a transformation built from this set of parameters would perform only a translation.

void

reverseRotation()

Inverts in-place the sign of rotation terms (rX, rY, rZ).

void

setPositionVectorTransformation(Matrix matrix, double tolerance)

Sets all Bursa-Wolf parameters from the given Position Vector transformation matrix.

void

setValues(double... elements)

Sets the parameters to the given values.

Methods inherited from class FormattableObject
print, toString, toString, toWKT

Methods inherited from class Object
finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details
- tX
  
  public double tX
  
  X-axis translation in metres (EPSG:8605). The legacy OGC parameter name is "dx".
- tY
  
  public double tY
  
  Y-axis translation in metres (EPSG:8606). The legacy OGC parameter name is "dy".
- tZ
  
  public double tZ
  
  Z-axis translation in metres (EPSG:8607). The legacy OGC parameter name is "dz".
- rX
  
  public double rX
  
  X-axis rotation in arc-seconds (EPSG:8608), sign following the Position Vector convention. The legacy OGC parameter name is "ex".
- rY
  
  public double rY
  
  Y-axis rotation in arc-seconds (EPSG:8609), sign following the Position Vector convention. The legacy OGC parameter name is "ey".
- rZ
  
  public double rZ
  
  Z-axis rotation in arc-seconds (EPSG:8610), sign following the Position Vector convention. The legacy OGC parameter name is "ez".
- dS
  
  public double dS
  
  The scale difference in parts per million (EPSG:8611). The legacy OGC parameter name is "ppm".
  Example
  If a distance of 100 km in the source coordinate reference system translates into a distance of 100.001 km in the target coordinate reference system, the scale difference is 1 ppm (the ratio being 1.000001).
Constructor Details
- BursaWolfParameters
  
  public BursaWolfParameters(GeodeticDatum targetDatum, Extent domainOfValidity)
  
  Creates a new instance for the given target datum and domain of validity. All numerical parameters are initialized to 0, which correspond to an identity transform. Callers can assign numerical values to the public fields of interest after construction. For example, many coordinate transformations will provide values only for the translation terms (tX, tY, tZ).
  Alternatively, numerical fields can also be initialized by a call to setPositionVectorTransformation(Matrix, double).
  
  Parameters:
  
  targetDatum - the target datum (usually WGS 84) for this set of parameters, or null if unknown.
  
  domainOfValidity - area or region in which a coordinate transformation based on those Bursa-Wolf parameters is valid, or null if unspecified.
Method Details
- getTargetDatum
  
  public GeodeticDatum getTargetDatum()
  
  Returns the target datum for this set of parameters, or null if unknown. This is usually the WGS 84 datum, but other targets are allowed.
  The source datum is the DefaultGeodeticDatum that contain this BursaWolfParameters instance.
  
  Returns:
  
  the target datum for this set of parameters, or null if unknown.
- getValues
  
  public double[] getValues()
  Returns the parameter values. The length of the returned array depends on the values:
  
  If this instance is an TimeDependentBWP, then the array length will be 14.
  
  Otherwise if this instance contains a non-zero dS value, then the array length will be 7 with tX, tY, tZ, rX, rY, rZ and dS values in that order.
  
  Otherwise if this instance contains non-zero rotation terms, then this method returns the first 6 of the above-cited values.
  
  Otherwise (i.e. this instance is a translation), this method returns only the first 3 of the above-cited values.
  
  Compatibility note
  The rules about the arrays of length 3, 6 or 7 are derived from the Well Known Text (WKT) version 1 specification. The rule about the array of length 14 is an extension.
  Returns:
  
  the parameter values as an array of length 3, 6, 7 or 14.
  
  Since:
  
  0.6
- setValues
  
  public void setValues(double... elements)
  Sets the parameters to the given values. The given array can have any length. The first array elements will be assigned to the tX, tY, tZ, rX, rY, rZ and dS fields in that order.
  
  If the length of the given array is not sufficient for assigning a value to every fields, then the remaining fields are left unchanged (they are not reset to zero, but this is not a problem if this BursaWolfParameters is a new instance).
  
  If the length of the given array is greater than necessary, then extra elements are ignored by this base class. Note however that those extra elements may be used by subclasses like TimeDependentBWP.
  Parameters:
  
  elements - the new parameter values, as an array of any length.
  
  Since:
  
  0.6
- isIdentity
  
  public boolean isIdentity()
  
  Returns true if a transformation built from this set of parameters would perform no operation. This is true when the value of all parameters is zero.
  
  Returns:
  
  true if the parameters describe no operation.
- isTranslation
  
  public boolean isTranslation()
  
  Returns true if a transformation built from this set of parameters would perform only a translation.
  
  Returns:
  
  true if the parameters describe a translation only.
- reverseRotation
  
  public void reverseRotation()
  
  Inverts in-place the sign of rotation terms (rX, rY, rZ). This method can be invoked for converting a Coordinate Frame Rotation transformation (EPSG operation method 9607) to a Position Vector transformation (EPSG operation method 9606). The latter convention is used by IAG and recommended by ISO 19111.
- invert
  
  public void invert()
  
  Inverts in-place the transformation by inverting the sign of all numerical parameters. The position vector transformation matrix created from inverted Bursa-Wolf parameters will be approximately equals to the inverse of the matrix created from the original parameters. The equality holds approximately only because the parameter values are very small (parts per millions and arc-seconds).
- getPositionVectorTransformation
  
  public Matrix getPositionVectorTransformation(Date time)
  Returns the position vector transformation (geocentric domain) as an affine transform. For transformations that do not depend on time, the formula is as below where R is a conversion factor from arc-seconds to radians:
  R = toRadians(1″) S = 1 + dS/1000000 ┌ ┐ ┌ ┐ ┌ ┐ │ X' │ │ S -rZ*RS +rY*RS tX │ │ X │ │ Y' │ = │ +rZ*RS S -rX*RS tY │ │ Y │ │ Z' │ │ -rY*RS +rX*RS S tZ │ │ Z │ │ 1 │ │ 0 0 0 1 │ │ 1 │ └ ┘ └ ┘ └ ┘
  This affine transform can be applied on geocentric coordinates. This is identified as operation method 1033 in the EPSG database. Those geocentric coordinates are typically converted from geographic coordinates in the region or timeframe given by getDomainOfValidity().
  If the source datum and the target datum do not use the same prime meridian, then it is caller's responsibility to apply longitude rotation before to use the matrix returned by this method.
  
  Time-dependent transformation
  Some transformations use parameters that vary with time (e.g. operation method EPSG:1053). Users can optionally specify a date for which the transformation is desired. For transformations that do not depends on time, this date is ignored and can be null. For time-dependent transformations, null values default to the transformation's reference time.
  Inverse transformation
  The inverse transformation can be approximated by reversing the sign of the 7 parameters before to use them in the above matrix. This is often considered sufficient since position vector transformations are themselves approximations. However, Apache SIS will rather use MatrixSIS.inverse() in order to increase the chances that concatenation of transformations A → B followed by B → A gives back the identity transform.
  Parameters:
  
  time - date for which the transformation is desired, or null for the transformation's reference time.
  
  Returns:
  
  an affine transform in geocentric space created from this Bursa-Wolf parameters and the given time.
  
  See Also:
  
  DefaultGeodeticDatum.getPositionVectorTransformation(GeodeticDatum, Extent)
- setPositionVectorTransformation
  
  public void setPositionVectorTransformation(Matrix matrix, double tolerance) throws IllegalArgumentException
  Sets all Bursa-Wolf parameters from the given Position Vector transformation matrix. The matrix shall comply to the following constraints:
  
  The matrix shall be affine.
  
  The sub-matrix defined by matrix without the last row and last column shall be skew-symmetric (a.k.a. antisymmetric).
  Parameters:
  
  matrix - the matrix from which to get Bursa-Wolf parameters.
  
  tolerance - the tolerance error for the skew-symmetric matrix test, in units of PPM or arc-seconds (e.g. 1E-8).
  
  Throws:
  
  IllegalArgumentException - if the specified matrix does not met the conditions.
  
  See Also:
  
  getPositionVectorTransformation(Date)
- getDomainOfValidity
  
  public Extent getDomainOfValidity()
  
  Returns the region or timeframe in which a coordinate transformation based on those Bursa-Wolf parameters is valid, or null if unspecified. If an extent was specified at construction time, then that extent is returned. Otherwise the datum domain of validity (which may be null) is returned.
  Returns:
  
  area or region or timeframe in which the coordinate transformation is valid, or null.
  
  See Also:
  
  DefaultExtent
- clone
  
  public BursaWolfParameters clone()
  
  Returns a copy of this object.
  
  Overrides:
  
  clone in class Object
  
  Returns:
  
  a copy of all parameters.
- equals
  
  public boolean equals(Object object)
  
  Compares the specified object with this object for equality.
  
  Overrides:
  
  equals in class Object
  
  Parameters:
  
  object - the object to compare with the parameters.
  
  Returns:
  
  true if the given object is equal to this BursaWolfParameters.
- hashCode
  
  public int hashCode()
  
  Returns a hash value for this object.
  
  Overrides:
  
  hashCode in class Object
  
  Returns:
  
  the hash code value. This value does not need to be the same in past or future versions of this class.
- formatTo
  
  protected String formatTo(Formatter formatter)
  
  Formats this object as a Well Known Text ToWGS84[…] element. The WKT contains the parameters in translation, rotation, scale order, like below:
  TOWGS84[tX, tY, tZ, rX, rY, rZ, dS]
  The element name is "ToWGS84" in the common case where the target datum is WGS 84. For other targets, the element name will be derived from the datum name.
  Compatibility note
  TOWGS84 is defined in the WKT 1 specification only.
  Specified by:
  
  formatTo in class FormattableObject
  
  Parameters:
  
  formatter - The formatter where to format the inner content of this WKT element.
  
  Returns:
  
  Usually "ToWGS84".
  
  See Also:
  
  FormattableObject.toWKT()
  
  FormattableObject.toString()

Class BursaWolfParameters

Source and target geodetic datum

When Bursa-Wolf parameters are used

Field Summary

Constructor Summary

Method Summary

Methods inherited from class FormattableObject

Methods inherited from class Object

Field Details

tX

tY

tZ

rX

rY

rZ

dS

Example

Constructor Details

BursaWolfParameters

Method Details

getTargetDatum

getValues

Compatibility note

setValues

isIdentity

isTranslation

reverseRotation

invert

getPositionVectorTransformation

Time-dependent transformation

Inverse transformation

setPositionVectorTransformation

getDomainOfValidity

clone

equals

hashCode

formatTo

Compatibility note