org.cts.op.transformation
Class SevenParameterTransformation

java.lang.Object
  org.cts.IdentifiableComponent
      org.cts.op.AbstractCoordinateOperation
          org.cts.op.transformation.SevenParameterTransformation

All Implemented Interfaces:

Identifiable, CoordinateOperation, GeoTransformation

public class SevenParameterTransformation
extends AbstractCoordinateOperation
implements GeoTransformation

Seven-Parameter transformations are mathematical similarities or Helmert transformations in a three dimensional space.

In the geodesy domain, formulas are often linearized, considering that rotation angles are small enough to replace sin(x) by x, cos(x) by 1 and sin(x)*sin(x) by 0. This is the case of Bursa-Wolf formulas and Coordinate- frame rotation. If you want to use non linearized formulas, please, use the createSevenParameterTransformation constructor

Geodesian also use two different conventions for rotation angle :

• The Position Vector convention, used in Bursa-Wolf formulas are widely used in Europe. It is used by the International Association of Geodesy and recommended by ISO 19111). In this convention, rx, ry and rz are the rotations to be applied to the point's vector.
• The CoordinateFrame convention use opposite values for rotations. In this convention, most used in USA and recommended by NATO, rotation parameters represent rotations to be applied to the frame.

Author:

Michaël Michaud

Field Summary

static int	COORDINATE_FRAME COORDINATE_FRAME sign convention is such that a positive rotation of the frame about an axis is defined as a clockwise rotation of the coordinate reference frame when viewed from the origin of the cartesian coordinate reference system in the positive direction of that axis, that is a positive rotation about the Z-axis only from source coordinate reference system to target coordinate reference system will result in a smaller longitude value for the point in the target coordinate reference system.
static boolean	LINEARIZED LINEARIZED when formulas use x (rad) instead of sin(x).
static boolean	NOT_LINEARIZED NOT_LINEARIZED when formulas use exact sin(x) function.
static int	POSITION_VECTOR POSITION_VECTOR sign convention is such that a positive rotation about an axis is defined as a clockwise rotation of the position vector when viewed from the origin of the cartesian coordinate reference system in the positive direction of that axis; e.g. a positive rotation about the Z-axis only from source system to target system will result in a larger longitude value for the point in the target system.

Fields inherited from class org.cts.op.AbstractCoordinateOperation

precision

Fields inherited from interface org.cts.Identifiable

DEFAULT, LOCAL, UNKNOWN

Method Summary

static SevenParameterTransformation	createBursaWolfTransformation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm) Create a Bursa-Wolf transformation with the default precision.
static SevenParameterTransformation	createBursaWolfTransformation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm, double precision) Create a Bursa-Wolf transformation with a specific precision.
static SevenParameterTransformation	createCoordinateFrameRotation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm) Create a CoordinateFrame rotation with the default precision.
static SevenParameterTransformation	createCoordinateFrameRotation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm, double precision) Create a Coordinate Frame rotation with a specific precision.
static SevenParameterTransformation	createSevenParameterTransformation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm, int rotationConvention, boolean linearized) Create a 7-Parameter transformation with a default precision.
static SevenParameterTransformation	createSevenParameterTransformation(double tx, double ty, double tz, double rx_sec, double ry_sec, double rz_sec, double ds_ppm, int rotationConvention, boolean linearized, double precision) Create a 7-parameter transformation with a specific precision.
boolean	equals(Object o) Returns true if object is equals to this.
int	hashCode() Returns the hash code for this GeocentricTranslation.
CoordinateOperation	inverse() Creates the inverse CoordinateOperation.
String	toString() Return this SevenParameterTransformation as a String.
String	toWKT() Returns a WKT representation of the seven parameter transformation.
double[]	transform(double[] coord) Transform coord values

Methods inherited from class org.cts.op.AbstractCoordinateOperation

getPrecision

Methods inherited from class org.cts.IdentifiableComponent

addAlias, addRemark, getAliases, getAuthorityKey, getAuthorityName, getCode, getComponent, getIdentifier, getName, getRemarks, getShortName, setIdentifier, setRemarks, setShortName

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.cts.Identifiable

addAlias, addRemark, getAliases, getAuthorityKey, getAuthorityName, getCode, getName, getRemarks, getShortName, setRemarks, setShortName

Field Detail

POSITION_VECTOR

public static final int POSITION_VECTOR

POSITION_VECTOR sign convention is such that a positive rotation about an axis is defined as a clockwise rotation of the position vector when viewed from the origin of the cartesian coordinate reference system in the positive direction of that axis; e.g. a positive rotation about the Z-axis only from source system to target system will result in a larger longitude value for the point in the target system. [EPSG : Coordinate Conversions and Transformations including Formulas - Revised April 2006]

See Also:

Constant Field Values

COORDINATE_FRAME

public static final int COORDINATE_FRAME

COORDINATE_FRAME sign convention is such that a positive rotation of the frame about an axis is defined as a clockwise rotation of the coordinate reference frame when viewed from the origin of the cartesian coordinate reference system in the positive direction of that axis, that is a positive rotation about the Z-axis only from source coordinate reference system to target coordinate reference system will result in a smaller longitude value for the point in the target coordinate reference system. [EPSG : Coordinate Conversions and Transformations including Formulas - Revised April 2006]

See Also:

Constant Field Values

LINEARIZED

public static final boolean LINEARIZED

LINEARIZED when formulas use x (rad) instead of sin(x).

See Also:

Constant Field Values

NOT_LINEARIZED

public static final boolean NOT_LINEARIZED

NOT_LINEARIZED when formulas use exact sin(x) function.

See Also:

Constant Field Values

Method Detail

createSevenParameterTransformation

public static SevenParameterTransformation createSevenParameterTransformation(double tx,
                                                                              double ty,
                                                                              double tz,
                                                                              double rx_sec,
                                                                              double ry_sec,
                                                                              double rz_sec,
                                                                              double ds_ppm,
                                                                              int rotationConvention,
                                                                              boolean linearized)

Create a 7-Parameter transformation with a default precision.

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds)

ry_sec - rotation parameter around y axis (seconds)

rz_sec - rotation parameter around z axis (seconds)

ds_ppm - scale factor in ppm (parts per million)

rotationConvention - convention used for the rotation (Position- Vector or Coordinate-Frame)

linearized - true if the formula is linearized (sin(x) = x)

createSevenParameterTransformation

public static SevenParameterTransformation createSevenParameterTransformation(double tx,
                                                                              double ty,
                                                                              double tz,
                                                                              double rx_sec,
                                                                              double ry_sec,
                                                                              double rz_sec,
                                                                              double ds_ppm,
                                                                              int rotationConvention,
                                                                              boolean linearized,
                                                                              double precision)

Create a 7-parameter transformation with a specific precision.

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds)

ry_sec - rotation parameter around y axis (seconds)

rz_sec - rotation parameter around z axis (seconds)

ds_ppm - scale factor in ppm (parts per million)

rotationConvention - convention used for the rotation (Position- Vector or Coordinate-Frame)

linearized - true if the formula is linearized (sin(x) = x)

precision - precision of the transformation in meters

createBursaWolfTransformation

public static SevenParameterTransformation createBursaWolfTransformation(double tx,
                                                                         double ty,
                                                                         double tz,
                                                                         double rx_sec,
                                                                         double ry_sec,
                                                                         double rz_sec,
                                                                         double ds_ppm)

Create a Bursa-Wolf transformation with the default precision.

Bursa-Wolf transformation (or simplified seven parameters transformation or linearized Helmert transformation) is a 3D similarity with very small rotations (< 2") making it possible to approximate sin(r) with r, cos(r) with 1 and sin(r)*sin(r) with 0, which is very helpful to compute the transformation parameters from two data sets using a mean square method.

This is the the most widely used method to transform coordinates between two different datums, specially in Europe, and it is recommended by the International Association of Geodesy and ISO 19111).

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds, point vector convention)

ry_sec - rotation parameter around y axis (seconds, point vector convention)

rz_sec - rotation parameter around z axis (seconds, point vector convention)

ds_ppm - scale factor in ppm (parts per million)

createBursaWolfTransformation

public static SevenParameterTransformation createBursaWolfTransformation(double tx,
                                                                         double ty,
                                                                         double tz,
                                                                         double rx_sec,
                                                                         double ry_sec,
                                                                         double rz_sec,
                                                                         double ds_ppm,
                                                                         double precision)

Create a Bursa-Wolf transformation with a specific precision.

Bursa-Wolf transformation (or simplified seven parameters transformation or linearized Helmert transformation) is a 3D similarity with very small rotations (< 2") making it possible to approximate sin(r) with r, cos(r) with 1 and sin(r)*sin(r) with 0, which is very helpful to compute the transformation parameters from two data sets using a mean square method.

This is the the most widely used method to transform coordinates between two different datums, specially in Europe, and it is recommended by the International Association of Geodesy and ISO 19111).

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds, point vector convention)

ry_sec - rotation parameter around y axis (seconds, point vector convention)

rz_sec - rotation parameter around z axis (seconds, point vector convention)

ds_ppm - scale factor in ppm (parts per million)

precision - mean precision of the geodetic transformation

createCoordinateFrameRotation

public static SevenParameterTransformation createCoordinateFrameRotation(double tx,
                                                                         double ty,
                                                                         double tz,
                                                                         double rx_sec,
                                                                         double ry_sec,
                                                                         double rz_sec,
                                                                         double ds_ppm)

Create a CoordinateFrame rotation with the default precision.

Coordinate frame rotation (sometimes called Helmert transformation or similarity) is the same transformation as Bursa-Wolf except it uses the opposite rotation angle convention. It is used in USA and recommended by NATO.

Formulas are linearized as in BursaWolf transformation.

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds, point vector convention)

ry_sec - rotation parameter around y axis (seconds, point vector convention)

rz_sec - rotation parameter around z axis (seconds, point vector convention)

ds_ppm - scale factor in ppm (parts per million)

createCoordinateFrameRotation

public static SevenParameterTransformation createCoordinateFrameRotation(double tx,
                                                                         double ty,
                                                                         double tz,
                                                                         double rx_sec,
                                                                         double ry_sec,
                                                                         double rz_sec,
                                                                         double ds_ppm,
                                                                         double precision)

Create a Coordinate Frame rotation with a specific precision.

Coordinate frame rotation (sometimes called Helmert transformation or similarity) is the same transformation as Bursa-Wolf except it uses the opposite rotation angle convention. It is used in USA and recommended by NATO.

Formulas are linearized as in BursaWolf transformation.

Parameters:

tx - translation parameter along x axis (meters)

ty - translation parameter along y axis (meters)

tz - translation parameter along z axis (meters)

rx_sec - rotation parameter around x axis (seconds, point vector convention)

ry_sec - rotation parameter around y axis (seconds, point vector convention)

rz_sec - rotation parameter around z axis (seconds, point vector convention)

ds_ppm - scale factor in ppm (parts per million)

precision - mean precision of the geodetic transformation

transform

public double[] transform(double[] coord)
                   throws IllegalCoordinateException

Transform coord values

Specified by:

transform in interface CoordinateOperation

Specified by:

transform in class AbstractCoordinateOperation

Parameters:

coord - the coordinate to transform

Returns:

a double array containing the output coordinate

Throws:

IllegalCoordinateException - if coord is not compatible with this CoordinateOperation.

inverse

public CoordinateOperation inverse()
                            throws NonInvertibleOperationException

Creates the inverse CoordinateOperation.

Specified by:

inverse in interface CoordinateOperation

Overrides:

inverse in class AbstractCoordinateOperation

Throws:

NonInvertibleOperationException

toString

public String toString()

Return this SevenParameterTransformation as a String.

Overrides:

toString in class IdentifiableComponent

toWKT

public String toWKT()

Returns a WKT representation of the seven parameter transformation.

Specified by:

toWKT in interface GeoTransformation

equals

public boolean equals(Object o)

Returns true if object is equals to this. Tests equality between the references of both object, then tests if the seven parameters values (tx, ty, tz, etc) used by each SevenParameterTransformation are equals.

Overrides:

equals in class IdentifiableComponent

Parameters:

object - The object to compare this ProjectedCRS against

hashCode

public int hashCode()

Returns the hash code for this GeocentricTranslation.

Overrides:

hashCode in class IdentifiableComponent