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 dx 8606 Y-axis translation dy 8607 Z-axis translation dz 8608 X-axis rotation ex 8609 Y-axis rotation ey 8610 Z-axis rotation ez 8611 Scale difference ppm Geocentric coordinates transformation from ( X s, Y s, Z s) to ( X t, Y t, Z t) (ignoring unit conversions) X t Y t Z t = ( 1 + dS ) ⋅ 1 - r z + r y + r z 1 - r x - r y + r x 1 × X s Y s Z s + t x t y t z The numerical fields in this BursaWolfParameters class use the EPSG abbreviations with 4 additional constraints compared to the EPSG definitions:.
Unit of scale difference is fixed to parts per million. Unit of translation terms (, ) is fixed to metres. Unit of rotation terms (, ) 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. When Bursa-Wolf parameters are used BursaWolfParameters are used in three contexts:.
Created as a step while creating a from the EPSG database. Associated to a with the WGS 84 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 been found in the EPSG database for a given pair of source and target CRS.
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 (, ).
Alternatively, numerical fields can also be initialized by a call to. 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 is unspecified. Method Detail. getTargetDatum public getTargetDatum.
Returns the parameter values. The length of the returned array depends on the values:. If this instance is an, then the array length will be 14. Otherwise if this instance contains a non-zero value, then the array length will be 7 with, and 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 ), this method returns only the first 3 of the above-cited values. Sets the parameters to the given values. The given array can have any length. The first array elements will be assigned to the, and 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.
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Note however that those extra elements may be used by subclasses like. Parameters: elements - the new parameter values, as an array of any length. Since: 0.6. isIdentity public boolean isIdentity. 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 + /1000000 ┌ ┐ ┌ ┐ ┌ ┐ │ X' │ │ S -.RS +.RS │ │ X │ │ Y' │ = │ +.RS S -.RS │ │ Y │ │ Z' │ │ -.RS +.RS S │ │ 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. If the source datum and the do not use the same, then it is caller's responsibility to apply longitude rotation before to use the matrix returned by this method. 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 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:. setPositionVectorTransformation public void setPositionVectorTransformation( matrix, double tolerance) throws. Sets all Bursa-Wolf parameters from the given Position Vector transformation matrix. The matrix shall comply to the following constraints:.
The matrix shall be. The sub-matrix defined by matrix without the last row and last column shall be (a.k.a. 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.
Throws: - if the specified matrix does not meet the conditions. Geocontrol2 pc serial key. See Also:. getDomainOfValidity public getDomainOfValidity.
ILWIS Download Documentation Applications This page contains information and downloadable executables or source code for:. The ILWIS add-ons are formally not part of the ILWIS package; questions on these tools cannot be handled by ILWIS support.
Inverse Molodensky (, 326 KB) This is a tool that enables the user to find Molodensky Datum shifts (D X, D Y, D Z) between the global WGS84 reference and a local geodetic reference. The user has to provide the following input:. The latitude, longitude and ellipsoidal height of 3 points in the WGS84 system. The latlons must be expressed in arcseconds, and the heights in meters above the ellipsoid. The parameters a, and 1/f of the ellipsoid used in the Local reference system (semi-major axis and inverse flattening). The latitude, longitude and ellipsoidal height of 3 corresponding points in the Local system (in arcseconds and meters resp.).
The Molodensky shifts are then calculated in meters (with cm precision). Remark: The program uses the average of the three point-coordinates in either system. It works fine also if one has only one or two control points available. In those cases one has simply to repeat the same coordinates in the other (two) boxes, because the actual program expects 3 control points and hence all input fields being used.
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Datum Transformation (, 344 KB) This is a tool that enables the user to apply a full Datum transformation between 2 geodetic reference systems (input, output). One of the systems can be the global WGS84 reference for instance, and the other can be any Local Reference System defined on any user-defined ellipsoid. The usual reference ellipsoids (Bessel, Clarke, Hayford (International), Airy, Everest etc.) are also provided. The transformation method uses 7 parameters (and optionally the 3 geocentric coordinates of a local centroid or pivot point). The method is known as Bursa-Wolf, Molodensky-Badekas (Leica) or Position-Vector (Esri) transformation.
The user has to provide the following input:. The 3 shift components of the position vector (in meters).
The 3 rotations of the coordinate frame about the respective axes (in 10e-9 radians, 'nano-radians'). The difference of scale (in 10e-9 m per meter). Optionally the geocentric coordinates (with respect to the axes of the input ellipsoid) of a local centroid (origin of Reference System 1). The ellipsoid parameters a and 1/f of the input system (provided in a combo box for many usual ellipsoids).
The ellipsoid parameters a and 1/f of the output system (provided for many usual ellipsoids). An input (terrain-) point P, given in latitude, longitude (decimal degrees) and height (m above the input ellipsoid). The computed output consists of:.
Geocentric coordinates of P in the input system (Reference System 1). Geocentric coordinates of P in the output system (Reference System 2). Ellipsoidal latitude, longitude and height of P in the output system (again in decimal degrees and m respectively). Datum Transformation in ArcMap (ESRI) (, 14 KB) In Esri 's ArcGis environment one can program VBA code to customize Spatial Reference possibilities. In ArcMap there is no tool to find or compute Datum transformation parameters from measured or observed control data. Below you can find VBA code to implement this as an interactive dialogue that can be started from a button control.
In the tool, two pointfiles are expected (ESRI shape format) with 3D geographic coordinates (lat, lon, height), each of them defined on a different but known spheroid. Common points (pertaining to identical locations) are used to calculate the Datum transformation parameters.
The user can select either of the two control point layers; the selected one will serve as the 'source map' whose correction to the spatial reference of the other layer will be calculated. Optionally this transformation is carried out in the current data frame. Finally, an option is offerd to store the transformation parameters in a custom geogtran file for later use.
Find datum transformation parameters - Method page Find datum transformation parameters Select transformation method This second page of the Datum transformation parameters wizard allows you to choose the method you wish to use to calculate the datum transformation parameters between the two sets of control points. The concept of each calculation method is shortly explained.
Dialog box options: Geo-centric datum shift: Calculates the translation vector (dX, dY, dZ, i.e. Differences in geocentric coordinates in meters) between:.
the centroid of all point-coordinates in the first point map, using a local (unknown) datum,. and the centroid of all point-coordinates in the second point map, using a global datum (preferably WGS 84), so that the point-coordinates of the first point map can be transformed to the second. Molodensky: Calculates the translation vector (dX, dY, dZ, i.e. Differences in geocentric coordinates in meters) between:. the centroid of all point-coordinates in the first point map, using a local (unknown) datum,. and the centroid of all point-coordinates in the second point map, using a global datum (preferably WGS 84),. and inverts the Molodensky transformation equations and avoids the use of geocentric coordinates, so that the point-coordinates of the first point map can be transformed to the second.
Bursa Wolf: Calculates translations (dX, dY, dZ, i.e. Differences in geocentric coordinates in meters), calculates rotations (Rot X, Rot Y, Rot Z in microradians and in arc seconds), and calculates the scale difference factor (dScale) between:. all point-coordinates in the first point map, using a local (unknown) datum,. and all point-coordinates in the second point map, using a global datum (preferably WGS 84),. using the center of the ellipsoid as the rotation center (pivot), so that the point-coordinates of the first point map can be transformed to the second. Compute scale and rotations first: When you selected the Bursa Wolf or the Molodensky Badekas method:.
Select this check box to have the scale factor and the rotations calculated first to obtain more accurate scale and rotation parameters (independent of the stochastic errors in the translations). Clear this check box to have the translation vector calculated first. Molodensky Badekas: Calculates translations (dX, dY, dZ, i.e. Differences in geocentric coordinates), calculates rotations (Rot X, Rot Y, Rot Z in microradians and in arc seconds), and calculates the scale factor (dScale) between:. all point-coordinates in the first point map, using a local (unknown) datum,. and all point-coordinates in the second point map, using a global datum (preferably WGS 84),. using a user-defined centroid (in X, Y, Z as geocentric coordinates) on the ellipsoid of the first point map as the rotation center (pivot), so that the point-coordinates of the first point map can be transformed to the second.
Bursa Wolf Transformation
Xo, Yo, Zo: When you selected the Molodensky Badekas method, you must specify a rotation center. As defaults, the centroids of the X, Y, Z geocentric coordinates on the ellipsoid of the first point map are given. If you wish, you can overrule these defaults, and specify your own Xo, Yo, Zo geocentric coordinates (on the ellipsoid of the first point map) as the rotation center. When you click the Next button, you will go to the where you can inspect, and optionally save, the calculated datum transformation parameters. Additional information The general process of the calculations is presented below. Conversions take place between map coordinates, latlon coordinates on the (local) ellipsoid, and geocentric coordinates.
Geographic Transformation Methods Moving your data between coordinate systems sometimes includes transforming between the geographic coordinate systems. Because the geographic coordinate systems contain datums that are based on spheroids, a geographic transformation also changes the underlying spheroid. There are several methods, which have different levels of accuracy and ranges, for transforming between datums. The accuracy of a particular transformation can range from centimeters to meters depending on the method and the quality and number of control points available to define the transformation parameters. A geographic transformation is always defined in a particular direction. When working with geographic transformations, if no mention is made of the direction, the command will handle the directionality automatically.
Werewolf Transformation
For example, if converting data from WGS 1984 to NAD 1927, you can pick a transformation called NAD1927toWGS19843 and the software will apply it correctly. A geographic transformation always converts geographic (longitude–latitude) coordinates. Some methods convert the geographic coordinates to geocentric (X,Y,Z) coordinates, transform the X,Y,Z coordinates, and convert the new values back to geographic coordinates. These include the Geocentric Translation, Molodensky, Coordinate Frame, and Molodensky-Badekas methods. Other methods, such as NADCON and NTv2 use a grid of differences and convert the longitude–latitude values directly. Equation-based methods Equation-based transformation methods can be classified into the following four method types. Usually the transformation parameters are defined as going from a local datum to WGS 1984 or another geocentric datum.
Three-parameter methods The simplest datum transformation method is a geocentric, or three-parameter, transformation. The geocentric transformation models the differences between two datums in the X,Y,Z coordinate system. One datum is defined with its center at 0,0,0. The center of the other datum is defined at some distance (DX,DY,DZ) in meters away.
The three parameters are linear shifts and are always in meters. Seven-parameter methods A more complex and accurate datum transformation is possible by adding four more parameters to a geocentric transformation. The seven parameters are three linear shifts (DX,DY,DZ), three angular rotations around each axis (rx,ry,rz), and a scale factor. The rotation values are given in decimal seconds, while the scale factor is in parts per million (ppm).
The rotation values are defined in two different ways. It's possible to define the rotation angles as positive either clockwise or counterclockwise as you look toward the origin of the X,Y,Z systems. The United States, Australia, New Zealand, and a few other countries define the equations such that the rotation values are positive counterclockwise. This method is called the Coordinate Frame Rotation transformation.
Europe uses a different convention called the Position Vector transformation. Both methods are sometimes referred to as the Bursa–Wolf method. In the Projection Engine, the Coordinate Frame and Bursa–Wolf methods are the same. Both Coordinate Frame and Position Vector methods are supported, and it is easy to convert transformation values from one method to the other simply by changing the signs of the three rotation values.
For example, the parameters to convert from the WGS 1972 datum to the WGS 1984 datum with the Coordinate Frame method are (in the order DX,DY,DZ,rx,ry,rz,s): (0.0, 0.0, 4.5, 0.0, 0.0, -0.554, 0.227) To use the same parameters with the Position Vector method, change the sign of the rotation so the new parameters are: (0.0, 0.0, 4.5, 0.0, 0.0, +0.554, 0.227) It's impossible to tell from the parameters alone which convention is being used. If you use the wrong method, your results can return inaccurate coordinates. The only way to determine how the parameters are defined is by checking a control point whose coordinates are known in the two systems. The Molodensky–Badekas method is a variation of the seven-parameter methods.
It has an additional three parameters that define the XYZ origin of rotation. Sometimes this point is known as the origin of the datum, or geographic coordinate system. Given the XYZ origin of rotation point, it is possible to calculate an equivalent Coordinate Frame transformation. The DX, DY, and DZ values will change but the rotation and scale values will remain the same.
Molodensky method The Molodensky method converts directly between two geographic coordinate systems without actually converting to an X,Y,Z system. The Molodensky method requires three shifts (DX,DY,DZ) and the differences between the semimajor axes (Da) and the flattenings (Df) of the two spheroids. The Projection Engine automatically calculates the spheroid differences according to the datums involved. Abridged Molodensky method The Abridged Molodensky method is a simplified version of the Molodensky method. Grid-based methods Grid-based transformation methods include the following: NADCON and HARN methods The United States uses a grid-based method to convert between geographic coordinate systems.
Grid-based methods allow you to model the differences between the systems and are potentially the most accurate method. The area of interest is divided into cells. The National Geodetic Survey (NGS) publishes grids to convert between NAD 1927 and other older geographic coordinate systems and NAD 1983. These transformations are grouped into the NADCON method. The main NADCON grid, CONUS, converts the contiguous 48 states. The other NADCON grids convert older geographic coordinate systems to NAD 1983 for:. Alaska.
Hawaiian islands. Puerto Rico and Virgin Islands. St. Lawrence, and St. Paul Islands in Alaska The accuracy is approximately 0.15 meters for the contiguous states, 0.50 for Alaska and its islands, 0.20 for Hawaii, and 0.05 for Puerto Rico and the Virgin Islands.
Accuracies can vary depending on how good the geodetic data in the area was when the grids were computed (NADCON, 1999). The Hawaiian islands were never on NAD 1927. They were mapped using several datums that are collectively known as the Old Hawaiian datums.
New surveying and satellite measuring techniques have allowed NGS and the states to update the geodetic control point networks. As each state is finished, the NGS publishes a grid that converts between NAD 1983 and the more accurate control point coordinates. Originally, this effort was called the High Precision Geodetic Network (HPGN).
It is now called the High Accuracy Reference Network (HARN). Four territories and 46 states have published HARN grids as of January 2004. HARN transformations have an accuracy approximately 0.05 meters (NADCON, 2000). The difference values in decimal seconds are stored in two files: one for longitude and the other for latitude. A bilinear interpolation is used to calculate the exact difference between the two geographic coordinate systems at a point. The grids are binary files, but a program, NADGRD, from the NGS, allows you to convert the grids to American Standard Code for Information Interchange (ASCII) format. Shown at the bottom of the page is the header and first row of the CSHPGN.LOA file.
This is the longitude grid for Southern California. The format of the first row of numbers is, in order, the number of columns, number of rows, number of z–values (always one), minimum longitude, cell size, minimum latitude, cell size, and not used. The next 37 values in this case are the longitude shifts from -122° to -113° at 32° N in 0.25°, or 15 minute, intervals in longitude. NADCON EXTRACTED REGION NADGRD 37 21 1 -122.00000.0.25.00000.007383.004806.002222.000347.002868.005296.007570.009609.011305.012517.013093.012901.011867.009986.007359.004301.001389.001164.003282.004814.005503.005361.004420.002580.000053.002869.006091.009842.014240.019217.025104.035027.050254.072636.087238.099279.110968 Send your comments to:.