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# Transformation

Transformation
The process that converts coordinates from one coordinate system to another through translation, rotation, and scaling.

Affine Transformation
affine transformation - [Euclidean geometry] A geometric transformation that scales, rotates, skews, and/or translates images or coordinates between any two Euclidean spaces. It is commonly used in GIS to transform maps between coordinate systems.

A common transformation in North American data is between NAD83 and WGS84, or between the GCS North American 1927 and GCS WGS 1984 geographic coordinate systems as shown below.

Geometric Transformations
This function is concerned with the registering of a data layer to a common coordinate scheme. This usually involves registering selected data layers to a standard data layer already registered. The term rubber sheeting is often used to describe this function.

00155: No transformation exists from the data frame's datum to WGS 1984 Major Auxiliary Sphere ...

Elastic body ~
A least-squares computer software program run against a raw digitized data source map to produce a geographically true "X" and "Y" coordinate database referenced to any standard map system.

This land use/land ~ modeling workshop will focus on three main themes: (1) the use of landscape ecology approaches for land ~/land use change modeling, and, in particular, the need to address the integration of the human dimensi ons and aspects of scale into modeling; ...

To Use Version 2 of the Canadian National ~
To Use the New High Accuracy GDA94 Datum
To Set Up a GDC File
To Set Up a GDC File for the United States
To Set Up a GDC File for France
To Set Up a GDC File for Australia and New Zealand ...

~s and Associative Procedures
In addition to nouns, our analysis requires associations. We need to model what we mean by properties NEAR subway stops. For this we will use many of the basic procedures of vector GIS: ...

B-56. The next step is derivation of ~ parameters between minimally constrained adjusted vectors and selected points in local geodetic system. This usually carried out together with a least-squares adjustment.

6.1.7 ~
~ is the conversion of coordinates from one coordinate system to another coordinate system.

Format ~s
Format is the pattern into which data are systematically arranged for use on a computer. Format ~s are used to get data into acceptable GIS format.

~ Parameter Computation: 5) Compute image-to-photo ~ parameters
6) Initialize exposure station parameters
7) Compute photo-to-target ~ parameters ...

The ~ phase of a Spatial ETL process allows a variety of functions; some of these are similar to standard ETL, but some are unique to spatial data.

The ~ from the latitude and longitude co-ordinates into the geocentric co-ordinates is rather straightforward and turns ellipsoidal latitude (j), longitude (l) and height (h) into X,Y and Z, using 3 direct equations that contain the ellipsoidal parameters a and e.

the ~ is made to the surface of a cone tangent at a small circle (tangent case) or intersecting at two small circles (secant case) on a globe ...

Affine ~ - A combination of linear transformations (rotation and scaling) followed by translation (shift of position). In geographic data processing, affine ~ is used to register maps of different scales and origins.
...

2. New ~ method for map projection using Delaunay Triangulation, in addition to the least square bi-linear method.
4. Added support to SDL format for MapGuide software. Digitize your maps and publish them directly to the Internet with R2V.

Topic 9: ~ of Raster Datasets
Supplemental references
Knuth, Donald., The Art of Computer Programming, Volume 3: Sorting and Searching. Second Edition, 1998, Addison-Wesley, MA. ISBN 0-201-89685-0.

DataGroup ~ Services
Architectural:
Editing Multiple Space
Roof Builde
New Handrail too
Slabs - DataGroup Placement and Modif
Flip/Side Offset for Wall Placemen
New Catalogs and Conten
Unified Casework Schema/Catalog ...

Coordinate ~s defined by mapping relations
Usually those relations are not functions, as the same point on the sphere may be represented by several points on the map.

However the ~ is easy to automatize if the data in their metadata header contain ~ parameters to a generally accepted local reference corresponding the site the data describe.

3) Apply the ~ matrix to each pixel on the image to map the old location to the new location. In the case of DEMs, each point has three dimensions while L1A data has two dimensions and involves only planar ~s.

map-to-page ~ The process of positioning and scaling a map on a graphic page. It controls how coverage coordinates are transformed into graphics on the display screen or plotter page. (Coverages are not maps; they contain the unscaled coordinates that ArcInfo uses to draw maps.) ...

The geometric ~s that arise during map reprojection efforts can cause problems for raster graphics and represent a third disadvantage to using the raster data model.

Provides point ~ from one coordinate reference system to another.
Includes ~ between datums.
Large number of projection classes supported.
Implemented Standards¶ ...

A mathematical ~ of he earth's surface to create a flat map sheet. The UTM projection is well suited for small areas.
Unzip/Zip ...

Area (containment): arcs containing a polygon with given area ~ The process of converting data from one coordinate system to another through translation, rotation, and scaling.

No map projection ~ can maintain scale everywhere. Angles, areas, distances and directions will be altered in the planar representation of the ellipsoidal earth. The distortions created during the map projection ~ may be analyzed using a measure of distortion.

For information on ~s to other grid systems:
New Zealand Map Grip from Land Information New Zealand, the official mapping agency of NZ ...

General Coordinate ~ Package (software); Geographic Coordinate ~ Package (software)
GD
Geologic Div. (USGS); Geospatial data; Graphic digitization ...

10 properties that remain unchanged despite ~s of the numbers used to represent a measurement. isolated object frameworks p.

coordinate ~ Source: GETIS glossary A mathematical operation on coordinates that includes a change of datum.

This can be distinguished from the ~s done within GIS analysis software by the fact that these changes are permanent, more complex and time consuming.

This is an error measurement that most GIS report during geometric ~ of data sets. It is mathematically the spatial equivalent to the standard deviation.

Not formed by a projecting light source, Mercator's projection is a completely mathematical ~ of the earth onto a rectangular map. It was presented in 1569 by Gerhard Kremer, known as Mercator, the Latinized version of his name.

Conversions from various formats and from raster to vector and vector to raster are examples of format ~.

A number of mathematical ~s can be employed to best depict the three-dimensional surface of the Earth on a flat map. However, these ~s do create some type of distortion artifact.

This is because in order to do operations that require raster ~s or other rater warping / clipping etc, PostGIS uses GDAL epsg files.

Geospatial data are encoded with certain units (feet, meters, degrees, etc.), the spatial components of each feature (lines, points) are projected using a mathematically defined ~. The earth is round and maps are flat, map projections flatten the round earth.

Contents > Map projections > Getting started with map projections > An overview of map projections Geographic coordinate systems (all topics) Projected coordinate systems (all topics) Geographic ~s (browse all topics) Supported map projections > List of supported map projections ...

This generally requires a systematic mathematical ~ of the earth's graticule of lines of longitude and latitude onto a plane.

[programming] Acronym for Extensible Style Language ~s. A language for transforming the tagged content in an XML document into an output document with another format. An XSL style sheet contains the XSLT code that defines each ~ to be applied.

Perhaps the most frequent geometric ~ is the conversion of lines to polygons. This happens a lot because many CAD programs often use line segments to build parcels (and other features), but within a GIS these features are best coded as polygons.

Commoditization implies the ~ of goods and services into a commodity thus becoming an undifferentiated product characterized solely by its price, rather than its quality and features.

Available under either a UNIX or Windows-NT operating system, ARC/INFO contains a comprehensive selection of advanced functions for data entry and editing, data conversion, coordinate projection and ~, spatial and tabular data management, spatial analysis, cartographic production, ...

~ is not a projection. ~ uses a linear formula to transform Cartesian coordinates in the x- and y-axes. There are three type of coordinate ~s that can be use: affine, projective, and similarity.

Because of the non-rigorous relationship between AGD66/84 and GDA94 and inaccuracies in AGD, the ~ parametres between the two vary across the country. The National ~ Grid overcomes this problem to a very large extent by developing local parameters based on a national grid.

Manufacturing "The Manufacturing sector comprises establishments engaged in the mechanical, physical, or chemical ~ of materials, substances, or components into new products.

the abbreviation for geographic information system. GIS are special-purpose digital databases in which a common spatial coordinate system is the primary means of reference. GIS contain subsystems for: 1) data input; 2) data storage, retrieval, and representation; 3) data management, ~, ...

ArcGIS 10.2 Delivers ~al Capabilities
The new release of ArcGIS transforms enterprise mapping with dramatic improvements in ease of use, real-time data access, and integration with existing IT infrastructures.

Projection A map projection is a mathematical ~ of the surface of a sphere (3D) onto a 2D plane. Due to the laws of the universe, each type of projection must make tradeoffs on how and what features it distorts. Raster A raster is a rectangular grid of pixels.

Conflation is a process by which two digital data layers, usually of the same area at different points in time, or two different data layers of the same area, are geographically "corrected" through geometrical and rotational ~s so that the different layers can be overlaid on one another.

Relational Database: A method of structuring data in the form of sets of records so that relationships between different entities and attributes can be used for data access and ~.

Before this information can be integrated, it must be transformed to the same scale (degree of detail or accuracy). This could be a temporary ~ for display purposes or a permanent one required for analysis.

The 'srtext' column is used to store the Well Known Text format of the spatial reference system, identifying datums, projections, prime meridians, units and other spatial references. Finally the 'proj4text' column utilizes the Proj4 open-source projections library to allow coordinate ~ ...

GIS standards categories COMPUTING STANDARDS hardware software data formats communications (cabling, network protocols) DATA COLLECTION AND ~ STANDARDS geodetic control, locational accuracy, base map coordinate-reference system mapping scale, resolution data content, ...

See also: What is the meaning of Transform, Information, Map, Coordinate, Model?