The Coordinate System dialog provides a system for choosing a coordinate system. The terms projection and coordinate system are used as interchangeable synonyms in Manifold. The dialog appears in three settings:
Assign Initial Coordinate System  If a component is imported from a format that fails to specify the coordinate system it should use, we must do so manually. Until we assign the initial coordinate system to use the coordinate system readout for that component will use red text. Once we assign the initial coordinate system the readout will switch to black text. This command should only be used once, immediately after initial import or linking of a component. The Coordinate System dialog appears in the Edit Coordinate System choice in the menu launched by this command.
Repair Initial Coordinate System  If people never made mistakes we would not need this option. Sometimes a component is imported from a format that incorrectly specifies the coordinate system it should use, and we must manually change that initial setting to the correct coordinate system. At other times, we might have used Assign Initial Coordinate System to specify the initial setting but we made a mistake and specified the wrong projection. This option allows us to repair such errors by specifying the correct initial coordinate system. The Coordinate System dialog appears in the Edit Coordinate System choice in the menu launched by this command.
Change Coordinate System  This is the routine command we use to reproject data into whatever projection we want. Suppose, for example, we import data that is in Latitude / Longitude format but we want it to be in pseudoMercator so it is a better match to web servers and so we can better measure distances. This option allows us to reproject the data as we like. The Coordinate System dialog appears in the Edit Coordinate System choice in the menu launched by setting a new coordinate system.
The Coordinate System dialog allows us to choose a coordinate system from three groups of available coordinate systems, totalling thousands of options:
Standard  A long list of coordinate systems known by text names, either as a result of wellestablished tradition in cartographic circles or by formal government or standards group designation in various countries. Standard names are useful because they are familiar, but they are imperfect due to different organizations using the same name for different coordinate systems.
EPSG  The gold standard. A staggeringly comprehensive list of coordinate systems from the EPSG Geodetic Parameter Dataset published by IOGP. EPSG coordinate systems are precisely, unambiguously defined with a level of care unprecedented in international cartographic and geodesic practice. EPSG coordinate systems are known formally by their EPSG codes but also have a text name to provide easier discussions in more casual settings.
Custom  The ability to define a custom coordinate system starting with a coordinate system type taken from a list of configurable types, choosing a base coordinate system (ellipsoid) and providing custom parameters allowed by that type.
Standard 
A long list of coordinate systems known by their names, either by wellestablished tradition or by government designation in various countries. 
EPSG 
A comprehensive list of coordinate systems from the EPSG Geodetic Parameter Dataset published by IOGP. 
Custom 
Specify a custom coordinate system by choosing a base coordinate system (ellipsoid) and a standard type from a list of configurable coordinate systems. 
(Filter Box) 
Our best friend when sifting through long lists. Enter text, such as Mercator into the filter box and only those projections which include that text in their names will be displayed. 
(list pane) 
Click on a coordinate system in the list to select it by highlighting it. 
(lower pane) 
Details for a highlighted coordinate system will be displayed in JSON format in the lower pane, as seen in the illustration below. 
Force XY axes 
Force the coordinate system to always use XY axis ordering. A defensive measure against data that specifies use of YX axis ordering but which in reality uses XY ordering. See the That YX Thing essay. 
The Filter box provides muchneeded help when trying to find a desired coordinate system in a very long list. The dialog displays only those coordinate systems which contain in their names the text entered into the Filter box. If Lambert is entered into the Filter box the list will display only those coordinate systems with Lambert in their names.
The EPSG tab provides a staggeringly long list of coordinate systems from the EPSG Geodetic Parameter Dataset published by IOGP. Each has a text name and the official EPSG code in parentheses. The only rational way to find a desired EPSG coordinate system is to use the Filter box to find it by entering the EPSG code into the Filter box.
The EPSG tab includes all EPSG codes, including those (marked with a red ! message icon) that have been deprecated or otherwise are discouraged by the EPSG system.
Clicking on a coordinate system will select it by highlighting it and will display details in the lower pane. Text comments from the EPSG database are provided as ordinary text while the coordinate system definition is reported in JSON format. To understand EPSG commentary, consult documentation published by IOGP.
Manifold provides the ability to create a custom coordinate system by customizing a starting coordinate system chosen from a list of configurable Types. Most custom coordinate systems are simply variations on a relatively limited list of frequently utilized coordinate system types so this approach can cover a very wide range of possibilities should a coordinate system be required that is not included in the thousands of EPSG plus standard coordinate systems.
A common use of Custom is usually to specify an azimuthal coordinate system, like Orthographic, or other coordinate system that is centered precisely upon a specific area of interest. See the Example: Change Projection of an Image topic for a typical example.
Provide a Name for the new system.
Choose a starting Type of coordinate system.
Choose a Base if an ellipsoid other than WGS84 is desired.
Specify desired parameters. Parameter boxes will be displayed as options for the selected Type allow.
Press OK.
Name 
Choose something more useful and selfdocumenting than the default of "Custom Coordinate System." That will help remind us what we did should we use this project or data years later. 
Type 
A list of configurable coordinate systems. Choosing one of those will configure the parameter boxes to provide allowed options. 
Base 
The "base coordinate system," also classically known as the ellipsoid or datum. 
Click to edit the Base Coordinate System, choose from a list of favorite base coordinate systems, or to edit the list of favorite base coordinate systems. 

(Parameter boxes) 
Configuration parameters allowed by the Type of configurable coordinate system selected. 
To learn how to add a favorite coordinate system or a favorite base coordinate system, see the Example: Adding a Favorite Coordinate System topic.
Custom coordinate systems are created by specifying custom parameters for a configurable coordinate system. Manifold provides a list of popular configurable systems in the Type box. To choose one of those we click on the down arrow icon at the right of the box.
Doing so opens up the list of available configurable coordinate systems. We choose a system by clicking on it to highlight it.
Above we have selected Orthographic as the Type. Once we choose a configurable Type we can customize the coordinate system by specifying parameters of interest.
Manifold will automatically provide option boxes for parameters that may be customized for a particular system. Option boxes have indicators what units of measure are used, for example, m for meters and deg for degrees. Enter values to customize the starting coordinate system to create the specific custom coordinate system desired. When finished, press OK.
For example, the default values for Center latitude and Center longitude for Orthographic projection, as with most projections, are 0 and 0, thus centering the projection on the 0,0 intersection of the Prime Meridian and the Equator in the ocean off the coast of Africa. To customize the Orthographic projection to create an azimuthal projection centered on our area of interest we enter the center coordinates of the area of interest. The illustration above shows Orthographic being customized to be centered on the state of Florida in the United States, a good choice for creating environmental maps of Florida.
When a starting Type of coordinate system provides too many options to fit at once into the display a scroll bar will appear to allow us to scroll through all of the options. The Modified Krovak Oblique Conformal Conic (North) coordinate system lives up to the promise of its long name by providing almost two pages of configurable parameters.
Tech Tip: Manifold provides a seemingly endless range of coordinate systems with seemingly endless options because over the course of centuries experts around the world have developed very many sophisticated and endlessly varied projections to match precisely the requirements of their tasks. There are very good reasons why the Krovak family of coordinate systems has so many options. Teaching such systems and how to correctly use them is beyond the scope of this documentation. Users who need to use them or who would like to learn more should take advantage of the world's extensive resources, many of which are online, that teach geodesy, computational cartography, mathematics and so on. Read a book or take a course at a local college  you may find yourself addicted to the field, as computational cartography often becomes a hobby for noncartographers. The most gifted computational cartographer of all in modern times, John Parr Snyder, began his career as an amateur hobby. He became a legendary professional in the field after solving a complex problem the professional cartographic bureau at USGS could not.
The Base option allows us to customize the coordinate system by choosing the base coordinate system, that is, the Earth ellipsoid model used. See the discussion in the Base Coordinate System dialog topic.
Synonyms  Cartographers favor the term projection while programmers seem to prefer coordinate system. This documentation uses the two terms interchangeably, with the term projection tending to be used more in GIS or display contexts and the term coordinate system tending to be used more when discussing programming, SQL or standards.
Bases are Basic  All coordinate systems are based upon a model of the Earth's sphere or ellipsoid that specifies the size and shape of the Earth using various parameters such as radius, eccentricity, center of rotation and so on. Such models have usually been referred to by cartographers and GIS people as the ellipsoid or datum but the more popular term among computer people now is becoming the base, short for base coordinate system. Manifold tends to use the terms base, base coordinate system, ellipsoid and datum as interchangeable synonyms since that is how most people working with spatial data know the terms.
All spatial data in any projection, including Latitude / Longitude, assumes some base even if the base is not explicitly specified as is often the case with data where latitude and longitude numbers specify a location. If precision is required it is important to know what base is assumed because different bases used with exactly the same type of coordinate system and exactly the same numeric data can result in differences of hundreds of meters in the position of a location.
We might not care about what base was used if we are creating maps that display all of Europe where it does not matter if the dots that represent cities vary in position by a few hundred meters, but in other applications such as guiding an emergency medical response vehicle to the correct entry portal for a hospital and not into water in an adjacent lake, or determining whether a specific real estate parcel falls within a special planning zone or taxation zone, a few hundred meters can matter very much. See the Latitude and Longitude are Not Enough topic for a visual example of how varying bases can move the position of exactly the same coordinates.
Assign Initial Coordinate System
Favorite Base Coordinate Systems
Example: Assign Initial Coordinate System  Use the Contents pane to manually assign an initial coordinate system when importing from a format that does not specify the coordinate system.
Example: Change Projection of an Image  Use the Change Coordinate System command to change the projection of an image, raster data showing terrain elevations in a region of Florida, from Latitude / Longitude to Orthographic centered on Florida.
Example: Adding a Favorite Coordinate System  Step by step example showing how to add a frequently used coordinate system to the Favorites system.
Example: Detecting and Correcting a Wrong Projection  A lengthy example exploring projection dialogs and a classic projection problem. We save a drawing into projected shapefiles and then show on import how a projection can be quickly and easily checked and corrected if it is wrong.
ReProjection Creates a New Image  Why changing the projection of an image creates a new image.
Latitude and Longitude are Not Enough