Projections

Projections are a very important idea in GIS and mapping. If you are not familiar with projections, please begin by reading the Projections Tutorial topic.

 

This documentation provides several paths through the general subject of working with projections in Manifold. Some material is repeated in the various topics so that essential material is covered no matter which path the reader takes through the Help system.

 

·      Experts may jump directly to the Projections Quick Reference topic for a terse introduction.

 

·      If you are a new user and are working completely within Manifold System, read this topic and then proceed to the Projecting a Map topic. Very little expertise in the inner workings of projections is required to make simple projections when working within Manifold System.

 

·      To permanently re-project a specific component we open it in a window and apply the Edit - Change Projection command. If the component appears in a map and we would like to re-project it to use the same projection as the map, we can right click its tab in the map and choose Project to Map.

 

·      If you must deal with maps in legacy formats such as ESRI .shp or AutoCAD .dxf, please read the Projections and Legacy Formats topic. Because legacy formats do not normally save information on projection parameters used, importing maps saved in legacy formats can require extensive knowledge of projections and coordinate systems.

 

·      If you are new to projections and coordinate systems in GIS and would like to learn more about the general concepts involved, consult the Projections Tutorial and subsequent topics.

 

·      The Projections Readings topics provide a classical introduction to projection concepts together with a guide to selecting projections based on the writings of John Parr Snyder, one of the greatest enthusiasts of map projections ever.

 

·      The Manifold Projections topics discuss the specific characteristics in summary form of various families of projections available within Manifold System. This is a reference section that should be consulted for summary information on a specific projection.

 

·      A topic related to projections is Georegistration , the process of matching an image or drawing to the geographic location and projection of a "known good" reference drawing, image, or map. If you wish to use an image within a geographic map please read the Georegistration topic.

 

·      Experts may specify custom units of measure, ellipsoids, datums and even customized coordinate systems (projections) by specifying customized projection presets. See the Customization topic.

 

·      Very Important: Do not use the Edit - Assign Projection dialog in an attempt to change the native projection of a component. This dialog is used only to complete the import of a projected component from a format that does not correctly save projection information. Instead, use the Edit - Change Projection dialog to re-project a component.

 

·      Maps are a special case because they are viewports that show their contents in whatever temporary projection is desired. They don't change their contents, they simply show them in a different form. The projection used by a map to display its contents is set in the Edit - Assign Projection dialog.

 

Why Use Projections?

 

In Manifold, projections are used for three main reasons:

 

·    To provide a more natural looking map,

·    To enable measurements of areas and lengths in printed maps.

·    To enable easy measurement in linear units such as meters when performing analyses.

 

Better Appearance

 

Geographic projections are confusing to many people but the idea is quite simple. Because the Earth is a round, three-dimensional body it’s not possible to show the shapes of large entities such as continents on a flat sheet of paper or a flat computer monitor without distorting their shapes. Anyone who has tried to flatten a deflated basketball knows that a rounded 3D surface cannot be perfectly flattened without distorting shapes on the surface.

 

"Geographic projections" are simply ways of transferring the shapes of things from a sphere onto a flat sheet of paper (or, the same thing, onto a flat computer monitor screen) in a way that minimizes distortions. The idea is to show an image that looks like what one would perceive if one were looking at a globe.

 

The simplest "projection" is sort of a non-projection: take the longitude and latitude coordinates of objects and plot them as if they were X and Y coordinates. This is a "cylindrical" projection of sorts. Along the Equator and middle latitudes, the distortion is not so bad. More northerly objects are very distorted. Manifold uses this "projection" by default because it is the simplest conceptually. If we are working with small-scale maps such as a map of a particular county near the Equator, we might never need to use another projection. However, if we are working with larger maps such as the entire United States or all of Europe we will probably wish to convert the map to a projection that shows the region in a closer approximation to the way it would appear if seen on a globe.

 

It is very important to note that no projection can show the entire world without distortion, and every projection to a greater or lesser extent causes some distortion within the map. All projections are therefore approximations. Various projections have been designed for different purposes so when they are used for the intended purpose they do a better job of minimizing distortions that are important for that purpose. For example, some projections are better at minimizing distortions when used to display broad, rectangular regions such as the continental United States. Other projections are better at displaying circular regions such as the Antarctic continent or oceanic coverage of the entire Pacific Ocean.

 

See the readings in projections provided in this documentation, including General Projections Concepts , The Earth as an Ellipsoid and Guide to Selecting Map Projections for more information on various projections and their uses.

 

Accurate Measurement

 

Projections are also used to create flat maps from which measurements can be made. Many people are familiar with the idea of taking a ruler to a paper map and measuring the distance between two points, perhaps by comparing the measured distance of a pencil line to a scale printed at the edge of the map. This is a simple and straightforward idea when the map shows a very small rectangle of the Earth’s surface because in such cases even a clumsy projection does not introduce distortions that are greater than the intrinsic accuracy of the map.

 

When maps cover larger areas of the Earth one must be more careful to choose a projection for the map so that the distortions introduced in the process of projection do not make it impossible to measure distances in the map reliably. The larger the area, the more difficult it is to draw a rectangular, flat map that will enable accurate measurements of length and area to be made at all locations in the map.

 

The usual solution is to use a projection that is mathematically arranged so that the area of a figure drawn on the globe (such as a country) is the same as that of the equivalent figure on the flat, rectangular map within the area of interest. If lengths are more important than areas, one chooses a projection that does a good job of preserving accurately measurable lengths in the region of interest. If measurement is not required because the map will be used for "thematic" presentation, one is free to use a projection such as the Robinson that allows no accurate measurement at all but that nonetheless delivers a pleasing aesthetic impression.

 

For work done on the computer screen Manifold will automatically compute areas and lengths of items that appear on screen so one can use whatever projection is desired for visual effect without losing the ability to measure lengths or areas. Because Manifold knows what the true Earth coordinates are supposed to be of every map, the system can re-compute on the fly what the correct areas and lengths should be if the items were laid out on the real, three-dimensional, ellipsoidal Earth.

 

For measuring lengths using the Tracker tool, Manifold will always compute the tracker length by great circle distance, that is, a straight line between the two points indicated as laid out over the surface of whatever Earth ellipsoid is currently specified as the map datum.

 

Projections are still important when printing maps because users may attempt measurements from the printed map. In such cases it is important to pick the projection which best preserves lengths or areas in the intended usage.

 

Projecting a Map

 

Once drawings have been imported into Manifold it is easy to show them in a map and to show the map within any projection desired. To do so, we open the map and use the Edit - Assign Projection dialog to change the projection to any projection desired.

 

Note that even though a map can show its layers in whatever projection desired, re-projecting the layers on the fly if their components are in a projection different from the one used by the map, at some point the reprojection on the fly process will take so long that users will be unhappy with the resultant performance of the map window for panning and zooming. We can make the map window work faster if both the map window and any large components it contains use the same projection.

 

See the Projecting a Map topic for more information.

 

Projections and GIS Formats

 

Manifold can work with data saved in both projected and unprojected coordinate systems from all standard GIS formats. Unprojected maps are usually easy to import automatically no matter how geographically unaware the GIS format. GIS data saved as projected maps might require user intervention in some cases if the format does not save the projection parameters necessary to use the data.

 

Once a drawing is imported, the projection parameters in use for that drawing may be seen at any time by viewing its coordinate properties. Click on the drawing in the project view to highlight it and then choose the Edit - Assign Projection dialog for that component. The coordinate properties tell Manifold how to interpret the data in that drawing. If these properties are changed, they simply change how Manifold uses the existing data. Changes in this dialog do not change the data itself. To change the native projection of the drawing, we use the Edit - Change Projection dialog.

 

Some GIS formats are "smart" and automatically save the projection parameters in use together with the data. During import, Manifold will fetch all necessary parameters from such "smart" formats automatically and will load the coordinates properties with the correct parameters necessary to use the data. Cool!

 

Other GIS formats (such as ESRI .shp "shapefile" format as commonly used) are legacy formats and do not save the projection parameters in use. When legacy formats are used to save projected maps they require users to keep track manually of the projections used in the file. This is usually done by accompanying the GIS data with a readme.txt file or other "metadata" documentation that specifies what projection parameters should be used with the file. Users must read the file's documentation to know what parameters to use. If we download the file and neglect to fetch the documentation that says how to use it we are in trouble. Ugly!

 

Since no one wants the hassle of keeping track of projection parameters manually, most people will use legacy formats only to save unprojected data. GIS data in legacy formats therefore is usually unprojected data that may be imported into Manifold with no special user intervention.

 

On those rare occasions when we encounter a projected map saved using a legacy format there is usually no warning within the format that the data it contains must be interpreted in a way known only to its author. When importing from legacy formats we should always keep in mind the possibility that the file being imported contains projected data. If we suspect projected data is involved we should keep an eye out for a readme.txt or other "metadata" documentation file that might explain what projection parameters are to be used with the file.

 

To use projected data from a legacy format we first import the drawing using default settings. We then manually add the projection parameters required. To do this, click on the new drawing to highlight it in project view, and then open the Edit - Assign Projection dialog. This will display the (wrong) parameters used during default import. We then enter the correct parameters intended to be used with that data. We only need do this once and then forever more Manifold will keep track of all projection parameters for us automatically.

 

Note: It's always a good idea to download any accompanying documentation when downloading GIS data from the web even when "smart" formats are used. This will help us speak accurately about the sources of data being used in our projects.

 

Verifying Projections

 

Once a component has been correctly imported into Manifold, the system will automatically manage projections from then on. The catch is getting a drawing or image or other component correctly imported into Manifold in the first place if it must be imported from a format that does not reliably capture projection information. Surprisingly many formats for drawings and images used in GIS work are very old formats that do not reliably capture projection information.

 

It is so important to make sure that a projection has been correctly assigned that Manifold tries to ascertain when a component is imported from a format that does not store projection information. In such cases, Manifold will take special measures to ask us to verify the projection assigned. The first time such a new component is opened, Manifold will overlay an info bar onto the window telling us that the projection used by the component has not yet been verified, and inviting us to click on the info bar to verify the projection.

 

Clicking on the info bar will launch the Edit - Assign Projection dialog. We should take a moment to review the settings shown by that dialog to verify that the projection is indeed what it should be. If it is, we can click OK and thereafter Manifold will not nag us about verifying the projection. If the projection is not what it should be, we can specify the desired projection. Once we verify the projection assigned, we can open the component without Manifold nagging us to verify the projection.

 

We can get rid of the info bar without launching the Assign Projection dialog by clicking the X sign at the right side of the info bar; however, Manifold will know that we've not yet verified the projection of this component and the info bar will appear again the next time the component is opened in a window.

 

If we do not want to verify projections of new components, once we acquire enough expertise not to want to verify projections anymore unless it is absolutely necessary, we can get rid of the info bar by changing the Prompt to verify projections of new components option in the Tools - Options dialog.

 

Conversely, if we would like Manifold to remind us to verify the projection of all new components, even those imported from formats that correctly store projection information, we can uncheck the Suppress prompt for non-default projections option in the Tools - Options dialog.

 

Note: The rule of thumb used by Manifold to decide if a component has been imported from a format that does not store projection information is to simply raise the info bar whenever a new component's projection is Orthographic, the default used for imports from formats that do not provide coordinate information, or if the component has been imported in Latitude / Longitude with coordinate locations outside the expected range (+/- 90 latitude and +/- 180 longitude).

 

That leads to some unnecessary use of the info bar as occasionally we will import a component from a perfectly expert GIS format where the component just happens to have truly been stored in Orthographic projection, but for a short hand rule of thumb it works surprisingly well.

 

More worrisome is that the rule of thumb will miss occasions when formats have some projection information but not complete projection information. The classic case is shapefiles using incomplete .prj accessory files or some image formats accompanied by "world" files. In that case, there may be enough information to cause a projection other than Orthographic to be used, so that the rule of thumb does not cause the info bar to be raised, but not sufficient information from the format to have all projection parameters correctly assigned. In that case, we have be alert enough as users to manually launch the Assign Projection dialog to verify the projection and to accurately specify all parameters if needed.

 

Beginning GIS users working with formats such as shapefiles or graphics formats using "world" files may want to uncheck the Suppress prompt for non-default projections option in the Tools - Options dialog so that they are reminded by Manifold to always verify projections on all new components.

 

Changing Projections of Drawings and Images

 

Changing the coordinates properties of a drawing or image simply changes how Manifold interprets the internal coordinate numbers that comprise the actual data set. The only time we would do this manually is if we import a projected drawing or image from a legacy format and need to tell Manifold (manually) what parameters are supposed to be used. When importing a projected map from a legacy format, the internal coordinate numbers are already correct but there is nothing in the format that can be imported as correct properties. We must add this information manually.

 

Changing the native projection within which the coordinate numbers are computed requires us to change the actual coordinate numbers themselves. To re-project a drawing or image into a new coordinate system we open the drawing or image and use the Edit - Change Projection dialog. The dialog opens with the projection parameters currently in use. If the drawing was imported correctly these parameters will be the exactly correct parameters required for the coordinates in the drawing to make sense.

 

When we use the Edit - Change Projection dialog to change these properties to cast the drawing into new projection, Manifold will re-compute the coordinates within the drawing to the equivalent numbers required by the new projection. All of this happens automatically. Henceforth, when we open either the projections dialog we will see the new parameters to match the new coordinate numbers. Re-projecting a drawing in this way permanently changes the internal coordinates used to define the drawing.

 

Because drawings are normally seen through map view within maps, it is not normally necessary to re-project them from whatever projection they were in when imported. Specifying the projection used by a map does not change any data - it simply changes the way the data is seen by computing "on the fly" how the drawing should look in the projection requested of that map view.

 

The only time we would re-project a drawing is to speed up map view. Map windows works much faster if the drawings they contain use the same projection requested of the map. This is especially true if many, large drawings and images are used in the map. If we re-project a drawing into the same projection used by our map we should make sure that the projection used for the drawing also uses the same parameters as the map. For example, using the same azimuthal projection with the same center latitude and longitude but using different datums is not using the same projection.

 

Very important: The above discussion of Edit - Change Projection assumes the drawing was correctly imported in the first place. A regrettable trap for the unwary is the use of some older formats, such as ESRI .shp or AutoCAD .dxf, to publish GIS data in projected form. Because these formats do not save projection information, the user must manually enter such information using the Edit - Assign Projection dialog. If you are importing projected data from such formats you must use the Edit - Assign Projection dialog to specify the correct information the format is unable to provide. Until you provide such information the drawing may appear visually correct but it is not yet correctly imported.

 

Formats such as ESRI .shp or AutoCAD .dxf should not be used to publish projected data but regrettably this is done all the time. See Projections and Legacy Formats for more information in this area.

 

Images

 

Although idea of projection is the same in both cases we tend to work differently with images and projections than we do with drawings and projections.

 

·      Images are often re-projected to achieve greater speed in a map view, because images usually contain many more pixels than drawings contain objects.

·      Images are usually highly localized views shot from directly overhead or very nearly so. They thus are already in Orthographic projection or are very close to Orthographic. In contrast, most drawings or imported maps are in Latitude / Longitude coordinates and are not in any specific geographic projection.

·      Images are often slightly off Orthographic projection, or they are shot at angles that result in a Tilted Perspective or Space Oblique projected view in the image; however, it is very rare that we have actual numeric parameters corresponding to a particular image.

 

Manifold deals with the above by providing a collection of interactive tools for simple image movement and distortion to transform an image into a correct projection by matching the image to a known good drawing. This process is often called georegistration and allows the use of images with drawings and surfaces in correct geographic position.

 

A Projections Strategy

 

For most interactive editing and map preparation work in middle latitudes a good strategy is to keep all drawings in Latitude / Longitude form and to work with them in maps using the Latitude / Longitude projection. This is the name given to the "unprojection" that uses simple degrees latitude and longitude instead of any other projection. Most GIS data is published in this form, so it's likely that this will be the native "projection" used by most drawings on import.

 

Use the map in Latitude / Longitude projection for most interactive editing. For fine-tuning the appearance of the map for presentation purposes, create a map that shows the project in whatever projection is desired for presentation.

 

Maps involving images such as aerial photographs can be conveniently kept in Orthographic projection because the images by default will be in Orthographic projection and because Orthographic provides a typical "view from space" appearance that most people associate with overhead imagery. If speed is an issue, the drawings involved in the map should also be re-projected into the same Orthographic projection.

 

One limitation of Orthographic is that the projection is defined only for the sphere datum. If other datums are to be used, an alternative "view from space" projection is the Stereographic projection.

 

If you have an especially fast system or are working with smaller maps you can simply keep drawings in whatever projection they were imported and use whatever projection you like in maps.

 

XML Files Created upon Export and Used on Import

 

Not all formats to which Manifold can export have the ability to correctly save projection information. As a safety measure to ensure that projection information is never lost, Manifold always writes an accompanying .xml file when exporting drawings, images, labels, maps or surface components to a file. The accompanying .xml file contains coordinate system information and some other metadata. The XML file is created for all formats, even those that correctly save coordinate system information.

 

When Manifold imports drawings, images, labels or surfaces, the system will check for an accompanying .xml file that might have been written by Manifold. If such an .xml file exists, Manifold will read it and use the information it contains to load a correct coordinate system.

 

In addition to the .xml file that is automatically created, Manifold projections dialogs such as the Edit - Change Projection dialog provide toolbar commands to manually write or read projection information from accessory files using generic XML, Golden Software GSR or ESRI PRJ files.

 

Automatic use of Custom Datum Transformations

 

Manifold uses high accuracy coordinate transformation mathematics when re-projecting data from one coordinate system to another. In certain parts of the world, custom transformation formulae are routinely used (and, at times mandated by law for certain uses) to convert datums during re-projection. If the Use custom datum transformations option is checked in the Tools - Options - Miscellaneous pane (checked by default) Manifold will use such custom datum transformations when available.

 

Currently, NADCON formulae are used to convert between NAD27 and NAD83 in North America and NTv2 formulae are used to convert Canadian, Australian and New Zealand datums supported by NTv2.

 

If a converted location is outside of the conversion domain supported by such custom methods, no datum conversion is done and Manifold will display a message box to that effect after the attempted re-projection. If desired, such a re-projection can be undone, the data set edited to fall entirely within the region supported by the custom method and re-projection attempted once more.

 

Note: the message box mentioned above appears only when a component is re-projected using Edit-Projection. It does not appear when a component is re-projected on-the-fly for display as part of a map view.

 

In general, if we attempt to make a datum conversion between any of the datum pairs shown below and the datum is not converted, that tells us part of the data set we are attempting to convert falls outside the service area of the custom transformation formulae.

 

Datum Pairs supported by Custom Transformations

 

North American 1927 (mean for CONUS)

< NADCON >

North American 1983 (mean for CONUS)

North American 1927 (mean for Canada)

< NTv2 >

North American 1983 (mean for CONUS)

Australian Geodetic 1966 (Australia, Tasmania)

< NTv2 >

Australian Geocentric 1994 (GDA94)

New Zealand Geodetic 1949 (New Zealand)

< NTv2 >

New Zealand Geodetic 2000

 

Custom datum transformations will be invoked only when converting between the above pairs in either direction. For example, they will be used when converting NAD27 to NAD83, or when converting from NAD83 to NAD27. Pairs shown above are listed using their full names as they appear in the datum box in Manifold projection dialogs, not using the abbreviated form commonly used. For example, North American 1983 (mean for CONUS) is referred to as NAD83 in abbreviated form.

 

The names of the above datums are significant, not the parameters used. For example, if we convert GRS80 (the parameters of which are identical to NAD83 so it is the same datum) to NAD27 (mean for Canada), Manifold will not use the custom NADCON conversion formulae. This is done on purpose, so we can use NAD83 as the name of the datum for conversion-sensitive North American data (so that the custom transformation will be used) and GRS80 as the name of the datum for all other data where we would like to use the general purpose routines.

 

Custom Datum Pairs for NTv2

 

Additional datum pairs may be added to those supported by Manifold for use in NTv2 transformations through customization. See the Custom Datum Grids for NTv2 topic for details.

 

A Technical Note on Datums

 

This technical note is intended for experts.

 

The most commonly used datums for many purposes (such as the default datums used by GPS devices) are WGS84 worldwide and NAD83 in North America. While in almost all cases these datums may be thought of as fixed, well-defined datums not subject to change, that is not true in all cases as sometimes the definitions of those datums will vary from the "standard" definitions embedded within Manifold's XML file definition and as used by virtually all GIS applications and almost all hardware (such as most GPS devices).

 

In actual fact both the WGS84 datum and the NAD83 datum change slightly over time to account for changes such as those caused by movements of tectonic plates. The working definitions of these datums as used in some high-precision applications will therefore change from the "standard" definitions of these datums.

 

To use a working definition for either WGS84 or NAD83, create a custom datum from the working definition and use that instead of the WGS84 or NAD83 datum built into Manifold. Such working definitions are not published within this documentation or with Manifold because the point of those definitions is that they change over time. Therefore, the user must find out exactly how such "working" datums are defined within the particular usage that employs them. This can be a major annoyance, especially if someone uses such an atypical definition for a very common standard like WGS84 without alerting users that something unusual is going on.

 

The need for such custom datums usually arises when working with GPS devices that employ working definitions of such datums instead of the prevailing standard definitions.

 

For example, certain Trimble devices equipped with WAAS will use a working definition of NAD83. To use data from such devices in Manifold, first find out what working definition is used by that device. Create a custom datum from that working definition using a distinct name of your choosing, such as "NAD83T."

 

Next, create a drawing in latitude / longitude using the standard NAD83 datum. Accept data from the Trimble device into that drawing. To correct the coordinate system used, launch the Edit - Assign Projection dialog and change the datum to use your custom NAD83T datum.

 

Note that some Trimble devices not equipped with WAAS will use a working definition of WGS84 instead of the "standard" WGS84 definition. These may be dealt with by using a custom datum created from the working WGS84 definition used by Trimble.