Rotated Views

Most projections show a "North Up" display.  The topic shows how to create rotated views where North is not up.   Rotated views are also covered in two videos, the Rotated Views video, which shows a simple way to create North arrows, and the Portable North Arrows video, which shows a more sophisticated technique also shown within the Example: Create Custom North Arrows with Manual Edits topic.


Download the sample project from the Examples page on the Manifold web site to follow along with this topic.


Creating a Rotated View


  1. Compose the desired scene in a map that uses default Pseudo-Mercator projection.  

  2. Save the current Location.

  3. Move the mouse cursor to the approximate center of the view, and note the latitude and longitude of the center of the view.

  4. In the Info pane, click on the coordinate picker button for the map and choose More... in the dropdown menu.

  5. In the Coordinate System dialog, click on the Custom tab.

  6. In the Custom tab, enter a memorable Name, and choose Hotine Oblique Mercator (B) as the Type.

  7. For the Center latitude and Center longitude, use the lat/lon values noted for the center of the view.

  8. Leave 0 for the Center line azimuth.

  9. Enter the rotation desired as the Rectified grid value.  For example to rotate 70 degrees counter-clockwise we would enter -70.  To rotate clockwise 45 degrees we enter 45.

  10. Press OK.

  11. Right-click on the saved Location and choose View in Active Window.


It is usually a good idea to include a drawing layer in the original, North-up map that has a vertical line with an arrowhead at the end, to use as a North arrow.  The rotated, Hotine Oblique Mercator map will rotate that drawing layer as well, so the result will be an arrow that points North in the Hotine map.


When experimenting, we can quickly make a copy of a map in the Project pane using Copy and Paste.  We can then tinker with rotated view experiments with the copy of the map.  If results are not to our liking, we can delete the copy and start fresh with a new copy of the original map.


To fit into this documentation, illustrations show an artificially small Manifold desktop, with only a few panes, docked to the right side.   In real life we use a much larger Manifold desktop, and all panes would be turned on, with some panes docked to the left and others docked to the right.


We will create a rotated view of Italy.  Basically, this is as easy as noting the center latitude and longitude of the desired view of our area of interest (which we can read out from the status bar) and then changing the projection of the map to use the Hotine Oblique Mercator (B) projection with that center latitude and longitude and the desired rotation angle.    


Rotating a view is therefore basically only one step: reprojecting into the desired, rotated, Hotine projection.   All the rest of the workflow illustrated in this topic covers various real-life conveniences that experienced users tend to apply.





We begin with a map that has a Bing street map web server layer.    The first layer added to a map sets the projection for that map, in this case, the Pseudo Mercator projection that Bing, Google and almost all web servers use.





We drag and drop a drawing of provinces in Italy into the map.  The layer comes from a free administrative units layer that may be downloaded from the Natural Earth website.  We have thematically formatted it to show provinces in different colors.   We have also created a Location for this view, so we can return to it easily.





We can double-click the location to open it.  The location provides a handy way to recall the center latitude and longitude of the view.  We can undock the location window and then refer to it when we change the projection. Shift-click the title tab for a window or a pane to undock it.  That saves us from trying to remember the center latitude and longitude when we are busy filling in boxes in a coordinate system dialog, when the status bar might not be visible, the mouse might not be in the center of the display, and so on.  


In this case, we see the view is centered on a longitude of 42 and a latitude of 13. That would be an amazing coincidence given the view was chosen by casually panning and zooming into the view, except that we have taken the liberty of editing the original numbers, which were almost exactly 42 and 13, to the exact numbers of 42 and 13.


 When experimenting with rotated views, it is convenient to work with a copy of the map.  There is no absolute need to work with a copy: we can simply change the coordinate system on the original map.  But given that it takes just a moment to make a copy (Ctrl-C and then Ctrl-V), and copies of maps require zero extra space in a project,  it can be very convenient to work with a copy.   





We click on the map and chose Copy in the toolbar.  We could also simply click on the map and then press Ctrl-C for Copy.





Next, we Paste a copy of the map by pressing the Paste button on the toolbar.  We could also simply press Ctrl-V for Paste.  The pasted copy appears using the name Map 2.


Maps are just windows that show their contents in a desired projection.  Maps store no data, as all the data they show remains, unchanged, within the drawings, images and data sources that appear in the map.  We can make as many copies of maps as we like without increasing the storage size of the project.  Each such map can use a different projection, with the various layers within the map being reprojected on-the-fly from their native projections into whatever projection the map uses.


We rename the pasted copy to Rotated Map, we double-click it to open it.





We double-click the Bing tab to turn that layer off, to reduce visual clutter.   We have used the Layers pane to set a background color of medium gray. We choose the Info pane.


 We click the coordinate system picker button to change the coordinate system (projection) used by the map.





In the menu that appears we choose More.   The Coordinate System dialog appears.



A rotated map view uses the Hotine Oblique Mercator (B) projection. "Hotine" in English is pronounced with the first syllable sounding like the "ho" part of "hot" and the second syllable sounding like "teen," with the stress on the first syllable.  It is named after the inventor, Brigadier General Martin Hotine, who led the UK's Ordnance Survey for many years.


Because the center latitude and longitude of the area of interest must be specified, each such use of the Hotine Oblique Mercator is a custom, one-of-a-kind coordinate system.    We provide a memorable name, Italy Rotated Hotine, and in the Type box we choose Hotine Oblique Mercator (B) from the long list of options.


To create a rotated view, we enter the center latitude and longitude, and then in the Rectified grid box we  enter the rotation angle in degrees (positive numbers for clockwise rotation, negative numbers for counterclockwise rotation).   The center latitude and longitude values we can read from the Location that we thoughtfully created and opened, in this case a Center latitude of 42 and a Center longitude of 13.    We want to rotate the display 45 degrees counterclockwise, so we enter a value of -45 into the Rectified grid box.  Press OK.





The display zooms to the full extent of all layers, including the worldwide Bing layer.  We can zoom in manually or choose the Location to get in the ballpark.





With a bit of panning and zooming we get the above display.  Italy is, indeed rotated 45 degrees counterclockwise.

Adding a North Arrow - One Click

When a projection shows "North up" a North arrow is less important to show orientation, but when a projection is rotated so North is no longer up, a North arrow is a good idea to show orientation.  Adding a North arrow is easy.  In the Layers pane, click on the North Arrow layer.





A default North arrow (actually, a four pointed compass rosette) appears.  The default North arrow shape is unlikely to be what we want, so we will customize it by clicking the North Arrow layer in the Layers pane, to launch the North Arrow dialog.



We tinker with settings in the North Arrow dialog as described in the North Arrow topic, pressing Apply to see how different combinations look in the map.  When we are happy with the settings, we press OK.





We add a North arrow to the Rotated Map in the same way, by clicking on the North Arrow layer:





We click the North Arrow layer to launch the North Arrow dialog.



We choose the above settings and press OK.  


Note that the Auto box in the Bearing control has been checked.




The result is a North arrow that automatically rotates to point to the correct bearing to North given the projection in use by the map, as well as the position of the North arrow within the map.


The use of rotated views continues in the Example: Create Custom North Arrows with Manual Edits topic, which uses the rotated view created in this topic to illustrate creation of objects in new drawing layers that can be used to produce custom North arrows.



Credits - This topic was inspired by a post in the forum by expert Manifold user Tim Baigent.  Thanks, Tim!


Download a sample PDF - The PDF created in this example may be downloaded from Italy_rotated.pdf.



Manifold Viewer - Rotated Views -  Learn how to create rotated views, to display maps where North is not always up.  The video shows how to create a rotated map of Italy in seconds, with perfect cartographic accuracy.  See how to create North arrows, labels, and how Manifold can instantly reproject on the fly to create rotated views of web served layers from Bing street maps, satellite photography and much more.   The video uses the free Manifold Viewer and works exactly the same in Release 9 as well.


Manifold Viewer - Portable North Arrows -  Continuing on from the preceding Rotated Views video, we explore a more sophisticated way of creating custom North arrows that can be easily repositioned and recycled.  Instead of creating a North arrow that is a combination of two objects, we use a tiny SQL expression to create a computed geometry field within a single object that automatically tracks any changes, such as creation of new North arrows, resizing or repositioning.  Amazing to see all this can be created in the free Viewer!  Works in Manifold Release 9 too!


See Also



North Arrow


Scale Bar












Project Pane






Info Pane


Layers Pane


North Arrows


Map Projection


Example: Create Custom North Arrows with Manual Edits - This topic uses the map of Italy created in the Rotated Views topic.  This topic shows how to add embellisments to a map by creating objects in drawing layers.  In this example we create custom North arrows as a way to learn how to create and edit objects in drawings.


Example: Create a Rotated View of a Map - Illustrates use of rotated views, that is, map displays which are not "North up," using a  Bing street map image server layer, to show how even layers fetched on the fly from a web server can be rotated.  The topic also shows an alternate way of creating North arrows that is initially simpler, but ultimately much less convenient than the more sophisticated method illustrated in the Rotated Views topic.