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Typical Projection of the Earth's Surface onto a 2D surface using Gerardus Mercator's method.

 

Flattening a full 360° spherical image onto a 2D surface involves different projection methods.  The most familiar to us is the “Mercator” projection, developed by Gerardus Mercator in 1569 that has been used for centuries to display the globe on a 2D map.  This image of Earth is typical of this method and is comfortable to us, but it is actually very distorted.  We all know that Antarctica is not 5 times the size of South America.   For various reasons we disregard these particular distortions. Mercator’s projection method makes immediate sense because moving up from any point on the map is always North. It’s helpful for navigation.

 

The Earth's features projected into 2D using a Hyperbolic method.

 

However, projecting a 3D surface onto a 2D map can be done in an infinite number of ways, but all will have some type of distortion. This image is using a “hyperbolic” projection method.  Note that the North and South Poles are of more typical size, but now Australia and Western North America are huge compared to other areas.  With these projections moving outward from any point on the map will lead you to the Pacific Ocean. This feature is of little help to navigators, but can become very useful in artistically describing spaces – as seen below.

 

 

Original Mercator Projection along with a Hyperbolic Projection, commonly called "Planet"

 

 

The left image is a traditional mercator or equirectangular projection of the statue “True Grit,”  a retriever,  at the entrance to UMBC. Pretty mundane image, perhaps.  The right image is a stereographic projection of the same 360° panorama.  In this case, moving from any point outwards leads to the sky.  This type of projection is commonly called a “Planet” and you regularly see them.  In fact, you can now make them from any of the panoramas from Street View in Google Maps. You will need WebGL activated in your browser (it probably is).  Here is one at the triple-decker bridge on the beltway around Baltimore.

 

Example of two projections methods for underneath a spruce tree canopy

 

 

This is another example of a panorama taken under the canopy of a large spruce tree.  The left image is traditional and the right image is a stereographic projection. In the stereographic one, moving outward from any point takes you to a position up in the tree.   To view a larger image, click here.

 

 

 

 

Traditional and Stereographic Projections of Crab Tree Falls

 

 

Another example, this time of Crab Tree Falls in North Carolina.  For the alternative projection, moving outward from any point in the image takes you to the puddle below the camera’s position. To view a larger image click here.