Maths - The Mercator Projection

Projecting surface of sphere onto plane

The Mercator Projection maps the north and south poles to lines this means that, at these points, the projection is many to one (more about this subject on this page):

earth projection

Singularities of Euler angles

Simarly we can map Euler angles to quaternions (4 dimensional hypersphere). This maps a one dimensional space (rotations around 0,1,0 axis) to a two dimensional plane in Euler terms. This is where attitude = 90° and heading, bank vary:

north pole

On this plane lines of common orientation are diagonal lines, that is rotation around 0,1,0 axis are given by angle = heading+bank.

Similarly for the south pole.

 

 

 

 

 

 

 

 



metadata block
see also:

 

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover Introduction to Topological Manifolds (Graduate Texts in Mathematics S.)

Other Books about Curves and Surfaces

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2017 Martin John Baker - All rights reserved - privacy policy.