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.









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

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