Multi Standard-Parallel Azimuthal Projections
ISBN 978-85-88783-11-9
Authors
1Lapaine, M.
1University of Zagreb, Faculty of Geodesy Email: mlapaine@geof.hr
Abstract
The author has lately been trying to explain and demonstrate that the approach to map projections which maps (using geometric principles) from a sphere onto an auxiliary surface (cylinder, cone), and is then developed into a plane, is limited, because it does not correspond to the mathematical basis of many useful map projections. In azimuthal pro-jections, the projection plane is often placed so that it touches or inter-sects the sphere, which means that the projection only has one zero dis-tortion point, or one zero distortion circle. In normal or polar aspect az-imuthal projections, this circle is the standard parallel. This paper shows that relating the projection plane to a projecting sphere does not make much sense. In fact, it can be demonstrated that an azimuthal projection with two, three and more standard parallels exists. How does one explain a plane intersecting a sphere in three con-centric circles? Obviously, this is not possible. Of course, such an azimuthal projection is unlikely to be applied widely. It was developed only to show how awkward and unnecessary it is to relate the projection plane to the sphere so that projection distortions can be explained. Furthermore, conic projections with any number of standard parallels can be created in the same way.
Keywords
azimuthal projections; distortions; standard parallels