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Map Projections
Published in Julio Sanchez, Maria P. Canton, William Perrizo, Space Image Processing, 2018
Julio Sanchez, Maria P. Canton
Parallels and meridians exist on the sphere (or the ellipsoid) but maps are often drawn on a flat surface. In order to transfer the graphic information from the surface of the sphere to a two-dimensional map, the cartographer must accept some distortion. A map projection is the representation of all or part of a spherical body, usually the earth, on a plane surface. Since it cannot be done without distortion, the cartographer selects which method of representation, or map projection, accurately shows the features that are most desirable for the purpose at hand. Usually, this implies sacrificing the accuracy with which other features are represented. The following list includes properties often considered desirable in map making: Areas in the map are in correct relative proportions. This means that if we place a coin on any part of the map, it covers an equal surface area.The shape of the physical features in the map is accurate. A map that shows true shapes is said to be conformal. A consequence of conformality is that local angles are correctly shown everywhere on the map.The scale of the map is consistent, therefore, it can be used for measuring distances.Azimuths of any point on the map are correctly shown with respect to the center.Rhumb lines or great circles are shown as straight lines.
Manipulate View
Published in Tamara Munzner, Visualization Analysis and Design, 2014
With the project design choice, all items are shown, but without the information for specific dimensions chosen to exclude. For instance, the shadow of an object on a wall or floor is a projection from 3D to 2D. There are many types of projection; some retain partial information about the removed dimensions, while others eliminate that completely. A very simple form of projection is orthographic projection: for each item the values for excluded dimensions are simply dropped, and no information about the eliminated dimensions is retained. In the case of orthographic projection from 3D to 2D, all information about depth is lost. Projections are often used via multiple views, where there can be a view for each possible combination of dimensions. For instance, standard architectural blueprints show the three possible views for axis-aligned 2D views of a 3D XYZ scene: a floor plan for the XY dimensions, a side view for YZ, and a front view for XZ. A more complex yet more familiar form of projection is the standard perspective projection, which also projects from 3D to 2D. This transformation happens automatically in our eyes and is mathematically modeled in the perspective transformation used in the computer graphics virtual camera. While a great deal of information about depth is lost, some is retained through the perspective distortion foreshortening effect, where distant objects are closer together on the image plane than nearby objects would be. Many map projections from the surface of the Earth to 2D maps have been proposed by cartographers, including the well-known Mercator projection. These projections transform from a curved to a flat space, and most of the design choices when creating them concern whether distorting angles or areas is less problematic for the intended abstract task.1
Computer Imaging of the Geoid
Published in Petr Vaníček, Nikolaos T. Christou, GEOID and Its GEOPHYSICAL INTERPRETATIONS, 2020
Map projections — The display of data related to the Earth, such as its shape, its bathymetry, its gravity field, etc. involves the representation of undulations of a three-dimensional curved surface on a flat map. This is the basic problem of map projections and many text-books have dealt with it.15,16 Here we are mainly concerned with the effect of these projections on the display of a data set: are two parallel lineations on the Earth also parallel in the projected map and how does the projection affect the shapes of objects and the distances between them?
Low-distortion symmetrical polyconic map projections of the world
Published in Journal of Spatial Science, 2022
The main goal of map projections is to represent spherical properties on the plane as similar to the original as possible. The key advantage of polyconic mappings lie here: they represent parallels as circular arcs, resembling the original circular parallels on the sphere. Such concepts will be applied consequently in this paper: a mapping with equidistant parallels, and another with rectangular graticule will be developed because real parallels are equidistant and the original spherical graticule lines meet at right angles.