By Donald Fenna
Geographic books regularly introduce map projections with no offering mathematical factors of projections and few delve into complicated mathematical improvement or hide the breadth of projections. From uncomplicated projecting to complicated modifications, Cartographic technological know-how: A Compendium of Map Projections, with Derivations is a accomplished reference that provides a proof of the technological know-how of cartography.
The ebook is a compilation of greater than 100 map projections, from vintage conics to modern alterations utilizing complicated variables. ranging from broadly defined geometric projecting onto flat paper, cylinder, and cone after which progressing via numerous layers of arithmetic to arrive smooth projections, the writer maximizes the appliance of 1 layer of complicated arithmetic sooner than carrying on with directly to the following. He additionally offers a variety of one-page tutorials that overview phrases and methodologies, supporting reduce the demanding situations of unusual mathematical territory.
Divided into 4 elements, the 1st part examines the form and dimension of the Earth, then proceeds to enquire the potential for bearing on the curved floor to a flat floor, and addresses scaling. It is going directly to conceal pertinent rules of projection together with literal projecting, real yet artificial projections, secantal projections, pseudocylindrical projections, and pseudoconical projections, in addition to the opposite versions of extra severe projections. The e-book concludes via elements influencing suggest Sea point and notes the cartographic facets of present developments.
Cartographic technological know-how: A Compendium of Map Projections, with Derivations explains the mathematical improvement for a wide variety of projections inside of a framework of the several cartographic methodologies. This conscientiously paced e-book covers extra projections, with light and revolutionary immersion within the arithmetic concerned, than the other publication of its variety
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Additional info for Cartographic Science: A Compendium of Map Projections, with Derivations
A couple of centuries earlier, hot-air balloons allowed a much more limited aerial viewing. Before then, only steeply elevated escarpments and a few tall buildings allowed any looking down on the surface that man inhabited. Images from any distance have effectively been available, however, through the many centuries since globes were first created. The picture in a viewer’s eye, likewise on the film of a viewing camera, derives from the converging light rays from the area viewed. Clearly, the rays from the outer fringes are closer together for a given increment in distance from the central point — the point immediately underneath the viewer in gravitational terms, and equally the nearest point on the surface — but at the outer limits of the viewed area the rays are tangential to the spherical source and merge.
24 PART A: The Curved World TUTORIAL 8 ELLIPSES AND ELLIPSOIDS Ellipse Canonical form Using the latter pair of axes and co-ordinates X, Y, Z of the 3-dimensional scene in anticipation of its use for the ellipsoid, the formula for an ellipse centred on the origin and passing through (±a, 0) and (0, ±b) is, for point P = (Y, Z), Because for any angle θ Y2 + Z2 =1 a2 b2 Its area equals π a b. If a = b, the ellipse is a circle. If a > b, giving a true ellipse as illustrated below, then a is called the semimajor axis, b the semiminor axis.
However expressed, any scale applies precisely only to a limited extent, and often is grossly misleading – what appears as a clearly stated fact can be a major fiction. The scale cited above for the Plate-Carrée applies precisely along the Equator and along all meridians (drawn and not drawn). But it obviously does not hold true along any parallels other than the Equator. Because the length on the globe of the parallel for latitude φ is only cosφ times that of the Equator, the map has 1 cm along the parallel representing only 3000cosφ km.
Cartographic Science: A Compendium of Map Projections, with Derivations by Donald Fenna