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A series of parallel profiles, taken at regular intervals on a map, can be combined to provide a more complete three-dimensional view of the area that appears on the topographic map. It is evident that, thanks to computer science, more sophisticated three-dimensional models of the landscape can be made from digital terrain data.
The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale. That parallel is called the standard parallel. By scaling the resulting map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them. This gives the map two standard parallels.
A map : between simply-connected CW complexes is a homotopy equivalence if and only if its mapping cone is contractible. More generally, a map is called n-connected (as a map) if its mapping cone is n-connected (as a space), plus a little more. [3] [page needed]
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection; that is, the projection is a conformal map in the mathematical sense. For example, if two roads cross each other at a 39° angle, their images on a map ...
Terrain cartography or relief mapping is the depiction of the shape of the surface of the Earth on a map, using one or more of several techniques that have been developed. Terrain or relief is an essential aspect of physical geography , and as such its portrayal presents a central problem in cartographic design , and more recently geographic ...
In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology.In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi ...
The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .