Search results
Results from the WOW.Com Content Network
The vectors v ∈ R n+1 such that Q(v) = -1 form an n-dimensional hyperboloid S consisting of two connected components, or sheets: the forward, or future, sheet S +, where x 0 >0 and the backward, or past, sheet S −, where x 0 <0. The points of the n-dimensional hyperboloid model are the points on the forward sheet S +.
Gnomonic projection of a portion of the north hemisphere centered on the geographic North Pole The gnomonic projection with Tissot's indicatrix of deformation. A gnomonic projection, also known as a central projection or rectilinear projection, is a perspective projection of a sphere, with center of projection at the sphere's center, onto any plane not passing through the center, most commonly ...
Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back. [5] [6] [7] 1879 Peirce quincuncial: Other Conformal Charles Sanders Peirce
In the past, the gnomonic projection was widely used for navigation charts, and also for polar charts. [29] Since the late 1970s, all charts at a scale of 1:50,000 or larger have used the transverse Mercator projection, [30] which is the projection used for the Ordnance Survey National Grid.
The computational cost of renormalizing a quaternion, however, is much less than for normalizing a 3 × 3 matrix. Quaternions also capture the spinorial character of rotations in three dimensions. For a three-dimensional object connected to its (fixed) surroundings by slack strings or bands, the strings or bands can be untangled after two ...
Cube mapping was first proposed in 1986 by Ned Greene in his paper “Environment Mapping and Other Applications of World Projections”, [3] ten years after environment mapping was first put forward by Jim Blinn and Martin Newell. However, hardware limitations on the ability to access six texture images simultaneously made it infeasible to ...
To keep the projection conformal, the projection increases the displayed distance between lines of latitude (north–south distances) in proportion; thus a square is shown as a square everywhere on the chart, but a square on the Arctic Circle appears much bigger than a square of the same size at the equator.
The stereographic projection, also known as the planisphere projection or the azimuthal conformal projection, is a conformal map projection whose use dates back to antiquity. Like the orthographic projection and gnomonic projection , the stereographic projection is an azimuthal projection , and when on a sphere, also a perspective projection .