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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 ...
Gnomonics (from the ancient Greek word γνώμων, pronounced [/ɡnɔ̌ː.mɔːn/], meaning 'interpreter, discerner') is the study of the design, construction and use of sundials. The foundations of gnomonics were known to the ancient Greek Anaximander (ca. 550 BCE), which augmented the science of shadows brought back from Egypt by Thales of ...
Since the Mercator projection is conformal, that is, bearings in the chart are identical to the corresponding angles in nature, courses plotted on the chart may be used directly as the course-to-steer at the helm. The gnomonic projection is used for charts intended for plotting of great circle routes.
Combined projections from the Klein disk model (yellow) to the Poincaré disk model (red) via the hemisphere model (blue) The Beltrami–Klein model (K in the picture) is an orthographic projection from the hemispherical model and a gnomonic projection of the hyperboloid model (Hy) with the center of the hyperboloid (O) as its center.
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.
Orthographic projection in cartography has been used since antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance.
The gnomonic projection of the hemisphere to the plane is a geodesic map as it takes great circles to lines and its inverse takes lines to great circles. Let (D, g) be the unit disc D ⊂ R 2 equipped with the Euclidean metric, and let (D, h) be the same disc equipped with a hyperbolic metric as in the Poincaré disc model of hyperbolic geometry.
Or if the environment is first considered to be projected onto a sphere, then each face of the cube is its Gnomonic projection. In the majority of cases, cube mapping is preferred over the older method of sphere mapping because it eliminates many of the problems that are inherent in sphere mapping such as image distortion, viewpoint dependency ...