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Summary Of: Stereographic projection

3D illustration of a stereographic projection from the north pole onto a plane below the sphere... 3D illustration of a stereographic projection from the north pole onto a plane below the sphere... 3D illustration of a stereographic projection from the north pole onto a plane below the sphere... the stereographic projection is a way of picturing the sphere as the plane... The stereographic projection was known to... aspect of the stereographic projection was commonly used for maps of the... gave the stereographic projection its current name in his 1613 work... Stereographic projection of the unit sphere from the north pole onto the plane z... Stereographic projection of the unit sphere from the north pole onto the plane z... Stereographic projection of the unit sphere from the north pole onto the plane... For the stereographic projection to be performed on a computer... The stereographic projection defined in the preceding section sends the... stereographic projection does not preserve area... The conformality of the stereographic projection implies a number of convenient geometric properties... Stereographic projection plots can be carried out by a computer using the explicit formulas given above... distorting property of the stereographic projection can be seen by comparing a grid sector near the center of the net with... Stereographic projection of the unit sphere from the north pole onto the plane z... Stereographic projection of the unit sphere from the north pole onto the plane z... Stereographic projection of the unit sphere from the north pole onto the plane... define stereographic projection from the north pole... Stereographic projection of a sphere from a point Q onto the plane E... Stereographic projection of a sphere from a point Q onto the plane E... Stereographic projection of a sphere from a point... one can define a stereographic projection from any point... All of the formulations of stereographic projection described thus far have the same essential properties... Stereographic projection of a snub 24... Stereographic projection of a snub 24... stereographic projection may be applied to the... then the stereographic projection of a point... Then the stereographic projection of a point... the stereographic projection is conformal and invertible outside of a... The stereographic projection presents the quadric hypersurface as a... Although any stereographic projection misses one point on the sphere... The stereographic projection from the north pole onto the equatorial plane is then... define a stereographic projection from the south pole onto the equatorial plane... So the stereographic projection also lets us visualize planes as points in the disk... Stereographic projection is also applied to the visualization of... stereographic projection from the unit circle provides a means to describe all primitive... stereographic projection from the north pole... then its inverse stereographic projection is the point... Stereographic projection is used to map the Earth... Stereographic projection is used to map the Earth... Stereographic projection is used to map the Earth... Stereographic projection falls into the second category... Use of lower hemisphere stereographic projection to plot planar and linear data in structural geology... Use of lower hemisphere stereographic projection to plot planar and linear data in structural geology... Use of lower hemisphere stereographic projection to plot planar and linear data in structural geology... In this context the stereographic projection is often referred to as the... use a stereographic projection to capture a wide angle view... The stereographic projection has been used to map spherical panoramas... the stereographic projection tends to produce especially visually pleasing panoramas...

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3D illustration of a stereographic projection from the north pole onto a plane below the sphere | | geometry | function | sphere | plane | smooth | bijective | conformal | angles | area | mathematics | complex analysis | cartography | geology | photography | computer | graph paper | Illustration by Rubens for "Opticorum libri sex philosophis juxta ac mathematicis utiles", by François d'Aiguillon. It demonstrates how the projection is computed. | | Rubens | François d'Aiguillon | Hipparchus | Ptolemy | Egyptians | Planisphaerium | celestial charts | planisphere | equatorial | Eastern | Western Hemispheres | François d'Aiguillon | Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section | | cross section | unit sphere | Cartesian coordinates | spherical coordinates | polar coordinates | trigonometric identities | cylindrical coordinates | unit circle | projective geometry | topological | homeomorphic | one point compactification | A 10x10 Cartesian grid on the plane appears distorted on the sphere. The grid lines are still perpendicular, but the areas of the grid squares shrink as they approach the north pole. | | A radius-5 polar grid on the plane appears distorted on the sphere. The grid curves are still perpendicular, but the areas of the grid sectors shrink as they approach the north pole. | | isometry | Gaussian curvature | transversally | real projective plane | The sphere, with various loxodromes shown in distinct colors | | loxodromes | loxodromes | equiangular spirals | Wulff net or stereonet, used for making plots of the stereographic projection by hand | | parallels | Russian | mineralogist | Illustration of steps 1–4 for plotting a point on a Wulff net | | central angle | Stereographic projection of the unit sphere from the north pole onto the plane z = −1, shown here in cross section | | Stereographic projection of a sphere from a point Q onto the plane E, shown here in cross section | | diffeomorphisms | Stereographic projection of a snub 24-cell. | | snub 24-cell | n-sphere | Euclidean space | hyperplane | quadric hypersurface | projective space | homogeneous coordinates | rational hypersurface | algebraic geometry | conformal geometry | parametrizations | orientation | surface | manifold | complex number | meromorphic functions | Riemann sphere | metric | Fubini-Study metric | Animation of tilt traverse between 4 of the 8 <111> zones in an fcc crystal. Planes edge-on (banded lines) intersect at fixed angles. | | real projective plane | embedded | antipodal points | quotient topology | beam compass | polytopes | Schlegel diagram | The rational points on a circle correspond, under stereographic projection, to the rational points of the line. | | arithmetic geometry | Pythagorean triples | rational number | Stereographic projection is used to map the Earth, especially near the poles, but also near other points of interest. | | map projections | statistical | integration | navigation | meridians | parallels | A crystallographic pole figure for the diamond lattice in [111] direction | | diamond lattice | [111] direction | Pole figure | crystallography | crystal | X-ray | electron diffraction | Visualization of lines and planes | electron diffraction | Kikuchi line | Ewald sphere | transmission electron microscope | Use of lower hemisphere stereographic projection to plot planar and linear data in structural geology, using the example of a fault plane with a slickenside lineation | | structural geology | foliation | lineation | fault | slickensides | Visualization of lines and planes | Lambert azimuthal equal-area projection | contouring | Spherical panorama projected using the stereographic projection | | fisheye lenses | citation needed | Panotools | nadir | zenith | Astrolabe | Astronomical clock | Apostol, Tom | ISBN 0070109052 | ISBN 0-13-212589-7 | doi | ISBN 0130652466 | ISBN 0-486-65812-0 | ISBN 0387548122 | Snyder | ISBN 0-226-76746-9 | ISBN 091409873X | Eric W. Weisstein | MathWorld | Categories | Cartographic projections | Projective geometry | Conformal mapping | Crystallography | All articles with unsourced statements | Articles with unsourced statements since July 2007 |
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