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Topic: Stereographic projection

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Map projection

Robinson projection

Orthographic projection (cartography)

Dymaxion projection

Conformal map

Riemann sphere

Mercator projection

Dandelin spheres

Transverse Mercator projection

Hyperbolic geometry

Cartography

Germinal Pierre Dandelin

Azimuth

Circle Line

Astrolabe

	Stereographic projection - Wikipedia, the free encyclopedia
		Let the points of the sphere be projected stereographically onto a plane which is tangent to the pole.
		There are a number of ways to perform stereographic projection onto a sphere, based on your choice of where you put the plane and the sphere.
		therefore a loxodrome on a stereographic projection is a equiangular spiral.
	en.wikipedia.org /wiki/Stereographic_projection (364 words)

	Labs 12 and 13: Miller Indices and Stereographic Projections (Site not responding. Last check: 2007-10-21)
		The stereographic projection is derived from the spherical projection by projecting the spherical poles to the south pole of the sphere; the points where lines of projection intersect the equatorial plane of the sphere are the stereographic poles of the faces, and the complete pattern is the stereographic projection of the crystal (Figure 3).
		On a stereographic projection it is customary to indicate a plane of symmetry by a solid line (a horizontal plane of symmetry appears on a stereographic projection as a solid line for the primitive circle, which is otherwise represented by a broken line, vertical planes of symmetry appear as solid diameters).
		The position of symmetry axes are also shown on a stereographic projection (or stereonet) and their type indicated by an appropriate symbol: a solid ellipse for a 2-fold axis, a triangle for a 3-fold axis; a square for a 4-fold axis, a hexagon for a 6-fold axis.
	www.clas.ufl.edu /users/jmartin/mineralogy/Fall/Labs_12&13.htm (895 words)

	4th Dimension Stereo-projection: Stereographic Projection
		Stereographic projection maps the sphere (minus the north pole) to the plane.
		Note that points near the north pole are projected to points far away from the sphere (since the rays of light are nearly parallel to the plane).
		One important property of stereographic projection is that it maps circles on the sphere to circles in the plane, except for the circle that pass through the north pole, which are projected to lines in the plane below.
	www.math.union.edu /%7Edpvc/math/4D/stereo-projection/welcome.html (801 words)

	Sphæra issue no. 7: article 10
		The common stereographic projection is made from the south celestial pole onto the plane of the equator.
		A universal projection, on the other hand, is made from a point on the plane of the equator in the direction of the sun at the equinoxes onto the solstitial plane - the plane through the poles and the sun's position at the summer and winter solstices.
		In the common stereographic projection, circles on the celestial sphere are preserved as circles when projected, and the angles between them are maintained.
	www.mhs.ox.ac.uk /sphaera/issue7/articl9.htm (1639 words)

	Projection from Spheres (Site not responding. Last check: 2007-10-21)
		The stereographic projection is one way of projecting the points that lie on a spherical surface onto a plane.
		Such projections are commonly used in Earth and space mapping where the geometry is often inherently spherical and needs to be displayed on a flat surface such as paper or a computer display.
		The general cylindrical projection is one where lines of latitude are projected to equally spaced parallel lines and lines of longitude are projected onto not necessarily equally spaced parallel lines.
	astronomy.swin.edu.au /~pbourke/projection/spherical (807 words)

	Sperical astronomy by analytical geometry
		Stereographic projection gives a map of the celestial sphere, and it is straightforward to use analytical geometry to find the equation of the projection of an arbitrary circle on the sphere.
		Projected points are described by complex numbers, and rotations of the sphere then correspond to the bilinear transformations.
		Stone, 'On the stereographic projection of the sphere', The Mathematical Gazette 40, 181-184 (1956).
	homepage.ntlworld.com /stone-catend/astron.htm (949 words)

	STEREOGRAPHIC PROJECTION (Site not responding. Last check: 2007-10-21)
		(Geom.), a method of representing the sphere in which the center of projection is taken in the surface of the sphere, and the plane upon which the projection is made is at right andles to the diameter passing through the center of projection.
		A map projection in which meridians and parallels are projected onto a tangent plane, with the point of projection on the surface of the sphere diametrically opposite to the point of tangency of the projecting plane.
		A similar projection used in optical mineralogy and structural geology, made on an equatorial plane (passing through the center of the sphere) with the point of projection at the south pole.
	www.websters-online-dictionary.org /definition/STEREOGRAPHIC+PROJECTION (404 words)

	Stereographic Projection (Site not responding. Last check: 2007-10-21)
		Stereographic projection is one way to make a flat map of the earth.
		Mathematically, a projection (or type of map) is described by a rule telling where (in the plane of the map paper) to draw the image of each point on the sphere.
		This angle property means that stereographic projection (like the Mercator map but unlike many other common map projections) is conformal: shapes of small regions are the same on the map as on the earth.
	torus.math.uiuc.edu /jms/java/ster1.2 (602 words)

	Stereographic projection: introduction
		Stereographic Projection is a method of representing and interpreting orientational data (such as the dips of bedding planes or joints).
		Equal Angle projection ensures that, measured along great circles, the size of an angle is proportional to its separation on the plot.
		Equal area projection ensures that if two regions have the same area plotted on the hemisphere then they will be the same size on the plot.
	www3.telus.net /public/nstuart/SGIntro.htm (735 words)

	Oblique Stereographic
		The Stereographic projection may be imagined to be a projection of the earth's surface onto a plane in contact with the earth at a single tangent point from the opposite end of the diameter through that tangent point.
		In order to reduce the scale error at the extremities of the projection area it is usual to introduce a scale factor of less than unity at the origin such that a unitary scale factor applies on a near circle centred at the origin and some distance from it.
		For Stereographic projections centred on points in the southern hemisphere, including the south Polar Stereographic, the signs of E, N, 0, , must be reversed to be used in the equations and * will be negative anyway as a southerly latitude.
	www.remotesensing.org /geotiff/proj_list/oblique_stereographic.html (707 words)

	Polar Stereographic Projection (Site not responding. Last check: 2007-10-21)
		projected surface than they are on the ellipsoid.
		For the GK Projection, the scale factor at the central meridian
		It is a conformal azimuthal projection that is
	www.tpub.com /content/USMC/mcwp3167/css/mcwp3167_62.htm (262 words)

	Stereographic Map Projection -- 3DSoftware.com (Site not responding. Last check: 2007-10-21)
		The Stereographic projection is an Azimuthal map projection.
		Geometric projection of the polar Stereographic projection, projected from
		The stereographic projection is used to map polar regions, and large continent-sized areas that extend similarly in all directions.
	www.3dsoftware.com /Cartography/USGS/MapProjections/Azimuthal/Stereographic (647 words)

	Map Projections: Deducing Braun's Stereographic Cylindrical Projection
		Imaginary development of stereographic cylindrical map, most of it shown from the reverse side; the Eastern hemisphere on the left was unrolled.
		Instead of a flat projection plane directly yielding the projected map, here the projection surface is a cylindrical sheet tightly rolled against the Equator.
		Due to projection constraints, the length of tube (therefore the map's height) is twice the sphere's diameter
	www.progonos.com /furuti/MapProj/Normal/CartHow/HowBraunC/howBraunC.html (228 words)

	07a.2.3 Map Projection Selection
		In the case of the Polar Stereographic projection, the orientation of the display is determined by designating a longitude line to be drawn vertically downward from the pole.
		Their point of projection is on the surface of the sphere at a point just opposite the point of tangency of the plane or the center point of the projection.
		The Cassini projection uses complex curves for the meridians and parallels, except for the central meridian, meridians 90 degrees from the central meridian, and the equator.
	www.microimages.com /refman/xhtml/BASIC020.HTM (3427 words)

	Azimuthal Projections (Site not responding. Last check: 2007-10-21)
		The gnomonic projection is the perspective, azimuthal projection with point of perspective at the center of the globe.
		Hence, with the gnomonic projection, the interior of a hemispherical region of the globe is projected to the
		The default clipping region for the gnomonic projection is a circle with a radius of 60 degrees at the center of projection.
	idlastro.gsfc.nasa.gov /idl_html_help/projections9.html (1384 words)

	Construction by Compasses Alone
		We'll show now that the stereographic projection of a sphere with diameter NS to the plane tangent to S is actually inversion in a sphere with center N and radius NS.
		We conclude that stereographic projection is inversion in a sphere.
		Since stereographic projection is an inversion in a circle, that plane will be inverted to a sphere, and that sphere will intersect the tangent plane is a circle.
	aleph0.clarku.edu /~djoyce/java/compass/compass4.html (827 words)

	Stereographic projection: Definition and Links by Encyclopedian.com - All about Stereographic projection (Site not responding. Last check: 2007-10-21)
		In cartography and geometry, the stereographic projection is a mapping that projects each point on a sphere onto a tangent plane along a straight line from the antipode of point of tangency, with one exception: the center of projection, antipodal to the point of tangency, is not projected to any point.
		Two remarkable properties of this projection were demonstrated mathematically by Hipparchus:
		This mapping transforms circles on the surface of the sphere that do not pass through the center of projection, to circles in the plane.
	www.encyclopedian.com /st/Stereographic-projection.html (127 words)

	Map Projections: Perspective Cylindrical Projections
		This projection's perspective is easily visualized by rolling a flexible sheet around the globe and projecting each point horizontally onto the tube so formed.
		Like most cylindrical projections, it is quite acceptable for the tropics, but practically useless at polar regions, which are rather compressed, resulting in a map much broader than tall.
		This is unfortunate, for projections must not be chosen due to a single feature or on the basis of publicity alone.
	www.progonos.com /furuti/MapProj/Normal/ProjCyl/ProjCEA/projCEA.html (710 words)

	SPECIFICATION OF
		Stereographic projection was firstly calculated using (001) or [001] as default projection direction.
		Stereographic projection with the selecting (hkl) or [uvw] projection direction was obtained by rotating the generated projection map so that (hkl) or [uvw] becomes the projection direction.
		The application of stereographic projection for specimen orientation adjustment was also described in the paper by C.T. Chou (1987).
	www.unl.edu /CMRAcfem/XZLI/jecp_sp/stereogram_specification.htm (630 words)

	[CF-metadata] Stereographic projection (Site not responding. Last check: 2007-10-21)
		I agree that the projection should be renamed "stereographic".
		I'd prefer their polar stereographic set: latitude_of_natural_origin longitude_of_natural_origin scale_factor_at_natural_origin false_easting false_northing because it's complete set, including the scale factor, and because it avoids using the word "center", which is liable to cause spelling mistakes by non-US users.
		I think we should note that the longitude_of_natural_origin is the straight vertical longitude from the pole of the FGDC terminology, and that polar stereographic is a special case with latitude_of_natural_origin being 90N or 90S.
	www.cgd.ucar.edu /pipermail/cf-metadata/2003/000277.html (132 words)

	Stereographic Projection
		Show that under stereographic projection the equator is mapped onto the unit circle, that is the circle
		Show that under stereographic projection the lower hemisphere is mapped into the interior of this circle, that is the disk
		Inversion: Another proof uses the fact that stereographic projection may be regarded as a particular case of inversion in three dimensions.
	www.geom.umn.edu /docs/doyle/mpls/handouts/node33.html (729 words)

	Fermilab/FMI Coordinate Systems
		The Double Stereographic Projection is performed in two steps: namely, the projection from the reference ellipsoid to a conformal sphere and from the sphere to a plane.
		The Stereographic projection of an ellipsoid of revolution can be approached by a double projection (hence double Stereographic projection), in which the biaxial ellipsoid is conformally mapped to a sphere, which is then "stereographically" projected to a plane.
		The Stereographic projection is the most widely used azimuthal projection, mainly used for portraying large areas of similar extent in all directions.
	ppd.fnal.gov /align/mi-0209.html (4146 words)

	The Sterographic Projection (Site not responding. Last check: 2007-10-21)
		Just as a map of the world is a projection of the spherical Earth on a flat sheet of paper, the astrolabe plate is a projection of the celestial sphere on an imaginary piece of paper placed through the flat plane of the equator.
		In the stereographic projection as used on the astrolabe, an imaginary line is drawn between a point on the celestial sphere and the south celestial pole.
		Circles on the celestial sphere are projected as circles on the projection.
	www.astrolabes.org /stereo.htm (279 words)

	Stereographic Projection, Chaucer and the Astrolabe (Site not responding. Last check: 2007-10-21)
		One particular kind of projection used for representing spheres and circles on spheres in two dimensions (ie on the climates of an astrolabe, or on some maps of the earth or celestial sphere) is stereographic projection.
		Also, a projection is defined by Webster’s Dictionary as "a systematic presentation of intersecting coordinate lines on a flat surface upon which features from the curved surface of the earth or the celestial sphere may be mapped".
		The lines of latitude, almucantar, azimuth, and hour angles are represented stereographically onto a plane (usually taken is the equatorial plane) and the climates are merely a scaled-down representation of this.
	www.math.ubc.ca /people/faculty/cass/courses/m309-01a/montero/math309project.html (6190 words)

	Gall's Stereographic Projection (Site not responding. Last check: 2007-10-21)
		Since the Mercator projection causes considerable distortion of size at latitudes approaching the poles, many attempts have been made to create map projections which, although similar to it, improve upon it in this respect.
		Note that because the northern and southern parts of the map are stretched horizontally, the map as a whole was stretched vertically; in this way, while tropical countries are stretched vertically, the map's standard parallels, where the stretching is balanced, are at 45 degrees north and south, allowing the temperate countries to be shown well.
		Some projections with such an overall stretch, though, were too notable to exclude, and do not have an alternate form without it, specifically the Mollweide projection and the Eckert IV projection.
	members.shaw.ca /quadibloc/maps/mcy0102.htm (233 words)

	org.geotools.ct.proj (Site not responding. Last check: 2007-10-21)
		The USGS equatorial case of the stereographic projection.
		The USGS oblique/equatorial case of the stereographic projection.
		when a map projection failed because the point is outside the envelope of validity.
	geotools.sourceforge.net /gt2docs/api/org/geotools/ct/proj/package-summary.html (102 words)

	Stereographic projection of Titan's surface seen from Huygens \| SpaceRef - Your Space Reference
		One particular kind of projection used for spheres in two dimensions (for example on some maps of Earth or the celestial sphere) is 'stereographic' projection.
		This type of projection is often found on maps used by navigators and aviators in determining the shortest distance between two points.
		On the stereographic view, like that through a 'fish-eye' lens, the bright area to the north (top of the image) and west is higher than the rest of the terrain, and covered in dark lines that appear to be drainage channels.
	www.spaceref.com /news/viewpr.html?pid=16894 (825 words)

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