stereographic double projection
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stereographic double projection by Donald B. Thomson

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Published by Dept. of Surveying Engineering, University of New Brunswick in Fredericton, N.B .
Written in English


Book details:

Edition Notes

Statementby Donald B. Thomson, Michael P. Mepham [and] Robin R. Steeves.
SeriesTechnical report / Dept. of Surveying Engineering, University of New Brunswick -- no.46
ContributionsMepham, Michael P., Steeves, Robin R., University of New Brunswick. Department of Surveying Engineering.
The Physical Object
Paginationiii,47p. :
Number of Pages47
ID Numbers
Open LibraryOL21254852M

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The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the was originally known as the planisphere projection. Planisphaerium by Ptolemy is the oldest surviving document that describes it. One of its most important uses was the representation of celestial charts. The term planisphere is still used to refer to such charts. A Star Atlas for Students and Observers, Showing Stars and Double Stars, Nebulae, &c. in Twelve Maps on the Equidistant Projection: With Index Maps on the Stereographic Projection by Proctor and Richard A. (Richard Anthony).   A stereographic projection, or more simply a stereonet, is a powerful method for displaying and manipulating the 3-dimensional geometry of lines and planes (Davis and Reynolds ).The orientations of lines and planes can be plotted relative to the center of a sphere, called the projection sphere, as shown at the top of Fig. The intersection made by the line or plane with the sphere's. Double projection means that the ellipsoidal data is first mapped conformally on a conformal sphere. Top of Page 6. What are the parameters for the NB Double Stereographic and Reference Systems? Over the years, New Brunswick has progressed using different datum or reference frames. The following table captures all the possible parameters.

The coordinate plane of the province’s Geographic Information System was realized by using a Double Stereographic Projection with parameters specific to this province as listed below and is referred to as the PEI Survey Reference System. The projection is referenced to the North American Datum of realized from the Canadian Spatial. Polar Stereographic projection 51 Polar Stereographic mapping equations 51 Finding (x,y) 51 Finding (0,x) 51 Alternate method for finding 4 53 Finding the point scale factor 54 Finding the convergence of the meridian 54 Accuracy 54 Area of Cited by: The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the was originally known as the planisphere projection. [1] Planisphaerium by Ptolemy is the oldest surviving document that describes it. One of its most important uses was the representation of celestial charts. [1] The term planisphere is still used to refer to such charts. Stereographic projection is one way of making maps, and it adopts the second strategy. It has been used since ancient times for this purpose, and at least one of its basic geometrical properties was known even then. This result is one of the first results in Apollonius' book on conics, and presumably one of the earliest non-trivial results.

An easy way to get intuition for this is to note that those formulas for the stereographic projection give equations for the point on the unit sphere (which you've labeled as $(x_1, x_2, x_3)$) if you draw a line through the north pole of the sphere (i.e. $(x_1, x_2, x_3) = (0, 0, 1)$) and the point in the plane. The stereographic projection is a projection of points from the surface of a sphere on to its equatorial plane. The projection is defined as shown in Fig. 1. If any point P on the surface of the sphere is joined to the south pole S and the line PS cuts the equatorial plane at p, then p is the stereographic projection of P. The importance of the. STEREOGRAPHIC PROJECTION IS CONFORMAL Let S2 = {(x,y,z) ∈ R3: x2 +y2 +z2 = 1} be the unit sphere, and let n denote the north pole (0,0,1). Identify the complex plane C with the (x,y)-plane in R3. The stereographic projection map, π: S2 −n−→ C, is described as follows: place a light source at the north pole n. For any pointFile Size: 58KB. In the right hand-diagram we see the stereographic projection for faces of an isometric crystal. Note how the ρ angle is measured as the distance from the center of the projection to the position where the crystal face plots. The Φ angle is measured around the circumference of the circle, in a clockwise direction away from the b crystallographic axis or the plotting position of the (