Universal transverse mercator utm and the universal polar stereographic ups grids. Q869 polar stereographic calculation help atp forum. Mar 20, 2017 stereographic projection, 2d map mapping on 3d i. More in detail, you can project in equal area, or you can choose to project in equeal projection.
Visualizing quaternions 4d numbers with stereographic projection duration. Q869 polar stereographic calculation help 11012007, 16. Rectangling stereographic projection for wideangle image. The pythagorean triple that is probably most commonly known is 3. Here we discuss the method used in crystallography, but it is similar to the method used in structural geology. The important advantage of the stereographic projection is. The center point is a pole in the common polar aspect, but can be any point. From the ancient greeks with their intimate knowledge of the mediterranean sea to modern data that can chart every border imaginable with great precision, it has been an interesting and useful tool to project the components of a threedimensional sphere. It also discusses computations for convergence from geographic positions and from grid coordinates for the utm grid, and convergence in the polar stereographic projection. This projection amounts to selecting the top standard parallel very near the pole, thus closing off the top of the map. Handbook for transformation of datums, projections, grids.
The stereographic map projection is most useful for maps of polar regions for navigation purposes or large continentsized areas of similar extent in all directions. Stereographic projection let a sphere in threedimensional euclidean space be given. Both mathematical and tabular methods are illustrated for the above items. Stereographic projections used to display crystal morphology. Stereographic projection an overview sciencedirect topics. Stereographic projection is about representing planar and linear features in a twodimensional diagram. Equalangle wulff b equalangle stereonets are used in crystallography because the plotted angular relationships are preserved, and can be measured directly from the stereonet plot. The stereographic projection if the light or centre of projection is placed at the south pole, s, figure 2 changes to figure 3 and the stereographic projection is obtained.
Introduction to stereonets a stereonet is a lower hemisphere graph on to which a variety of geological data can be plotted. The orientation of a plane is represented by imagining the plane to pass through the centre of a sphere fig. The findings can be used by the airline industry and the faa to identify factors of interest in managing the polar airspace which in the future will be shared between manned and unmanned aircrafts, as well as establishing new requirements. The origin of the polar and equatorial stereographic projections can be traced back to hipparchos d. Polar stereographic projection and grid nsidcs polar stereographic projection specifies a projection plane or grid tangent to the earths surface at 70 degrees northern and southern latitude.
Illustrated above are the stereographic projections for triclinic point groups 1 and 1. The term planisphere is still used to refer to such charts. The universal polar stereographic ups coordinate system is used in conjunction with the universal transverse mercator utm coordinate system to locate positions on the surface of the earth. In geology, we overlay the 2d projection with a grid of meridians, or great circles analogous to longitudes, and parallels or small circles. Therefore stereographic projection maps all points on the sphere except. In all likelihood the source of this problem is the astronomer. Describe a conformal map projection that transforms circles on a globe sphere into circles of the map. Rectilinear equirectangular mercator stereographic pannini ours figure 1.
Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. Rectangling stereographic projection for wideangle image visualization chehan chang1 minchun hu2 wenhuang cheng3 yungyu chuang1. Stereographic projections we will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents general form hkl. The second step maps the projection on the swung surface onto the im. Ppt stereographic projections powerpoint presentation. Illustrated above are the stereographic projections. History of the stereographic projection and its early use in.
The value is in terms of an internal ncl loop that calculates new starts. The stereographic map projection is conformal but not. In geology, we overlay the 2d projection with a grid of meridians, or great circles analogous to. Stereographic projection mathematica stack exchange. History of the stereographic projection and its early use. Zenithal projections also known as azimuthal projections are a class of projections in which the surface of projection is a plane. How can i plot polar stereographic projection learn more about polar stereographic projection, plot, nsidc seaice data. Stereographic projection involves plotting 3d data. Mention should also be made of the polar stereographic projection that is favored by meteorologists. Essays on automorphic forms stereographic projection.
On a polar stereographic projection, the observers perspective comes from looking down at either the north or south pole. This is a perspective projection on a plane tangent at the center point from the point antipodal to the center point. Consider a meridional section of the sphere through the point p as in fig. M obius transformations and stereographic projection.
The native coordinate system is such that the polar axis is orthogonal to the plane of projection, whence the meridians are projected as equispaced rays emanating from a central point, and the parallels are mapped as concentric. The projection surface is a plane, tangent at one of the s and the projecting lines originate from the. The stereographic projection and its uses christopher hammond. The intersection made by the line or plane with the spheres. Examples of equatorial stereographic nets by the astronomer al. Comparisons of the proposed projection model with several popular projection models.
It is conformal, being free from angular distortion. Here we discuss the method used in crystallography, but it. This means we have a polar stereographic projection and the map boundaries. Presumably, the advantages of this projection are its. Geometrical properties of stereographic projection continued 1.
The purpose of the stereographic projection in crystallography the stereographic projection is a projection of points from the surface of a sphere on to its equatorial plane. Stereographic projection we talked about stereographic projection a little bit already, but there is a lot more fun stu we can do with it. The equatorial projection became an essential tool in astronomy and from the 2nd to. The polar stereographic projection is used for all regions not included in the utm coordinate system, regions north of 84 n and south of 80 s. Pdf history of the stereographic projection and its early. Pdf history of the stereographic projection and its. A stereographic projection, or more simply a stereonet, is a powerful method for displaying and manipulating the 3dimensional geometry of lines and planes davis and reynolds 1996. Important properties of the stereographic projection. The stereographic projection was known to hipparchus, ptolemy and probably earlier to the egyptians. Usually one cares about either the area or the angle.
Polar stereographic projection and grid national snow and. The point p can be inserted using the protractor and joined to s. To determine nq in this case, we must first show that nsq 12 900 0, whence nq 2r tan 2 900 0. The projection we are looking for, which is called a stereographic or polar projection is very important in cartography. Planar perspective projection, where one pole is viewed from the other pole. Stereographic projection the basics geological digressions. In general, it is not possible to map a portion of the sphere into the plane without introducing some distortion. One can also associate a point u,v,w on the unit sphere s u,v,w. Stereographic projections 32 pointgroups crystal classes. It was originally known as the planisphere projection.
Stereonets are used in many different branches of geology and can be used in a range of ways beyond those which are discussed here see references for further uses. It is used by universal polar stereographic ups maps showing areas north of 84 north and south of 80 south that arent included in the universal transverse mercator utm coordinate system. This unique vantage point allows operational weather forecasters to watch, for example, the movements of weather system over long distances. The equatorial projection became an essential tool in astronomy and from the 2nd to mid. Making stereographic projections of crystals is great fun. Next, it turns to the construction of the stereographic projection of a cubic crystal, the use of the polar and wulff nets, noncubic crystals distinguishing between plane normals and zone axes, and applications of the stereographic projection representation of point group symmetry, orientation relationships between crystals, preferred. Polar stereographic projection and grid national snow. The polar stereographic is a conformal azimuthal projection, where parallels of latitude appear as unevenly spaced concentric circles and meridians appear as straight lines, centered on and radiating from the pole, respectively. Like the utm coordinate system, the ups coordinate system uses a metricbased cartesian grid laid out on a conformally projected surface. Handbook for transformation of datums, projections, grids and.
Feb 26, 2016 how can i plot polar stereographic projection learn more about polar stereographic projection, plot, nsidc seaice data. Stereographic projection is all about representing planes e. Software for stereographic projection there are several pieces of software that youd like to check out for that purposes. A geometric construction known as stereographic projection gives rise to a onetoone correspondence between the complement of a chosen point a on the sphere and the points of the plane z. Mapmaking has existed on planet earth for thousands of years. The universal grids and the transverse mercator and polar. This planar grid is designed so that the grid cells at 70 degrees latitude are exactly the nominal grid resolution.
Universal polar stereographic coordinate system wikipedia. Planisphaerium by ptolemy is the oldest surviving document that describes it. The sphere that we have chosen for our stereographic projection only has some very identified details equator, poles, polar diameter, reason why it shines a transparent point to our curious eyes. This tlp covers the use of the stereographic projection and wulff nets. Such a conic projection is conformal over most of its domain. The stereographic projection is appropriate for mapping the polar regions at large scales, such as navigational and topographic maps. One of its most important uses was the representation of celestial charts. Next, it turns to the construction of the stereographic projection of a cubic crystal, the use of the polar and wulff nets, noncubic crystals distinguishing between plane normals and zone axes, and applications of the stereographic projection representation of point group. The line of intersection between the plane and the sphere will then represent a circle, and this circle is formally known as a. Electronic navigation system based on the use of alternate.
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