The Projector module has input ports for several pyramids and lattices and modifies the coordinates of its input to produce a projection. The first pyramid is designated the map and its z coordinate may be transformed to place the map above or below the data.
All lattices (including the base lattices of the pyramids) are assumed to have three coordinate variables. Any lattice with uniform or perimeter coordinates is also assumed to be three dimensional. All coordinates are assumed to represent longitude, latitude, and altitude (depths should be negative values). Longitude and latitude should be in degrees. Longitude may take on any value, but should be consistently within a range of 360 degrees and the Base Longitude parameter (see below) should be set to compensate.
The implemented projections are listed below along with a brief explanation of their properties, utility, and parameters. Projections are classified according to their properties. A projection may be conformal, preserving the shapes of structures while distorting their scale, equivalent, preserving the area of structures, or equidistant, preserving distances in one or more directions. A Projection may also be azimuthal, based on some projection of the globe onto a plane tangent at one point, cylindrical, based on the projection of the globe onto a cylinder tangent (usually) at the equator, or conic, based on the projection of the globe onto a cone which intersects the globe at one or two standard parallels.
Available Projections
Cartesian
Parameters: Base Long., Base Lat.
Properties: None
Longitude and Latitude map directly to x and y except that they are scaled to make equatorial and meridian distances correct in proportion to altitudes. This projection is seldom seen on maps, is considered cylindrical, and preserves no particular quality. The parameters only set the center of the map.
Mercator Cylindrical
Parameters: Base Long., Base Lat.
Properties: Conformal
This is the standard Mercator projection. It is a cylindrical conformal projection. This projection goes to infinity as latitude approaches the poles, therefore such data should be cropped. The parameters only set the center of the map.
Lambert Cylindrical
Parameters: Base Long., Base Lat.
Properties: Equivalent
This is an equivalent projection. Structures at the poles become flat in this projection. The parameters only set the center of the map.
Gnomonic Azimuthal
Parameters: Base Long., Base Lat.
Properties: None
Projection is made from a perspective point at the center of the globe onto a plane which is tangent to the globe at (Base Longitude, Base Latitude). As with all azimuthal projections, great circles on the globe passing through the tangent point appear as straight lines radiating from it. This is the simplest azimuthal projection but has no special properties. Care should be taken in cropping data to avoid points which appear on the other side of the world from the tangent point, as this will produce undesirable results.
Stereographic Azimuthal
Parameters: Base Long., Base Lat.
Properties: Conformal
Projection is made as above but from a perspective point on the surface of the globe exactly opposite the tangent point. This projection has the added property of being conformal. As above, all data points should be on the same side of the globe as the tangent point.
Orthonormal Azimuthal
Parameters: Base Long., Base Lat.
Properties: None
Projection is made onto a plane as above from a point at infinity. This projection gives the effect of looking a a globe, but the projection is flat. Data points should be on the same side of the globe as the tangent point. To achieve the effect of looking at a globe, the actual Globe projection is recommended.
Postel Azimuthal
Parameters: Base Long., Base Lat.
Properties: Equidistant
Also known as the azimuthal equidistant projection, this is useful for determining distances from a given origin. The distance from the point (Base Longitude, Base Latitude) to any other point on the map will be equal to that actual distance on the surface of the earth.
Lambert Azimuthal
Parameters: Base Long., Base Lat.
Properties: Equivalent
Lambert's azimuthal equivalent projection. There is no distortion of area and the minimal distortion of shape occurs at the base point.
Lambert Conical
Parameters: Base Long. & Lat., 1st. & 2nd. St. Par.
Properties: Conformal
Lambert's conformal conical projection. Minimal distortion of area occurs at in the region between the 1st. Standard Parallel and the 2nd. Standard Parallel. The Base Longitude and Latitude parameters set the center of the map.
Albers Conical
Parameters: Base Long. & Lat., 1st. & 2nd. St. Par.
Properties: Equivalent
Albers' equivalent projection. Minimal distortion of shape occurs at in the region between the 1st. Standard Parallel and the 2nd. Standard Parallel. The Base Longitude and Latitude parameters set the center the map. An interesting property of this projection is that the pole maps to a section of a circle, effectively truncating the cone.
Cassini-Soldner
Parameters: Base Long., Base Lat.
Properties: Equidistant
This is a cylindrical equidistant projection in which the cylinder lies at a right angle to the earth's axis. It is useful only for areas which extend mainly in the north-south direction. The Base Longitude parameter sets the meridian of contact for the cylinder and horizontal distances from this central meridian are correct. The Base Latitude parameter sets the center of the map. Distortion occurs mostly in the vertical direction and increases with distance from the central meridian.
Bonne Conical
Parameters: Base Long., Base Lat.
Properties: Equivalent
Actually Bonne's pseudo conical equivalent projection. Scale is preserved only on the central meridian, set by the Base Longitude parameter, and along the parallels. Minimal shape distortion is achieved along the Base Latitude. This projection produces highly curved maps which are useful mainly for projections of an entire hemisphere.
Werner
Parameters: Base Long., Base Lat.
Properties: Equivalent
The Werner projection produces an equivalent heart shaped map, centered on the Base Longitude and is actually a form of Bonne's projection. The Base Latitude determines which hemisphere is at the top of the heart and sets the center of the map. Useful for viewing the entire globe.
Sanson-Flamsteed
Parameters: Base Long., Base Lat.
Properties: Equivalent
The Sanson-Flamsteed projection produces an equivalent symmetric map, centered on the Base Longitude and the equator. This is also a form of Bonne's projection and is useful for viewing the entire globe. The Base Latitude parameter sets the center of the map.
Globe
Parameters: None
Properties: No distortion
This produces an actual three-dimensional globe with radius Globe Radius. If necessary (as when displaying the entire globe) the module SimpleSphere may be used to place a sphere inside the globe in order to avoid seeing through it.
jcphill@uiuc.edu