eqarea – The eqarea module

Routines for computing an equal area grid.

Specifically, Sergej’s equal area 8000 element grid of the Earth (or any sphere like object). See GISTEMP code, subroutine GRIDEA

Global Variables

band_altitude

Array of altitudes from the equatorial plane.

Altitude refers to the distance from the equatorial plane. The “North” pole being at altitude 1, the “South” pole being at altitude -1.

band_altitude[n] gives the northern altitude of band n, n from 0 to 3. band_altitude[n+1] gives the southern altitude of band n.

Note

These are the sines of the latitude.

band_boxes

Number of horizontal boxes in each band.

To ensure equal area these should be proportional to the thickness of each band (Archimedes’ Hat Box Theorem).

Functions

centre(box)

Return the (latitude,longitude) pair for the centre of box/subbox.

This the the “equal area” centre in the sense that the area to the north will equal the area to the south, and the same for east/west. box is specified as a 4-tuple (as returned as an element of grid() for example).

Return Value

A tuple of (latitude,longitude).

grid()

Generator: Yields 80 boxes comprising equal area divisions of a sphere.

Each box is yielded as a 4-tuple of its boundaries: (southern, northern, western, eastern).

Co-ordinates are given as (fractional) degrees of latitude (for northern and southern borders) and longitude (for western and eastern borders).

grid8k()

As gridsub(), but returns a single generator for all 8000 subboxes.

Not used by real code, but it useful for debugging.

gridJSON()

As gridR3 but in JSON (http://www.json.org/) format.

Return Value

A string matching a JSON array production.

gridR3()

As grid but each box is described in a right-hand 3-dimensional euclidean co-ordinate system.

The sphere is centred at the origin (0,0,0). The equator lies on the plane containing the x- and y-axes (z=0). The north pole has co-ordinate (0,0,1); the intersection of the eqautor and the prime meridian (0 longitude at equator) is (1,0,0). That should be enough for you to deduce that longitude 90 on the equator is at (0,1,0).

Each box is a quadrilateral described by its corners; from the viewpoint of a distant observer viewing the side of the sphere with the box on, the corners are in a counter-clockwise order (so this consistent ordering can be used for face culling if desired).

Each box is yielde as a 4-tuple of 3-tuples. Note polar boxes have co-incident corners.

gridsub()

Generator: Yields 80 boxes, each divided into subboxes.

Each box containts, in a general sense, 100 subboxes. The 80 boxes are those obtained from the generator grid(). A box is yielded as a tuple pair (bound, subgen), where bound is the 4-tuple as returned by grid() (boundaries in degrees for S N W E edges), and subgen is a generator for the 100 subboxes.

The order of the boxes is the same as grid().

The subboxes are returned as 4-tuples using the same latitude/longitude box representation as for grid().

Note that Sheffield, +53.40-001.50, is in subbox 759:

>>> subbox=list(list(gridsub())[7][1])[59]
>>> subbox[0] < 53.4 < subbox[1]
True
>>> subbox[2] < -1.5 < subbox[3]
True

and Vostok, -78.40+106.90, is in subbox 7921:

>>> subbox=list(list(gridsub())[79][1])[21]
>>> subbox[0] < -78.4 < subbox[1]
True
>>> subbox[2] < 106.9 < subbox[3]
True

lerp(x, y, p)

Return a value interpolated between x and y by the fraction p.

Return Value

When p == 0 x will be returned, when p == 1 y will be returned. Note that p is not restricted to being between 0 and 1.

northern40()

Generator: Yields each of the 40 northern hemisphere boxes.

Each box is yielded as a tuple of (southern, northern, western, eastern).

See grid() for more details about what a box is.

southern40()

As northern40() but for southern hemisphere.