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Cahill 1909

Cahill-Keyes Octant Graticule:
Principles and Specifications

with Perl programs and OpenOffice.org 2.0 macros
for 1/1,000,000 Megamap

Gene Keyes
2010-08-20

Continued from page 2

11) Complete x-y coordinates for
Cahill-Keyes Octant Graticule Template
(and 1/1,000,000 Megamap)

Notes by Gene Keyes and Mary Jo Graça

Mary Jo's first of two Perl programs (p. 2) outputs this complete data set of all the x-y coordinates for all one degree geocells of a horizontal half octant (including the very narrow polar geocells from 90° to 85°), plus meridian joints, octant border, etc. The original format was a text-file of tab-separated values [shown as .csv, comma-separated values], which is convertible to a spreadsheet. But that complete table is presented here in HTML. Because of the different orientation, its x-y coordinates differ from Gene's hand-calculated, whole-octant values, but the segment lengths and geocell dimensions remain the same.

Mary Jo's abbreviations and arrangement:

All coordinates, distances and lengths are in millimeters for a 1/1,000,000 map. (A millimeter in this scale represents one kilometer.)

Column headers from 0 to 45 refer to each meridian, central (0°) to outer (45°), and are listed from left to right. (Meridian 0 is seen as the horizontal base AG in Mary Jo's half-octant version.)

File "Hashes8.csv", as shown in HTML below, includes these eight tables with values of arrays (called "hashes" in Perl) from the program:

Table dP: Distance between parallels along each meridian:

0: Polar zone — 90°-75° of latitude
1: Polar supple zone — 75°-73° of latitude
2: Middle zone — 73°-15° of latitude
3: Equatorial zone — 15°-0° of latitude

Table L: Lengths of meridian segments

0: Polar — from point A to first joint
1: Middle — from first joint to second joint
2: Equatorial — from second joint to Equator
3: Middle + equatorial — sum of 1 and 2
4: Total length — from A to Equator
5: Length from 73° to 0° of latitude, along meridian

Tables xJ and yJ: x- and y-coordinates, respectively, of important meridian points — joints and end points:

0: Start of drawn meridian — Although all calculations are done with every meridian starting at point A, coordinates on this line are the start of the drawn meridian: major meridians (every 5°, bolded) are shown from point A, while all other meridians (minor) are drawn starting at parallel 85°.
1: First joint
2: Second joint
3: Equator-meridian intersections

Tables xP and yP: x- and y-coordinates, respectively of parallel-meridian intersections.

Parallels from Equator (0°) to last before Pole (89°) are listed in ascending order in the left hand column.

Table of Points: x- and y-coordinates of points on the scaffold triangle and semi-octant. Point labeled Center is the center for the circular arc defining part of parallel 15°.

Table of Lengths: lengths of segments and combined segments of the scaffold triangle and semi-octant. Length labelled R is the radius of the circular arc defining part of parallel 15°.