map projections

[riis]

Does anyone here know a good site dealing with map projections? Including formulas, of course. Almost all sites I've seen don't have any formulas.

[Jim Brown]

Riis, I don't know. But a good place to start might be www.nationalgepgraphic.com

If they can't help, don't worry. It's such a good site you can goof off there for ages!

[da_silvy]

goof off?



I think browsing it is more appropriate

[Guv]

The Mercator projection which is a very common transformation maps the sphere to a cylinder and then unrolls the cylinder, making a plane. Note that local geometry on a cylinder is exactly the same as plane geometry. This projection tends to be fairly accurate near the Equator. The further from the Equator, the more distorted is the resulting map.

I think this projection is very good when used to plot routes from one place to another. You just draw a straight line between the two points and note the indicated route. This is one reason the projection is used.

The formulae for the transforms are extremely simple, another reason for using this projection.

X = A * Longitude, with Longitude from 0 to 360 degrees.
Y = B * Latitude, with Latitude from -90 (South Pole) to +90 (North Pole) degrees.

Where (X, Y) are Cartesian coordinates and (Latitude, Longitude) are the spherical coordinates. A & B are scaling constants.

The equator maps to a piece of the X-Axis. Each pole maps to a line parallel to the equator and equal in length to the equator.

One inch for each ten degrees of Longitude would make the Equator 36 inches long (A = 1/10 inches per degree). Since the Equator is approximately 25,000 miles, each inch at the equator would represent about 694 miles.

The same scale for latitude seems reasonable. One inch per each ten degrees of latitude would make the Pole to Pole distance 18 inches (B = 1/10 inches per degree). Each inch along a line of constant Longitude would once again be approximately 694 miles.

A World Almanac or some Web Site can provide exact values for Pole to Pole and equatorial circumference. Note that the earth is an oblate spheroid, not a sphere. The poles are closer to the center than the equator.

I do not know the formulae for any other projections.