A cartographic map projection is a systematic
transformation (also called mapping) from a round surface
to a plane. There are many different projections, since there are
several interesting or useful properties to fulfill. For instance,
it would be desirable to keep shape, distance and area
relationships exactly as in the original surface. Unfortunately,
it can be proved that there is not and there will never be such a
perfect projection: every one is bound to distort at least part of
the mapped region.

Therefore, cartography is an art and science of trade-offs and
guidelines for designing and choosing the least inappropriate
projection for each purpose.

My Own Projection

I have always liked playing with world maps and wondered how
computers could be used for mapping. I spent a good time
deducing formulas
for projecting radius, latitude and longitude
into cartesian x and y. Of course, I could only
draw coordinate grids until the day I got a public-domain
database of geographical coordinates (at first my PC-XT
computer spent over one hour to draw a rough map).

After some time I started devising my "own" projections (actually
I had little access to map bibliography, so I could have
reinvented the wheel). My favorite design is an equal-area flat-polar
inspired by both Sanson's,
Flamsteed's and Eckert's works. It closely resembles
Eckert's V
and VI, and also some of Wagner's
projections.

I wrote a simple application to draw maps; it is somewhat
restricted but effective (luckily nowadays it
takes seconds, not hours).

What You Can Learn Here

The next pages present basic projection concepts, which
properties are important for each map application, why there is
a diversity of maps, how projections are designed, how maps can be
misleading and how to choose a good projection for world maps.

More
than a catalog of projections, I have attempted to present
cartographical concepts in context; unavoidably, several
important projections are discussed in more than one place
(e.g., while explaining its mathematical foundations and when
listing projections with similar features).