Map Projections

## Introduction

 One of my renditions of a generalized, transverse polyconic projection

### An Interest in Map Projections

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.
 My pseudo-Eckert projection
This projection's mathematical derivation is presented in Uma Projeção Cartográfica Equivalente, Portuguese gzipped PostScript and Portuguese PDF.

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).

 An Estonian translation by Karolin Lohmus.

 www.progonos.com/furuti    July 31, 2017