ABSTRACT
Usually we try to choose the map projection that has the smallest deformation. But some urban maps for travel need to show detailed streets in the business center, in scenic spots and at historical sites, and for other service facilities such as restaurants and hotels. The key elements of such detail are nearly always focused in the center of a city or region. So this area needs to be expressed at a larger scale. Applying the deformation information for a map projection, we can edit a map to have arbitrary different scales. On the map we can make the scale of every region vary, one at a time, two at a time or not the same everywhere. In addition, for a large regional map if we need to stress an important area we can use the surrounding area as a background, or we can make the different areas have a different kind of areal deformation to satisfy the requirement of various thematic map uses. For example, in epidemiology rates can be shown on a base stretched to equal the number of susceptibles, or, for political purposes on a base of voters. This kind of map is usually called a variable-scale map. In Russia they are known as varivalent projections, in France as anamorphoses, in the Anglo-American literature as ‘area cartograms' (Dorling 1996; Tobler 1963, 1986a). It can be shown that all equal-area map projections are the special case of ‘constant importance'. We can obtain variable-scale map projections in many ways. These will be introduced as follows.
