All major web mapping services use the web Mercator projection. This is a poor choice for maps of the entire globe or areas of the size of continents or larger countries because the Mercator projection shows medium and higher latitudes with extreme areal distortion and provides an erroneous impression of distances and relative areas. The web Mercator projection is also not able to show the entire globe, as polar latitudes cannot be mapped. When selecting an alternative projection for information visualization, rivaling factors have to be taken into account, such as map scale, the geographic area shown, the map_s height-to-width ratio, and the type of cartographic visualization. It is impossible for a single map projection to meet the requirements for all these factors. The proposed composite map projection combines several projections that are recommended in cartographic literature and seamlessly morphs map space as the user changes map scale or the geographic region displayed. The composite projection adapts the map_s geometry to scale, to the map_s height-to-width ratio, and to the central latitude of the displayed area by replacing projections and adjusting their parameters. The composite projection shows the entire globe including poles; it portrays continents or larger countries with less distortio, optionally without areal distortion); and it can morph to the web Mercator projection for maps showing small regions.