A visual basic algorithm for the Winkel Tripel projection

National Geographic Society (NGS) has made several changes throughout the years in their choice of map projection for their world reference maps. The Van der Grinten I map projection was used from 1922 to 1988. Then, in 1988, it was replaced by the Robinson projection. Beginning in 1998, the Winkel Tripel became the map projection of choice for NGS' world maps. Given this change, cartographers and others who make maps may be interested in using the Winkel Tripel for custom applications. The goal of this paper is to show how Winkel Tripel's complex projection equations can be programmed using Visual Basic. Those who use other languages such as C++ can use this programming example to help them create a similar algorithm in their language of choice.