About the Globe Navigator
Presenting Images of an Early Globe on the Web
The goal for this project was to develop a technique that provides a comprehensive digital view of an historically important globe; in this case Mercator's terrestrial globe of 1541. Because of their rarity, such globes are not readily accessible to scholars or others interested in cartography. Most maps can be made accessible on the web through a single digitized image. In order to view all parts of a globe, however, multiple images must be produced, to cover the entire surface of the sphere. In addition, a mechanism is needed that allows the user to navigate over these images in order to view any desired location on the globe's surface. This page describes the approach taken to provide this capability.
Problem 1: Partitioning the surface of the globe into areas for imaging.
In order to avoid excess overlapping of the surface areas covered by different images, an approach was chosen that would allow the different images to cover, as evenly as possible, the globe's surface. The approach was based on the solid geometry of regular polyhedra. Consider a box in the shape of a cube, exactly large enough to contain a particular globe. The cube has six surfaces, and, when the globe is placed in the box, the centerpoint of each surface will touch the globe, identifying six evenly-distributed points which could serve as the centerpoints for a set of photographic images. However, in order for the six images to cover all parts of the globe, the area that would have to be included by each image would be too large to produce a satisfactory result. The curvature of the photographed surface would result in images that are distorted and out-of-focus at the edges, and the large area covered by each image would make it difficult to produce digitized images with legible detail. To decrease the surface-area coverage required for each individual image, one must base the imaging on a higher-order polyhedron than a cube. Of the five regular polyhedra, the icosahedron, consisting of 20 equilateral triangles (meeting at 12 vertices), has the most surfaces. So, an imaginary icosahedron built around a globe would locate 20 points touching the globe's surface (the centerpoints of each triangle) which could then be used as the centerpoints for a set of images.
Though an icosahedron is a large improvement over a cube, an even better solution is a truncated icosahedron. This polyhedron is created by truncating each of the 12 vertices of an icosahedron a third of the way down the sides of each triangle. The result of this is a 32-sided polyhedron, with 20 hexagons (where the 20 triangles of the original icosahedron were) and 12 pentagons (where the 12 vertices of the icosahedron were).
The shape of a truncated icosahedron is familiar. It is the shape used in the construction of soccer balls. It is also the shape of an unusual 60-atom carbon molecule (C60) discovered in the 1980's and named the 'buckyball' or 'fullerene', in tribute to Buckminster Fuller, the visionary scientist and creator of geodesic dome houses, whose structures resembled this polyhedral shape. When applied to a medium-sized (16" diameter) globe, the surface area covered by each of the 32 images (whose centerpoints correspond to the centerpoints of each of the 32 polygons) need only be approximately 5" x 5" to ensure that the entire surface of the globe is covered. This creates an image small enough to reduce the effect of curvature on the area being photographed, and also makes it possible for each image to be shown with enough magnification to allow all of the globe's surface detail to be legible. An arbitrary choice has to be made as to the alignment between the truncated icosahedron and the underlying globe to be imaged. It was decided to align the poles with pentagon centerpoints and to align a hexagon centerpoint with the prime meridian. The use of a polyhedron to map the surface of a sphere is not a new idea. Buckminster Fuller produced such a map, projecting a globe image onto a 'buckyball' and unfolded it to produce a flat, but broken up, world map. He called it a "dymaxion map", whose virtues included a low degree of distortion in all parts of the earth, and the ability to unfold the polyhedron such that no land areas are cut into by edges of the map. Even many centuries earlier, Albrecht Dürer, in 1538, had described the idea of projecting a globe's surface onto a polyhedron (including an icosahedron).
Problem 2: Navigating among the 32 images.
As Ptolemy pointed out:
[With a globe] one cannot fix one's eye at the same time on the whole sphere, but one or the other must be moved, that is, the eye or the sphere, if one wishes to see other places. (Geography, Book I-Chap. 20)
The limitation described by Ptolemy is even more true when the globe is not at hand, to be rotated or walked around, but is being viewed through images on a web browser. To work around this limitation a "globe navigation device" was created, seen to the left. This device is a small image of the earth, with a representation of the present-day geography displayed on its surface. In addition, the mesh of the truncated icosahedron, used to define the image locations, is superimposed on the earth image. The navigation device can be rotated by clicking on the visible polygons, causing the clicked-on area to rotate into the center position. A separate pop-up list can also be used to choose any of the 32 center-point locations by long/lat value. Whether chosen from the pop-up list or by clicking on the globe image, the two stay synchronized, displaying the current, selected location. Additional buttons let you flip to the opposite point on the globe or to spin the globe image, until the desired side of the globe comes into view. Once the desired location is chosen, the "Load Image" button can be clicked to load the photographic image of the corresponding section of the globe.
When used for navigating among images of an early globe, the coastlines of continents and islands shown on the navigation device may not correspond exactly to those shown on the globe itself. With the Mercator 1541 globe, for example, at the expected position of Japan (approximately 140° East, 35° North) one finds neither Japan nor even the eastern coast of Asia, but an area roughly corresponding to Tibet. This is because Mercator (like other cartographers of his day) greatly overestimated the combined longitudinal extent of Europe and Asia. However the correspondence between what you expect to see and what is actually displayed will usually be close enough so that given the currently displayed image, along with the earth image on the navigation device, one can easily find, and navigate to, the image segment you are looking for. Also, the prime meridian on an old globe will not correspond with the current (Greenwich) prime meridian, but this difference has no effect on the approach taken here; it simply results in the old globe's longitude markings being offset by some constant amount from the modern coordinates used by the navigation device. On the Mercator globe, the prime meridian is drawn through the Canary Islands, 14 degrees west of the Greenwich prime meridian (but only 12 degrees west of the location of Greenwich as shown on the Mercator globe).Arbitrarily, all images (except for the two polar images) are presented with north at the top. For the North Pole, the image is taken with the (Greenwich) prime meridian going downwards from the (polar) centerpoint, and for the South Pole, the image is taken with the prime meridian going upwards from the (polar) centerpoint. When manipulating the navigation device, the positioning of the globe image also reflects the orientation choices described here.
The coordinates shown for each image/polygon center are the longitude and latitude rounded to the nearest degree. The longitudes are, in fact, exact degrees. The non-polar latitudes, shown as 11, 27, and 53 degrees (both north and south), are, more precisely, 10°48', 26°35', and 52°37', respectively.