Three-Dimensional Map Construction

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Science  18 Nov 1966:
Vol. 154, Issue 3751, pp. 857-864
DOI: 10.1126/science.154.3751.857


Three-dimensional maps are useful tools which have been neglected for some time. They shouldbe more commonly used, and familiarity with the techniques discussed in this article should dispel any qualms anyone might ve about needing artistic talent to nstruct them. The saving in time esulting from the use of an anamorphoser provides a further incentive.

The anamorphoser transformations discussed above were all prepared by using straight slits, oriented at right angles to each other and placed so that all planes of the elements were parallel to each other. It is possible to vary these conditions in an infinite number of ways and thereby produce nonparallel tranceformations. Some of these variations are illustrated in Fig. 10. All the illustrations in Fig. 10 are transformations of the planimetric weather map shown in Fig. 8A. The variations used for the maps of Fig. 10 are as follows. (A) All planes parallel, with a curved rear slit; (B) all planes parallel, with curved slits front and rear; ( C) all planes parallel, with S-shaped rear slit; (D) all planes parallel, with an undulating rear slit; (E) all planes parallel, with curved front and undulating rear slit; (F) plane of the original rotated on the horizontal axis—both slits curved; (G) plane of the original rotated on thevertical axis— both slits curved; (H) plane of the original rotated on the horizontal axis —both slits straight.

These are only a few of the many transformations which can be made with an anamorphoser, butthey do point toward some interesting possibilities. For example, it appears that maps based onone projection might be altered to satisfy the coordinates of a completely different projection. Note, for example, the change of parallels from concave to convex curves (Figs. 8A and 10A) and the change from converging meridians to diverging meridians (Figs. 8A and l0G). Similarly, the grids of maps B, F, and H of Fig. 10 approximate projections which are quite different from the original.

Other possible, and noncartographic, uses also come to mind. For example, transformations offront and side views of architectural and engineering drawings could be made to show views fromdifferent elevations and orientations. Or a geologist might be able to illustrate folding of sedimentary strata by preparing a drawing of a series of horizontal beds and then using an anamo-rephoser with an undulating slit to alter the beds to any degree of folding desired. With a movie camera and a moving lens mount this "folding" process could be photographed with different settings, so that the parallel beds would gradually and continuously change to irregularly folded beds.

The transformations shown in Fig. 10 resulted from uncontrolled experimentation with the anamorphoser, and as yet no geometric solutions for setting up the transformation elements are available. Similarly, the suggested uses are mere flights of fancy, and no claim is made for theirpracticality. It is hoped, however, that they will stimulate the reader's imagination and lead him to look for uses of the anamorphoser in fields other than cartography (9).