Medial-axes in Caspian Sea
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THE DELIMITATION OF SEA BOUNDARIES

In these pages we inform on a fully automated procedure that traces sea limits taking due account of all points and sinuosities in the shoreline, contrary to the commonly used solutions that require the manual selection of input points as well as the insertion of straight baselines (see publications from UNCLOS, the United Nations Law of the Sea), contrivances that have triggered all sorts of injudicious claims against the freedom of the seas.
        The development of this automated procedure grew out of the understanding that the central problem in sea delimitation is one of recognition and handling of shapes. Its basic component is computer waterlining (see elsewhere in this site), a sure-footed tool to obtain abstractions of shapes and the modern counterpart of the device used by cartographers of old to mark out water areas in maps. This procedure operates either on a projection plane, on a sphere or on the terrestrial ellipsoid, and yields correct and ambiguities-free results in general and special cases of outer, equidistant and median limits.
        This procedure was applied in cases such as the determination of the natural entrance points to a bay; delineations considering the so-called full-effect and the half effect, and configurations that call for proportionality between areas and coastline lengths, with clear advantages over the manual solutions proposed in the literature. Those tests, carried out with digital shorelines in the public domain, put in doubt complex limits and awkward pockets (see UNCLOS publications) as grounds for the principle of Straight Baselines.
        The data for the map on the left, shorelines and land boundaries for the five coastal states, were extracted from the Digital Chart of the World (DCW), a digitalization of world maps at the 1:1,000,000 scale. With that data the Caspian Sea was waterlined on the ellipsoid and its medial-axes traced, shown at right as a network of black lines. All that was executed in fully automated mode. In the same mode the medial-axes was shaved of its superfluous branches. The lines in red, commonly designated as median lines, are the result of that operation; they partition the Caspian Sea into the areas that could in all fairness be assigned to each coastal state. The fact that the accuracy of DCW is very low relative to what modern tools could provide today is irrelevant in this context: any shoreline file, even compiled from GPS signals, would serve equally well.
        Other discussions and illustrations on these procedures can be found in the NEXT pages.