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The two-dimensional ``hidden-line'' problem is the problem of determining, by means of a computer algorithm, which edges or parts of edges of an arbitrary, nonintersecting polygon are visible from a specified vantage point in the plane of the polygon. The problem is an important one in the field of computer graphics, and is encountered, for example, in using a computer to determine the portion of an island's coastline visible from a ship offshore. Some propositions are introduced that facilitate the solution of this problem. A general algorithm for the solution is described, and illustrative examples are given of hidden-line problems solved with a digital computer.