LIPIcs.COSIT.2024.4.pdf
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We propose a theoretical framework for qualitative spatial representation and reasoning about curves on a two-dimensional plane. We regard a curve as a sequence of segments, each of which has its own direction and convexity, and give a symbolic expression to it. We propose a reasoning method on this symbolic expression; when only a few segments of a curve are visible, we find missing segments by connecting them to create a global smooth continuous curve. In addition, we discuss whether the shape of the created curve can represent that of a real object; if the curve forms a spiral, such a curve is sometimes not appropriate as a border of an object. We show a method that judges the appropriateness of a curve, by considering the orientations of the segments.
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