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Qualitative Formalization of a Curve on a Two-Dimensional Plane

Author Kazuko Takahashi

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Author Details

Kazuko Takahashi
  • School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

Funding

This research is supported by JSPS Kakenhi JP21K12020.

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Kazuko Takahashi. Qualitative Formalization of a Curve on a Two-Dimensional Plane. In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.COSIT.2024.4

Abstract

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Artificial intelligence
Keywords
  • qualitative spatial reasoning
  • knowledge representation
  • logical reasoning
  • shape information

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