On Embedding a Qualitative Representation in a Two-Dimensional Plane

@article{Takahashi2008OnEA,
  title={On Embedding a Qualitative Representation in a Two-Dimensional Plane},
  author={Kazuko Takahashi and Takao Sumitomo and Izumi Takeuti},
  journal={Spatial Cognition \& Computation},
  year={2008},
  volume={8},
  pages={26 - 4}
}
Abstract This paper discusses embedding in a two-dimensional plane a symbolic representation for spatial data using the simple objects, points (P), lines (L), circuits (C), and areas (A). We have proposed PLCA as a new framework for a qualitative spatial reasoning. In a PLCA expression, the entire figure is represented in a form in which all the objects are related. We investigate the conditions for two-dimensional realizability of a PLCA expression, and derive the relation that the numbers of… 
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TLDR
An algorithm for generating a figure in a two-dimensional plane from a qualitative spatial representation of PLCA is described and a genetic algorithm is used to determine the locations and the sizes of circles in the last step of the algorithm.
A Qualitative Representation of a Figure and Construction of Its Planar Class
TLDR
A method of constructing PLCA expressions inductively is described, and it is proved that the resulting class coincides with that of the planar PCLA.
Qualitative Spatial Representation Based on Connection Pattern and Convexity
TLDR
The goal is to represent not only the shape of the outer circuit of a single region, but that of the boundaries between regions, by utilizing a convex-hull of each area to give a qualitative shape representation.
Construction of a Planar PLCA Expression: A Qualitative Treatment of Spatial Data
TLDR
This paper describes a method of constructing a PLCA expression inductively, and proves that the defined class coincides with a subclass of P LCA that can be realized on a two-dimensional plane.

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