On Embedding a Qualitative Representation in a Two-Dimensional Plane

  title={On Embedding a Qualitative Representation in a Two-Dimensional Plane},
  author={Kazuko Takahashi and Takao Sumitomo and Izumi Takeuti},
  journal={Spatial Cognition \& Computation},
  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… 
Drawing a Figure in a Two-Dimensional Plane for a Qualitative Representation
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
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
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
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.


The Qualitative Treatment of Spatial Data
A new framework called PLCA is proposed, which provides a symbolic representation for the figure in a two-dimensional plane, focusing on the connections between regions, based on four simple objects: points, lines, circuits and areas.
PLCA: A Framework for Qualitative Spatial Reasoning Based on Connection Patterns of Regions
Throughout the study, the authors discovered many topics that relate QSR to other research areas such as topology, graph theory, and computational geometry, while achieving the research goals, indicating that QSR is a very fruitful research area.
On the Equivalence of Topological Relations
This paper refines the model of empty/non-empty 4-intersections with further topological invariants to account for more details about topological relations.
A Pointless Theory of Space Based on Strong Connection and Congruence
We present a logical theory of space where only tridimensional regions are assumed in the domain. Three distinct primitives are used to describe their mereological, topological and morphological
Qualitative Spatial Representation and Reasoning: An Overview
The paper is a overview of the major qualitative spatial representation and reasoning techniques including ontological aspects, topology, distance, orientation and shape, and qualitative spatial reasoning including reasoning about spatial change.
Splitting Ratios: Metric Details of Topological Line-Line Relations
This paper develops a model that captures metric details for line-line relations through splitting ratios, which are normalized values of lengths and areas of intersections that apply to the 9-intersection’s nonempty values, thereby providing refinements of topological properties.
A Spatial Logic based on Regions and Connection
An interval logic for reasoning about space is described, which supports a simpler ontology, has fewer functions and relations, yet does not su er in terms of its useful expressiveness.
Qualitative Spatial Reasoning with Topological Information
  • Jochen Renz
  • Medicine
    Lecture Notes in Computer Science
  • 2002
This work Enumeration of the Relations of the Maximal Tractable Subsets of RCC-8 and Empirical Evaluation of Reasoning with R CC-8 shows positive results in terms of tractability and representation.
Topological Inference
The computational problems involved in developing a relational consistency and planarity inference system are studied, and polynomial-time algorithms for several important special cases are developed and proved to be NP-hard.
Spatial and Temporal Reasoning
From the Publisher: Qualitative reasoning about space and time - a reasoning at the human level promises to become a fundamental aspect of future systems that will accompany us in daily activity.