Modeling Cardinal Direction Relations in 3D for Qualitative Spatial Reasoning

2014 ◽  
pp. 199-214 ◽  
Author(s):  
Chaman L. Sabharwal ◽  
Jennifer L. Leopold
Keyword(s):  
Spatial Reasoning ◽  
Qualitative Spatial Reasoning ◽  
Cardinal Direction ◽  
Direction Relations ◽  
Cardinal Direction Relations

scholarly journals Reasoning about Topological and Cardinal Direction Relations Between 2-Dimensional Spatial Objects

2014 ◽  
Vol 51 ◽  
pp. 493-532 ◽  
Author(s):  
A. G. Cohn ◽  
S. Li ◽  
W. Liu ◽  
J. Renz
Keyword(s):  
Spatial Reasoning ◽  
Spatial Information ◽  
Qualitative Spatial Reasoning ◽  
Topological Information ◽  
Directional Information ◽  
Spatial Objects ◽  
Cardinal Direction ◽  
Direction Relations ◽  
Consistency Problem ◽  
Cardinal Direction Relations

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints.

scholarly journals A Hybrid Reasoning Model for “Whole and Part” Cardinal Direction Relations

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Ah-Lian Kor ◽  
Brandon Bennett
Keyword(s):  
Hybrid Model ◽  
Binary Relations ◽  
Single Piece ◽  
Cardinal Direction ◽  
Hybrid Reasoning ◽  
Direction Relations ◽  
Cardinal Directions ◽  
To Come ◽  
Cardinal Direction Relations ◽  
Constraints Model

We have shown how the nine tiles in the projection-based model for cardinal directions can be partitioned into sets based on horizontal and vertical constraints (called Horizontal and Vertical Constraints Model) in our previous papers (Kor and Bennett, 2003 and 2010). In order to come up with an expressive hybrid model for direction relations between two-dimensional single-piece regions (without holes), we integrate the well-known RCC-8 model with the above-mentioned model. From this expressive hybrid model, we derive 8 basic binary relations and 13 feasible as well as jointly exhaustive relations for the x- and y-directions, respectively. Based on these basic binary relations, we derive two separate 8×8 composition tables for both the expressive and weak direction relations. We introduce a formula that can be used for the computation of the composition of expressive and weak direction relations between “whole or part” regions. Lastly, we also show how the expressive hybrid model can be used to make several existential inferences that are not possible for existing models.

On Internal Cardinal Direction Relations

2005 ◽  
pp. 283-299 ◽  
Author(s):  
Yu Liu ◽  
Xiaoming Wang ◽  
Xin Jin ◽  
Lun Wu
Keyword(s):  
Cardinal Direction ◽  
Direction Relations ◽  
Cardinal Direction Relations

scholarly journals Composing cardinal direction relations

2004 ◽  
Vol 152 (2) ◽  
pp. 143-171 ◽  
Author(s):  
Spiros Skiadopoulos ◽  
Manolis Koubarakis
Keyword(s):  
Cardinal Direction ◽  
Direction Relations ◽  
Cardinal Direction Relations
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