Qualitative spatial reasoning using orientation, distance, and path knowledge

Zimmermann, Karsten; Freksa, Christian

doi:10.1007/bf00117601

Cited by 150 publications

(74 citation statements)

References 11 publications

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“…In this method, a double-cross matrix captures the relative position (or orientation) of any two line segments in a polyline by describing it with respect to a double cross based on the start-ing points of these line segments (Freksa (1992); Zimmermann and Freksa (1996)). For an overview of the use of constraint calculi in qualitative spatial reasoning, we refer to (Renz and Nebel (2007)).…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

“…As mentioned in the Introduction, in the double-cross formalism, the relative position (or orientation) of two (located) vectors of a polyline is encoded by means of a 4-tuple, whose entries come from the set {−, 0, +} (Freksa (1992); Zimmermann and Freksa (1996)). Such a 4-tuple expresses the relative orientation of two vectors with respect to each other.…”

Section: The Double-cross Matrix Of a Polylinementioning

confidence: 99%

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On the realisability of double-cross matrices by polylines in the plane

Kuijpers

Moelans

2017

Journal of Computer and System Sciences

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We study a decision problem that emerges from the area of spatial reasoning, but that is also of interest to the area of computational algebraic geometry. This decision problem concerns the use of constraint calculi in qualitative spatial reasoning. One such qualitative calculus describes polylines in the plane by means of their double-cross matrix. In such a matrix, the relative position (or orientation) of each pairs of line segments of a polyline is expresses by means of a 4-tuple, whose entries come from the set {−, 0, +}. However, not any N ×N matrix of 4-tuples from {−, 0, +} is the double-cross matrix of a polyline with N line segments. This gives rise to the following decision problem: given an N × N matrix of 4-tuples from {−, 0, +}, decide whether it is the double-cross matrix of a polyline with N line segments, and if it is, given an example of a polyline that realises the matrix.It is known that this problem is decidable, but it is NP-hard and the best, known algorithms have exponential time complexity. In this paper, we give polynomial time algorithms for the case where the attention is restricted to polylines in which consecutive line segments make angles that are multiples of 90 • or 45 • , respectively. For the more complicated case of 45 • -polylines, we also introduce the polar-coordinate representation of double-cross matrices.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Section: The Double-cross Matrix Of a Polylinementioning

confidence: 99%

On the realisability of double-cross matrices by polylines in the plane

Kuijpers

Moelans

2017

Journal of Computer and System Sciences

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“…Works by Cohn (Cohn & Hazarika, 2001;Cohn & Renz, 2008) augment spatial representation and reasoning with the concepts of: ontology, mereology, mereotopology, mereogeometry (the study and mathematics of part-whole relationships), spatial relations, direction and orientation, shape, distance and size, spatial vagueness and uncertainty. Freksa (1992) and Zimmermann & Freksa (1996) discuss qualitative spatial reasoning based on directional orientation information. In their work, 15 qualitatively different relations are defined between a point and a vector (directed line segment).…”

Section: Qualitative Spatial Representation and Reasoningmentioning

confidence: 99%

Investigating Geosparql Requirements for Participatory Urban Planning

Mohammadi

Hunter

2015

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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Commission VI, WG VI/4KEY WORDS: GeoSPARQL, PGIS, Urban Planning, Spatial Reasoning, Urban Patterns, Spatial Relations ABSTRACT:We propose that participatory GIS (PGIS) activities including participatory urban planning can be made more efficient and effective if spatial reasoning rules are integrated with PGIS tools to simplify engagement for public contributors. Spatial reasoning is used to describe relationships between spatial entities. These relationships can be evaluated quantitatively or qualitatively using geometrical algorithms, ontological relations, and topological methods. Semantic web services utilize tools and methods that can facilitate spatial reasoning. GeoSPARQL, introduced by OGC, is a spatial reasoning standard used to make declarations about entities (graphical contributions) that take the form of a subject-predicate-object triple or statement. GeoSPARQL uses three basic methods to infer topological relationships between spatial entities, including: OGC's simple feature topology, RCC8, and the DE-9IM model. While these methods are comprehensive in their ability to define topological relationships between spatial entities, they are often inadequate for defining complex relationships that exist in the spatial realm. Particularly relationships between urban entities, such as those between a bus route, the collection of associated bus stops and their overall surroundings as an urban planning pattern. In this paper we investigate common qualitative spatial reasoning methods as a preliminary step to enhancing the capabilities of GeoSPARQL in an online participatory GIS framework in which reasoning is used to validate plans based on standard patterns that can be found in an efficient/effective urban environment.

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“…Its functions in spatial database construction (Kim and Um, 1999), qualitative spatial reasoning (Frank, 1996;Sharma, 1996;Clementini et al, 1997;Mitra, 2002;Wolter and Lee, 2010;Mossakowski, 2012), spatial computation (Ligozat, 1998;Bansal, 2011) and spatial retrieval (Papadias and Theodoridis, 1997;Hudelot et al, 2008) have attracted researchers' interest. Direction relation has also been used in many practical fields (Zimmermann and Freksa, 1996;Kuo et al, 2009), such as combat operations (direction relation helps soldiers to identify, locate, and predict the location of enemies), driving (direction relation helps drivers to avoid other vehicles), and aircraft piloting (direction relation assists pilots to avoid terrain, other aircrafts and environmental obstacles).…”

Section: Introductionmentioning

confidence: 99%

An approach to computing direction relations between separated object groups

Yan

Wang

2013

Geosci. Model Dev.

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Abstract. Direction relations between object groups play an important role in qualitative spatial reasoning, spatial computation and spatial recognition. However, none of existing models can be used to compute direction relations between object groups. To fill this gap, an approach to computing direction relations between separated object groups is proposed in this paper, which is theoretically based on gestalt principles and the idea of multi-directions. The approach firstly triangulates the two object groups, and then it constructs the Voronoi diagram between the two groups using the triangular network. After this, the normal of each Voronoi edge is calculated, and the quantitative expression of the direction relations is constructed. Finally, the quantitative direction relations are transformed into qualitative ones. The psychological experiments show that the proposed approach can obtain direction relations both between two single objects and between two object groups, and the results are correct from the point of view of spatial cognition.

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Qualitative spatial reasoning using orientation, distance, and path knowledge

Cited by 150 publications

References 11 publications

On the realisability of double-cross matrices by polylines in the plane

On the realisability of double-cross matrices by polylines in the plane

Investigating Geosparql Requirements for Participatory Urban Planning

An approach to computing direction relations between separated object groups

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