The Four Intersection-and-Difference Model for Line-Line Topological Relations

The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.

An Approach to Reasoning Topological Relations Between Areal Objects Under Randomness

This paper describes the geometric and statistical properties of areal object under randomness. In order to describe formally such a uncertain topological relation, a new formal model (i.e. 4ID model) is proposed. On the basis of this, the effects of positional uncertainty on topological relations between areal objects are investigated in detail. Some possibility functions for the determination of relations are constructed based on the assumption that randomness of point location complies with a normal distribution, and the concept of uncertain sets of topological relations under randomness is introduced.

Topological relations between spherical spatial regions with holes

There is growing interest in globally modelling the entire planet.Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated,few studies have focused on the topological relations between spherical spatial regions with holes.The 16-intersection model(16IM)is proposed to describe the topological relations between spatial regions with holes.A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes.The results show that(1)3 disjoint relations,3 meet relations,66 overlap relations,7 cover relations,3 contain relations,1 equal relation,7 coveredBy relations,3 inside relations,1 attach relation,52 entwined relations,and 28 embrace relations can be distinguished by the 16IM and that(2)the formalisms of attach,entwined,and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different,whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.

Qualitative spatial reasoning on topological relations by combining the semantic web and constraint satisfaction

Qualitative spatial reasoning on topological relations can extract hidden spatial knowledge from qualitatively described topological information,which is of significant importance for decisionmaking and query optimization in spatial analysis.Qualitative reasoning on spatial topological information based on semantic knowledge and reasoning rules is an efficient means of reducing both the known relations and the corresponding rules,which can result in enhanced reasoning performance.This paper proposes a qualitative reasoning method for spatial topological relations based on the semantic description of reasoning rules and constraint set.Combined with knowledge from the Semantic Web,the proposed method can easily extract potential spatial results consistent with both unique and non-unique rules.The Constraint-Satisfactionbased approach,describing constraint set with semantic expressions,is then used together with an improved path consistency algorithm to verify the consistency of the unique-rules-based and non-unique-rules-based reasoning results.The verification can eliminate certain reasoning results to ensure the reliability of the final results.Thus,the task of qualitative spatial reasoning on topological relations is completed.

Definitions of Natural-Language Spatial Relations: Combining Topology and Directions

Because SQL for querying data from spatial databa se s is ineffective, the query based on natural or visual language becomes an attra ctive research field gradually. However, how to define and represent natural lan guages related to spatial data are still gigantic problems. Because existing mod els of direction relations can’t describe by use of some common concepts. First of all, detailed direction relations are proposed to describe the directions re lated to the interior of spatial objects, such as "east part of a region","ea st boundary of a region", and so on. Secondly, by integrating the detailed dire ctions with exterior direction relations and topological relations, several NLSR s are defined, such as "a road goes across the east part of a lake", "a river goes along the east boundary of a province", etc. Finally, based on the NLSRs abovementioned, a natural spatial query language (NSQL) is formed to retrieve da ta from spatial databases.

DEALING WITH SPATIAL RELATIONS FOR SPATIAL OBJECTS WITH RANDOMNESS IN GIS

To design retrieval algorithm of spatial relations for spatial objects with randomness in GIS,this paper builds up the membership functions based on set theory idea,used for determination of topological spatial relations between random objects,such as between point and point,point and line or polygon,which provides theoretical basis for retrieving spatial relations between certain and random objects.Finally,this paper interprets detailed methods and steps of realizing them by means of some simple examples under the GIS’s environment.

Topological Recursion Relations from Pixton Relations

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.

A genus-4 topological recursion relation for Gromov-Witten invariants

In this paper,we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton’s relations on the moduli space of curves.As an application,we prove that Pixton’s relations imply a known topological recursion relation on Mg,1 for genus g≤4.

Application of Ray Scanning Method in Color Measurement

A new method based on the traditional method of ray scanning has been introduced to resolve the problem of judging the color in the chromaticity diagram by employing the line segments approximate curve—— using polygonal approximate closed curve. Then a vector coordinate could be used to describe the curve instead of curve equations. So it is easy to judge the topology relation between an area and a point or a locus. And any data processing method has been used to save memory, which makes the improved ray scanning method is quite useful in the measurement of color.

Two topological approaches to resonance energy and the relation between them

Two of the present authors recently put forward a novel approach to resonance energy which is based on a similar topological reasoning as a previously elaborated resonance energy concept. It is shown that these two approaches are not completely equivalent. Several other properties of the new resonance energy are pointed out.

Relativization of dynamical properties

In the past twenty years,great achievements have been made by many researchers in the studies of chaotic behavior and local entropy theory of dynamical systems.Most of the results have been generalized to the relative case in the sense of a given factor map.In this survey we offer an overview of these developments.