CN109658506A - A kind of complex three-dimensional topological relation describes method - Google Patents
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Abstract
The invention discloses a kind of complex three-dimensional topological relations to describe method, including summing up 10 kinds of topological relations that can describe two-dimentional three-dimensional space object, and definition is made to it；It summarizes the basic topology relationship between point, line, surface, body space sub-goal and it is finely divided；Whether will intersect between spatial object sub-goal as criteria for classifying to topological relation by carrying out hierarchical reasoning to subdivision roughly；Using decomposition-combination method, by each self intersection of the sub-goal of spatial object, acquires and whether intersect, intersect dimension, intersection separation number, propose " 9PDS " universal expression model, complex three-dimensional spatial topotaxy is expressed；By topological relation hierarchical reasoning and expression model, the basis of complex three-dimensional topological relation reasoning is established.The present invention provides a kind of general expression for topological relation, is conducive to the differentiation expression of two and three dimensions spatial topotaxy, while solving the problems, such as that complex topology relationship is beyond expression of words, enables topological relation Unified Expression.
Description
Technical field
The invention belongs to topology of geographic information system relationship expression fields, are a kind of topological relations by spatial object
The hierarchical relationship and " 9PDS " descriptive model of complex three-dimensional topological relation are defined, established, realizes complex three-dimensional spatial topotaxy
Can be from detail to outline, the sight from microcosmic to middle, then the method that describes of reasoning to macro-level.
Background technique
It expresses the relationship between the feature and target of extraterrestrial target with will be clear that, must just be gone in the form of certain specific
Them are described, their connection is usually expressed with spatial relationship.Spatial relationship includes metric relation, position relation and opens up
Three kinds of relationship are flutterred, wherein topological relation occupies center-stage, is the basis for studying spatial relationship.
The description of present three-dimensional topology relationship rests on the expression of simple Three dimensional Targets topological relation mostly,
Ability to express is very limited on the topological relation of complex target.Due to the difference of Three dimensional Targets element shape and size,
Many kinds of, these extraterrestrial targets can have having for the case where a variety of topological relations, the topological relation infinitely segmented and the mankind
Limit cognition can generate contradiction, and complex topology relationship is beyond expression of words.
Compared to two-dimensional topology relationship and simple Three dimensional Targets topological relation, complex three-dimensional spatial topotaxy
Can be realized the more careful and comprehensive expression of D spatial features, the spatial information for making it possible to utilize greatly increases,
It can preferably observe and understand space and geographical things.
Summary of the invention
The purpose of the present invention is to provide a kind of complex three-dimensional topological relations to describe method, to solve above-mentioned background technique
The problem of middle proposition.
Technical solution used by the present invention solves the above problems is:
A kind of complex three-dimensional topological relation describes method, including following sections:
(1), 10 kinds of topological relations that can describe two-dimentional three-dimensional space object are summed up, and 10 kinds of topological relations are made
It defines out.
(2), the topological relation between point, line, surface, body spatial object is summed up, is existed for different topological relations
The case where identical topological relation describes the characteristics of according to different topology relational graph, is finely divided name to basic topology relationship
It is distinguish, finally by topological relation instance graph, subdivision name, nine friendship models and the decimal coded after subdivision to scheme
The form of table indicates.
(3), according to the overlapping relation between the sub-goal of space, existing topological relation is carried out by roughly to subdivision
Hierarchical classification carries out hierarchical reasoning.
(4), it proposes " 9PDS " expression model, expresses complex three-dimensional spatial topotaxy, pushed away by the level in (three)
Reason figure and expression model combine content described in (one) and (two), infer the description of complex three-dimensional topological relation.
As further technical solution of the present invention, in the content (one), closed in 8 kinds of topologys that Egenhofer is proposed
Summarizing is carried out on the basis of system, theoretical based on point set topology, in conjunction with topological relation description rule, summing up 10 kinds can
It describes the topological relation of two and three dimensions spatial object: equal (Equal), meeting (Meet), is overlapped (Overlap), covering
(Cover), comprising (Contain), on side (On the edge), contact (Touch), intersection (Intersect), pass through
(Cross) and mutually definition is provided respectively from (Disjoint), and to this 10 kinds of topological relations.
As further technical solution of the present invention, in the content (two), according to topological relation description rule, summarize
Point and point, Points And lines, point and face, point and body, line and line, line and face, line and body, face and face, face and body and body and 10 kinds of body out
Three-dimensional topology relationship between fundamental space object, it is corresponding in the analysis of similar topological relation for a kind of description of topological relation
Different topological relation figures the characteristics of according to different topology relational graph, is finely divided name to basic topology relationship and is subject to area
Point, the topological relation after subdivision is finally handed over to the shape of model and decimal coded chart with instance graph, subdivision name, nine
Formula indicates.
As further technical solution of the present invention, in the content (three), whether to intersect between spatial object sub-goal
For division rule, according to analytic hierarchy process principle, existing topological relation is carried out by roughly to the hierarchical classification segmented, into
The description of row hierarchical reasoning.
As further technical solution of the present invention, in the content (four), expressed using extraterrestrial target decomposition and combination,
It proposes " 9PDS " expression model, complex three-dimensional spatial topotaxy is expressed, and pass through topological relation hierarchical reasoning and table
Up to model, the descriptive model of complex three-dimensional topological relation is proposed.
Compared with prior art, the beneficial effects of the present invention are: the present invention solve topological relation describe level confusion and
The problem of complex topology relationship expression scarce capacity.In the present invention, summed up the description of 10 kinds of topological relations and point, line,
Three-dimensional topology spatial relationship between face, body, and the case where different topology relationship is described there are identical topological relation is directed to topology
Relationship has carried out subdivision name, solves the problems, such as that topological relation describes level confusion；9IM is reduced to decimal coded, point
Analysis decimal coded and topological relation contact, and summarize the expression rule of decimal coded, are conducive to improve computer for opening up
Flutter the judging efficiency of relationship；Based on analytic hierarchy process principle, the relational graph between the topological relation of different the level of detail is constructed,
Realize the hierarchical reasoning of different levels spatial relationship；" 9PDS " model is proposed for describing complex three-dimensional topological relation, to open up
The relationship of flutterring provides unified expression, solves the problems, such as that complex topology relationship is inenarrable.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the Compound Topology relational graph of recombination line and recombination line；
Fig. 3 is the Compound Topology relational graph of recombination line and composite surface；
Fig. 4 is the Compound Topology relational graph of composite surface and composite surface；
Fig. 5 is the Compound Topology relational graph of recombination line and complex；
Fig. 6 is the Compound Topology relational graph of composite surface and complex；
Fig. 7 is the Compound Topology relational graph of complex and complex；
Fig. 8 is that topological relation segments table.
Specific embodiment
The technical solution in present example is clearly and completely described below, it is clear that described example is only
It is only a part of example of the invention, rather than whole examples.Based on the example in the present invention, ordinary skill people
Member's every other example obtained under the premise of not making creative labor, shall fall within the protection scope of the present invention.
A kind of complex three-dimensional topological relation describes method.Flow chart is as shown in Figure 1, include following key content:
(1), for the topological relation of basic extraterrestrial target, from the difference of dimension between extraterrestrial target and there may be
Topological relation analysis as a result, we have concluded that following 10 kinds can not only describe two dimension but also Three dimensional Targets can be described
Specific topological relation.Wherein, the point, line, surface in space and body are indicated with P, L, S and V respectively.Two spaces target is set
Inside, boundary and external representation for target A and target B, A are Ao、And A-, inside, boundary and the external representation of B is Bo、And B-.The intersection of space sub-goal indicates with " ∩ ", as a result there are two types of: intersectionWith it is non-intersectingSame item
It is connected between part with " ∨ ", indicates "or"；Condition, which merges, uses " ∧ ", indicate " and ".
(1) equal (Equal)
Equal occurs between same dimension target, and inside, boundary and the outside of two spaces target are completely coincident, referred to as phase
Deng.Equal contextual definition is as follows:
(2) meet (Meet)
Meet occurs between L/L, L/S, L/V, S/S, S/V and V/V, and the boundary of two extraterrestrial targets is in contact, but internal
Between, it is non-intersecting between boundary and inside, be known as meeting.Meet contextual definition is as follows:
(3) it is overlapped (Overlap)
Overlap occurs between L/L, S/S and V/V, and two the same as dimension space object boundary and boundary, internal and inside
Intersection, but be not completely equivalent, the dimension of the part of intersection is identical as former space dimensionality, is referred to as overlapped.Overlap contextual definition
It is as follows:
(4) (Cover) is covered
Cover occurs between L/L, S/S and V/V of same dimension, and two completely the same with dimension space target internal, part
Boundary is met, and is referred to as covered.Cover contextual definition is as follows:
(5) it is contained in (Inside)
Inside occurs between P/L, P/S, P/V, L/L, L/S, L/V, S/S, S/V and V/V, and an extraterrestrial target exists
The inside of another extraterrestrial target, boundary are not met, and are known as being contained in.Inside contextual definition is as follows:
(6) on side (On the edge)
On the edge occurs between P/L, P/S, P/V, L/S, L/V, S/S, S/V and S/V, extraterrestrial target
Part or all is on the boundary of another extraterrestrial target, referred to as on side.On the edge relationship is defined as follows:
(7) (Touch) is contacted
Touch occurs between L/L, L/S and S/S, the inside weight of the boundary of an extraterrestrial target and another extraterrestrial target
It closes, but does not penetrate, referred to as contacting this is between a kind of n dimension element, in the relationship that n+1 dimension space could occur.Touch relationship
It is defined as follows:
(8) intersect (Intersect)
Intersect occurs between L/S, L/V, S/S (three-dimensional) and S/V, and an extraterrestrial target a part is internal another
The inside of one extraterrestrial target, but do not penetrate, referred to as intersect.Intersect contextual definition is as follows:
(9) (Cross) is passed through
Cross occurs between L/L, L/R, L/V, R/R and S/V, and an extraterrestrial target intersects with another extraterrestrial target
And penetrate, referred to as across.Cross contextual definition is as follows:
(10) mutually from (Disjoint)
Disjoint occur between P/P, P/L, P/S, P/V, L/L, L/S, L/V, S/S, S/V and V/V, referred to as mutually from.
The inside and boundary for indicating two extraterrestrial targets are mutually disjointed.Disjoint contextual definition is as follows:
Respectively to equal (Equal), meet (Meet), be overlapped (Overlap), covering (Cover), include
(Contain), on side (On the edge), contact (Touch), intersection (Intersect), pass through (Cross) and phase from
(Disjoint) 10 kinds of topological relation descriptions are made definitions, and close the topology between extraterrestrial target with this 10 kinds of topological relations
System expresses.And this relationship of V/V can both be retouched because of the particularity of its topological relation figure with Overlap
It states, can also be described with Cross, can also be described with Intersect.The symmetry for handing over model due to 9, because only considered
With the topological relation between dimension space target and between low-dimensional and higher dimensional space, partial-topology relationship has its corresponding inverse
Relationship, the reverse-power of covering (Cover) are capped (Covered by)；Be contained in (Inside) reverse-power be comprising
(Contain)；The reverse-power of contact (Touch) is to be contacted (Touched by)；Reverse-power across (Cross) is to be worn
Cross (Crossed by).
(2) using low-dimensional object and high dimensional object and with the topological relation between dimensional object as goal in research, it is contemplated that point
Opening up between point, point and line, point and face, point and body, line and line, line and face, line and body, face and face, face and body and body and body
The all situations of relationship are flutterred, relationship situation can be showed with example graphical, 9 friendship models and decimal coded respectively.We
Topological relation that may be present between two and three dimensions extraterrestrial target is considered respectively, is summarized between point, line, surface, body spatial object
Three-dimensional topology relationship, it is found that the three-dimensional topology relationship description of complex object wherein having is too general, it is different in practice
The instance graph of complex three-dimensional topological relation may correspond to identical topological relation description.This general description is unfavorable for multiple
The differentiation of miscellaneous three-dimensional topology relationship, therefore we are finely divided existing topological relation, the name specifically segmented and in fact
Example diagram shape, nine friendship models and decimal coded are indicated with diagrammatic form.Different target in example figure is with different color tables
Show.
Description is finely divided according to the feature of existing different topology relational graph.(On the edge) it will be divided on side
Part at upper (Part on edge) and all while on (All on edge), intersect (Intersect) and be divided into full cut phase
It hands over (Whole cut intersect), part cut phase hands over (Part cut intersect) and non-boundary to intersect (None edge
intersect).It is divided into boundary across (Edges cross) across (Cross), non-boundary passes through (None edge cross)
(Cut Cross) is passed through with crosscutting, overlapping (Overlap) is divided into line segment overlapping (Lines overlap) and face overlapping
(Regions overlap), as shown in Figure 8.
(3), the basic principle of binding hierarchy analytic approach, existing known 10 kinds of topological relations and corresponding subdivision are opened up
Relationship is flutterred, according to A between the sub-goal of spaceo∩Bo,A-∩BoWithFriendship is
Empty or this 6 conditions of non-empty carry out step analysis as the criterion of step analysis.Cognition based on the mankind to space, by target
Inside whether intersect as first judgment criterion by topological relation be divided into intersection (Intersect, Overlap, Cross,
Cover, Inside, Equal) and non-intersecting (Disjoint, Touch, Meet, On the Edge) two major classes, then with boundary
Whether intersection as next criterion, is classified, by classification respectively in the two class results whether upper one layer of inside intersects
As a result the classification that criterion carries out next level is assigned, until being layered only a kind of topological relation in result.From top to bottom
Topological relation of the topological relation of extraterrestrial target from outline to subdivision is expressed out by layering, convenient for quickly distinguishing every kind of relationship
Feature, the similar relationship of condition is found, while providing the foundation for the reasoning of topological relation, in particular so that different levels
On topological relation reasoning have theory and method basic.Judgment criterion corresponding to each topological relation is different, passes through
The different hierarchy of criteria is divided into most thin topological relation, it is possible thereby to which most detailed topological relation is passed through identical criterion
Infer rough topological relation.
(4) 9PDS descriptive model
By the way of subdivision, complex target is refined into most basic extraterrestrial target, considers that each is substantially empty comprehensively
Between topological relation between target, by complex three-dimensional extraterrestrial target " 9PDS (9IM+Partial topological
Relations+Dimension+Separation number) " model tormulation comes out.Intersection dimension and intersection separation number are pressed
According to the form of 9IM, the matrix write as.
For the topological relation of partial 3 d extraterrestrial target A and B, the inside of target A is represented by Ao, boundary is according to sky
Between the specific number of boundary of target be expressed asThen the boundary sub-goal of A is represented byExternal representation is A-；The inside of target B, boundary and outside with target A as, internal representation Bo, side
Boundary is expressed as according to the number of boundary of extraterrestrial targetThen the boundary sub-goal of B is represented byOutside is B-, the local topology relationship of A and B are the expression matrix of each sub-goal intersection.According to space mesh
It marks actual number of boundary the topological relation of the part of target is showed by matrix, guarantees that the topology of each part is closed
System all considers.In order to unified, local space topological relation (Partial topological relations, PTR) is used
Formula (1-1), matrix form expression:
Above formula is directed to the extraterrestrial target A that boundary number is m and the extraterrestrial target B that boundary number is n, respectively to two skies
Between the sub-goal of target ask friendship.Space sub-goal element is non-intersecting to be expressed as -1, intersects at a point and is expressed as 0, intersects at one
Line is expressed as 1, intersects at a face and is expressed as 2, intersects at an individual and be expressed as 3.By all offices in the model tormulation of front
The intersection situation of portion's extraterrestrial target is expressed with dimension, for the topological relation of two complex spatial objects of intuitive judgment, later
Dimension and separation number expression in, topological relation between each subset is merged, thus dimension take same type intersect dimension
Maximum value, value range is, separation number takes the sum of same type intersection separation number, and value range is [0 ,+∞], formula (1-2)
The merging of representation dimension (Dimension), formula (1-3) indicates the addition of separation number (Separation number), with 3
× 3 expression matrix.
It is that reasoning of the method to several complex three-dimensional topological relations is described using above-mentioned complex three-dimensional topological relation below
With expression.
The boundary of complex three-dimensional topological relation such as Fig. 3, recombination line A of recombination line A and recombination line B composition are point P1And P2,
The boundary of recombination line B is point P3And P4。
Formula (1-4) is " 9PDS " expression formula of Fig. 3, and " ∪ " is indicated and by 9IM, local topology relationship, intersection in formula
Maximal dimension and total separation number of intersection merge.
The all elements of composite space target are all accounted for, carry out hierarchical reasoning using local topology relational matrix
The topological relation of Fig. 3 is obtained, the topological relation reasoning of formula (1-4) is as follows:
(1)
(2)
The first step judges whether recombination line A intersects with the inside of recombination line B, result be it is non-intersecting, then topological relation is
Disjoint, Touch, Meet and On the edge.Second step judges whether recombination line A intersects with the boundary of recombination line B, knot
Fruit is a part intersection, a part of non-intersecting, should be discussed in two kinds of situation at this time.If non-intersecting between boundary, topological relation
For Disjoint and Touch, then judge whether the inside of recombination line A intersects with the boundary of recombination line B, result be it is non-intersecting, then
Topological relation is Meet；If intersecting between boundary, topological relation is Meet and On the edge, then judges the side of recombination line A
Whether boundary intersects with the inside of recombination line B, and result is intersection, topological relation Touch.According to 9 hand over models, intersection dimension with
The topological relation of separation number comprehensive analysis, recombination line A and composite surface B are Meet ∪ Touch, and being reduced to decimal coded is R
(095)∪R(111)。
Complex three-dimensional topological relation such as Fig. 4 of recombination line A and composite surface B composition, the boundary of recombination line are the P of 0 dimension1、P2。
Formula (1-5) is the topological relation with " 9PDS " model tormulation." ∪ " in formula indicate simultaneously, by 9IM, local topology relationship,
The total separation number for intersecting maximal dimension and intersection merges:
Composite space target is not only needed to consider individual element, is needed all inside, boundary and the outside of target
Consider together, carries out hierarchical reasoning using local topology relational matrix to obtain result.Formula (1-5) reasoning process is as follows:
(1)
(2)
(3)
The first step judges whether recombination line A intersects with the inside of composite surface B, result be it is non-intersecting, then topological relation is
Disjoint, Touch, Meet and On the edge.Second step judges whether recombination line A intersects with the boundary of composite surface B, knot
Fruit is a part intersection, a part of non-intersecting, should be discussed in two kinds of situation at this time.If non-intersecting between boundary, topological relation
For Disjoint and Touch, then judging whether the boundary of recombination line A intersects with the inside of composite surface B, result is two kinds of situations,
Non-intersecting is Disjoint, is intersected for Touch；If intersecting between boundary, topological relation is Meet and On the edge, then is sentenced
Whether the inside of disconnected recombination line A intersects with the boundary of composite surface B, is as a result similarly two kinds of situations: non-intersecting for Meet, intersection
For On the edge.And On the edge includes the topological relation of subdivision, so continuing third step, judges that recombination line A's is interior
Whether portion intersects with the outside of composite surface B, and result is intersection, then topological relation is Part on edge.Model, phase are handed over according to 9
The topological relation of friendship dimension and separation number comprehensive analysis, recombination line A and composite surface B are Touch ∪ On the edge, are reduced to
Decimal coded is R (111) ∪ R (223)
Topological relation such as Fig. 5 of composite surface A and composite surface B.
Formula (1-6) is that corresponding topological relation expresses formula:
The reasoning process of formula (1-6) is as follows:
(1)
(2)
(3)
None edge cross is not used in the topological relation in description face and face, needs to exclude, and Lines Overlap is used for
The topological relation for describing line and line, also excludes.Therefore the topological relation of composite surface A and composite surface B is Edge Cross ∪ None
Edge, corresponding decimal coded are R (463) ∪ R (495).
Topological relation such as Fig. 6 of recombination line A and complex B, there are two point, the boundary of complex is 6 on the boundary of recombination line
A face.
Formula (3-15) is that corresponding topological relation expresses formula:
The reasoning process of formula (1-7) is as follows:
(1)
(2)
(3)
(4)
Model, intersection dimension and separation number are handed in conjunction with 9, the topological relation of recombination line A and complex B is Cross, corresponding
Decimal coded be R (463).
Topological relation such as Fig. 7 of composite surface A and complex B, the boundary of composite surface have 4, and the boundary of complex is 6
Face.
Formula (1-8) is that corresponding topological relation expresses formula:
The reasoning process of formula (1-8) is as follows:
(1)
(2)
Wherein None edge cross, None edge intersect and Cut cross are not used in description face/body and open up
Relationship is flutterred, therefore is excluded.Model, intersection dimension and separation number are handed in conjunction with 9, the topological relation of composite surface A and complex B is Part
Cut Intersect ∪ Whole cut Intersect, corresponding decimal coded are R (223) ∪ R (479).
Topological relation such as Fig. 7 of complex A and complex B.
Formula (1-9) is that corresponding topological relation expresses formula:
Formula (1-9) reasoning process is as follows:
(1)
(2)
(3)
The topological relation of complex A and complex B is Meet, and corresponding decimal coded is R (111).
Claims (5)
1. a kind of complex three-dimensional topological relation describes method, which is characterized in that including following main contents:
(1), the topological relation of two and three dimensions spatial object can be described by analyzing and summing up 10 kinds, and is given 10 kinds and opened up
Flutter the definition of relationship.
(2), the topological relation between point, line, surface, body spatial object is summed up, there are identical for different topological relations
The case where topological relation describes the characteristics of according to different topology relational graph, is finely divided name to basic topology relationship and is subject to area
Point, finally graphically by topological relation instance graph, subdivision name, nine friendship models and the decimal coded after subdivision
It indicates.
(3), according to the overlapping relation between the sub-goal of space, existing topological relation is carried out by roughly to the level of subdivision
Classification carries out hierarchical reasoning.
(4), it proposes " 9PDS " expression model, expresses complex three-dimensional spatial topotaxy, pass through the hierarchical reasoning and table in (three)
Up to content described in models coupling (one) and (two), complex three-dimensional topological relation inference pattern is proposed.
2. complex three-dimensional topological relation as described in claim 1 describes method, it is characterised in that: in the content (one), base
In point set topology theory, in conjunction with topological relation description rule, to equal (Equal), meets (Meet), is overlapped (Overlap), covers
Lid (Cover), comprising (Contain), on side (On the edge), contact (Touch), intersection (Intersect), pass through
(Cross) and mutually 10 kinds from (Disjoint) topological relations provide definition.With this 10 kinds of topological relations can by extraterrestrial target it
Between topological relation express out.
3. complex three-dimensional topological relation as described in claim 1 describes method, it is characterised in that: in the content (two), always
Bear a little with point, point and line, point and face, point and body, line and line, line and face, line and body, face and face, face and body and body and body it
Between topological relation all situations.It is wherein corresponded in the analysis of similar topological relation for a kind of description of topological relation different
The case where topological relation figure, the characteristics of according to different topology relational graph, is finely divided name to basic topology relationship and is distinguish,
Finally indicated in the form of chart by instance graph, subdivision name, nine friendship models and decimal coded.
4. complex three-dimensional topological relation as described in claim 1 describes method, it is characterised in that: in the content (three), base
In the mankind's spatial cognition the characteristics of, whether to intersect between spatial object sub-goal for division rule, according to analytic hierarchy process principle,
Existing topological relation is carried out by roughly to the hierarchical classification of subdivision, is realization spatial relationship from detail to outline, from microcosmic
Theoretical basis has been established to middle sight, then to the reasoning of macro-level.
5. complex three-dimensional topological relation as described in claim 1 describes method, it is characterised in that: in the content (four), benefit
With extraterrestrial target decomposition-combinational expression, proposes " 9PDS " expression model, complex three-dimensional spatial topotaxy is expressed, and
By topological relation hierarchical reasoning and expression model, realize spatial relationship from detail to outline, the sight from microcosmic to middle, then to macroscopic view
The reasoning of level.
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| CN117422810A (en) * | 2023-12-19 | 2024-01-19 | 深圳大学 | Structure and parameter guided indoor element regularization and relationship reasoning method and terminal |
| CN117422810B (en) * | 2023-12-19 | 2024-05-17 | 深圳大学 | Structure and parameter guided indoor element regularization and relationship reasoning method and terminal |
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