CN103927771B - Self adaptation arranges the Linear element displacement method of Snakes mould shapes parameter - Google Patents

Abstract

The invention discloses a kind of self adaptation and the Linear element displacement method of Snakes mould shapes parameter is set, including: use the Priority level for location of linear target and the relation of form parameter to obtain the form parameter of linear target；Identifying and bend in linear target, the relation of curvature based on bending and form parameter obtains the form parameter of bending；The form parameter using the bending of finite element unit place builds finite element matrix, and uses Linear element displacement method based on Snakes model to shift map center line shape target.The inventive method not only inherits global optimization's feature of displacement method based on Snakes model, and account for the semantic relation between different map elements and the graphic feature within map objects to a certain extent, it is more beneficial for the holding of map elements spatial relationship and positional precision.

Description

Self adaptation arranges the Linear element displacement method of Snakes mould shapes parameter

Technical field

The invention belongs to Automated Map Generalization technical field, Snakes mould shapes ginseng is set particularly to a kind of self adaptation The Linear element displacement method of number.

Background technology

During Map Generalization, due to scale compression, map space reduces therewith, and partial element is had to greatly simultaneously Symbol in actual size exaggerates expression, consequently, it is possible to cause on map neighbouring conflict, vision conflict and sky between adjacent target Between conflict of relationships.In order to keep the clarity of map, it is necessary to use choose, merge, exaggerate, these conflicts are added by the operation such as displacement To process, wherein displacement is to solve a kind of operation that this type of conflict is the most frequently used.

Linear element (such as road, river etc.) on map, can regard the skeleton of map as, and it has a very wide distribution, structure Complicated.Associated Automated Map Generalization problem is typically the displacement that the emphasis of research is also difficult point, especially Linear element Problem, relates to the spatial relationship between the holding of each linear target geometric shape and linear goal and safeguards, more seem intricate. Nickerson^[2]Use basic method of geometry that Linear element is shifted, more comprehensively solve between two lines shape target Conflict, but be difficult to solve multiobject sophisticated collision problem.Burghardt and Meier^[5]Propose is based on Snakes model Shifting algorithm is the Global Optimization Algorithm For Analysis of a kind of applicable wire map elements displacement, has more excellent to multiobject challenge Effect.This algorithm use minimum energy principle, descriptions of energy is represented by most basic shift amount, with displacement before and after wire will The geometry change of element describes internal energy, describes external energy with the Steric clashes of neighbouring Linear element, passes through finite element Optimum shape after the displacement of analysis method calculated curve and position.

Form parameter (elastic parameter α and rigidity parameters β) in Snakes model determines the elasticity of Linear element with just Property, reflect model attributes, displacement effect is had certain control action.Burghardt and Meier^[5]、Bader^[10]And Wu Xiao Fang^[11]All discussion is expanded around the offering question of form parameter, it is proposed that the basic principle that parameter is arranged, but mesh Deng scholar Before still lack effective parameter setting method.

Literary composition relates to following list of references:

[1]Lichtner W.Computer-Assisted Processes of Cartographic Generalization in Topographic Maps[J].Geo-Processing,1979Vol.1No.1.

[2]Nickerson B G.Automated Cartographic Generalization for Linear Features[J].Cartographica,1988Vol.25No.3.

[3]Mackaness W A.An Algorithm for Conflict Identification and Feature Displacement in Automated Map Generalization[J].Cartography and Geographic Information Systems,1994Vol.21No.4.

[4]Ruas A.A Method for Building Displacement in Automated Map Generalisation[J].International Journal of Geographic Information Science, 1998Vol.12No.7.

[5]Burghardt D,Meier S.Cartographic Displacement Using the Snakes Concept[A].Semantic Modeling for the Acquisition of Topographic Information from Images and Maps[C],ed.By Wand L Plümer,1997.

[6]Harrie L E.The Constraint Method for Solving Spatial Conflicts in Cartographic Generalization[J].Cartography and Geographic Information Science,1999Vol.26No.1.

[7]P.Solving Local and Global Space Conflicts in Map Generalization:Using a Finite Element Method[J].Cartography and Geographic Information Science,2000Vol.27No.1.

[8]Ware J M,Jones C B.Conflict Reduction in Map Generalization Using Iterative Improvement[J].GeoInformatica,1998Vol.2No.4.

[9]Wilson I D,Ware J M,Ware J A.A Genetic Algorithm approach to cartographicmap generalization.Computers in Industry,2003Vol.52No.3.

[10]Bader M.Energy Minimization Methods for Feature Displacement in Map Generalization[D].Zurich:University of Zürich,2001.

[11] Wu little Fang, Du Qingyun, Hu Yueming etc. process [J] based on the road network Steric clashes improving Snake model. Mapping journal, 2008Vol.37No.2.

[12] Ai Tinghua. the displacement [J] of groups of building based on Field Analysis. mapping journal, 2004Vol.35No.1.

Summary of the invention

In order to overcome form parameter in Linear element displacement method based on Snakes model to arrange the deficiency of existence, this A kind of self adaptation of bright proposition arranges the Linear element displacement method of Snakes mould shapes parameter.

For solving above-mentioned technical problem, the present invention adopts the following technical scheme that:

Self adaptation arranges the Linear element displacement method of Snakes mould shapes parameter, including:

(1) Priority level for location and the relation of form parameter of linear target are used $\left\{\begin{array}{c}{\mathrm{\α}}_R={h_{\mathrm{\α}}}^{(g-1)}\mathrm{\α}\\ {\mathrm{\β}}_R={h_{\mathrm{\β}}}^{(g-1)}\mathrm{\β}\end{array}\right.$ Obtain linear target Form parameter α_RAnd β_R, wherein, α and β is form parameter initial value, rule of thumb pre-sets；G represents the location of linear target Priority, pre-sets as the case may be, and Priority level for location is the biggest, and during displacement, positional precision and shape to linear target are protected The requirement held requires the highest；h_αAnd h_βIt is respectively form parameter α of linear target_RAnd β_RCommon ratio, experience of charting according to the map Pre-set；

(2) identify and bend in linear target, curvature based on bending and the relation of form parameterWithObtain form parameter α of bending_CAnd β_C, wherein, k For bending curvature, k₀For narrow curved threshold value, k₀＞ 1；α_RAnd β_RForm parameter for bending place linear target；C ＞ 1, k₀It is both needed to pre-set as the case may be with c；

(3) form parameter using the bending of finite element unit place builds finite element matrix K_L, and use based on Map center line shape target is shifted by the Linear element displacement method of Snakes model, and described finite element unit refers to wire mesh Put on the straightway of adjacent point-to-point transmission.

Map center line shape target is entered by the Linear element displacement method based on Snakes model that uses described in step (3) Row displacement farther includes sub-step:

2.1 set finite element matrix K_LObtain the overall stiffness matrix K of linear goal, by wire mesh in original map Put on external force suffered by each conflict point and constitute the initial stressed vector f of linear goal⁽⁰⁾, by initial displacement vector d⁽⁰⁾In each element set It is set to 0；

2.2 by the overall situation stiffness matrix K, the shift vector d of last iteration^(t-1)Stress vector f with last iteration^(t-1)Generation Enter (I+ γ K) d^(t)=d^(t-1)+γf^(t-1)Equation, it is thus achieved that the shift vector d of current iteration^(t), then, perform step 2.3, its In, d^(t-1)Initial value be step 2.1 obtain initial displacement vector d⁽⁰⁾；f^(t-1)Initial value is at the beginning of described in step 2.1 Beginning stress vector f⁽⁰⁾；K is overall situation stiffness matrix, and in iterative optimization procedure, K keeps constant；I is unit matrix；γ is iteration step Long, it is configured as the case may be；

2.3 motion-vector d based on current iteration^(t)Map center line shape target is shifted, then, performs step 2.4；

2.4 update the stress vector f of last iteration according to stress of conflicting in the map after displacement^(t-1)Obtain current iteration Stress vector f^(t), by the motion-vector d of current iteration^(t)With stress vector f^(t)Motion-vector and stress as last iteration Vector, re-executes step 2.2, until meeting the condition of convergence preset.

The condition of convergence described in sub-step 2.4 includes that the map after shifting does not exists conflict, iterations reaches default Maximum iteration time or current iteration by maximum in force vector less than preset value.

In identification linear target described in step (2), a kind of detailed description of the invention of the method for bending is:

It is bent into the set of one group of consistent finite element unit of moving direction on linear target line, by by linear target The point that finite element unit moving direction changes is as the terminal of bending, the point that finite element unit moving direction changes Judgement can be by the most adjacent every 4 P in detection linear target₁、P₂、P₃, and P₄Realize, then finite element unit moving side To at P₂The necessary and sufficient condition that point changes is $(\stackrel{\&RightArrow;}{P_1{P}_2}\&times;\stackrel{\&RightArrow;}{P_2{P}_3})\&CenterDot;(\stackrel{\&RightArrow;}{P_2{P}_3}\&times;\stackrel{\&RightArrow;}{P_3{P}_4})<0.$

Compared to the prior art, the present invention has a characteristic that

Bend in linear target as fundamental figure unit in map, set up curved shape feature, linear target respectively Quantitative relationship between Priority level for location and Snakes mould shapes parameter, enhances the controlled of form parameter in Snakes model Property, preferably account for the semanteme in map and graphic constraint condition.The inventive method not only inherits based on Snakes model Global optimization's feature of displacement method, and account for the semantic relation between different map elements and map to a certain extent The graphic feature of target internal, is more beneficial for the holding of map elements spatial relationship and positional precision.

Accompanying drawing explanation

Fig. 1 is the parabola signal reflecting quantitative relationship between the curvature of bending and Snakes mould shapes parameter in the present invention Figure；

Fig. 2 is modeling language (UML) the class figure of road network model and Snakes shifting algorithm in the present invention；

Fig. 3 is that the global parameter of Snakes model arranges interface；

Fig. 4 is that the category of roads parameter of Snakes model arranges interface；

Fig. 5 is that the bending curvature parameter of Snakes model arranges interface；

Fig. 6 is the calculating schematic diagram of external force suffered by conflict point in linear target；

Fig. 7 is curved-ray tracing Method And Principle schematic diagram；

Fig. 8 is each element pass corresponding with line segment endpoint number, position in overall situation stiffness matrix in finite element matrix System；

Fig. 9 is the particular flow sheet of the inventive method；

Figure 10 is the result using the inventive method that certain mountain area segment path net carries out collision detection；

Figure 11 is traditional shift result based on Snakes model displacement method and the comparison diagram of original road network；

Figure 12 is shift result and the comparison diagram of original road network of the inventive method；

Figure 13 is the partial enlarged drawing of the shift result of the inventive method and traditional method, and wherein, (a) is original map, B () is the shift result of traditional method, (c) is the shift result of the inventive method.

Detailed description of the invention

Existing theory, inventive concept and the detailed description of the invention that the present invention relates to will be described in detail below.

1, Linear element displacement theory based on Snakes model

Linear element displacement method of the present invention uses Linear element displacement method based on Snakes model, the description of energy Use most basic shift amount to represent, with displacement before and after Linear element geometry change describe internal energy, use adjacent threads The Steric clashes of shape key element describes external energy.

Based on minimum energy principle, calculate the optimum shape after linear target displacement and position.The mathematical expression of shift amount Formula is: s → d (s)=(x (s)-x⁰(s),y(s)-y⁰(s))^T, 0≤s≤l, wherein, l represents the length of linear target；S is table Showing the parametric variable of the position of any point in linear target, for arbitrfary point in linear target, the s of its correspondence is linear target Starting point is along linear target to the distance of this point；x⁰、y⁰Represent original line coordinate, i.e. line coordinates before displacement；After x, y represent displacement Line coordinates；D (s) is the parameter expression of shift amount.

Based on shift amount, gross energy E (d)=∫ is described_l(E_int+E_ext) ds, wherein, E_intIt is internal energy, E_extIt is outside Energy.Internal energyD'(s) and d " (s) be shift amount d (s) respectively about The first derivative of s and second dervative, reflect the size of the change of shape that linear target produces due to displacement；α (s) and β (s) Determine the elasticity of Snakes model and rigidity, the attribute of reflection Snakes model, be used for controlling to shift effect, generally by α (s) and β (s) is referred to as the form parameter of Snakes model.External energy E_extBy the overlapping generation of map symbol, its value when producing conflict It is directly proportional to overlapping region size, by external energy E_extPromote linear target movement and deformation, thus solve conflict.

It is minimum that the principle of displacement of Snakes model is to maintain gross energy, accordingly, it would be desirable to wire mesh when asking E (d) to take minima The shift amount of mark each point.Utilize Eulerian equation, Finite Element Method, through a series of mathematic(al) manipulations, obtain the overall situation of Kd=f form Matrix equation, Xie Zhi, linear target shift amount everywhere can be obtained.Wherein, K is stiffness matrix；D is to be moved by each point in linear target Position amount and the shift vector of first derivative composition thereof, be the unknown number of matrix equation Kd=f；F is by being in conflict in linear target Suffered by each point of scope external force constitute by force vector.

According to Finite Element Method, the local matrix K that in linear target, each line segment is corresponding_L、d_L、f_LAs follows, " line segment " here The straightway of adjacent point-to-point transmission in finger linear target:

$K_L=\left[\begin{array}{cccc}\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}\\ -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}\end{array}\right]$

$d_L=\left[\begin{array}{c}d\left(x_0\right)\\ d^{\text{'}}\left(x_0\right)\\ d\left(x_1\right)\\ d^{\&prime;}\left(x_1\right)\end{array}\right];$

$f_L=\left[\begin{array}{c}\frac{1}{2}\mathrm{hf}\left(x_0\right)\\ \frac{1}{12}\mathrm{hf}\left(x_0\right)\\ \frac{1}{2}\mathrm{hf}\left(x_1\right)\\ -\frac{1}{12}\mathrm{hf}\left(x_1\right)\end{array}\right];$

Wherein, α and β is α (s), the constant form of β (s), i.e. the form parameter of line segment place bending；H is line segment length； x₀、x₁It is respectively line segment starting point coordinate and terminal point coordinate；d(x₀) and d (x₁) represent that line segment beginning and end is moved in x direction respectively Position amount, d'(x₀) and d'(x₁) represent the line segment beginning and end first derivative at x direction shift amount, f (x respectively₀) and f (x₁) Represent external force component in the x direction suffered by line segment beginning and end.

When linear targets all on view picture map are carried out shifting processing, need constituting each line segment of linear target respectively Build its local matrix, and successively local matrix is gathered in the overall situation matrix K, f；Then, complete on x and y direction respectively Office's matrix equation solves, and obtains the shift amount of each point in linear target.

During overall situation matrix equation solves, owing to K is singular matrix, it is impossible to try to achieve its inverse matrix, so cannot be directly to entirely Office's matrix equation solves.Accordingly, it would be desirable to increase boundary condition in matrix equation, singular matrix K is converted to conventional square Battle array, is allowed to solve.

It addition, if conflict area target is not the most intensive, conflict just may have been resolved in once-through operation, but actual Upper most conflict area situation is complicated, and the target participating in conflict is more, is not that once-through operation can be fully solved all conflicts. Now it is necessary to repeatedly carry out shifting function, progressively solve conflict.Iteration optimization process specifically can be used progressively to solve all punchings Prominent, iterative formula is shown in formula (1):

(I+γK)d^(t)=d^(t-1)+γf^(t-1)(1)

In formula (1), I is unit matrix, and t is iterations, d^(t)With d^(t-1)It is shift vector during the t time iteration respectively With shift vector during (t-1) secondary iteration, f^(t-1)The stress that when being (t-1) secondary iteration, in linear target, each point stress is constituted Vector, γ is iteration step length, and iteration step length is rule of thumb configured.

2, Snakes mould shapes parameter arranges basic principle and binding target

When using Snakes model to carry out Linear element displacement, need to consider further semantic constraint and the figure of Linear element Shape retrains, by Linear element weight and the deformation arranging the size and shape controlling displacement of Snakes mould shapes parameter. Such as, when road network is shifted, need to arrange corresponding form parameter according to category of roads, road local buckling feature. But about the setting of form parameter, have no relatively effective method at present, only refer to following basic principle and rule of thumb arrange:

When increasing the most simultaneously or reduce parameter alpha and β, the most obvious to shift result impact effect, α and β is the biggest, and deformation is more Little；α and β is the least, deforms the biggest；

2. β is constant, and during the change of α value, α value is the biggest, and shift amount is the fewest, deforms the least；α value is the least, and shift amount is the biggest, with former Linear target position is away from more；

3. α is constant, and during β value change, β value is the biggest, deforms the least；β value is the least, deforms the biggest；

4. the impact that displacement is produced by the change of α value is than parameter beta larger.

In order to set up the quantitative relationship between Snakes mould shapes parameter and map objects feature, with wire on map The curvature of the Priority level for location of target and each section of bending is binding target, designs Snakes from semantic respectively in terms of two, figure The method to set up of mould shapes parameter.

(1) Priority level for location of linear target and the relation of Snakes mould shapes parameter

On map, each Linear element has the importance information that it is the most intrinsic, and this importance information can be as shifting The Priority level for location of different map objects in journey.Such as, all highways are divided by China according to the volume of traffic of highway function and adaptation For: highway, Class I highway, Class II highway, Class III highway, Class IV highway.In Snakes model, linear target can be set up Association between Priority level for location with corresponding wire target shape parameter.The Priority level for location of linear target is the highest, displacement time pair The requirement that the positional precision of linear target and shape keep is the highest, and the shape parameter values of corresponding linear target just should be arranged The highest.Otherwise, linear target Priority level for location is the lowest, and corresponding form parameter just should arrange the lowest.

The present invention use Geometric Sequence function (2) represent linear target Priority level for location and form parameter between pass System:

$\left\{\begin{array}{c}{\mathrm{\&alpha;}}_R={h_{\mathrm{\&alpha;}}}^{(g-1)}\mathrm{\&alpha;}\\ {\mathrm{\&beta;}}_R={h_{\mathrm{\&beta;}}}^{(g-1)}\mathrm{\&beta;}\end{array}\right.---\left(2\right)$

In formula (2), α and β is original shape parameter, and original shape parameter is empirical value, and user is rule of thumb given；α_R And β_RFor the form parameter of linear target R, g ∈ 1,2 ..., n} represents the Priority level for location of linear target, and Priority level for location is more Height, corresponding g value is the biggest, starts g is carried out assignment from 1 the most respectively according to the Priority level for location of linear target, i.e. fixed The linear target that position priority is minimum, the g of its correspondence is 1；h_αAnd h_βIt is respectively form parameter α_RAnd β_RCommon ratio, according to the map Drawing experience sets.

(2) curvature bent and the relation of Snakes mould shapes parameter

In numerical map, linear target is to be made up of the bending of differently curved degree, and bending can regard the son of linear target as Section, is demonstrated by the local figure feature of in linear target each section respectively.Shifting function linear target will necessarily be carried out displacement and Deformation, in Snakes model, this displacement and deformation are under the effect of interior external enwergy, travel to linear target everywhere.And from map Drawing angle is seen, linear target shifts everywhere and the degree that deforms different, and this is relevant with the tortuous of bending.Straight line Or the deformation of near linear part is more easy to discover than sweep, it is not that line shifting becomes in actual mechanical process sweep Suitably, so straightway should arrange bigger form parameter, straight limit deforms；General bending, in shifting process, Deformation is difficult to discover, and bending can be allowed in shifting process " to absorb " bigger shift amount and deformation, so should arrange less to bending Form parameter.

But being not that curvature is the biggest, deformable degree is the biggest.Narrow curved on curve is it is considered to be one is notable Graphic feature, to keep narrow curved shape invariance as far as possible in shifting process.Therefore, when bending curvature k the least or the biggest time, All should not produce moderate finite deformation, now need to arrange bigger form parameter.For straightway, its curvature k=1；And it is narrow curved Song is a relative concept, and its curvature does not clearly define value, needs to determine as the case may be.In practical operation, Curvature threshold k can be set as required₀, by curvature k >=k₀Bending be classified as narrow curved.

For straight line and narrow curved, their form parameter can be set to maximum；And for curvature between 1 and k₀ Bending, its Snakes mould shapes parameter with curvature increase generally in first drop the trend risen afterwards, i.e. when curvature k from 1 growth To k₀Time, form parameter first increases along with curvature and reduces, and increases along with curvature again and increase after arriving marginal value.Might as well use The symmetrical parabola of opening upwards come matching bending form parameter with the change procedure of curvature, see Fig. 1.

The above analysis, according to the piecewise function of the form parameter of bending curvature design bending:

In formula (3) and (4), k₀For narrow curved threshold value, k₀＞ 1；α_RAnd β_RShape ginseng for bending place linear target Number, can calculate according to formula (2) and obtain；f₁(k) and f₂K () all represents that opening upwards, axis of symmetry are (1+k₀)/2 and 1 and k₀ Place takes the parabola of maximum, sees Fig. 1,C is for when being bent into straight line or narrow During narrow bending condition, its form parameter relatively belonging to the multiple of linear target form parameter, c ＞ 1；Parameter c and k₀It is both needed to basis Concrete condition is chosen.

Describe the detailed description of the invention of the present invention in detail below in conjunction with above-mentioned theory and thinking, idiographic flow sees Fig. 9.

Step 1, builds the topological relation between map linear target according to digital map data.

This step belongs to the known technology in this area, for ease of understanding, and figure wire mesh over the ground as a example by road network below Between mark, the foundation of topological relation illustrates.

Calculate needs according to Snakes rigidity of model matrix with by force vector, design road network topology data model, this mould Type defines road object, link vertex object, road endpoint object and the triangular topological correlation that road network is comprised Relation, is shown in Fig. 2, road network class in figure, road class, apex coordinate class and close tie-point class be respectively used to describe road network, road, Summit in road network and the attribute of a few class object of end points and method.Between these classes, interrelated formation one comprises substantially Topology information and the road network model of coordinate information.In road network model, road network by road list, vertex list and End points list is constituted；Article one, road comprises a starting point, a terminal and two and above summit, and beginning and end is referred to as End points, summit is to constitute each point on the digital curve that road is axial；End points is also summit simultaneously, can be as the starting point of road or end Point is associated with one or more road.It addition, category of roads class is used for describing road class attribute feature, it is that wall scroll road is set One of basic foundation of road form parameter.

Step 2, arranges the basic parameter of Snakes model, obtains determining of linear target according to Snakes model basic parameter The curvature of position priority and the quantitative relationship of form parameter and bending and the quantitative relationship of form parameter.

In Fig. 2, the Snakes class of algorithms is that shifting algorithm based on Snakes model realizes, and the Snakes class of algorithms defines The basic parameter list of Snakes model, parameter arranges interface and sees Fig. 3～5.

The global parameter of Snakes model is set, sees Fig. 3, including between the minimum between map objects scale, map objects Every threshold value, original shape parameter, maximum iteration time and iteration step length.The original shape parameter of Snakes model rule of thumb obtains , concretely: the random original shape parameter that obtains, employing original shape parameter carries out shifting function, adjusts according to displacement effect Whole current original shape parameter, the original shape parameter more excellent to obtain displacement effect.Maximum iteration time and iteration step length root Arranging according to experience, the minimum interval threshold value drawing norm according to the map between map objects scale, map symbol is arranged.This is concrete In enforcement, map objects scale is set to 1:500000, and the minimum interval threshold value between map symbol is set to 0.2mm, initially Form parameter α is set to 10,000,000, β be set to 1,000,000, maximum iteration time is set to 2, and iteration step length is set to 0.1。

The category of roads parameter of Snakes model is set, sees Fig. 4, including form parameter α and the common ratio h of β of linear target_α And h_β, the Priority level for location g of linear target and the symbol intervals of linear target.Symbol intervals drawing norm according to the map is arranged. Common ratio h_αAnd h_βDrawing experience sets according to the map；Positioning precision and shape holding are wanted by Priority level for location g according to linear target Ask and be configured.Originally in being embodied as, common ratio h_αAnd h_βIt is respectively set to 3 and 5, the linear target such as highway, national highway, provincial highway Priority level for location to set gradually be 3,2,1.Location according to original shape parameter, form parameter common ratio and linear target is preferential Level, uses formula (2) to obtain the form parameter of each linear target.

The bending curvature parameter of Snakes model is set, sees Fig. 5, including narrow curved threshold value k₀With maximum parameter c, basis Narrow curved threshold value k is set in being embodied as₀=1.8, maximum parameter c=10.According to narrow curved threshold value k arranged₀And maximum Value parameter c obtains parabola $f_1\left(k\right)=f_2\left(k\right)=4(c-1)\frac{{(k-\frac{1+k_0}{2})}^2}{{(k_0-1)}^2}+1.$

Step 3, the initial space conflict between detection map Linear Objects, and collision table is shown as in Snakes model By force vector.

Use the initial space conflict between buffer zone analysis and overlay analysis detection map Linear Objects, if there is punching Prominent, then collision table is shown as the form by force vector in Snakes model, then performs step 4；Otherwise, directly terminate, no Carry out shifting function.

Collision detection can call the space topological computing interface in ArcGIS Engine secondary development components (ITopologicalIOperator), spatial relationship computing interface (IRelationalOperator), spatial neighbor analysis connect Mouth (IProximityOperator) and overlay analysis interface (IBasicGeoProcessor), owing to collision detection belongs to ability Known technology in territory, does not repeats.

Conflict is expressed as in this step the power with direction and size visually, and the linear target that there is conflict is respectively conflicted External force f suffered by some P_PIt is represented by:

$f_P=\underset{i\&NotEqual;j}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}}\left\{\begin{array}{c}\frac{v_i}{\left|v_i\right|}(r_{\mathrm{ij}}-\min \left(\right|v_i|,r_{\mathrm{ij}})),\mathrm{if}(P\&RightArrow;P+v_i>2r_{\mathrm{ij}})\\ 0,\mathrm{otherwise}\end{array}\right.$

In formula (5):

N is linear target number, and i, j are linear target numbering；

r_ijRepresent linear target L_iAnd L_jThe minimum interval reached required between, the most intersymbol minimum interval threshold Value obtains, after suing for peace the half of linear target i and the symbol intervals of linear target j, between the minimum added between map symbol Every threshold value, it is r_ij；

v_iFor conflict point P to linear target L_iThe vector of upper closest approach, it is considered to close the special circumstances at tie-point, make P → P+ v_iRepresent and arrive L from a P along the route network_iThe path length of upper closest approach, as P → P+v_i＞ 2r_ijJust think wire mesh Mark L_iAnd L_jThere is conflict, otherwise it is assumed that be to close the normal condition at tie-point.

The calculating of external force suffered by conflict point P can be found in Fig. 6, and n the linear target related to during this calculating refers to all ginsengs With the linear target of conflict probe, such as, when shifting road, the linear target participating in conflict probe includes in road network All road targets and other linear target that may clash with road target, such as river.

External force f suffered by each conflict point P in linear target during initial space is conflicted_PAssemble the stress in Snakes model Vector.

Step 4, identifies all bendings in linear target in map, and obtains the form parameter that each bending is corresponding.

Use Wang and M ü ller(1998) the curved recognition methods (reference based on straightway moving direction that proposes Document: Wang Zeshen, M ü ller J.Line Generalization Based on Analysis of Shape Characteristics[J].Cartography and Geographic Information Systems, 1998Vol.25No.1.) all bendings obtained in map in linear target, and calculate the curvature of each bending.This curved-ray tracing Method is defined as the set of one group of adjacent straight line segment that straightway moving direction is consistent on line bending, by by straight line on curve The point that section moving direction changes, as the terminal of bending, blocks curve and forms bending.Digital curve upper curve section around The judgement of the some position that dynamic direction changes can be by the most adjacent 4 P₁、P₂、P₃, and P₄(the most every 3 not conllinear) Carry out detecting realizing, see Fig. 7, by four orderly some P₁、P₂、P₃、P₄Form three in orderVector, Then moving is at P₂The necessary and sufficient condition that point changes is:Bending curvature k=l/d, l are Bending length, d is the line of the bending length of base, i.e. terminal.

After identifying all bendings, formula (3)～(4) is used to calculate the corresponding form parameter of each bending.

Step 5, builds Snakes model overall situation stiffness matrix.

According to finite element matrix K bending corresponding form parameter acquisition Snakes model_L, gather finite element rigidity Matrix K_LObtain the overall stiffness matrix K of linear goal.

The detailed description of the invention of this step is as follows:

To comprising the Snakes model on n summit, there is n-1 bar limit, i.e. line segment, each limit is as a finite element list Unit, stiffness matrix K is by the stiffness matrix K of each finite element unit for the overall situation_LSet forms, and overall situation stiffness matrix K is a size Banding symmetrical matrix for 2n*2n.

Owing to step 1 (including start-stop end points, intermediate node and adjacent wire mesh to the summit in all linear targets Pass tie-point between mark) carry out Unified number, the set of matrix can be carried out by summit numbering.First, overall situation rigidity square is initialized Battle array, i.e. creates overall situation stiffness matrix by summit quantity in linear target, and matrix element is initialized as 0；Then, by line segment institute Form parameter and line segment length in bending substitute into finite element matrix K_LComputing formula, obtain finite element matrix K_L； Finally, " sit in the right seat ", by finite element matrix K by the numbering of line segment two-end-point_LIn each element value be added to the overall situation respectively Stiffness matrix K.Finite element matrix K_LIn the computing formula of each element as follows:

$K_L=\left[\begin{array}{cccc}\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}\\ -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}\end{array}\right]---\left(6\right)$

Fig. 8 gives each element position and line segment point numbering i in overall situation stiffness matrix in finite element matrix, j's Corresponding relation, such as, the 1st element of the 1st row in finite element matrixIt is positioned at 2i in overall situation stiffness matrix Row 2i arranges, the 2nd element of the 1st row in finite element matrixIt is positioned at 2i row the in overall situation stiffness matrix 2i+1 arranges.

Step 6, realizes linear target is carried out shifting function by iterative optimization method.

By initial displacement vector d⁽⁰⁾Be set to [0,0 ..., 0]^T, initial stressed vector f is set to conflict probe in original map The stress vector f obtained⁽⁰⁾, overall situation stiffness matrix K tries to achieve according in step 5, is iterated solving to shift vector d:

(1) by the overall situation stiffness matrix K, the shift vector d of last iteration^(t-1)Stress vector f with last iteration^(t-1)Generation Enter (I+ γ K) d^(t)=d^(t-1)+γf^(t-1)Equation, it is thus achieved that the shift vector d of current iteration^(t), perform step (2)；d^(t-1)At the beginning of Initial value is d⁽⁰⁾, f^(t-1)Initial value is the stress vector f that in original map, conflict stress is constituted⁽⁰⁾；K is overall situation stiffness matrix, repeatedly During generation optimization, K keeps constant；I is unit matrix；γ is iteration step length, and being originally embodied as middle γ is 0.1.

(2) motion-vector d based on current iteration^(t)Map center line shape target is shifted, then, performs step (3)；

(3) judging whether iterations t reaches the maximum iteration time arranged, if reaching, then terminating iteration optimization；Otherwise Perform step (4).

(4) whether the map after detection displacement exists conflict, if there is conflict, performs step (5)；Otherwise terminate iteration excellent Change.

(5) the stress vector f of last iteration is updated according to stress of conflicting in the map after displacement^(t-1)Obtain current iteration Stress vector f^(t), make iterations add 1, will the motion-vector d of current iteration^(t)With stress vector f^(t)As last iteration Motion-vector and by force vector, re-execute step (1).

The condition of convergence of iterative optimization procedure is not limited in this detailed description of the invention be carried, it would however also be possible to employ other convergences Condition, such as currently can be less than preset value by the maximum in force vector is the condition of convergence.

Application note beneficial effects of the present invention below in conjunction with the present invention.

Figure 10 is the result using the inventive method that certain mountain area segment path net carries out collision detection, comprises at a high speed in figure Highway, national highway, provincial highway, river four class Linear element.By symbol under 1:50 ten thousand scale relative to the width on ground along each bar road Drawing relief area with the centrage in river, the lap in different buffering intervals is under target proportion chi produced symbol weight Folded conflict.For ease of discussing, having divided tri-battlegrounds of A, B and C, A battleground is highway and the conflicting of river；B conflicts District is highway and the conflicting of provincial highway；C battleground is national highway and the conflicting of provincial highway.River has higher location in map Required precision, therefore, is set to irremovable by river in this application example.All of road key element constitutes a network structure, Overall situation displacement is carried out by Snakes model.

Being respectively adopted traditional method and the inventive method and Figure 10 carries out overall situation displacement, Figure 11 is traditional based on Snakes The shift result of model displacement method and the comparison diagram of original road network, Figure 12 is the shift result of the inventive method and original road The comparison diagram of road network.It can be seen that displacement deformation from collision position initiate, propagate across the network to everywhere, Figure 11～ 12 overall structure and the topological relations that all can preferably keep road network.

Contrast tri-battlegrounds of A, B, C respectively, find that the displacement effect of the present invention is substantially better than traditional method, see Figure 12～ 13.In Figure 11, the shift size of each conflict point is only strong and weak to conflict relevant, do not account for any other semanteme and graphic constraint Condition, A battleground high speed highway displacement is too big, and the conflict in C battleground is the most unresolved, and the displacement of narrow curved away from From the biggest with the anglec of rotation.In Figure 12, arranging form parameter owing to have employed Geometric Sequence, the highway of A battleground moves Position and deformation receive certain suppression, and in B battleground, the provincial highway of " weak tendency " is being forced in the antagonism of the highway of " surging " Mobile bigger distance.Owing to the form parameter of bending has been carried out personal settings, narrow curved has obtained higher shape Parameter, in C battleground, the narrow curved on national highway is protected, and the general bending on provincial highway is forced mobile bigger distance.

Figure 13 be target proportion chi be ten thousand times shift result display effects of 1:50, wherein, in Figure 13, (a) is original map； In Figure 13, (b) is traditional shift result based on Snakes model displacement method；In Figure 13, (c) is the displacement of the inventive method Result.The further whole structure of (c) in (b) and Figure 13 in contrast Figure 13, although in Figure 13 (b) move generally more greatly away from From, there is displacement excessive (such as A battleground) in the most preferably solving conflict, subrange and conflict the most effectively solves The problem of (such as C battleground).Comparatively speaking, in Figure 13, in (c), integral shift effect is more preferable, and positional precision is the highest.

Claims (4)

1. self adaptation arranges the Linear element displacement method of Snakes mould shapes parameter, it is characterized in that, including:

(1) Priority level for location and the relation of form parameter of linear target are usedObtain the shape of linear target Parameter alpha_RAnd β_R, wherein, α and β is form parameter initial value, rule of thumb pre-sets；G represents that the location of linear target is preferential Level, pre-sets as the case may be, and Priority level for location is the biggest, during displacement keeps the positional precision of linear target and shape Require the highest；h_αAnd h_βIt is respectively form parameter α of linear target_RAnd β_RCommon ratio, according to the map drawing experience pre-set；

(2) identify and bend in linear target, curvature based on bending and the relation of form parameter WithObtain form parameter α of bending_CAnd β_C, wherein, k is bending curvature, k₀For narrow curved Bent threshold value, k₀＞ 1；α_RAnd β_RForm parameter for bending place linear target；C ＞ 1, k₀It is both needed to pre-set as the case may be with c；

(3) form parameter using the bending of finite element unit place builds finite element matrix K_L, and use based on Snakes mould Map center line shape target is shifted by the Linear element displacement method of type, and described finite element unit refers in linear target adjacent The straightway of point-to-point transmission.

2. self adaptation as claimed in claim 1 arranges the Linear element displacement method of Snakes mould shapes parameter, its feature It is:

The described Linear element displacement method based on Snakes model that uses carries out displacement further to map center line shape target Including sub-step:

2.1 set finite element matrix K_LObtain the overall stiffness matrix K of linear goal, by linear target in original map External force suffered by each conflict point constitutes the initial stressed vector f of linear goal⁽⁰⁾, by initial displacement vector d⁽⁰⁾In each element be set to 0；

2.2 by the overall situation stiffness matrix K, the shift vector d of last iteration^(t-1)Stress vector f with last iteration^(t-1)Substitute into (I+ γK)d^(t)=d^(t-1)+γf^(t-1)Equation, it is thus achieved that the shift vector d of current iteration^(t), then, perform step 2.3, wherein, d^{(t -1)}Initial value be step 2.1 obtain initial displacement vector d⁽⁰⁾；f^(t-1)Initial value is the initial stressed described in step 2.1 Vector f⁽⁰⁾；K is overall situation stiffness matrix, and in iterative optimization procedure, K keeps constant；I is unit matrix；γ is iteration step length, according to Concrete condition is configured；

2.3 motion-vector d based on current iteration^(t)Map center line shape target is shifted, then, performs step 2.4；

2.4 update the stress vector f of last iteration according to stress of conflicting in the map after displacement^(t-1)Obtain the stress of current iteration Vector f^(t), by the motion-vector d of current iteration^(t)With stress vector f^(t)As the motion-vector of last iteration with by force vector, Re-execute step 2.2, until meeting the condition of convergence preset.

3. self adaptation as claimed in claim 2 arranges the Linear element displacement method of Snakes mould shapes parameter, its feature It is:

The described condition of convergence includes that the map after shifting does not exists conflict, iterations reaches default maximum iteration time or this Secondary iteration by maximum in force vector less than preset value.

4. self adaptation as claimed in claim 1 arranges the Linear element displacement method of Snakes mould shapes parameter, its feature It is:

In described identification linear target bending method particularly as follows:

It is bent into the set of one group of consistent finite element unit of moving direction on linear target line, by by limited in linear target The point that unit unit moving direction changes is as the terminal of bending, sentencing of the point that finite element unit moving direction changes Breaking can be by the most adjacent every in detection linear target 4 P₁、P₂、P₃, and P₄Realize, then finite element unit moving direction exists P₂The necessary and sufficient condition that point changes is