CN102800116A - Method for rapidly creating large-scale virtual crowd - Google Patents

Method for rapidly creating large-scale virtual crowd Download PDF

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CN102800116A
CN102800116A CN2012102042936A CN201210204293A CN102800116A CN 102800116 A CN102800116 A CN 102800116A CN 2012102042936 A CN2012102042936 A CN 2012102042936A CN 201210204293 A CN201210204293 A CN 201210204293A CN 102800116 A CN102800116 A CN 102800116A
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sample
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tile
crowd
color
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CN102800116B (en
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王欣捷
申晶晶
金小刚
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Zhejiang University ZJU
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Abstract

The invention discloses a method for rapidly creating a large-scale virtual crowd, and is used for creating a virtual crowd in a scene area input by a user. People are deemed to be particles with distribution and role information, a sample base is established by acquiring a sample containing small-scale crowd particle information from a true picture, a Wangs brick set is produced by using a sample based on a Wangs brick method, and a scene area is spliced and covered by using the Wangs brick aperiodically so as to rapidly generate various virtual crowds in the scene of any scales. The creating method is simple and rapid, and the crowd can be created rapidly just by inputting a plurality of samples and a scene area to be covered by crowds; and besides, the crowd with true complex characteristics in a true picture is used as the sample, so that the created virtual crowd is different in appearance and has realness and naturalness.

Description

A kind of quick establishment large-scale virtual crowd's method
Technical field
The present invention relates to the virtual reality field, the field of virtual crowd creation in particular is used for reproducing various crowd realistically at virtual scene.
Background technology
The people is one of component most important and the most basic in the real world; Virtual role has the meaning of no less important for virtual world; Utilize colony's analogue technique; In the computing machine span, create and the simulating reality world in colony and motion thereof, can greatly improve the sense of reality and the feeling of immersion of virtual world.In recent years, along with the continuous development of computer cluster n-body simulation n technology, it is used also more and more widely, and the field that relates to comprises simulated training, computer game animation, video display special efficacy and public safety Aided Design etc.Such as, can the scene that comprise a large amount of crowd activities be realized through computer simulation in the tv screen, thereby improve the efficient of special efficacy making and reduce cost of manufacture; Through to the daily stream of people or in emergency circumstances crowd's motion process simulate and analyze, for fabric structure designs, large-scale activity passenger flow management, public place emergency preplan are formulated and played good directive function.
For thousands of crowd, if desired successively to each character carry out the position, towards etc. the simulation association attributes be provided with and revise, concerning the user, will be a huge loaded down with trivial details task.If just these attributes are set at random, then can cause the result not meet true group characteristic, very difficult control reaches the required effect of user.If adopt simple rule that the crowd is arranged, can cause the too regular or repetition of result, simultaneously, complicated crowd's distribution rule is difficult to describe with math equation.
For large scale scene and crowd's simulation, how to accomplish crowd's initial distribution and state setting quickly and efficiently, and make it have diversity and authenticity, be a urgent problem.
Aspect the virtual crowd creation, existing department pattern is suggested, for example flocking model (the Reynolds C. of Reynolds; Flocks, Herds and Schools:A distributed behavioralmodel [J] .Computer Graphics, 1987; 21 (4): 25-34.), the social force model of Helbing (Helbing D., Molnar P.; Social force model for pedestrian dynamics. [J] .Physical Review E; 1995,51 (5): 4282-4286.), can be used to simulate crowd's distribution that generation has certain complicacy; But be difficult to control final effect, also be difficult to simulation and reach the user and specify effect through the adjustment local rule.(the Ulicny B. of Crowdbrush system of Ulciny; Ciechomski O.and Thalmann D.; Crowdbrush:Interactive authoring of real-time crowdscenes [C] .In Proceedings of ACM SIGGRAPH/Eurographics Symposium onComputer Animation; 2004,243-252.) the user real time creation and the crowd's of drafting method is provided, edit and control persona information through using brush; Because that operation more is directed against is single or several roles, needs a large number of users mutual.People such as Yersin propose large scale scene crowd creation and animation method (Yersin B., Maim J., the Pettre J.andThalmann D. based on Crowd Patch; Crowd patches:populating large-scale virtual environments forreal-time applications [C] .In Proceedings of the 2009symposium onInteractive 3D graphics and games; 2009,207-214.), through in advance the movement locus of character being stored among the Patch; Splicing obtains final effect; The complex design of Patch in this method, it is continuous to satisfy space and time, institute can a simulated person crowd distribute and the animation kind very limited; Simultaneously, the user can't revise spliced crowd's scene.People such as Ju have proposed crowd's analogy method (Ju E., Choi M., Park, the M. based on data-driven; Lee J., Lee K., Takahashi S., Morphablecrowds [J] .ACM Trans.Graph.; 2010,29 (6): Article 140.), classification learning obtains on a small scale crowd's sample that distributes from real video; In the simulation, whether in sample set, add individuality and controlled motion, owing to need to detect the similarity of each individual adjacent domain and whole sample set through every group distribution among the detection crowd; Crowd's aggregate velocity is very slow, and synthetic result is rule very, is not suitable for the synthetic fast of extensive various crowd.People such as Guy have proposed method (the Guy S.J. based on psychological model parametric description character behavioral trait; Kim S.; Lin M.C., Manocha D., Simulating heterogeneous crowd behaviors using personality trait theory [C] .In Proceedings of ACM SIGGRAPH/Eurographics Symposium on ComputerAnimation; 2011; 43-52.), generate various crowd's movement effects, concern be the relevant parameter setting of control role movement.In addition; Macro approach based on the global speed field is also arranged; Comprise that these methods can only be used for global motion control effect based on cartographic information, user interactions control navigation, based on continuum theory, based on fluid model etc., the uncontrollable local crowd effect that distributes.
Summary of the invention
The objective of the invention is to propose a kind of virtual crowd creation method, be used for creating fast the large-scale virtual crowd based on true picture in order to solve complicated operation and too regular problem when the virtual crowd.
The invention provides a kind of quick establishment large-scale virtual crowd's method, be used in the scene areas of user's input, creating virtual crowd, comprise step:
(1) creates virtual crowd sample storehouse based on true picture;
(2) based on the virtual crowd sample storehouse of creating, synthetic Wang Shi brick Wang Tile sets up the set of Wang Shi brick;
(3) use the Wang Tile in the set of Wang Shi brick that the scene areas splicing that the user imports is covered.
Further, said step (1) is created virtual crowd sample storehouse based on true picture, specifically comprises step:
(1.1) initialization sample square;
(1.2) from true picture, choose the square area of concern;
(1.3) selected individual and gather its distributed intelligence and role attribute information from the square area of choosing; From the three dimensional character model bank, select to meet the actor model of role attribute information; According to the distributed intelligence persona model of gathering carry out the position and towards conversion; Put into the sample square area, as a sample;
(1.4) for each sample is provided with a various colors coding, sample is put into the sample storehouse.
For authenticity and the naturality that guarantees virtual crowd; The present invention adopts and creates the sample storehouse based on true picture; The sample storehouse is big more to provide abundant more sample; The distributed intelligence and the role attribute information of the individuality in therefore can collection real pictures as much as possible make up sample as much as possible, the scale of the virtual crowd that will make according to the later stage, and it also is feasible coming suitably to set up the sample storehouse.
Further, the step of synthetic Wang Shi brick Wang Tile comprises in the said step (2):
(2.1) branch is respectively selected a sample four times from said sample storehouse; A bigger sample block is formed in 4 sample splicings; Has certain coincidence district in twos between the sample; 0.1~0.35,4 foursquare diagonal line of sample that overlap the length of side and be sample length of side diamond-shaped area of forming that intersects each other is Wang Tile;
(2.2) in diamond-shaped area; Particle collection in the adjacent sample overlapping region is carried out Voronoi to be divided; Select a cut-off rule of forming by the Voronoi limit; Make the particle furthest that is separated to keep left samples particle that is positioned at the cut-off rule left side and the right side sample particles that is positioned at the cut-off rule right side respectively, guarantee the naturality of distribution of particles in the overlapping region;
(2.3) rotation after the cutting diamond-shaped area and be positioned at its particle, obtain square WangTile, its limit, upper and lower, left and right is labeled as N, S, W, E respectively, and the color coding on corresponding Wang Tile limit is set according to sample of color;
(2.4), travel through all 4 samples combinations, set up the set of Wang Shi brick, make the Wang Shi brick set of setting up be complete Wang Shi brick set.
The present invention sets up Wang Shi brick set completely through the combination of 4 samples in the traversal sample storehouse, and the optional color in every the limit that makes is whole sample storehouse.
Further, said sample storehouse comprises storehouse, first subsample and storehouse, second subsample, and the sample that will be used for following splicing is put into the first sample storehouse, and the sample that will be used for the right sides splicing is put into the second sample storehouse.When adopting said sample storehouse to synthesize Wang Tile, the optional color of last bottom is only selected from storehouse, first subsample, and the optional color of right sides is only selected from storehouse, second subsample.Through said method, can be so that the horizontal and vertical characteristic distributions of crowd be different.
Further, said step (3) also comprises:
(3.1), user's appointment polygon scene areas of needing virtual crowd to cover, select longest edge to need the border of alignment as coverings, the structure rectangular area comprises the polygon scene areas that the user specifies needs the crowd to cover;
(3.2), the color on the restrained boundary of appointment needs alignment;
(3.3), begin to select the Wang Tile of Satisfying Matching Conditions to arrange the rectangular area from restrained boundary;
(3.4), according to former input scene areas, deletion is positioned at its outer particle, obtains the virtual crowd in final covering scene zone.
Color on the restrained boundary that said appointment need be alignd be specify said rectangular area go up a whole piece and the borderline color of the first from left whole piece most.Saidly begin to select the Wang Tile of Satisfying Matching Conditions to arrange the rectangular area from restrained boundary to be meant, to arrange direction from top to bottom, from left to right; The Wang Tile of said Satisfying Matching Conditions be meant selected Wang Tile the top color must with its top Wang Tile following identical, left side color must be identical with the right of its left Wang Tile; The color on remaining two limits is specified by system at random, but different with the color on the limit of the Wang Tile that has arranged on every side.
Preferably; Synthetic Wang Tile is recorded in the concordance list of a four-dimension; Four components of said four-dimensional concordance list are respectively the color of 4 samples of synthetic this Wang Tile, when the splicing scene areas, only need provide the color of the four edges up and down of said Wang Tile; From said four-dimensional concordance list, find corresponding Wang Tile, can accomplish splicing fast.
The invention discloses a kind of quick establishment large-scale virtual crowd's method; The people is regarded as having the particle that distributes with Role Information,, sets up the sample storehouse through from true picture, obtaining the sample that comprises small-scale crowd particle information; And based on Wang Shi brick method; Use sample to make the set of Wang Shi brick, use Wang Shi brick aperiodicity splicing covering scene zone, thereby generate the various virtual crowd in the random scale scene rapidly.Creation method of the present invention is simply quick, and the user only need import some samples and the scene areas that needs the crowd to cover, and just can accomplish building work fast.
The present invention is based on the crowd who has true complex characteristic in the true picture and make sample; And gather a plurality of different samples and form the samples storehouse; In follow-up use; Use mode such as splice, synthesize, duplicate to produce the large-scale virtual crowd who comes in every shape in a large number, for the virtual crowd creation provides great facility, the while has also had authenticity and naturality.
Description of drawings
Fig. 1 creates large-scale virtual crowd method flow diagram fast for the present invention;
Fig. 2 sets up sample storehouse flow chart of steps for the present invention;
Fig. 3 sets up the flow chart of steps of Wang Tile for the present invention;
Fig. 4 splices the flow chart of steps of Wang Tile for the present invention.
Embodiment
Below in conjunction with accompanying drawing and embodiment technical scheme of the present invention is explained further details, following examples do not constitute qualification of the present invention.
The present invention at first sets up virtual crowd sample storehouse based on true picture in order to create the large-scale virtual crowd fast, utilizes the sample storehouse to set up Wang Shi brick (Wang Tile) then, at last Wang Tile is spliced, and forms the large-scale virtual crowd.The practical implementation method is as shown in Figure 1, may further comprise the steps:
Step 101, create virtual crowd sample storehouse based on true picture.
Step 102, based on the virtual crowd sample storehouse of creating, synthetic Wang Shi brick Wang Tile sets up the set of Wang Shi brick.
Wherein Wang Shi brick notion is proposed in 1961 by mathematical logic man Wang Hao, is one group of square Tile that size is identical, to all given a kind of color in every limit of Tile, if the adjacent side color of two Tile is identical, then can these two Tile splicings be put.
Synthetic Wang Shi brick Wang Tile, its limit, upper and lower, left and right is labeled as N, S, W, E respectively, and the color coding on corresponding Wang Tile limit is set according to sample of color.The Wang Shi brick set of setting up is complete Wang Shi brick set, and promptly every optional color in limit is whole sample storehouse.
Wang Tile in step 103, the set of use Wang Shi brick covers the scene areas splicing of user's input, obtains the interior crowd's particle assembly of scene areas.
Promptly, use Wang Shi brick aperiodicity to splice covering fast, obtain crowd's particle assembly in the scene according to the scene areas of user's input.
For authenticity and the naturality that guarantees virtual crowd, the present invention adopts and creates the sample storehouse based on true picture, and is as shown in Figure 2, creates virtual crowd sample storehouse based on true picture and may further comprise the steps:
Step 201, initialization sample square are changed to 1 unit length with the length of side, and the crowd's positional information correspondence that comprises zooms to 0~1.0 unit length.
Step 202, from true picture, choose the square area of concern.
Step 203, selected individual and gather its distributed intelligence and role attribute information from the square area of choosing; From the three dimensional character model bank, select to meet the actor model of role attribute information; According to the distributed intelligence persona model of gathering carry out the position and towards conversion; Put into the sample square area, as a sample.
Particularly, exactly each individuality among the crowd is regarded as particle, each particle comprises its initial distribution information, role attribute information.Initial distribution information is position P (P x, P y) and towards O (O x, O y), if role attribute information spinner personage three-dimensional model attribute information comprises sex Gender, age Age, attitude Pose (being the respective action sequence).After extracting these information, these information are applied on the qualified actor model, then these have been used in the real pictures actor model of individual distributed intelligence and role attribute information and put in the sample square area, form a sample.
Step 204, for each sample is provided with various colors coding, sample is put into the sample storehouse.
Particularly; Repeating step 201-step 204; Form a plurality of samples and form the samples storehouse, the sample storehouse is big more to provide abundant more sample, and the distributed intelligence and the role attribute information of the individuality in therefore can collection real pictures as much as possible make up sample as much as possible; The scale of the virtual crowd that will make according to the later stage, it also is feasible coming suitably to set up the sample storehouse.
After having created the sample storehouse, each sample has a color coding, next just can synthesize the Wang Shi brick based on the sample storehouse of creating, and handles the distribution that the inner adjacent sample of Wang Tile overlaps the interior particle in zone, and is as shown in Figure 3, specifically comprises the following steps:
Step 301, branch are respectively selected a sample four times from the sample storehouse; A bigger sample block is formed in 4 sample splicings; Has certain coincidence district in twos between the sample; 4 foursquare diagonal line of sample diamond-shaped area of forming that intersects each other is Wang Tile, the length of side Overlap_size ∈ (0.1,0.35) of intersection.
Step 302, in diamond-shaped area; Particle collection in the adjacent sample overlapping region is carried out Voronoi to be divided; Select a cut-off rule of forming by the Voronoi limit; Make the particle furthest that is separated to keep left samples particle that is positioned at the cut-off rule left side and the right side sample particles that is positioned at the cut-off rule right side respectively, guarantee the naturality of distribution of particles in the overlapping region.
Step 303, rotation after the cutting diamond-shaped area and be positioned at its particle, obtain square Wang Tile, its limit, upper and lower, left and right is labeled as N, S, W, E respectively, and the color coding on corresponding Wang Tile limit is set according to sample of color.
Step 304, travel through all 4 samples combinations, set up the set of Wang Shi brick, make the Wang Shi brick set of setting up be complete Wang Shi brick set, promptly every optional color in limit is whole sample storehouse.
In order to obtain Wang Shi brick set completely; Need the combination of each 4 sample in the traversal sample storehouse; The Wang Tile that it is synthetic records in the concordance list of a four-dimension; Four components of this four-dimension concordance list are respectively the color of 4 samples, i.e. the color of the N/S/W/E four edges of the synthetic Wang Tile of these 4 samples.In subsequent step, only need provide the color of N/S/W/E four edges, just can in four-dimensional concordance list, find corresponding Wang Tile.
Wang Shi brick set is completely laid a good foundation for the extensive virtual crowd of creating; In virtual scene; The polygonal region that user's appointment needs the crowd to cover, the border of selecting longest edge need align as Wang Tile splicing makes up a rectangular area that covers this polygonal region.Calculate required Wang Tile number H_NUM and the required Wang Tile number C_NUM of every row of every row in this rectangular area according to the length of square boundary and the boundary length of wide and Wang Tile then; In the rectangular foot-print territory; Random choose from the set of Wang Shi brick (or part is specified) H_NUM * C_NUM Tile meets the splicing of arranging of matched rule, and after all Wang Tile put together, total HNUM+1 was capable for widthwise edge (N/S limit); Every capable C NUM, with a two-dimensional matrix B N[H_NUM+1] [C_NUM] representes; The total C NUM+l row of vertical edge (W/E limit), every row HNUM, with a two-dimensional matrix B W[C_NUM+1] [H_NUM] representes.
Aperiodicity splicing step is as shown in Figure 4 at random, comprises step:
The polygon scene areas that step 401, user's appointment need virtual crowd to cover, the border of selecting longest edge need align as covering makes up the polygon scene areas that the rectangular area comprises that the user specifies needs virtual crowd to cover;
Step 402, appointment need the color on the restrained boundary of alignment, and that specifies the rectangular area usually goes up a whole piece and the borderline color of the first from left whole piece, i.e. two-dimensional matrix B most NIn lastrow B N[H_NUM+1] and two-dimensional matrix B WIn the first from left row B WThe color value of [C_NUM+1].Boundary constraint both can be specified by the user, also can be specified automatically by system.
Step 403, begin to select the Wang Tile of Satisfying Matching Conditions to arrange the zone, arrange direction from N to S, from W to E from restrained boundary.The Wang Tile of Satisfying Matching Conditions is: the N limit color of selected WangTile must be identical with the S limit of its top Wang Tile, W limit color must be identical with the E limit of its left Wang Tile; The color on remaining two limits can be specified by system at random, but will be as far as possible different with the color on the limit of the Wang Tile that has arranged on every side.After the four edges color of Wang Tile had all been confirmed, this Wang Tile of acquisition put into and arranges the zone from concordance list INDEX.After arranging end, obtain the crowd's particle CrowdParticles in the rectangular area.
Step 404, according to former input scene areas, deletion is positioned at its outer particle, if having barrier in the scene areas, deletion is positioned at the particle within the barrier polygon, obtains crowd's particle CrowdParticles of final covering scene.
Need to prove; Because the Tile in the Wang Shi brick set is kept in the four-dimensional concordance list according to the color of its four edges component as four-dimensional concordance list; Color through four edges (N/S/W/E) can be searched its position in concordance list fast, wants the Wang Tile that uses to splice the covering scene zone thereby find.
What need especially explanation here is and since the N limit of sample only with the splicing of S limit, the W limit only with the splicing of E limit, in order to generate the crowd neatly, also can be, and storehouse, another one subsample 2 is set for the W/E limit for the N/S limit is provided with storehouse, an optional subsample 1.When the sample storehouse further comprises the storehouse, subsample; The array mode of selecting sample during for synthetic Wang Tile changes to some extent; Promptly when at synthetic Wang Tile, the optional color in N/S limit is only selected from storehouse, subsample 1, and the optional color in W/E limit is only selected from storehouse, subsample 2.
The user also can put into storehouse, subsample 1 and storehouse, subsample 2 (for example: the crowd density in storehouse, subsample 1 is bigger, and the crowd density in the storehouse, subsample 2 is less or the like) according to characteristics autonomous sample of selecting to want from the sample storehouse of sample.Through said method, can be so that the horizontal and vertical characteristic distributions of crowd be different.
Above embodiment is only in order to technical scheme of the present invention to be described but not limit it; Under the situation that does not deviate from spirit of the present invention and essence thereof; Those of ordinary skill in the art work as can make various corresponding changes and distortion according to the present invention, but these corresponding changes and distortion all should belong to the protection domain of the appended claim of the present invention.

Claims (10)

1. a method of creating the large-scale virtual crowd fast is used in the scene areas of user's input, creating virtual crowd, it is characterized in that, comprises step:
(1) creates virtual crowd sample storehouse based on true picture;
(2) based on the virtual crowd sample storehouse of creating, synthetic Wang Shi brick Wang Tile sets up the set of Wang Shi brick;
(3) use the Wang Tile in the set of Wang Shi brick that the scene areas splicing that the user imports is covered.
2. establishment large-scale virtual crowd's as claimed in claim 1 method is characterized in that, and is said based on true picture establishment virtual crowd sample storehouse, comprises step:
(1.1) initialization sample square;
(1.2) from true picture, choose the square area of concern;
(1.3) selected individual and gather its distributed intelligence and role attribute information from the square area of choosing; From the three dimensional character model bank, select to meet the actor model of role attribute information; According to the distributed intelligence persona model of gathering carry out the position and towards conversion; Put into the sample square area, as a sample;
(1.4) for each sample is provided with a various colors coding, sample is put into the sample storehouse.
3. establishment large-scale virtual crowd's as claimed in claim 1 method is characterized in that, the step of said synthetic Wang Shi brick Wang Tile comprises:
(2.1) branch is respectively selected a sample four times from said sample storehouse; A bigger sample block is formed in 4 sample splicings; Has certain coincidence district in twos between the sample; 0.1~0.35,4 foursquare diagonal line of sample that overlap the length of side and be sample length of side diamond-shaped area of forming that intersects each other is Wang Tile;
(2.2) in diamond-shaped area; Particle collection in the adjacent sample overlapping region is carried out Voronoi to be divided; Select a cut-off rule of forming by the Voronoi limit; Make the particle furthest that is separated to keep left samples particle that is positioned at the cut-off rule left side and the right side sample particles that is positioned at the cut-off rule right side respectively, guarantee the naturality of distribution of particles in the overlapping region;
(2.3) rotation after the cutting diamond-shaped area and be positioned at its particle, obtain square WangTile, its limit, upper and lower, left and right is labeled as N, S, W, E respectively, and the color coding on corresponding Wang Tile limit is set according to sample of color;
(2.4), travel through all 4 samples combinations, set up the set of Wang Shi brick, make the Wang Shi brick set of setting up be complete Wang Shi brick set.
4. establishment large-scale virtual crowd's as claimed in claim 2 method; It is characterized in that: said sample storehouse comprises storehouse, first subsample and storehouse, second subsample; The sample that will be used for following splicing is put into the first sample storehouse, and the sample that will be used for the right sides splicing is put into the second sample storehouse.
5. establishment large-scale virtual crowd's as claimed in claim 4 method; It is characterized in that: when adopting said sample storehouse to synthesize Wang Tile; The optional color of last bottom is only selected from storehouse, first subsample, and the optional color of right sides is only selected from storehouse, second subsample.
6. establishment large-scale virtual crowd's as claimed in claim 1 method is characterized in that: said step (3) also comprises:
(3.1), user's appointment polygon scene areas of needing virtual crowd to cover, select longest edge to need the border of alignment as coverings, make up the polygon scene areas that the rectangular area comprises that the user specifies needs the virtual crowd covering;
(3.2), the color on the restrained boundary of appointment needs alignment;
(3.3), begin to select the Wang Tile of Satisfying Matching Conditions to arrange the rectangular area from restrained boundary;
(3.4), according to former input scene areas, deletion is positioned at its outer particle, obtains the virtual crowd in final covering scene zone.
7. establishment large-scale virtual crowd's as claimed in claim 6 method is characterized in that: the color on the restrained boundary that said appointment need be alignd be specify said rectangular area go up a whole piece and the borderline color of the first from left whole piece most.
8. establishment large-scale virtual crowd's as claimed in claim 6 method is characterized in that: saidly begin to select the Wang Tile of Satisfying Matching Conditions to arrange the rectangular area from restrained boundary to be meant, to arrange direction from top to bottom, from left to right; The Wang Tile of said Satisfying Matching Conditions be meant selected Wang Tile the top color must with its top Wang Tile following identical, left side color must be identical with the right of its left Wang Tile; The color on remaining two limits is specified by system at random, but different with the color on the limit of the Wang Tile that has arranged on every side.
9. establishment large-scale virtual crowd's as claimed in claim 3 method; It is characterized in that; Said method also comprises step: synthetic Wang Tile is recorded in the concordance list of a four-dimension, and four components of said four-dimensional concordance list are respectively the color of 4 samples of synthetic this Wang Tile.
10. establishment large-scale virtual crowd's as claimed in claim 9 method; It is characterized in that; The Wang Tile of said selection Satisfying Matching Conditions is meant the color of the four edges up and down that provides said Wang Tile, from said four-dimensional concordance list, finds corresponding Wang Tile.
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