CN105653881B - Flow field visualization method based on multi-density level - Google Patents
Flow field visualization method based on multi-density level Download PDFInfo
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Abstract
The present invention relates to Study on Flow Field technical fields, to realize in the visualization result of multi-density, there is the result of high density level less streamline, user can be clearly observed the general configuration in flow field, in the streamline result of low-density level, user is observed that more details.The technical solution adopted by the present invention is, flow field visualization method based on multi-density level, the visualization result of low-density is generated using a kind of hybrid algorithm first, in the hybrid algorithm, ensure the spreadability of streamline first with the seed point Algorithms of Selecting based on entropy, then ensures the uniformity of streamline in the way of control grid；It finally in the visualization result of low-density, is screened using based on streamline attribute flow line, the final visualization result for obtaining different densities；In the visualization result of multi-density, the result of high density level has less streamline.Present invention is mainly applied to Study on Flow Field occasions.
Description
Technical field
The present invention relates to visualization in scientific computing, the technical fields such as Study on Flow Field specifically are related to being based on multi-density level
Flow field visualization method.
Background technology
In the big data epoch, be visualized as data processing provides new tool.It all deposits in the fields such as medicine, meteorology, emulation
In a large amount of flow field phenomenons, confusor channel is found from the experimental data of large-scale complex, flow field is clearly observed and is characterized in
Common problem in scientific research.Visualization technique can provide good solution thus.
Stream field phenomenon carry out visualization be one of the mainstream research direction in visualization in scientific computing field, there are many
The research of related fields, main research method include direct visualizztion, flow-field visualized, feature based the stream based on texture
It is field visualized and flow-field visualized etc. based on geometry.Direct visualizztion generally places sampled point in flow field, by sampling
The vector value of point point is shown, can also show that the information in flow field, this method are real using modes such as color or arrows
It is now simple, but it is unable to the inner link of display data.Visualization based on texture mainly shown using the mode of texture, often
Have with method：Spot noise method [1], Line integral convolution method [2], texture advection method [3] etc., what the mode of texture can be apparent from paints
Image detail is made, but it is higher to calculate cost.The visualization Main Basiss flow field topological structure of feature based shows flow field
Structural information, this mode can simplify data volume, hold flow field essence, but are easily lost flow field portion information.Based on several
The flow-field visualized of what describes flow field with line, face, body, geometric element, can obtain good visual perception, but be easy in higher-dimension
In the case of cause confusion and block.
Flow-field visualized main method based on geometry is streamline visualization, i.e., obtains Field Characteristics according to particles track
Line.There are many seed point-generating algorithms in two and three dimensions flow field, such as equidistant fabric strategy [4] is based on flow field topology
The fabric method [5] of guiding, farthest seed point method [6], the seed point Placement Strategy [7] based on image, based on antithesis streamline
Fabric method [8], the fabric method [9] etc. based on entropy theory.Its moderate distance fabric strategy is intuitive it can be readily appreciated that but due to adopting
With the strategy of local optimum, it can not ensure whole streamlines being uniformly distributed in figure；Fabric method based on the guiding of flow field topology
Seed point placement is carried out based on critical point, the feature around critical point is apparent from, but cannot be guaranteed the uniformity of streamline；Farthest kind
The strategy that sub- point method uses is not suitable for being applied to large data collection, and the discontinuous situation of streamline is in addition will appear when density increases；
Seed point Placement Strategy based on image generates uniform streamline with energy function, but takes longer；Fabric based on antithesis streamline
Method has used the thought of greedy algorithm to generate streamline, ensure that the spreadability and continuity of streamline, and can expand to
On curved surface, but it is difficult to expand to field of three dimension；Streamline seed point selection algorithm based on entropy theory has used vector field information-based
Information frame, with unique visual angle annotated streamline generation informative.It proposes and is based in addition, domestic king lacks honor et al.
The fabric strategy [10] for going out in-degree defines one and goes out the difference matrix that becomes a mandarin, and major advantage is that solve visually effect not connect
Continuous problem.2014, Wang Shaorong et al. also proposed the bivector field visualization method [11] based on cluster.This method has very
Good robustness, but it is limited only to two-dimensional vector field.In streamline visualization other than seed point choosing method, Gunther
Et al. propose the optimization algorithm [12] based on streamline, this algorithm is first random to generate streamline, and then flow line carries out global optimization
Processing, major advantage are to allow to browse entire flow field in real time in the case where ensureing that important structural information does not lack, but nothing
Method handles large-scale dataset.
Bibliography：
[1]Van Wijk J J.Spot noise texture synthesis for data visualization
[A]In：Proceedings ofACMSIGGRAPH Computer Graphics[C].Las Vegas,USA：1991,25 (4)
∶309-318.
[2]Cabral B,Leedom L C.Imaging vector fields using line
integralconvolution[A]In：Proceedings ofthe 20th annual conference on Computer
graphicsand interactive techniques[C].Anaheim,CA,USA：1993∶263-270.
[3]Max N,Crawfis R,Williams D.Visualizing wind velocities by
advectingcloudtextures[A]In：Proceedings ofthe 3rd conference on
Visualization'92[C].Boston,Massachusetts,USA；1992∶179-184.
[4]Jobard B,Lefer W.Creating evenly-spaced streamlines of arbitrary
density[M].Austria：Springer Vienna,1997.43-55
[5]Verma V,Kao D,Pang A.A flow-guided streamline seeding strategy[A]
In：Proceedings ofthe conference on Visualization'00[C].ILos Alamitos,CA,USA：
2000∶163-170.
[6]MebarkiA,AlliezP,Devillers O.Farthest point seeding for efficient
placement ofstreamlines[A]In：Proceedings ofIEEEVisualization2005[C]
.Baltimore,Maryland.：2005∶479-486.
[7]Li L,Shen H W.Image-based streamline generation and rendering[J]
.Visualization and Computer Graphics,2007,13(3)∶630-640.
[8]Rosanwo O,Petz C,Prohaska S,et al.Dual streamline seeding[A]In：
Proceedings ofPacific Visualization Symposium[C].Beijing,China：2009∶9-16.
[9]Xu L,Lee T Y,Shen H W.An information-theoretic framework for flow
visualization[J].Visualization and Computer Graphics,2010,16(6)：1216-1224.
[10] Wang Shaorong, Wu Di, a kind of streamline placement methods of the flat of Wang state [J] Journal of Software, 2012,23 (2)：42-52.
[11] Wang Shaorong, field visualized [J] the CADs of bivectors of the flat of Wang state based on cluster and figure
Journal, 2014,26 (10)：1593-1602.
[12]Günther T,C,Theisel H.Opacity optimization for 3D line
fields[J].ACM Transactions on Graphics(TOG),2013,32(4)∶120.
Invention content
In order to overcome the deficiencies of the prior art, it realizes in the visualization result of multi-density, the result of high density level has
Less streamline, user can be clearly observed the general configuration in flow field, in the streamline result of low-density level, use
Person is observed that more details, can be applied in two dimension or three-dimensional flow field.The technical solution adopted by the present invention is to be based on
The flow field visualization method of multi-density level generates the visualization result of low-density using a kind of hybrid algorithm first, mixed at this
In hop algorithm, ensure the spreadability of streamline first with the seed point Algorithms of Selecting based on entropy, then utilizes control grid
Mode ensures the uniformity of streamline；Finally in the visualization result of low-density, sieved using based on streamline attribute flow line
Choosing, the final visualization result for obtaining different densities；In the visualization result of multi-density, the result of high density level have compared with
Few streamline, user can be clearly observed the general configuration in flow field, in the streamline result of low-density level, user
It is observed that more details.
Streamline generation based on hybrid algorithm includes two steps：Seed point Algorithms of Selecting based on entropy and it is based on grid
Null field filling algorithm,
1.1 initial point selection algorithms
The seed point set comprising critical point is selected using Shannon entropy, stream can be selected by choosing the larger point of entropy
The critical point of field：
H (X) is the entropy of certain point in formula (1), and P (x) is the probability that this direction x occurs in the vertex neighborhood, and x is indicated
Vector direction, by each neighborhood of a point entropy in calculation visualization region come select the larger point of entropy be used as seed point come
Draw streamline；
After the completion of seed point is chosen, streamline is calculated using fourth-order Runge-Kutta method；
1.2 null field filling algorithms
Null field filling algorithm is that entire flow field is divided into many small grids, and the size of grid is complete by User Defined
At then the grid for then marking streamline to be passed through when generating streamline detects connected blank grid, blank is represented with it
Domain generates streamline then using the center of each null field as seed point.Then it recalculates null field and repeats above-mentioned behaviour
Make, when the scale of null field is less than a certain threshold value, will stop drawing；
1.2.1 grid mark
The work marked into row bound initialization and streamline according to current streamline：First, current flow field is entirely flowed
The determination of field border grid, it is assumed that the size of flow field grid is N × N, and the grid that a circle has been labeled is defined in two dimensional field surrounding,
So that the quantity of unmarked grid is (N-1) × (N-1)；
In addition to net boundary is marked, when carrying out null field filling, also need according to current streamline indicia grid, tool
The process of body is：Assuming that label line segment (a, b), solves the grid where endpoint a, b first, it is being then pair by line segment (a, b)
Judge one by one in the rectangular area of linea angulata grid whether with line segment intersection；
1.2.2 null field detects
Null field is detected using using breadth first search, in three-dimensional flow field, since streamline can not be by three-dimensional flow field
It is divided into multiple null fields, therefore using improvement breadth-first search in three-dimensional flow field；
1.2.3 seed point is chosen
In two-dimensional flow field, using the geometric center of null field as new seed point coordinates, if the coordinate generated is at this
In null field, then streamline is generated as new seed point；If the coordinate generated is done not in the null field in the point
The parallel lines in the directions x and the directions y solve the line segment that two lines intersect with null field, compare the length of line segment in both direction, select
The longer line segment midpoint of length is as new seed point；
In three-dimensional flow field, after detecting null field, using the geometric center of null field as seed point-rendering streamline, together
Two dimension similarly, when the geometric center of null field is not in null field, will be parallel to reference axis in x, tri- directions y, z
Then straight line detects the length that each direction straight line intersects line segment with null field, select the midpoint of longest line segment in three directions
Streamline is generated as seed point.
Streamline screening based on streamline attribute
2.1 streamline attributes
Using streamline length, apart from both attributes between streamline and flow field；
Streamline length, that is, length of a curve, streamline indicate that the length of streamline can use consecutive points by a point sequence
Distance and indicate, reject some too short streamlines using streamline length, distance l between streamline and flow field on two-dimensional flow fields
It calculates as follows：
ls=min { ltop,ldown,lleft,lright} (2)
In above-mentioned formula, ltop,ldown,lleft,lrightPositive direction of the x-axis in two dimension is respectively represented, negative direction of the x-axis, y-axis is just
Direction, distance, l between flow field and flow field in negative direction of the y-axislineThe length of streamline, p is top or down, q be left or
Right, (3) formula illustrate that the distance in positive direction of the x-axis, calculation process are, regard streamline as set a little, dotted line direction
For positive direction of the x-axis, every bit is calculated in this direction at a distance from marked grid, is then calculated adjacent 2 points and curve
The region surrounded is considered as trapezoidal area, finally using area divided by streamline length as streamline in this direction with flow field away from
From equally calculating negative direction of the y-axis, x-axis square, streamline and flow field distance on these three directions of negative direction of the x-axis, finally choose four
On a direction minimum value as streamline at a distance from flow field；
When three-dimensional flow field is drawn, way two-dimensional flow field is consistent, i.e.,：According to the length of streamline and streamline and flow field away from
From rejecting too short streamline and overstocked streamline, the length of wherein streamline remain calculate each section length and, but count
Calculate streamline at a distance from flow field when, due to dimension rise, need to compare the distance on six direction, wherein in each direction away from
It is consistent with the computational methods under two dimension from computational methods；
2.2 filtering algorithm
It is being chosen by the seed point based on entropy, after the null field filling based on grid, streamline collection is being obtained, in the stream
Line is concentrated, and streamline is first carried out descending sort according to the entropy of its seed point.Grid is then initialized, successively according to streamline sequence
Streamline is placed in field, when the length of streamline is less than a certain threshold value σlOr distance is less than a certain threshold value σ between streamline and flow fieldtWhen,
The streamline will be deleted, until all streamlines are examined.
9 points around the certain point chosen in two-dimensional flow field are used as neighborhood, and entropy, which calculates the threshold value chosen after the completion, is
0.7；27 points chosen in three-dimensional flow field around certain point are used as neighborhood, and initial kind is chosen using the method for proportional sampling
Sub- point：I.e. in the point that entropy is more than 0.97 times of maximum entropy, using 1: 10 oversampling ratio, it is more than 0.95 times of maximum in entropy
Entropy is less than in the point of 0.97 times of maximum entropy, using 1: 20 oversampling ratio.
The features of the present invention and advantageous effect are：
The present invention proposes the method for visualizing based on multi-density level, generates low-density using a kind of hybrid algorithm first
Visualization result ensures the spreadability of streamline first with the seed point Algorithms of Selecting based on entropy, so in the hybrid algorithm
Ensure the uniformity of streamline in the way of control grid afterwards.Finally in the visualization result of low-density, using based on streamline
Attribute flow line is screened, the final visualization result for obtaining different densities.In the visualization result of multi-density, high density
The result of level has less streamline, and user can be clearly observed the general configuration in flow field, in low-density level
In streamline result, user is observed that more details.
Description of the drawings：
Fig. 1 method flow diagrams.
The present invention mainly realizes effect flow-field visualized in two and three dimensions, and Isabel numbers are shown in Fig. 2, Fig. 3
According to collection different time under piece visualization result, Isabel data sets essentially describe hurricane field different time piece shape
State, size are 500 × 500 × 100；The two-dimensional visualization of the same layer in different time under piece data set is shown in Fig. 2
As a result, its size is 500 × 500；For more preferably effect of visualization, shown in Fig. 3 compressed in different time under piece
Three-dimensional visualization is as a result, its size is 100 × 100 × 100, and left side shows the visualization result under low-density level in figure,
Right side shows the visualization result under high density level in figure.
Fig. 4 is calculated between streamline and flow field apart from schematic diagram.
Specific implementation mode
The present invention proposes the flow-field visualized of multi-density level for the uniformity, spreadability, continuity of visualization result
Method.Wherein uniformity refers to that streamline distribution is uniform, and spreadability, which refers to streamline, cannot lose important structure feature, and continuity refers to streamline
It to grow as much as possible.
In the research of stream field phenomenon, it is often necessary to which convection current field data carries out visualization processing and then observes flow field spy
Sign.It being visualized relative to two-dimensional flow field, three-dimensional flow field is visualized closer to reality, but since streamline is mutual on three dimensions
Blocking causes effect of visualization bad, and existing three-dimensional flow field is visualized for the processing in terms of streamline uniformity in three-dimensional not
It is good.
For the uniformity of occlusion issue and visualization result in three-dimensional, the present invention propose based on multi-density level can
Depending on changing method, the visualization result of low-density is generated using a kind of hybrid algorithm first, in the hybrid algorithm, first with base
Ensure the spreadability of streamline in the seed point Algorithms of Selecting of entropy, then ensures the uniform of streamline in the way of control grid
Property.Finally in the visualization result of low-density, is screened using based on streamline attribute flow line, finally obtain different densities
Visualization result.In the visualization result of multi-density, the result of high density level has a less streamline, and user can be with
It is clearly observed the general configuration in flow field, in the streamline result of low-density level, user is observed that more thin
Section.
The general frame of the present invention is shown in Fig. 1, includes mainly following steps：
1. the streamline based on hybrid algorithm generates (Fig. 1 (b) (c))：The present invention is chosen using the seed point based on entropy and is calculated
Method and null field filling algorithm based on grid generate the visualization result of least density level.The result meet uniformity,
Spreadability, continuity.
2. the streamline screening (Fig. 1 (d)) based on streamline attribute：The present invention according to streamline between flow field at a distance from and streamline it is long
It spends both attribute flow line collection to be screened, controls the stream that can generate different densities between streamline and flow field apart from this attribute
Knot fruit.This attribute of control flow field length can reject shorter streamline, and final streamline result is made to meet continuity.
The present invention can provide to the user 2 dimensions or 3 dimension it is flow-field visualized as a result, can be used for related Study on Flow Field field
In understand flow field integral structure characteristic, provide the flow-field visualized result being faster more readily understood to the user.
Testing machines configuration of the present invention is as follows：Intel Core i53500mq, 8G RAM, ATI Radeon HD
7450M, Windows7, VS2012.
Present invention be described in more detail with specific example below in conjunction with the accompanying drawings.
1. the streamline based on hybrid algorithm generates
A kind of hybrid algorithm is employed herein to generate the maximum streamline collection of density.Main in the algorithm includes two
A part：Seed point Algorithms of Selecting based on entropy and the null field filling algorithm based on grid, the seed based on entropy click
Taking can make streamline visualization result include the important feature feature in flow field；Null field filling algorithm based on grid can make
Visualization result is more uniform.
1.1 initial point selection algorithms
The present invention selects the seed point set comprising critical point using Shannon entropy, and what Shannon entropy was weighed is one group of vector institute
The information content contained, vector between difference it is bigger, entropy is bigger；In flow field, the direction around critical point is widely different, therefore
Entropy is very high, therefore, the critical point in flow field can be selected by choosing the larger point of entropy.
H (X) is the entropy of certain point in formula (1), and P (x) is the probability that this direction x occurs in the vertex neighborhood, and x is indicated
The direction of vector.The present invention is used as kind by each neighborhood of a point entropy in calculation visualization region to select the larger point of entropy
Son is put to draw streamline.In the experiment of this paper, 9 points of (including point sheets around the certain point that we choose in two-dimensional flow field
Body) it is used as neighborhood, threshold value that this experiment is chosen after the completion of entropy calculating is 0.7；We choose certain point week in three-dimensional flow field
27 points (including the points itself) enclosed are used as neighborhood, since three dimensional field data volume is larger, if directly choosing more than a certain threshold value
When entropy point, the quantity of entropy point will be very much, therefore, choose initial seed using the method for proportional sampling herein
Point.I.e. in the point that entropy is more than 0.97 times of maximum entropy, using 1: 10 oversampling ratio, it is more than 0.95 times of maximum entropy in entropy
Value is less than in the point of 0.97 times of maximum entropy, using 1: 20 oversampling ratio etc..The quantity control of final initial seed point exists
1000 or so.
After the completion of seed point is chosen, streamline is calculated using fourth-order Runge-Kutta method herein.
1.2 null field filling algorithms
After being chosen by the seed point based on entropy, there may be white spaces for visualization result, and the present invention is at this
How introduction limits the distance between streamline using grid, and final effect of visualization is made to meet uniformity.Null field
Filling algorithm is a kind of iterative algorithm based on spatial gridding, the general idea is that entire flow field is divided into many small nets
The size of lattice, grid can be completed by User Defined, then the grid for then marking streamline to be passed through when generating streamline is examined
Connected blank grid is surveyed, null field is represented with it, then using the center of each null field as seed point, generates streamline.
Then it recalculates null field and repeats aforesaid operations, when the scale of null field is less than a certain threshold value, will stop drawing.
1.2.1 grid mark
In the null field filling algorithm of the present invention, the definition of null field needs to detect the presence on boundary, so of the invention
The work that can be marked first into row bound initialization and streamline according to current streamline.First, entire flow field is carried out to current flow field
The determination of boundary mesh, it is assumed that the size of flow field grid is N × N, then as shown in Fig. 2, having defined a circle in two dimensional field surrounding
Labeled grid so that the quantity of unmarked grid is (N-1) × (N-1).
In addition to net boundary is marked, when carrying out null field filling, initial streamline is chosen by entropy
What seed point generated, therefore we also need according to current streamline indicia grid.In the present invention, since streamline is by many small
Line segment is constituted, so label streamline need to only detect line segment and intersect with which grid.Its specific process is：Assuming that mark line
Section (a, b) solves the grid where endpoint a, b first, is being then to sentence one by one in cornerwise rectangular area by line segment (a, b)
Suspension lattice whether with line segment intersection.
1.2.2 null field detects
Null field is the white space being made of streamline in flow field.In the algorithm based on grid, null field is continuous
The set of unmarked grid, boundary be labeled grid, so the size of null field is by constituting the grid of null field
Quantity determines.When seeking null field, its adjacent unmarked grid can be searched for, therefore solve null field by a little
Process can also regard a search problem as.It is used herein that null field is detected using breadth first search.In three-dimensional flow
In, since three-dimensional flow field can not be divided into multiple null fields by streamline, in three-dimensional flow field, breadth First is improved herein and is searched
Rope algorithm.
1.2.3 seed point is chosen
In two-dimensional flow field, using the geometric center of null field as new seed point coordinates, if the coordinate generated is at this
In null field, then we generate streamline as new seed point.If generate coordinate not in the null field, we
The parallel lines in the directions x and the directions y are done in the point, the line segment that two lines intersect with null field is solved, compares line segment in both direction
Length selects the longer line segment midpoint of length as new seed point.Show two-dimensional flow field after null field filling in Fig. 1
Visualization result.Drawing result can be seen that the drawing result based on null field is filled with white space, drawing result well
Middle streamline distribution is uniform, and drawing result shows the general configuration feature in entire flow field.
In three-dimensional flow field, after detecting null field, we are using the geometric center of null field as seed point-rendering stream
Line, similarly with two dimension, when the geometric center of null field is not in null field, we will do in tri- directions parallel in x, y, z
In the straight line of reference axis, the length that each direction straight line intersects line segment with null field is then detected, selects longest in three directions
The midpoint of line segment generates streamline as seed point.
Null field filling algorithm based on grid can uniformly draw out entire flow field according to predefined sizing grid,
The size of grid is related with the flow field density drawn out.
2. the streamline screening based on streamline attribute
After completing streamline and generating, we can obtain the flow-field visualized of lower level as a result, however two dimensional visible
Streamline is too close in change result, may not meet user's expectation, while streamline distribution is intensive in three-dimensional visualization result, mutually blocks
Seriously, it therefore introduces multi-level density in this section herein and shows how to be screened using streamline attribute flow line, produce
Raw better effect of visualization.
2.1 streamline attributes
Streamline simplification is a common sub- direction in streamline visualization, mainly passes through the streamline attribute progress to generation
Compare, then therefrom selected section streamline as last visualization result.Common streamline attribute has the length of streamline, streamline
Between distance, streamline linear entropy etc..Streamline length is mainly used herein, apart from both attributes between streamline and flow field.
Streamline length, that is, length of a curve, streamline herein indicate that the length of streamline can be used by a point sequence
It the distances of consecutive points and indicates.Herein some too short streamlines are rejected using streamline length.Streamline and stream on two-dimensional flow field
Distance l betweensIt calculates as follows：
ls=min { ltop,ldown,lleft,lright} (2)
In above-mentioned formula, ltop,ldown,lleft,lrightPositive direction of the x-axis in two dimension is respectively represented, negative direction of the x-axis, y-axis is just
Direction, distance, l between flow field and flow field in negative direction of the y-axislineThe length of streamline, p is top or down, q be left or
right.(3) formula illustrates the distance in positive direction of the x-axis, calculates schematic diagram such as Fig. 4, we regard streamline as set a little,
Calculating every bit at a distance from marked grid, then calculates streamline in this direction and the surrounded area in flow field in positive direction of the x-axis
The area (region that adjacent 2 points and curve surround is considered as trapezoidal calculate) in domain, finally by area divided by streamline length
As streamline in this direction at a distance from flow field, negative direction of the y-axis, x-axis square, negative direction of the x-axis these three sides are equally calculated
Upward streamline and flow field distance, it is final to choose on four direction minimum value as streamline at a distance from flow field.
When three-dimensional flow field is drawn, way two-dimensional flow field is consistent, i.e.,：According to the length of streamline and streamline and flow field away from
From rejecting too short streamline and overstocked streamline.The length of wherein streamline remain calculate each section length and, but count
When calculating streamline at a distance from flow field, since dimension rises, it would be desirable to compare the distance on six direction, wherein in each direction
Distance calculating method with two dimension under computational methods it is consistent.
2.2 filtering algorithm
It is being chosen by the seed point based on entropy, after the null field filling based on grid, we have obtained a streamline
Collection is concentrated in the streamline, and streamline is first carried out descending sort by us according to the entropy of its seed point.Grid is then initialized, is pressed
Streamline is placed in field successively according to streamline sequence, when the length of streamline is less than a certain threshold value σlOr distance is small between streamline and flow field
When a certain threshold value σ t, we will delete the streamline, until all streamlines are examined.
Claims (3)
1. a kind of flow field visualization method based on multi-density level, characterized in that generated first using a kind of hybrid algorithm low
The visualization result of density ensures covering for streamline in the hybrid algorithm first with the seed point Algorithms of Selecting based on entropy
Then Gai Xing ensures the uniformity of streamline in the way of control grid；Finally in the visualization result of low-density, base is used
It is screened in streamline attribute flow line, the final visualization result for obtaining different densities；In the visualization result of multi-density,
The result of high density level has less streamline, and user can be clearly observed the general configuration in flow field, in low-density
In the streamline result of level, user is observed that more details；Streamline generation based on hybrid algorithm includes two steps
Suddenly：Seed point Algorithms of Selecting based on entropy and the null field filling algorithm based on grid；
1.1 initial point selection algorithms
The seed point set comprising critical point is selected using Shannon entropy, flow field can be selected by choosing the larger point of entropy
Critical point：
H (X) is the entropy of certain point in formula (1), and P (x) is the probability that this direction x occurs in the vertex neighborhood, and x indicates vector
Direction, seed point is used as selecting the larger point of entropy by each neighborhood of a point entropy in calculation visualization region and is drawn
Streamline；
After the completion of seed point is chosen, streamline is calculated using fourth-order Runge-Kutta method；
1.2 null field filling algorithms
Null field filling algorithm is that entire flow field is carried out mesh generation, and the size of grid is completed by User Defined, then existed
The grid that label streamline is passed through when generating streamline, then detects connected blank grid, null field is represented with it, then will be every
The center of one null field generates streamline as seed point, then recalculates null field and repeats aforesaid operations, works as null field
Scale be less than a certain threshold value when, by stop draw；
1.2.1 grid mark
The work marked into row bound initialization and streamline according to current streamline：First, entire flow field side is carried out to current flow field
The determination of boundary's grid, it is assumed that the size of flow field grid is N × N, and the grid that a circle has been labeled is defined in two dimensional field surrounding so that
The quantity of unmarked grid is (N-1) × (N-1)；
In addition to net boundary is marked, when carrying out null field filling, also need according to current streamline indicia grid, specifically
Process is：Assuming that label line segment (a, b), solves the grid where endpoint a, b first, it is being then diagonal line by line segment (a, b)
Rectangular area in judge one by one grid whether with line segment intersection；
1.2.2 null field detects
Null field is detected using using breadth first search, in three-dimensional flow field, since three-dimensional flow field can not be divided by streamline
Multiple null fields, therefore using improvement breadth-first search in three-dimensional flow field；
1.2.3 seed point is chosen
In two-dimensional flow field, using the geometric center of null field as new seed point coordinates, if the coordinate generated is in the blank
In domain, then streamline is generated as new seed point；If the coordinate generated does the side x not in the null field in the point
To the parallel lines with the directions y, the line segment that two lines intersect with null field is solved, compares the length of line segment in both direction, selection length
Longer line segment midpoint is spent as new seed point；
In three-dimensional flow field, after detecting null field, using the geometric center of null field as seed point-rendering streamline, with two dimension
Similarly, when the geometric center of null field is not in null field, the straight of reference axis will be parallel in x, tri- directions y, z
Then line detects the length that each direction straight line intersects line segment with null field, the midpoint of longest line segment in three directions is selected to make
Streamline is generated for seed point.
2. the flow field visualization method as described in claim 1 based on multi-density level, characterized in that based on streamline attribute
Streamline screens：
2.1 streamline attributes
Using streamline length, apart from both attributes between streamline and flow field；
Streamline length, that is, length of a curve, streamline indicated by a point sequence, the length of streamline can use consecutive points away from
From with indicate, reject some too short streamlines using streamline length, distance l between streamline and flow field on two-dimensional flow fieldsIt calculates
It is as follows：
ls=min { ltop,ldown,lleft,lright} (2)
In above-mentioned formula, ltop,ldown,lleft,lrightRespectively represent positive direction of the x-axis in two dimension, negative direction of the x-axis, positive direction of the y-axis, y
Distance between flow field and flow field, l in axis negative directionlineIt is the length of streamline, p is top or down, and q is left or right, (3) formula
Illustrating the distance in positive direction of the x-axis, calculation process is, calculates every bit in positive direction of the x-axis at a distance from marked grid,
The area of streamline and the surrounded region in flow field in this direction is then calculated, i.e., is considered as the region that and curve surround at adjacent 2 points
It is trapezoidal to be calculated, finally y-axis is equally calculated in this direction at a distance from flow field using area divided by streamline length as streamline
Negative direction, x-axis square, streamline and flow field distance on these three directions of negative direction of the x-axis, minimum value on final selection four direction
As streamline at a distance from flow field；
When three-dimensional flow field is drawn, way two-dimensional flow field is consistent, i.e.,：According to the length of streamline and streamline at a distance from flow field come
Reject too short streamline and overstocked streamline, the length of wherein streamline remain calculate each section length and, but calculate stream
When line is at a distance from flow field, since dimension rises, need to compare the distance on six direction, wherein distance meter in each direction
Calculation method is consistent with the computational methods under two dimension；
2.2 filtering algorithm
It is being chosen by the seed point based on entropy, after the null field filling based on grid, streamline collection is being obtained, in the streamline collection
In, streamline is first subjected to descending sort according to the entropy of its seed point, then initializes grid, successively will according to streamline sequence
Streamline is placed in field, when the length of streamline is less than a certain threshold value σlOr distance is less than a certain threshold value σ between streamline and flow fieldtWhen, it will
The streamline is deleted, until all streamlines are examined.
3. the flow field visualization method as claimed in claim 2 based on multi-density level, characterized in that chosen in two-dimensional flow field
Certain point around 9 points be used as neighborhood, it is 0.7 that entropy, which calculates the threshold value chosen after the completion,；Certain point is chosen in three-dimensional flow field
27 points of surrounding are used as neighborhood, and initial seed point is chosen using the method for proportional sampling：It is more than 0.97 times in entropy
In the point of maximum entropy, using 1:10 oversampling ratio is more than 0.95 times of maximum entropy in entropy and is less than 0.97 times of maximum entropy
Point in, using 1:20 oversampling ratio.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101694725A (en) * | 2009-10-10 | 2010-04-14 | 北京理工大学 | Topological driven plane flow field streamline placement method |
| CN102646288A (en) * | 2012-02-23 | 2012-08-22 | 北京理工大学 | Three-dimension flow line placing method with basically uniform intervals |
| CN102930563A (en) * | 2012-08-13 | 2013-02-13 | 北京理工大学 | Dual control grid-based streamline placement method for two-dimensional flow fields |
| CN104318591A (en) * | 2014-10-16 | 2015-01-28 | 南京师范大学 | Dynamic drawing method with boundary plane flow field |
-
2016
- 2016-03-04 CN CN201610123731.4A patent/CN105653881B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101694725A (en) * | 2009-10-10 | 2010-04-14 | 北京理工大学 | Topological driven plane flow field streamline placement method |
| CN102646288A (en) * | 2012-02-23 | 2012-08-22 | 北京理工大学 | Three-dimension flow line placing method with basically uniform intervals |
| CN102930563A (en) * | 2012-08-13 | 2013-02-13 | 北京理工大学 | Dual control grid-based streamline placement method for two-dimensional flow fields |
| CN104318591A (en) * | 2014-10-16 | 2015-01-28 | 南京师范大学 | Dynamic drawing method with boundary plane flow field |
Non-Patent Citations (2)
| Title |
|---|
| 一种流线放置方法;王少荣 等;《软件学报》;20140201;第23卷(第3期);第42-52页 * |
| 基于聚类的二维向量场可视化;王少荣 等;《计算机辅助设计与图形学学报》;20141031;第26卷(第10期);第1595-1598页第2-4节 * |
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