CN115964546B - Vortex migration channel extraction and visualization method based on edge binding - Google Patents
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Abstract
The invention discloses a vortex migration channel extraction and visualization method based on edge binding, and belongs to the technical field of ocean observation. The method comprises the following steps: dynamic visualization based on a Cesium platform is realized on global vortex motion track data by utilizing a particle system; selecting a vortex track typical test area for edge binding, and obtaining characteristic vortex track data; binding the characteristic vortex track data by using a force-based edge binding algorithm to realize extraction of a vortex channel; the vortex channels obtained by extraction are classified, and a main channel and a bypass channel of the vortex motion track are extracted. The binding diagram obtained by the invention simplifies the edge disorder, reduces the ambiguity information, highlights the ocean vortex main channel and realizes the ocean vortex main channel extraction based on force.
Description
Technical Field
The invention belongs to the technical field of ocean observation, and particularly relates to a vortex migration channel extraction and visualization method based on edge binding.
Background
Mesoscale vortices are known as "storms" in the ocean and are an important component of ocean currents, typically on the spatial scale of tens to hundreds of kilometers and on the temporal scale of days to hundreds of days. The mid-scale vortex has been widely observed in various areas of the world ocean since the first discovery by marine scientists in the 70 s of the last century. The mesoscale vortex has profound and wide effects on aspects such as ocean physics, chemistry and ecological environment, and therefore becomes one of research hotspots of oceanographic students.
With the development of ocean observation technology in recent years, mesoscale vortex is rapidly developed in the aspect of identification and detection, and track tracking is also an important point of ocean scientific research. The method for accurately predicting the mesoscale vortex propagation track has important scientific significance for researching the propagation process and evolution characteristics of the vortex, and has important practical values for the design of a marine observation system, fishery planning, underwater sound detection and the like. Compared with vortex identification, the research work of marine mesoscale vortex tracking is later in development, and three common mesoscale vortex track tracking methods exist at present: "pixel method", "distance method", "similarity method". Later scholars put forward a "density peak value based clustering algorithm" on the basis of the "similarity" algorithm.
Physical phenomena such as wind field, flow field, ocean vortex motion and the like are different in motion direction and speed in each area, and specific motion characteristics of the physical phenomena cannot be observed according to observed values, so that special processing is required for the data, and abstract observed data are visualized to intuitively reflect internal motion rules and information of ocean vector data. Vector field visualization is one of the most challenging subjects in the field of scientific computational visualization, and is now widely used in the fields of aerodynamics, atmospheric physics, meteorology, and marine science. Currently, there are many methods for vector field visualization, mainly generalized as direct visualization, geometric visualization, texture-based visualization and feature visualization.
Since the 90 s of the 20 th century, the swirling motion characteristics have become one of the research hotspots. The common ideas of people are: the motion of mesoscale vortices is disordered and is ubiquitous in the ocean. For vortices at some large areas, while there may be one or more prominent directions visually, the long-time series of ocean vortex motion trajectories are in a disordered distribution throughout the basin. In fact, the motion characteristics of the vortex are very complex in the motion direction, and the development and evolution process of the vortex are influenced by various factors such as the topography of the sea bottom, wind jet flow, background flow and the like. In addition, for the motion track of the marine mesoscale vortex, the previous research is mainly focused on the statistical analysis of the propagation direction and distance of the vortex, and the research on the movement characteristic of the large-area vortex is lacking.
Disclosure of Invention
The invention aims to realize the extraction and dynamic visualization of the global mesoscale vortex track by using a flow field-based visualization algorithm so as to make up the defects of the prior art.
Edge bundling techniques cluster edges with similar attributes together to reduce visual clutter, and current edge bundling techniques either implicitly or explicitly cluster groups of individual edges or partial edges together based on these attributes. According to the invention, by comparing the visualization effects of various edge binding technologies and setting the edge compatibility measurement according to the characteristics of ocean vortex motion, a force-based edge binding algorithm is provided.
In order to achieve the aim and based on the principle, the invention adopts the following specific technical scheme:
a vortex migration channel extraction and visualization method based on edge binding comprises the following steps:
s1: dynamic visualization based on a Cesium platform is realized on global vortex motion track data by utilizing a particle system;
s2: selecting a vortex track typical test area for edge binding on the basis of the step S1, and obtaining characteristic vortex track data;
s3: binding the characteristic vortex track data by using a force-based edge binding algorithm to realize extraction of a vortex channel;
s4: and (3) classifying the vortex channels obtained by the step (S3) to extract a main channel and a bypass channel of the vortex motion track.
Further, the step S1 specifically includes:
s1-1: generation of particles: the generation of vortex particles is controlled by utilizing a random function, and the random function controls the generation position, life cycle and number of particles generated in unit time interval of the particles, so that newly generated particles are randomly distributed in the grid;
s1-2: particle attribute initialization: initializing the vortex particle attributes represents which attributes the newly generated vortex particles possess; in the vortex visualization process, particle generation, movement and extinction are realized by changing particle properties;
s1-3: movement of particles: after attribute assignment is carried out on vortex particles through a random function, the attribute of the vortex particles changes along with the time, and the update of the particle attribute occurs in the time step of each frame; drawing a line segment according to the current frame position and the next frame position of the vortex particle, and repeating the steps to obtain the movement track of the vortex particle; the longitude and latitude of the position of the next frame of the particle are calculated through the speed of the particle, and the speed of the particle is obtained through bilinear interpolation;
s1-4: particle extinction: as the particles move, the life cycle of the particles gradually decreases, and when the life cycle of the particles decreases to zero, the particles die;
s1-5: drawing particles: vortex dynamic visualization is implemented on a visualization platform.
Further, the step S3 specifically includes:
s3-1: setting the number P of subdivision points of each edge 0 : holding the end points of each edge fixed, dividing each edge by an edge dividing point P i Equally subdividing into a plurality of parts;
s3-2: calculating the spring constant k p : the global spring constant k is used to control the number of edge bindings in the graph by determining the stiffness of the edge; since the edges have different initial lengths and are subdivided into segments, a local spring constant k is calculated for each segment of the edge p ， k p Is to calculate the spring force F s Important parameters of (2); k (k) p The same for each segment of the edge, the calculation formula is k p =k/|p|, where |p| is the initial length of the edge P;
s3-3: calculating the spring force F s : for each edge there is a linear attractive spring force F between each pair of successive subdivisions s Subdivision Point P i Force F of spring on s The calculation formula of (2) is as follows:
wherein P is i-1 Is the subdivision point P i P of (C) i+1 Is the subdivision point P i Is the next point of (2);
s3-4: setting an edge compatibility metric C e (P, Q): the edge compatibility measurement is the consideration judgment of the relation between the edges, removes the edge binding between the irrelevant edges, and optimizes the force-based edge binding visualization effect; if the edge compatibility metric C between the two sides of P and Q e If the (P, Q) is smaller than a certain threshold value, the two sides are considered to have smaller relevance and are not bound; between two sides of P and QEdge compatibility metric C e (P,Q)∈[0,1]The definition is as follows:
wherein C is a (P, Q) is angle compatibility, C s (P, Q) is proportional compatibility, C p (P, Q) is position compatibility, C v (P, Q) is visibility compatibility;
s3-5: calculating electrostatic force F e : an electrostatic attraction force F is provided between each corresponding subdivision point of the pair of interacting edges e For the edge P, it is subjected to the following electrostatic force formula:
where E is the set of all edges that interact with P except edge P, C e (P, Q) is an edge compatibility metric, P i Is the edge subdivision point on edge P, q i Is the edge subdivision point of all interacted edges except edge P;
s3-6: calculating the resultant force at each edge subdivision point: each edge point is subjected to two forces, one being the spring force F exerted on that point by the adjacent subdivision point of that point s One being the electrostatic force F exerted on the point by the subdivision of the interacting edge e Resultant force F pi The calculation formula is as follows:
s3-7: setting an initial step S 0 : the step size determines the distance a point moves in the direction of the resultant force applied to it;
s3-8: setting a fixed number of cycle times C: performing a fixed number of iterative steps I in each loop; i 0 Is the number of iterative steps during the first cycle; after one cycle is performed, the next cycle is startedBefore, the number of subdivision points P is doubled, and the step length S is halved; the iteration step I of each period is also reduced according to the previously set iteration times reduction rate;
s3-9: and the side binding and visualization of the vortex motion track are realized.
Still further, in S3-4:
for angle compatibility C a (P, Q): typically, the nearly vertical edges should not be bundled together, introducing angular compatibility C a (P,Q)∈[0,1]The method comprises the following steps:
wherein P and Q are two sides,
is the angle between P and Q, the greater the angle between edges P and Q, C a The smaller (P, Q); if P and Q are orthogonal, C a (P, Q) is 0, if P and Q are parallel, C a (P, Q) is 1;
for proportional compatibility C s (P, Q): typically, edges of widely varying lengths should not be bundled together; doing so may result in significant stretching and bending of the short edges to accommodate the shape of the long edges; thus, introducing dimension compatibility C s (P,Q)∈[0,1]The method comprises the following steps:
wherein P and Q are two sides,
is the average length of the two sides P and Q, < >>
Is the length of the short side between the two sides P and Q, < >>
The length of the long side between the two sides P and Q; if the lengths of P and Q are equal, C s (P, Q) is 1, cs (P, Q) is 0 if the ratio between the longest and shortest edges is close to ≡;
for position compatibility C p (P, Q): for the positions of the two edges, the edges which are far away from each other should not be bound together; introducing site compatibility C p (P,Q)∈[0,1]The concept of (2) is:
wherein P, Q is two sides, P m And Q m Is the center point of sides P and Q,
is P m And Q m A distance therebetween; if P m And Q m Consistent, C p (P, Q) is 1, if P m – Q m I is close to ≡c p (P, Q) is 0.
Compatibility C for visibility v (P, Q): in addition to the above compatibility, two edges may appear parallel, of equal length and close to each other, but they may still have a fairly low binding compatibility between them, e.g. opposite sides of a parallelogram. To solve this problem, visibility compatibility C is introduced v (P,Q)∈[0,1]：
Where V (P, Q) is the visibility of side P to side Q, and V (Q, P) is the visibility of side Q to side P; the visibility for the sides P to Q is obtained by extending a "line of sight band" from Q, and the intersection of the extension line of P and the "line of sight band" is I 0 And I 1 ，P m Is the midpoint of the line segment P, I m Is I 0 And I 1 Is a midpoint of (2); if P m And I m Overlap, C v (P, Q) is 1, otherwise C v (P, Q) is 0.
Further, in the step S4, an array is defined in the edge binding process to store the correlation between each edge and other edges, if the other edges associated with one edge are greater than 10 edges of the other edges, the edge is the edge of the main channel, otherwise, the edge is the edge of the bypass channel, and the edges are recorded in the array and respectively rendered.
The invention has the following advantages and technical effects:
(1) The dynamic visualization of the global vortex track is realized on the basis of the flow field visualization, so that the movement direction of the vortex track can be observed macroscopically, and some detailed information of the vortex track movement can be observed.
(2) By comparing various edge binding algorithms and setting compatibility measures, the force-based edge binding algorithm is provided for binding vortex data, so that edge disorder is simplified, ambiguity information is reduced, an ocean vortex main channel is highlighted, and force-based ocean vortex main channel extraction is realized.
(3) Traditional vortex track analysis mainly focuses on observation and statistics analysis, focuses on observing the movement direction of a vortex track of a small area, and the patent places a visual angle on a large ocean area, researches the characteristics of the large area or global ocean vortex movement trend, and adopts a visualization method to realize extraction of a large-area ocean vortex migration channel.
(4) The algorithm in the computer graphics is applied to the field of ocean vortex visualization, multi-disciplinary cross fusion is realized, and the method has higher research and application values.
Compared with the existing edge binding method, the binding diagram obtained by the invention simplifies the edge disorder, reduces the ambiguity information, highlights the ocean vortex main channel and realizes the ocean vortex main channel extraction based on force. According to the invention, the characteristic vortex track line segments of the test area are extracted through the force-based edge binding algorithm, so that the continuous tracking observation of the mesoscale vortex channels is realized, and a new research thought is provided for researching the mesoscale vortex motion characteristics and material transportation in the ocean.
Drawings
Fig. 1 is a basic flow chart of the present invention.
Fig. 2 is a diagram of a mesoscale vortex trajectory dynamic visualization based on Cesium.
Fig. 3 is a graph of the results of the south ocean mesoscale vortexes after binding based on the edge binding algorithm.
Fig. 4 is a graph of the result of extraction of the main and side branch channels of the south ocean mesoscale vortex after binding based on the edge binding algorithm.
Detailed Description
The technical scheme of the invention is further described and illustrated below by combining with the embodiment.
Example 1:
a vortex migration channel extraction and visualization method based on edge binding is shown in the flow chart of figure 1.
The specific operation comprises the following steps:
the data used in this example was derived from http:// www.aviso.oCEanobs.com, and the data used was a sea level anomaly data (SLA) dataset covering (1 month in 2000 to 12 months in 2020) with a temporal resolution of 1 day, a spatial resolution of (1/4) × (1/4) °, and a data coverage of global ocean.
1. Dynamic visualization based on a Cesium platform is realized on global vortex motion track data by using a particle system:
(1) Generation of particles: the generation of vortex particles is controlled by a random function that controls the location of particle generation, lifecycle, and number of particle generation per unit time interval. The random distribution of the newly generated particles in the grid can be achieved by means of a random function.
(2) Particle attribute initialization: initialization of the vortex particle properties represents which properties the newly created vortex particle possesses. In the vortex visualization process, particle generation, movement and extinction are realized by changing particle properties. The properties in this experiment were set as follows: the initial x position of the particle, the initial y position of the particle, the initial longitude of the particle, the initial latitude of the particle, the longitude of the particle to be moved next, the latitude of the particle to be moved next, the life cycle of the particle, the moving speed of the particle, and the like.
(3) Movement of particles: after attribute assignment is performed on the vortex particles through a random function, the attribute of the vortex particles changes along with the time, and the update of the particle attribute occurs in the time step of each frame. And drawing line segments according to the current frame position and the next frame position of the vortex particles, and repeating the steps to obtain the movement track of the vortex particles. The longitude and latitude of the position of the next frame of the particle are calculated by the speed of the particle, which is obtained by bilinear interpolation, and the formula is as follows:
where u is the radial velocity of the particle, v is the latitudinal velocity of the particle, g00, g10, g01, g11 are the coordinates of the four vertices of the mesh in which the particle is located, g00[0] represents the x-coordinate of the point, g00[1] represents the y-coordinate of the point, and the other points are the same. lng, lat are longitude and latitude coordinates of the particle on the current frame image. next lng, next is the longitude and latitude coordinates of the particle on the next frame image, and speedRateU and speedrateev are the moving rates in the longitude and latitude directions.
(4) Particle extinction: as the particles move, the life cycle of the particles gradually decreases, the life cycle decreases by 1 with each frame number, and when the life cycle decreases to zero, the particles die.
(5) Drawing particles: the steps of particle generation, particle attribute initialization, particle movement and the like are realized, and vortex drawing is realized by using a Cesium visual platform. Fig. 2 is a diagram of a mesoscale vortex trajectory dynamic visualization based on Cesium.
2. Selecting a vortex track typical test area for edge binding on the basis of the step 1:
since the south ocean is one of the most active regions of the global ocean in-scale vortex motion, and a vortex with high kinetic energy and large amplitude exists, research on the motion direction of the south ocean vortex is necessary. By comparing the global vortex dynamic visualization results, the test selects the south ocean area as the test area of edge binding. The global mesoscale vortex data of 2000-2020 are identified and tracked, and then the south ocean (30 DEG S, south) vortex data are extracted. In order to effectively extract a south ocean mesoscale vortex motion channel and describe motion characteristics and rules of the south ocean mesoscale vortex motion channel, the embodiment screens characteristic vortex track line segments with the life cycle of more than thirty days for experiments.
3. Binding the vortex track data obtained in the step 2 by using a force-based edge binding algorithm to realize extraction of the vortex channel:
(1) Setting the number P of subdivision points of each edge 0 : holding the end points of each edge fixed, dividing each edge by an edge dividing point P i On average, subdivided into several portions. The number of initialized subdivision points is 1, and the number of subdivision points becomes 2 times the number of subdivision points at the last time for each iteration.
(2) Calculating the spring constant k p : the global spring constant k is used to control the number of edge bindings in the graph by determining the stiffness of the edge. Since the edges have different initial lengths and are subdivided into segments, a local spring constant k is calculated for each segment of the edge p ， k p Is to calculate the spring force F s Is of the weight of (2)Parameters are required. k (k) p The same for each segment of the edge, the calculation formula is k p =k/|p|, where |p| is the initial length of the edge P. The global spring constant k=0.1 is set in this experiment.
(3) Calculating the spring force F s : for each edge there is a linear attractive spring force F between each pair of successive subdivisions s Subdivision Point P i Force F of spring on s The calculation formula of (2) is as follows:
wherein P is i-1 Is the subdivision point P i P of (C) i+1 Is the subdivision point P i Is the next point of (2);
(4) The edge compatibility measurement is the consideration judgment of the relation between the edges, can remove the edge binding between the irrelevant edges, and optimizes the force-based edge binding visualization effect. If the edge compatibility metric C between the two sides of P and Q e If (P, Q) is smaller than a certain threshold, the two sides are considered to have smaller relevance, and no binding is performed. We will measure the edge compatibility between P and Q sides, C e (P,Q)∈[0,1]The definition is as follows:
wherein C is a (P, Q) is angle compatibility, C s (P, Q) is proportional compatibility, C p (P, Q) is position compatibility, C v (P, Q) is visibility compatibility.
For angle compatibility C a (P, Q): typically, the nearly vertical edges should not be bundled together. Therefore, the invention introduces angle compatibility C a (P,Q)∈[0,1]The method comprises the following steps:
wherein P and Q are two sides,
is the angle between P and Q, the greater the angle between edges P and Q, C a The smaller (P, Q). If P and Q are orthogonal, C a (P, Q) is 0, if P and Q are parallel, C a (P, Q) is 1.
For proportional compatibility C s (P, Q): typically, edges of widely varying lengths should not be bundled together, which may result in significant stretching and bending of the short edges to accommodate the shape of the long edges. Thus, introducing dimension compatibility C s (P,Q)∈[0,1]The method comprises the following steps:
wherein P and Q are two sides,
is the average length of the two sides P and Q, < >>
Is the length of the short side between the two sides P and Q, < >>
Is the length of the long side between the two sides P and Q. If the lengths of P and Q are equal, C s (P, Q) is 1, and Cs (P, Q) is 0 if the ratio between the longest and shortest edges is close to ≡.
For position compatibility C p (P, Q): for the position of the two edges, the edges that are farther apart should not be bound together. Therefore, we introduce location compatibility C p (P,Q)∈[0,1]The concept of (2) is:
wherein P, Q is two sides, P m And Q m Is the center point of sides P and Q,
is P m And Q m Distance between them. If P m And Q m Consistent, C p (P, Q) is 1, if P m – Q m I is close to ≡c p (P, Q) is 0.
Compatibility C for visibility v (P, Q): in addition to the above compatibility, two edges may appear parallel, of equal length and close to each other, but they may still have a fairly low binding compatibility between them, e.g. opposite sides of a parallelogram. To solve this problem, the present patent introduces visibility compatibility C v (P,Q)∈[0,1] ：
Where V (P, Q) is the visibility of side P to side Q and V (Q, P) is the visibility of side Q to side P. The visibility for the sides P to Q is obtained by extending a "line of sight band" from Q, and the intersection of the extension line of P and the "line of sight band" is I 0 And I 1 ，P m Is the midpoint of the line segment P, I m Is I 0 And I 1 Is defined by a central point of the lens. If P m And I m Overlap, C v (P, Q) is 1, otherwise C v (P, Q) is 0.
Because the lengths of the vortex trajectories are different, in order to optimize the edge binding effect, different compatibility thresholds are set for the vortex trajectory binding with different lengths in the experiment, the compatibility threshold is set to be 0.6 for the long edge, and the compatibility threshold is set to be shortThe edge sets the compatibility threshold to 0.5. I.e. for edges of length greater than 25
It is considered that both sides satisfy the binding condition, and +.>
The binding condition is satisfied.
(5) Calculating electrostatic force F e : an electrostatic attraction force F is provided between each corresponding subdivision point of the pair of interacting edges e For the edge P, it is subjected to the following electrostatic force formula:
where E is the set of all edges that interact with P except edge P, C e (P, Q) is an edge compatibility metric, P i Is the edge subdivision point on edge P, q i Is the edge subdivision point of all interacting edges except the edge P.
(6) Calculating the resultant force at each edge subdivision point: each edge point is subjected to two forces, one being the spring force F exerted on that point by the adjacent subdivision point of that point s One being the electrostatic force F exerted on the point by the subdivision of the interacting edge e Resultant force F pi The calculation formula is as follows:
(7) Setting an initial step S 0 : the step size determines the distance a point moves in the direction of the resultant force applied to it. The initial step S is set in the experiment 0 = 0.1。
(8) Setting a fixed number of cycle times C: a fixed number of iterative steps I are performed in each loop. I 0 Is the number of iterative steps during the first cycle. In executing a loopAfter that, the number of subdivision points P is doubled and the step size S halved before the next cycle is started. The iteration step I of each cycle is also reduced at the previously set rate of reduction of the number of iterations. The number of loops c=6, the number of iterative steps I during the first loop was set in this experiment 0 Rate of iteration number reduction i_rate=2/3=90.
(9) Side binding and visualization are realized on vortex motion tracks: fig. 3 is a graph of the result of the binding of the south ocean mesoscale vortex based on the edge binding algorithm, and the white area is the south ocean vortex channel.
4. Classifying the vortex track bound in the step 3, and extracting a main channel and a bypass channel of the vortex motion track:
defining an array in the edge binding process to store the correlation of each edge and other edges, if the other edges associated with the edge are more than 10 for a certain edge, the edge is the edge of the main channel, otherwise, the edge of the side channel is recorded in the array and rendered respectively. Fig. 4 is a graph of the result of extraction of a main channel and a bypass channel of a south ocean mesoscale vortex after binding based on an edge binding algorithm, wherein a white area is the main channel of the south ocean mesoscale vortex extracted after the edge binding, and a black area is the bypass channel.
The present invention has been described in detail with reference to the above embodiments, and the functions and actions of the features in the present invention will be described in order to help those skilled in the art to fully understand the technical solution of the present invention and reproduce it.
Finally, although the description has been described in terms of embodiments, not every embodiment is intended to include only a single embodiment, and such description is for clarity only, as one skilled in the art will recognize that the embodiments of the disclosure may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (4)
1. The vortex migration channel extraction and visualization method based on edge binding is characterized by comprising the following steps of:
s1: dynamic visualization based on a Cesium platform is realized on global vortex motion track data by utilizing a particle system;
s2: selecting a vortex track typical test area for edge binding on the basis of the step S1, and obtaining characteristic vortex track data;
s3: binding the characteristic vortex track data by using a force-based edge binding algorithm to realize extraction of a vortex channel; the method comprises the following steps:
s3-1: setting the number P of subdivision points of each edge 0 : holding the end points of each edge fixed, dividing each edge by an edge dividing point P i Equally subdividing into a plurality of parts;
s3-2: calculating the spring constant k p : the global spring constant k is used to control the number of edge bindings in the graph by determining the stiffness of the edge; since the edges have different initial lengths and are subdivided into segments, a local spring constant k is calculated for each segment of the edge p ，k p Is to calculate the spring force F s Important parameters of (2); k (k) p The same for each segment of the edge, the calculation formula is k p =k/|p|, where |p| is the initial length of the edge P;
s3-3: calculating the spring force F s : for each edge there is a linear attractive spring force F between each pair of successive subdivisions s Subdivision Point P i Force F of spring on s The calculation formula of (2) is as follows:
F S ＝k P ·(||p i-1 -p i ||+||p i -p i+1 ||)
wherein P is i-1 Is the subdivision point P i P of (C) i+1 Is the subdivision point P i Is the next point of (2);
s3-4: setting an edge compatibility metric C e (P, Q): the edge compatibility measurement is the consideration judgment of the relation between the edges, removes the edge binding between the irrelevant edges, and optimizes the force-based edge binding visualization effect; if the edge compatibility metric C between the two sides of P and Q e If (P, Q) is less than a certain threshold, then the correlation between the two edges is considered to be small,binding is not performed; measure C of edge compatibility between P and Q sides e (P,Q)∈[0,1]The definition is as follows:
C e (P，Q)＝C a (P，Q)·C S (P，Q)·C p (P，Q)·C v (P，Q)
wherein C is a (P, Q) is angle compatibility, C s (P, Q) is proportional compatibility, C p (P, Q) is position compatibility, C v (P, Q) is visibility compatibility;
s3-5: calculating electrostatic force F e : an electrostatic attraction force F is provided between each corresponding subdivision point of the pair of interacting edges e For the edge P, it is subjected to the following electrostatic force formula:
where E is the set of all edges that interact with P except edge P, C e (P, Q) is an edge compatibility metric, P i Is the edge subdivision point on edge P, q i Is the edge subdivision point of all interacted edges except edge P;
s3-6: calculating the resultant force at each edge subdivision point: each edge point is subjected to two forces, one being the spring force F exerted on that point by the adjacent subdivision point of that point s One being the electrostatic force F exerted on the point by the subdivision of the interacting edge e Resultant force F pi The calculation formula is as follows:
s3-7: setting an initial step S 0 : the step size determines the distance a point moves in the direction of the resultant force applied to it;
s3-8: setting a fixed number of cycle times C: performing a fixed number of iterative steps I in each loop; i 0 Is the number of iterative steps during the first cycle; after executing one cycle, the subdivision point is followed by starting the next cycleThe number of P is doubled, and the step length S is halved; the iteration step I of each period is also reduced according to the previously set iteration times reduction rate;
s3-9: edge binding and visualization are realized on the vortex motion track;
s4: and (3) classifying the vortex channels obtained by the step (S3) to extract a main channel and a bypass channel of the vortex motion track.
2. The method for extracting and visualizing a vortex migration channel according to claim 1, wherein the step S1 is specifically:
s1-1: generation of particles: the generation of vortex particles is controlled by utilizing a random function, and the random function controls the generation position, life cycle and number of particles generated in unit time interval of the particles, so that newly generated particles are randomly distributed in the grid;
s1-2: particle attribute initialization: initializing the vortex particle attributes represents which attributes the newly generated vortex particles possess; in the vortex visualization process, particle generation, movement and extinction are realized by changing particle properties;
s1-3: movement of particles: after attribute assignment is carried out on vortex particles through a random function, the attribute of the vortex particles changes along with the time, and the update of the particle attribute occurs in the time step of each frame; drawing a line segment according to the current frame position and the next frame position of the vortex particle, and repeating the steps to obtain the movement track of the vortex particle; the longitude and latitude of the position of the next frame of the particle are calculated through the speed of the particle, and the speed of the particle is obtained through bilinear interpolation;
s1-4: particle extinction: as the particles move, the life cycle of the particles gradually decreases, and when the life cycle of the particles decreases to zero, the particles die;
s1-5: drawing particles: vortex dynamic visualization is implemented on a visualization platform.
3. The vortex migration channel extraction and visualization method of claim 1 wherein in S3-4:
for angle compatibility C a (P, Q): introduction of angle compatibility C a (P,Q)∈[0,1]：
C a (P，Q)＝|cos(α)|
Where P, Q are two edges, α is the angle between P, Q, the greater the angle between edges P and Q, C a The smaller (P, Q); if P and Q are orthogonal, C a (P, Q) is 0, if P and Q are parallel, C a (P, Q) is 1;
for proportional compatibility C s (P, Q): introducing scale compatibility C s (P,Q)∈[0,1]：
Wherein P, Q are two sides, l avg The average length of two sides P and Q is that min (P and Q) is that of the short side between the two sides P and Q, and max (P and Q) is that of the long side between the two sides P and Q; if the lengths of P and Q are equal, C s (P, Q) is 1, cs (P, Q) is 0 if the ratio between the longest and shortest edges is close to ≡;
for position compatibility C p (P, Q): introducing site compatibility C p (P,Q)∈[0,1]：
C p (P，Q)＝l avg /(l avg +||P m -Q m ||)
Wherein P, Q is two sides, P m And Q m Is the center point of sides P and Q, ||P m -Q m I is P m And Q m A distance therebetween; if P m And Q m Consistent, C p (P, Q) is 1, if P m –Q m I is close to ≡c p (P, Q) is 0;
compatibility C for visibility v (P, Q): introducing visibility compatibility C v (P,Q)∈[0,1]：
C v ＝(P，Q)＝min(V(P，Q)，V(Q，P))
Where V (P, Q) is the visibility of side P to side Q, and V (Q, P) is the visibility of side Q to side P; the visibility for the sides P to Q is obtained by extending a "line of sight band" from Q, and the intersection of the extension line of P and the "line of sight band" is I 0 And I 1 ，P m Is the midpoint of the line segment P, I m Is I 0 And I 1 Is a midpoint of (2); if P m And I m Overlap, C v (P, Q) is 1, otherwise C v (P, Q) is 0.
4. The method for extracting and visualizing a scroll migration channel according to claim 1, wherein in S4, an array is defined in the edge binding process to save each edge having a correlation with other edges, and if the other edge associated with a certain edge is greater than 10 edges of the main channel, otherwise the edge of the bypass channel is recorded in the array and rendered separately.
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