CN115035211A - WebGL-based visual rendering method for generating digital twin thermodynamic diagram image projection fusion - Google Patents
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Abstract
The invention relates to the technical field of digital twinning, in particular to a visual rendering method for generating digital twinning thermodynamic diagram image projection fusion based on WebGL, which comprises the steps of cloning and extracting a region model needing generating thermodynamic diagram textures in a virtual scene constructed based on a physical scene, and carrying out cube UV mapping on the extracted model textures; mapping a scatter set of the distribution of the heat source in the entity domain in a texture mapping UV coordinate system to generate a square picture with the distribution of the heat source in the entity domain; constructing a twin-domain heat source distribution two-dimensional coordinate in a Canvas, naming and identifying a twin-domain three-dimensional model, and then storing and exporting a GLTF format file; analyzing a GLTF format file based on WebGL, obtaining model information for storing UV mapping information, and constructing the mapping between a thermal image projection fusion twin domain and an entity domain. The invention effectively solves the technical problems in the prior art.
Description
Technical Field
The invention relates to the technical field of digital twinning, in particular to a visual rendering method for generating digital twinning thermodynamic diagram image projection fusion based on WebGL.
Background
Digital twin (digitaltrin) is to utilize big data technology to store data information of the physical world in a big data cluster in a virtual simulation mode, so that the data storage and calculation of the real world are more efficiently improved; in recent years, with the development of CPS (Cyber-Physical Svstems) technology, the digital twinning technology is gradually becoming a focus of research. By constructing twin of physical entities in the digital space, and virtual-real symbiosis of the physical space and the digital space, the comprehensive, real and objective mapping of the digital world to the physical world is realized. By virtue of the above technical advantages, the digital twinning technology continues to develop rapidly. The application field of the method is gradually expanded to the fields of product design, product manufacturing, medical analysis, engineering construction and the like, and a great promoting effect is generated in the related fields. The technical advantages of the digital twin technique bring a qualitative fly-through to model-based application analysis.
When the digital twin technology is actually applied, taking applications such as loss monitoring of industrial facility equipment, early warning monitoring of sensors (natural gas stations, gas collecting stations, water conservancy sewage treatment stations and the like), passenger flow monitoring, visitor volume monitoring and the like (smart cities, smart parks and the like) as examples, the digital twin technology can fully utilize physical models and sensor data, integrate multidisciplinary, multi-physical quantity and multi-scale simulation processes, and complete mapping in a virtual space, so that the full life cycle process of a corresponding entity is reflected. However, an interface of thermal image projection fusion is lacked, monitoring data obtained in the entity domain cannot be transmitted and reflected in the twin domain, result diagnosis and prediction in a subsequent stage are influenced, and processing efficiency is reduced.
Disclosure of Invention
In view of the above, the present invention provides a visual rendering method for generating a digital twin thermodynamic diagram image projection fusion based on WebGL, so as to solve the above technical problems in the prior art.
In order to achieve the purpose, the visual rendering method for generating the digital twin thermodynamic diagram image projection fusion based on the WebGL adopts the following technical scheme:
the visual rendering method for generating the digital twin thermodynamic diagram image projection fusion based on the WebGL comprises the following steps of:
in a virtual scene constructed based on a physical scene, carrying out clone extraction on a region model needing to generate thermodynamic diagram textures, and carrying out cube UV mapping on the extracted model textures;
mapping a scatter set of entity domain heat source distribution in a texture mapping UV coordinate system to generate a square picture with entity domain heat source distribution, constructing a twin domain heat source distribution two-dimensional coordinate in a Canvas, naming and identifying a twin domain three-dimensional model, and then storing and exporting a GLTF format file;
constructing a twin-domain heat source distribution two-dimensional coordinate interface in a Canvas based on a thermodynamic diagram principle, and drawing an initialized square thermodynamic diagram texture;
analyzing a GLTF format file based on WebGL, obtaining model information for storing UV mapping information, and constructing the mapping between a thermal image projection fusion twin domain and an entity domain.
Further, in a virtual scene constructed based on a physical scene, clone extraction of model mesh vertex information is performed on an Area needing generating a thermodynamic texture, a three-dimensional mesh model HeatMap _ Area01 independent of the original virtual scene is generated, and cube UV mapping is performed on the texture of the three-dimensional mesh model HeatMap _ Area 01.
Further, the implementation step of the UV mapping of the cube includes: mapping the two-dimensional texture space T (u, v) to a cube surface T '(x', y ', z') by S mapping using a cube intermediate space;
and mapping the texture on the surface of the cube to the three-dimensional grid model surface O (x, y, z) through O mapping to generate a grid model HeatMap _ Arae01_ UV with square UV texture information, wherein the UV coordinate points corresponding to all grid vertexes of the HeatMap _ Arae01_ UV are mapped in a square with the side length of 1.
Further, processing the three-dimensional mesh model: and generating a Texture _ Square picture with heat source distribution information by using spatial point information { P1, P2,. multidot.p 19, P20} of a physical heat source distributed on the three-dimensional grid model, and a scatter set { Q1, Q2,. multidot.q 19, Q20} in a space coordinate system corresponding to the HeatMap _ Arae01_ UV Texture.
Further, processing the square picture: based on a Canvas label in Html5, mapping the scattered point set point location information with the distribution of the heat source in the picture Texture _ Square into a Square Canvas with the length and the width of 1000 pixels respectively, thereby obtaining a two-dimensional coordinate array of a Position scattered point set of the heat source point location in the 2D Canvas.
Further, in a virtual scene constructed based on a physical scene, texture mapping is carried out on other areas in the scene needing to generate a heat source, new grid models which are mapped are named as HeatMap _ Arae02_ UV, HeatMap _ Area03_ UV and HeatMap _ Arean _ UV in sequence, and information is stored and exported for the three-dimensional grid models which are subjected to the texture mapping and the scene grid models by using a GLTF model format.
Further, the step of drawing the initialized square thermodynamic texture comprises: taking two-dimensional coordinate values of the Position scatter set as a circle center, taking [ (0,255,255), (0,255,0), (255,0,0) ] cyan, green, yellow and red as color band gradients, respectively drawing radial gradient circles in a square 2D Canvas with the length and width of 1000 pixels by taking Radius equal to 10 pixels and Radius equal to a section [1,30] random value pixels, and generating a square initialization thermal Texture map Texture _ HeatMap _ Init with the side length of 1000.
Further, processing the square initialization thermal texture map: processing the square initialization thermal texture map: and transferring the square initialization thermal Texture map Texture _ HeatMap _ Init to the material of the HeatMap _ Arae01_ UV, so that the physical domain thermal source distribution point location information is transferred to the two-dimensional Canvas at the space position of the twin-domain three-dimensional mesh model through the UV coordinate system and the rendering fusion of the initialization thermal Texture is carried out in the twin domain.
Further, the specific steps of mapping and rendering fusion of the magnitude of the entity domain heat source in the thermal texture of the three-dimensional mesh model in the twin domain include: multiplying the radius R of the radial gradual change circle by a weight value K of a magnitude, wherein the K is the ratio of the magnitude of the entity domain at a certain moment to the maximum value Kmax of the magnitude interval: radius = R (K/Kmax), generating a square thermal Texture map Texture _ HeatMap _ R (K/Kmax) in the twin domain, mapping the magnitude in the entity domain, and transferring the thermal Texture map Texture _ HeatMap _ R (K/Kmax) to the material of the HeatMap _ Arae01_ UV mesh model, wherein the magnitude of the entity domain heat source is also mapped and rendered in the thermal Texture of the three-dimensional mesh model in the twin domain.
The visual rendering method based on the WebGL generated digital twin thermodynamic diagram image projection fusion has the advantages that:
1) mapping an entity domain heat source space information interface in a twin domain three-dimensional model texture space;
2) mapping an entity domain heat source magnitude information interface in the twin domain heat pattern;
3) an interface for thermal image projection fusion is provided for the digital twin field in the related fields of passenger flow monitoring, facility equipment loss monitoring and sensor early warning monitoring in the industrial field;
4) monitoring data such as sensors and the like in the entity domain can be transmitted and embodied in the twin domain;
5) the method provides an efficient and feasible solution for the related fields of digital twin field passenger flow volume monitoring, industrial field facility equipment loss monitoring, sensor early warning and monitoring, and result diagnosis and prediction in the subsequent stage.
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FIG. 1 is a schematic diagram of the UV mapping of the cube of the texture of the extracted region model in step S1 according to the present invention;
FIG. 2 is a block diagram of a texture mapping UV coordinate system for mapping a set of physical domain thermal source distribution scatters to generate a square image with physical domain thermal source distribution;
FIG. 3 is a diagram of a picture with entity domain heat source distribution point location information mapped into an interval [0, 1000] two-dimensional array in a canvas according to the present invention;
FIG. 4 is a thermal texture diagram of the present invention, wherein the coordinate of the distribution point of the thermal source in the entity domain is used as the center of a circle, and different colors are used as color bands, and the thermal texture diagram is initialized;
FIG. 5 is a schematic diagram of analyzing a GLTF file based on WebGL, obtaining model information for storing UV mapping information, and performing rendering of an initialization thermal texture map and a thermal texture map with entity domain value weight values;
FIG. 6 is a thermal image projection fusion mapping result diagram of multi-region solid domain and twin domain in the present invention;
fig. 7 is a flowchart of a visualization rendering method for generating a digital twin thermodynamic diagram image projection fusion based on WebGL.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It should be apparent that the described embodiments are only some of the embodiments of the present invention, and not all of them. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention, are within the scope of the invention.
The invention aims to solve the problem that a thermal image projection fusion interface is provided for the digital twin technology in the related fields of passenger flow volume monitoring, loss monitoring of facility equipment in the industrial field and early warning and monitoring of a sensor, so that monitoring data such as the sensor in an entity domain can be transmitted and reflected in the twin domain, and an efficient and feasible solution is provided for result diagnosis and prediction in the related fields of passenger flow volume monitoring, loss monitoring of facility equipment in the industrial field and early warning and monitoring of the sensor.
Based on the above object, the visual rendering method for generating digital twin thermodynamic diagram image projection fusion based on WebGL provided by the invention comprises the following steps:
in a virtual scene constructed based on a physical scene, carrying out clone extraction on a region model needing to generate thermodynamic diagram textures, and carrying out cube UV mapping on the extracted model textures;
mapping a scatter set of entity domain heat source distribution in a texture mapping UV coordinate system to generate a square picture with entity domain heat source distribution, constructing a twin domain heat source distribution two-dimensional coordinate in a Canvas, naming and identifying a twin domain three-dimensional model, and then storing and exporting a GLTF format file;
constructing a twin-domain heat source distribution two-dimensional coordinate interface in a Canvas based on a thermodynamic diagram principle, and drawing an initialized square thermodynamic diagram texture;
analyzing a GLTF format file based on WebGL, obtaining model information for storing UV mapping information, and constructing the mapping between a thermal image projection fusion twin domain and an entity domain.
For digital three-dimensional mesh models, there are two most important coordinate systems. One is a three-dimensional space coordinate system (x, y, z) for constructing vertex information of a three-dimensional model mesh structure; the other is the UV coordinate system (u, v) which is resident on the polygon mesh vertex and is used for defining the two-dimensional texture space of the three-dimensional model. UV points are points associated with vertices of the polygon mesh, and pixel points on the texture map may be mapped to vertices on the model mesh to provide position information required for applying texture to an object, and thus, in the present application, a UV coordinate system is employed to provide position information required for applying texture to an object.
As shown in fig. 1, in a virtual scene constructed based on a physical scene, clone extraction of model mesh vertex information is performed for an Area where a thermodynamic texture needs to be generated, a three-dimensional mesh model HeatMap _ Area01 independent of the original virtual scene is generated, and cube UV mapping is performed on the texture of the three-dimensional mesh model HeatMap _ Area 01.
The implementation steps of the UV mapping of the cube comprise: based on a two-step texture mapping technology, firstly using a cube intermediate space, and mapping a two-dimensional texture space T (u, v) to a cube surface T '(x', y ', z') through S mapping; and mapping the texture on the surface of the cube to the surface O (x, y, z) of the three-dimensional grid model HeatMap _ Area01 through O mapping to generate a grid model HeatMap _ Area01_ UV with square UV texture information, wherein the UV coordinate points corresponding to all grid vertexes of the HeatMap _ Area01_ UV are mapped in a square with the side length of 1, namely the scattered point set P (u, v) of the HeatMap _ Area01_ UV texture space is in the interval of [0, 1 ].
As shown in fig. 2, spatial point information (P1, P2, a.., P19, P20) of a physical heat source distributed on a three-dimensional mesh model HeatMap _ Arae01 mesh model, a scatter set (Q1, Q2, a.., Q19, Q20) in a corresponding HeatMap _ Area01_ UV Texture spatial coordinate system, a scatter set Square picture Texture _ Square having heat source distribution information is generated; as shown in fig. 3, based on a Canvas tag in Html5, a scatter set having entity domain heat source distribution in a picture Texture _ Square is mapped in a Square Canvas with a length and a width of 1000 pixels, so as to obtain a two-dimensional coordinate array of a Position scatter set of heat source points in the 2D Canvas, where the two-dimensional coordinate array is the mapping point information of the entity domain heat source in the twin domain, and is also a parameter value used in constructing a twin domain heat source distribution two-dimensional coordinate interface.
Similarly, texture mapping can be performed on other areas needing to generate a heat source in a virtual scene constructed based on a physical scene, new mesh models which are mapped are named as HeatMap _ Arae02_ UV, HeatMap _ Area03_ UV and HeatMap _ Arean _ UV in sequence, and information of the three-dimensional mesh models which are subjected to texture mapping and the scene mesh models is stored and exported by using a GLTF model format;
based on the thermodynamic principle, a graphical representation of the geographical area in which the visitor is located is displayed in a particularly highlighted form. In reality, we need at least two dimensional parameters to obtain thermodynamic diagram representation of a certain geographic area. One is the position of the area, namely the coordinate value; the other is the number of people gathered in the area or the temperature, i.e., magnitude, of the area.
Based on the Canvas tag in Html5, graphics can be dynamically drawn in a 2D Canvas two-dimensional Canvas. And displaying the thermodynamic diagram of the magnitude value of a certain coordinate point in the corresponding entity domain, and only drawing a transparency Alpha radial gradient circle corresponding to the magnitude value at each coordinate point, and simultaneously rendering customized color band values for pixel points with different Alpha gradient gradients in the Canvas. A special highlighted version of the diagram can be drawn in accordance with the thermodynamic diagram principle.
As shown in fig. 4, the step of drawing the initialized square thermodynamic texture includes: taking two-dimensional coordinate values of the Position scatter set as a circle center, taking [ (0,255,255), (0,255,0), (255,0,0) ] cyan, green, yellow and red as color band gradients, respectively drawing radial gradient circles in a square 2D Canvas with the length and width of 1000 pixels by taking Radius equal to 10 pixels and Radius equal to a section [1,30] random value pixels, and generating a square initialization thermal Texture map Texture _ HeatMap _ Init with the side length of 1000.
As shown in the left half of fig. 5, the square initialization thermal texture map is processed: and transferring the square initialization thermodynamic Texture map Texture _ HeatMap _ Init to a material of HeatMap _ Area01_ UV, so that the physical domain thermodynamic source distribution point location information is transferred to the two-dimensional Canvas at the space position of the twin-domain three-dimensional mesh model through a UV coordinate system, and rendering fusion of the initialization thermodynamic Texture, namely a coordinate interface of digital twin thermodynamic map image projection fusion, is carried out in the twin domain.
In addition, in addition to the heat source coordinate information, the entity domain also has heat source quantity values (i.e. temperature values, customer flow values, visitor quantity values, etc. in the actual service demand).
The specific steps of mapping and rendering fusion of the magnitude of the entity domain heat source in the thermal texture of the three-dimensional mesh model in the twin domain comprise: multiplying the radius R of the radial gradual change circle by a weight value K of a magnitude, wherein the K is the ratio of the magnitude of the entity domain at a certain moment to the maximum value Kmax of the magnitude interval: radius = R (K/Kmax), generating a square thermal Texture map Texture _ HeatMap _ R (K/Kmax) in the twin domain, mapping the magnitude in the entity domain, and transferring the thermal Texture map Texture _ HeatMap _ R (K/Kmax) to the material of the HeatMap _ Arae01_ UV mesh model, wherein the magnitude of the entity domain heat source is also mapped and rendered in the thermal Texture of the three-dimensional mesh model in the twin domain, namely, the magnitude interface of the digital twin heat map image projection fusion. Up to this point, a method for generating a visualization rendering of digital twin thermodynamic image projection fusion based on WebGL has been implemented.
In actual service requirements, an entity domain is integrated into one region by a plurality of heat source distribution points, and thermodynamic diagram representation of multiple regions in the twin domain and multiple gradients in the regions is performed. As shown in fig. 6, by using the method for multiple times, thermal image projection fusion between the multi-region entity domain and the twin domain can be realized.
It is emphasized that the most critical point of the digital twin thermal image projection fusion is: firstly, a mapping relation of spatial information of heat source distribution in an entity domain in a texture space coordinate system of a three-dimensional mesh model of a twin domain is constructed. Secondly, constructing a twin-domain heat source distribution two-dimensional coordinate interface in a Canvas based on a thermodynamic diagram principle and drawing a thermodynamic diagram texture. Thirdly, mapping interfaces of point location information and magnitude information in the entity domain based on the thermodynamic diagram principle in the twin domain thermodynamic diagram texture are respectively constructed; aiming at the three key points, namely, the projection mapping and the fusion of the heat source space information and the magnitude value information of the entity domain in the texture space of the twin-domain three-dimensional mesh model are communicated and connected, so that the transmission and the presentation of data between the virtual domain and the real domain are feasible.
The specific flow block diagram can refer to fig. 7, and the visual rendering method for generating the digital twin thermodynamic diagram image projection fusion based on the WebGL has the advantages that:
1) mapping an entity domain heat source space information interface in a twin domain three-dimensional model texture space;
2) mapping an entity domain heat source magnitude value information interface in the twin domain heat pattern;
3) an interface for thermal image projection fusion is provided for the digital twin field in the related fields of passenger flow monitoring, facility equipment loss monitoring and sensor early warning monitoring in the industrial field;
4) monitoring data such as sensors and the like in the entity domain can be transmitted and embodied in the twin domain;
5) the method provides an efficient and feasible solution for the related fields of passenger flow monitoring in the digital twin field, facility equipment loss monitoring in the industrial field and sensor early warning and alarm monitoring in the subsequent stage.
In the present invention, unless otherwise explicitly specified or limited, for example, it may be fixedly attached, detachably attached, or integrated; can be mechanically or electrically connected; the terms may be directly connected or indirectly connected through an intermediate, and may be communication between two elements or interaction relationship between two elements, unless otherwise specifically limited, and the specific meaning of the terms in the present invention will be understood by those skilled in the art according to specific situations.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (9)
1. The visual rendering method for generating digital twin thermodynamic diagram image projection fusion based on WebGL is characterized by comprising the following steps of:
in a virtual scene constructed based on a physical scene, carrying out clone extraction on a region model needing to generate thermodynamic diagram textures, and carrying out cube UV mapping on the extracted model textures;
mapping a scatter set of entity domain heat source distribution in a texture mapping UV coordinate system, generating a square picture with entity domain heat source distribution, constructing a twin domain heat source distribution two-dimensional coordinate in a Canvas, naming and storing and exporting a GLTF format file after a twin domain three-dimensional model is named and identified;
constructing a twin-domain heat source distribution two-dimensional coordinate interface in a Canvas based on a thermodynamic diagram principle, and drawing an initialized square thermodynamic diagram texture;
analyzing a GLTF format file based on WebGL, obtaining model information for storing UV mapping information, and constructing the mapping between a thermal image projection fusion twin domain and an entity domain.
2. The WebGL-based generation of the visualization rendering method for projection fusion of the digital twin thermodynamic diagram based on the WebGL of claim 1, wherein: in a virtual scene constructed based on a physical scene, clone extraction of model mesh vertex information is carried out on an Area needing to generate a thermodynamic diagram texture, a three-dimensional mesh model HeatMap _ Area01 independent of the original virtual scene is generated, and cube UV mapping is carried out on the texture of the three-dimensional mesh model HeatMap _ Area 01.
3. The WebGL-based visual rendering method for generating digital twin thermodynamic diagram image projection fusion as claimed in claim 2, wherein the implementation step of the cube UV mapping comprises the following steps: mapping the two-dimensional texture space T (u, v) to a cube surface T '(x', y ', z') by S mapping using a cube intermediate space;
and mapping the texture on the surface of the cube to the three-dimensional grid model surface O (x, y, z) through O mapping to generate a grid model HeatMap _ Arae01_ UV with square UV texture information, wherein the UV coordinate points corresponding to all grid vertexes of the HeatMap _ Arae01_ UV are mapped in a square with the side length of 1.
4. The WebGL-based visual rendering method for generating digital twin thermodynamic diagram image projection fusion of claim 3, wherein the three-dimensional mesh model is processed by: and generating a scatter-point set Square picture Texture _ Square with heat source distribution information by using spatial point information { P1, P2,. multidot., P19, P20} of a physical heat source distributed on the three-dimensional grid model, and a scatter set { Q1, Q2,. multidot., Q19, Q20} in a spatial coordinate system corresponding to the HeatMap _ Arae01_ UV Texture.
5. The WebGL-based visual rendering method for generating digital twin thermodynamic diagram image projection fusion as claimed in claim 4, wherein the square picture is processed by: based on a Canvas label in Html5, mapping the scattered point set point location information with the distribution of the heat source in the picture Texture _ Square into a Square Canvas with the length and the width of 1000 pixels respectively, thereby obtaining a two-dimensional coordinate array of a Position scattered point set of the heat source point location in the 2D Canvas.
6. The visual rendering method based on WebGL generation digital twin thermodynamic diagram image projection fusion of any one of claims 3 to 5, characterized in that: in a virtual scene constructed based on a physical scene, texture mapping is carried out on other areas in the scene needing to generate a heat source, new grid models which are mapped are named as HeatMap _ Arae02_ UV, HeatMap _ Area03_ UV and HeatMap _ Arean _ UV in sequence, and information is stored and exported for the three-dimensional grid models which are subjected to the texture mapping and the scene grid models by using a GLTF model format.
7. The WebGL-based visual rendering method for generating digital twin thermodynamic diagram projection fusion according to claim 5, wherein the step of drawing an initialized square thermodynamic diagram texture comprises: taking two-dimensional coordinate values of the Position scatter set as a circle center, taking [ (0,255,255), (0,255,0), (255,0,0) ] cyan, green, yellow and red as color band gradients, respectively drawing radial gradient circles in a square 2D Canvas with the length and width of 1000 pixels by taking Radius equal to 10 pixels and Radius equal to a section [1,30] random value pixels, and generating a square initialization thermal Texture map Texture _ HeatMap _ Init with the side length of 1000.
8. The WebGL-based visual rendering method for generating digital twin thermodynamic diagram image projection fusion of claim 7, wherein the square initialization thermodynamic texture map is processed by: and transferring the square initialization thermal Texture map Texture _ HeatMap _ Init to the material of the HeatMap _ Arae01_ UV, so that the physical domain thermal source distribution point location information is transferred to the two-dimensional Canvas at the space position of the twin-domain three-dimensional mesh model through the UV coordinate system and the rendering fusion of the initialization thermal Texture is carried out in the twin domain.
9. The WebGL-based visual rendering method for generating digital twin thermodynamic map image projection fusion as claimed in claim 8, wherein the specific steps of mapping and rendering fusion of magnitude of an entity domain heat source in a thermal texture of a three-dimensional mesh model in a twin domain include: multiplying the radius R of the radial gradual change circle by a weight value K of a magnitude, wherein the K is the ratio of the magnitude of the entity domain at a certain moment to the maximum value Kmax of the magnitude interval: radius = R (K/Kmax), generating a square thermal Texture map Texture _ HeatMap _ R (K/Kmax) in the twin domain, mapping the magnitude in the entity domain, and transferring the thermal Texture map Texture _ HeatMap _ R (K/Kmax) to the material of the HeatMap _ Arae01_ UV mesh model, wherein the magnitude of the entity domain heat source is also mapped and rendered in the thermal Texture of the three-dimensional mesh model in the twin domain.
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| CN116681871B (en) * | 2023-07-31 | 2023-10-31 | 山东捷瑞数字科技股份有限公司 | Digital twinning-oriented model vision auxiliary positioning method and device |
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