CN113495933A

CN113495933A - Vector tile display method and system

Info

Publication number: CN113495933A
Application number: CN202010196936.1A
Authority: CN
Inventors: 曾刚; 曾飞传; 王焰辉
Original assignee: Zhongke Star Map Co ltd
Current assignee: Zhongke Star Map Co ltd
Priority date: 2020-03-19
Filing date: 2020-03-19
Publication date: 2021-10-12

Abstract

The invention discloses a method and a system for displaying vector tiles, wherein the method comprises the steps of obtaining required vector tiles according to a next view, and determining newly added vector tiles and removed vector tiles compared with the next view; requesting vector data corresponding to the newly added vector tiles from a server; and drawing the vector data corresponding to the newly added vector tile acquired from the server and displaying the next view. By applying the scheme of the invention, the dynamic scheduling of the vector data on the Cesum can be realized, and the scheduling and calculation amount of the vector data is reduced; and all vector drawing objects are drawn in batch, so that the vector data can be drawn efficiently.

Description

Vector tile display method and system

[ technical field ] A method for producing a semiconductor device

The invention relates to a computer application technology, in particular to a vector tile display method and a system.

[ background of the invention ]

With the fact that the Web GIS is deeper and deeper into the life of people, the requirements of people on the aspects of response efficiency, interactivity, rendering effect and the like of the Web GIS are higher and higher, and the vector tile map technology can well solve the problems aiming at the performance bottleneck of the grid tile map in the aspects of high-definition screen display, data updating and user exchange.

The vector tile map technology is the same as the grid tile map technology, the LOD pyramid technology is also adopted in the vector tile map technology, vector data sources with different scales are cut into vector tiles with corresponding levels, the tiles are stored in a GeoJson or protobuf vector format at a server side to issue a tile service function, when a client side initiates a tile data request, the server side returns the vector tiles, and the client side directly or indirectly draws the vector data on a graphic display device after receiving the vector data.

In recent years, the use of the dynamic scheduling vector tile technology in a two-dimensional geographic information system has matured, and currently, a two-dimensional display client has matured in the aspect of drawing and displaying, typically, display components such as MapBox, OpenLayers and the like. However, there is still a difficult breakthrough in the three-dimensional geographic information system, a typical usage mode is to deploy vector data at a server and divide the vector data into vector tiles, and a client sends a tile data request to the server through a scheduling mechanism, and there are two processing modes at this time: one is that the server side renders the corresponding vector tiles into pictures and transmits the pictures to the client side for rendering and display; the other mode is that the server side directly transmits the vector tiles to the client side, and the client side renders the vector tiles into pictures for rendering and displaying. In either case, we can see that the finally displayed vector data is actually not a true vector object, but rather a non-modifiable semi-transparent picture.

The vector tile technology is mainly divided into two parts, namely data deployment and release of a server and display of a client. The functions of the server side, such as tile segmentation, storage, quick retrieval, service release and the like, are very mature, and the display part of the client side, particularly the display part on the three-dimensional platform, is still rough. The method mainly shows that vector data is rasterized and attached to the three-dimensional earth as a picture, and the attribute and the function which the vector data should have are lost. The display effect is visualized as blurring or jagging, and no vector data is smooth and fine.

For example, cesum is a geographic information three-dimensional earth engine developed based on Web GL, which can run on most browsers and mobile terminals, and has been widely used and popularized in recent years. As a visualization software for geospatial data, the amount of data carried by the software is limited, especially for displaying vector data, and in order to solve the problem of vector data display efficiency, the dynamic scheduling vector tile technology is researched and used more and more frequently. The mode adopted by the Cesium three-dimensional engine is the second mode, and in the three-dimensional rendering client, after the client receives the vector data, the vector tiles are drawn into two-dimensional pictures, and then the two-dimensional pictures are rendered and drawn on the earth model in a raster picture mode. The display mode has the advantages that the vector data can be rapidly displayed on the three-dimensional earth without occupying too large computing resources, the display mode is almost equivalent to the display of image data in efficiency, but the defects are obvious, and because the vector quantity is rasterized, when the vector data is displayed on the earth surface, the shape or the display effect of the vector data is greatly reduced after the image is stretched, for example, lines are not smooth, characters are attached to the surface, objects cannot be clicked to inquire the attributes, and the like.

[ summary of the invention ]

Aspects of the present application provide a vector tile display method, system, device, and storage medium capable of displaying a vector tile.

In one aspect of the present application, a method for displaying vector tiles is provided, which includes the following steps:

acquiring a required vector tile according to a next view, and determining a newly added vector tile and a removed vector tile compared with the next view;

requesting vector data corresponding to the newly added vector tiles from a server;

and drawing the vector data corresponding to the newly added vector tile acquired from the server and displaying the next view.

The above aspect and any possible implementation further provide an implementation, where the obtaining the required vector tiles according to the next view includes:

the number of the vector tile corresponding to the next view is obtained.

The above-described aspect and any possible implementation further provides an implementation, wherein the determining new vector tiles and removed vector tiles compared to the next view further comprises:

and updating the vector tile list of the current view to be used as the vector tile list of the next view.

As to the foregoing aspect and any possible implementation manner, there is further provided an implementation manner, where requesting, from a server, vector data corresponding to the newly added vector tile includes:

and sending the number of the newly added vector tile to a server to request corresponding vector data.

As to the foregoing aspect and any possible implementation manner, there is further provided an implementation manner, where the drawing and displaying the vector data corresponding to the newly added vector tile obtained from the server includes:

creating a corresponding vector drawing object for the newly added vector tiles;

and deleting the corresponding vector drawing object for the removed vector tile.

As for the above-mentioned aspect and any possible implementation manner, further providing an implementation manner, where creating, for the newly added vector tile, a corresponding vector drawing object includes:

inquiring the newly added vector tile in a currently displayed vector drawing object list according to the ID of the newly added vector tile;

if the query is not found, creating a vector drawing object for the query, and adding the vector drawing object into a currently displayed vector drawing object list;

and if the vector drawing object is inquired, merging.

The above aspect and any possible implementation further provide an implementation in which the rendering the corresponding vector rendering object includes;

and drawing the vector data in batch.

In another aspect of the present invention, there is provided a vector tile display system comprising:

the calculation module is used for acquiring the required vector tiles according to the next view and determining the newly added vector tiles and the removed vector tiles compared with the next view;

the request module is used for requesting the server for the vector data corresponding to the newly added vector tiles;

and the drawing module is used for drawing the vector data corresponding to the newly added vector tile acquired from the server and displaying the next view.

In another aspect of the present invention, a computer device is provided, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method as described above when executing the program.

In another aspect of the invention, a computer-readable storage medium is provided, on which a computer program is stored, which program, when being executed by a processor, is adapted to carry out the method as set forth above.

Based on the introduction, the scheme of the invention can realize the dynamic scheduling of the vector data on the Cesum, and reduce the scheduling and calculation amount of the vector data; and all vector drawing objects are drawn in batch, so that the vector data can be drawn efficiently.

[ description of the drawings ]

FIG. 1 is a flow chart of a method for displaying vector tiles in accordance with the present invention;

FIG. 2 is a block diagram of a vector tile display system according to the present invention;

fig. 3 illustrates a block diagram of an exemplary computer system/server 012 suitable for use in implementing embodiments of the invention.

[ detailed description ] embodiments

In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

FIG. 1 is a flowchart of an embodiment of a method for displaying vector tiles according to the present invention, as shown in FIG. 1, including the following steps:

step S11, acquiring the required vector tiles according to the next view, and determining the newly added vector tiles and the removed vector tiles compared with the next view;

step S12, requesting the vector data corresponding to the newly added vector tile from the server;

and step S13, drawing the vector data corresponding to the newly added vector tile acquired from the server and displaying the next view.

The execution body of the method is a three-dimensional display client.

In one preferred implementation of step S11,

and acquiring required vector tiles according to the next view, and determining the vector tiles which are added and removed compared with the current view.

Preferably, the data request of the user, that is, the next view of the earth model that the user intends to show, is obtained according to the operation of the user on the earth model in the three-dimensional display client, and then the vector tile corresponding to the next view is obtained.

Preferably, the three-dimensional rendering server stores the vector data that has been cut in advance. The vector tile map technology adopts a pyramid model to segment vector data sources with different scales into vector tiles of corresponding levels. Preferably, the vector data source is a description line file of vector data, the current vector slice is mainly stored in a GeoJson or protobuf vector format at a server, and a quadtree space index is respectively established for each vector tile in the storage process.

Preferably, the pyramid model adopts an 18-degree pyramid model; the tile numbers are coded by 14 characters, a quadtree space index is established for each vector tile to form a tile storage index array, and the position offset of each vector tile in the tile storage index array is the number of the tile in the pyramid model.

Preferably, in the slicing process of the vector data source, Web mercator projection is adopted to ensure the consistency of the map data slices, so that the rapid conversion from the three-dimensional space coordinate of the client to the row-column system structure value to the geodetic coordinate is realized.

Preferably, in order to obtain the vector data corresponding to the vector tile corresponding to the next view, first, the vector tile number array corresponding to the next view needs to be obtained; and then acquiring the corresponding vector data according to the vector tile number array.

Preferably, the data request of the user includes a data layer range corresponding to a next view, and the attributive hierarchy and the corresponding number of the vector tile corresponding to the next view in the quadtree are determined according to the data layer range, where the number is a tile number (layer row and column) in a pyramid model constructed by a sesium three-dimensional earth GIS engine. For example, the tile golden tower is organized by a quadtree model, each map tile can be uniquely identified by its layer number 1, row number X and column number y in the quadtree, and the number of the map tile is < l-X-y >.

Preferably, an interface for acquiring a quad tree scheduling object, namely, a quad tree, a variable named by surface in the global, is added to the global object, where the global object is stored in a Scene object, and the Scene object is a monolithic object inside the cesum. Since the Data Source can acquire the Scene object, the quad tree scheduling object quadruplicate is acquired indirectly through the global object. Therefore, the tile number array corresponding to the next view can be obtained from the Quadtree Primitive object for each frame. And if the scheduling result, namely the tile number array, is available, corresponding vector data can be obtained according to the tile number array.

Preferably, the three-dimensional display client sends a vector Data request to the server according to a pre-designed universal Provider, and the vector Data is acquired from the server and then transmitted back to the Data Source. Preferably, the vector data request includes a tile number array corresponding to the next view.

Preferably, in order to realize dynamic scheduling of vector data, the scheduling and calculation amount of the vector data is reduced; before sending a tile data request to the server, the new vector tiles and the removed vector tiles of the next view need to be calculated first.

Preferably, a two-dimensional key value table of the tile number and the vector Data of the vector tile corresponding to the current view is stored in the Data Source so as to calculate the added vector tile and the removed vector tile of the next view. Preferably, the two-dimensional key value table is stored in the existing caching mechanism tilereplcation Queue of Cesium.

Preferably, comparing the tile number array corresponding to the next view with the vector tile list of the current view stored in the Data Source, calculating which vector tiles need to be newly added and which vector tiles need to be removed, and updating the vector tile list of the current view to serve as the vector tile list of the next view.

In one preferred implementation of step S12,

and requesting the vector data corresponding to the newly added vector tile from a server.

Preferably, the number of the newly added vector tile is sent to the server, and the corresponding vector data is requested, so that the newly added vector tile is dynamically converted into a vector drawing object according to the requested vector data.

Preferably, the server sends the corresponding vector data to the client according to the tile number data.

In one preferred implementation of step S13,

Preferably, if the original vector tile in the Data Source is not deleted, the corresponding vector rendering object is not deleted, and the tile number of the vector tile corresponding to the current view and the vector rendering object list of the vector rendering object are stored. Preferably, the vector drawing object list is stored in the existing caching mechanism Tile replace Queue of cesum. Therefore, only the newly added vector tiles need to be considered, drawing is carried out according to the requested vector data, and the vector tiles are converted into vector drawing objects.

Preferably, for the newly added vector tile, we proceed as follows:

inquiring all vector tiles in the newly added vector tiles in a currently displayed vector drawing object list according to the IDs of the vector tiles;

if the vector drawing object is inquired, merging processing is carried out, namely the newly added vector drawing object of the vector tile and the inquired vector drawing object are merged;

the list of dependent vector tile numbers is recorded, whether it is a newly created vector object or a merged vector object.

Preferably, considering that some vector tiles in the current frame need to be replaced with vector data corresponding to vector tiles at the parent level or ancestor level of the vector because the vector data corresponding to the vector tiles cannot be found. For example, the tile in layer 12, row 100 and column 200 is replaced by computing the corresponding vector data in layer 11 because its vector data is not requested, but if the vector data in layer 12, row 100 and column 201 is also not requested, the vector data in layer 11 is also replaced, and at this time, the repeated vector tiles in layer 11 (two sub-tiles share a parent tile) appear, and at this time, the two sub-tiles need to be merged into one vector tile for display.

For the removed vector tile, we proceed as follows:

inquiring a currently displayed vector drawing object list according to the tile number of the current vector drawing object list;

if the vector drawing object is inquired, deleting the tile number from the subordinate vector tile number list of the vector drawing object;

and traversing all the vector drawing objects, judging whether the dependent vector tile number list is empty, and deleting the vector drawing objects if the dependent vector tile number list is empty.

Through the steps, the vector tiles are dynamically converted into displayable vector drawing objects. The vector tile is the requested data corresponding to the vector number (layer row and column), and is a pure data object. The vector drawing object is a Cesium drawing object created by the data object, and can be displayed in a scene only by converting the data object into the drawing object and adding the drawing object into a Cesium scene object.

Preferably, the rendering and rendering of the vector data adopts a texture-based vector rendering method, firstly, the vector data is loaded and an outsourcing rectangular range of the two-dimensional projection of the terrain tile is obtained, then screening a corresponding vector element set from the two-dimensional vector data through a screener according to the outsourcing rectangle, reading and rendering the screened vector element set in real time through a two-dimensional drawing module Render, deriving off-screen textures and superposing the terrain tiles (forming off-screen textures with coordinate attributes through transparentization), then, three-dimensional display and online rendering are carried out in WMS service released by a GIS server, specifically, texture mapping technology is utilized, when each terrain tile is rendered, the corresponding area in the off-screen texture is bound into the tile, and meanwhile, a mapping table containing vector elements and each rendering tile is established, so that subsequent vector clicking and query are facilitated.

Preferably, based on the WebGl rendering principle, all vector data can be stored in a Geometry Instance mode, and uniformly added to a prime or a group prime for batch rendering, so that the vector rendering efficiency is exerted to the highest.

Preferably, in this embodiment, the data calculation and the data scheduling of the three-dimensional display client are separated, and a calculation engine role is served by the three-dimensional rendering engine, and is responsible for updating the tile number array displayed by the current frame, and sending the vector data to be finally rendered to the GPU for rendering; and the data scheduling engine is specially responsible for processing the vector data request and reading and discarding the vector data.

According to the above-described embodiments of the present invention,

1) the dynamic scheduling of the vector data on the Cesum is realized, and the scheduling and calculation amount of the vector data is reduced;

2) by drawing all vector drawing objects in batch, efficient vector object drawing of vector data is achieved.

It should be noted that, for simplicity of description, the above-mentioned method embodiments are described as a series of acts or combination of acts, but those skilled in the art will recognize that the present application is not limited by the order of acts described, as some steps may occur in other orders or concurrently depending on the application. Further, those skilled in the art should also appreciate that the embodiments described in the specification are preferred embodiments and that the acts and modules referred to are not necessarily required in this application.

The above is a description of method embodiments, and the embodiments of the present invention are further described below by way of apparatus embodiments.

FIG. 2 is a flowchart of an embodiment of the present invention, as shown in FIG. 2, comprising:

a calculating module 21, configured to obtain a required vector tile according to a next view, and determine a newly added vector tile and a removed vector tile compared to the next view;

a request module 22, configured to request, from the server, vector data corresponding to the newly added vector tile;

and the drawing module 23 is configured to draw the vector data corresponding to the newly added vector tile obtained from the server and display a next view.

It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the terminal and the server described above may refer to corresponding processes in the foregoing method embodiments, and are not described herein again.

In the several embodiments provided in the present application, it should be understood that the disclosed method and apparatus may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments of the present application may be integrated into one processor, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.

Fig. 3 illustrates a block diagram of an exemplary computer system/server 012 suitable for use in implementing embodiments of the invention. The computer system/server 012 shown in fig. 3 is only an example, and should not bring any limitations to the function and the scope of use of the embodiments of the present invention.

As shown in fig. 3, the computer system/server 012 is embodied as a general purpose computing device. The components of computer system/server 012 may include, but are not limited to: one or more processors or processors 016, a system memory 028, and a bus 018 that couples various system components including the system memory 028 and the processors 016.

Bus 018 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures. By way of example, such architectures include, but are not limited to, Industry Standard Architecture (ISA) bus, micro-channel architecture (MAC) bus, enhanced ISA bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus.

Computer system/server 012 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system/server 012 and includes both volatile and nonvolatile media, removable and non-removable media.

System memory 028 can include computer system readable media in the form of volatile memory, such as Random Access Memory (RAM)030 and/or cache memory 032. The computer system/server 012 may further include other removable/non-removable, volatile/nonvolatile computer system storage media. By way of example only, storage system 034 may be used to read from and write to non-removable, nonvolatile magnetic media (not shown in FIG. 3, commonly referred to as a "hard drive"). Although not shown in FIG. 3, a magnetic disk drive for reading from and writing to a removable, nonvolatile magnetic disk (e.g., a "floppy disk") and an optical disk drive for reading from or writing to a removable, nonvolatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In such cases, each drive may be connected to bus 018 via one or more data media interfaces. Memory 028 can include at least one program product having a set (e.g., at least one) of program modules configured to carry out the functions of embodiments of the present invention.

Program/utility 040 having a set (at least one) of program modules 042 can be stored, for example, in memory 028, such program modules 042 including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each of which examples or some combination thereof might include an implementation of a network environment. Program modules 042 generally perform the functions and/or methodologies of embodiments of the present invention as described herein.

The computer system/server 012 may also communicate with one or more external devices 014 (e.g., keyboard, pointing device, display 024, etc.), hi the present invention, the computer system/server 012 communicates with an external radar device, and may also communicate with one or more devices that enable a user to interact with the computer system/server 012, and/or with any device (e.g., network card, modem, etc.) that enables the computer system/server 012 to communicate with one or more other computing devices. Such communication may occur through an input/output (I/O) interface 022. Also, the computer system/server 012 may communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN), and/or a public network such as the internet) via the network adapter 020. As shown in fig. 3, the network adapter 020 communicates with the other modules of the computer system/server 012 via bus 018. It should be appreciated that although not shown in fig. 3, other hardware and/or software modules may be used in conjunction with the computer system/server 012, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, among others.

The processor 016 executes programs stored in the system memory 028 to perform the functions and/or methods of the described embodiments of the present invention.

The computer program described above may be provided in a computer storage medium encoded with a computer program that, when executed by one or more computers, causes the one or more computers to perform the method flows and/or apparatus operations shown in the above-described embodiments of the invention.

With the development of time and technology, the meaning of media is more and more extensive, and the propagation path of computer programs is not limited to tangible media any more, and can also be downloaded from a network directly and the like. Any combination of one or more computer-readable media may be employed. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).

It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.

Claims

1. A method of displaying vector tiles, comprising the steps of:

2. The method of claim 1, wherein obtaining the required vector tiles from the next view comprises:

the number of the vector tile corresponding to the next view is obtained.

3. The method of claim 2, wherein determining new vector tiles and removed vector tiles compared to a next view further comprises:

4. The method of claim 3, wherein the requesting the server for the vector data corresponding to the added vector tile comprises:

5. The method of claim 1, wherein the rendering vector data corresponding to the newly added vector tile obtained from the server and displaying a next view comprises:

6. The method of claim 5, wherein creating a corresponding vector render object for the added vector tile comprises:

and if the vector drawing object is inquired, merging.

7. The method of claim 5, wherein said rendering the corresponding vector rendered object comprises;

and drawing the vector data in batch.

8. A vector tile display system, comprising:

9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program implements the method of any one of claims 1 to 8.

10. A computer-readable storage medium, on which a computer program is stored, which program, when being executed by a processor, carries out the method according to any one of claims 1 to 8.