Static map generation method and system, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a static map generation method and system, electronic equipment and a storage medium, and belongs to the field of simulation testing. The method comprises the following steps: selecting a target map area according to a test requirement of the driving assistance system, and extracting a basic road in the target map area; classifying the basic roads to generate a plurality of road libraries of different types; and extracting cross nodes among the roads in the plurality of road libraries, and classifying the cross nodes into simple intersections and complex intersections. Basic roads are extracted from a map, different road libraries are formed through classification, different intersections are generated, a static map is generated for hardware-in-the-loop simulation test of the driving assistance system, and the hardware-in-the-loop simulation test is completed by adding other road participants and road facilities on the static map. The construction efficiency of the test map can be greatly improved, the generated map is extracted from a real road environment, the real road condition can be better reflected, and the coverage degree is higher.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a method, system, electronic device and storage medium for generating a static map. Background Art

[0002] With the rapid development of driver assistance systems, the comfort and safety of drivers and passengers have been greatly improved. However, since the driver assistance system is a joint ecosystem composed of many active safety systems, including warning functions (such as lane departure warning function, forward collision warning function) and control functions (such as lane keeping assist system, emergency braking system), a large number of tests are required at different stages of research and development to verify and improve the safety and reliability of the functions.

[0003] During the development process of the driving assistance system, real vehicle testing and hardware-in-the-loop simulation testing are required. Real vehicle testing can test the functional performance of the driving assistance system more realistically, but it is difficult to test dangerous working conditions, and during the test process, the tester needs to manually operate the vehicle to test and record the test process, which has low testing efficiency and high cost. Hardware-in-the-loop simulation testing can get rid of the limitations of test scenarios, and is more flexible in setting up test scenarios. It can make up for the gaps in real vehicle testing in dangerous working conditions, and has high testing efficiency. However, hardware-in-the-loop simulation testing requires the construction of a large number of test scenarios to test the functional performance of the driving assistance system under different working conditions. It can be seen that the test map is the basis of simulation testing, and the quality of the map library will directly affect the quality of hardware-in-the-loop simulation testing. At present, most simulation tests focus on manual scene construction, which has low construction efficiency and the quality of the constructed map is limited by the experience of testers. It is difficult to fully reflect the real road scene. Therefore, it is urgent to find a map generation method that can truly and effectively reflect the road characteristics, improve the coverage of the test, and increase the speed of map scene generation. Summary of the invention

[0004] The purpose of the embodiments of the present invention is to provide a method, system, electronic device and storage medium for generating a static map, which are used to completely or at least partially solve the technical problems existing in the above-mentioned prior art.

[0005] In order to achieve the above object, an embodiment of the present invention provides a method for generating a static map, which is applied to a hardware-in-the-loop simulation test of a driving assistance system, comprising: Selecting a target map area according to the test requirements of the driving assistance system, and extracting basic roads in the target map area; Classifying basic roads in the target map area to generate multiple road libraries of different types; The intersection nodes between roads in multiple road libraries are extracted, and the intersection nodes are classified into simple intersections and complex intersections.

[0006] Optionally, selecting a target map area according to the test requirements of the driving assistance system, and extracting basic roads in the target map area, includes: Select the target map area according to the test requirements of the driving assistance system and download the corresponding OSM map from the OSM website; The downloaded OSM map is read and processed through the simulation engine, and all lanes in the OSM map are extracted through the ID information and road type tags in the OSM map; All lanes in the OSM map are traversed, lanes with the same starting point and the same end point are classified as the same basic road, and the basic road is stored in the map template.

[0007] Optionally, the basic roads in the target map area are classified to generate multiple road libraries of different types, including: A sampling point is set at a preset distance on the basic road, and the heading angle, the heading angle change rate and the distance of each sampling point along the basic road relative to the first sampling point are calculated; Divide the basic road whose heading angle change rate meets the preset threshold into a straight road and a right-angle curve; For basic roads other than straight roads and right-angle curves, a clustering method is used to obtain the number of curves in the road; The basic roads are classified into straight roads, right-angle roads and different numbers of curves to generate different types of road libraries.

[0008] Optionally, for basic roads other than straight roads and right-angle curves, a clustering method is used to obtain the number of curves in the road, including: All sampling points are recorded as independent clusters by clustering method, and the maximum distance between two sampling points on the adjacent roads at the turn is set. If the distance between two sampling points on the adjacent roads at the turn is greater than the maximum distance, it is determined that the two sampling points belong to two different turns. If the distance between two sampling points on the adjacent roads at the turn is less than the maximum distance, it is determined that the two sampling points belong to the same turn. The relationship between the distance between two sampling points on the adjacent roads at each turn and the maximum distance is traversed to obtain the number of turns in the road.

[0009] Optionally, the heading angle of the i-th sampling point is calculated according to the following formula:

[0010] In the formula, si [ x ] is the i Sampling points x coordinate, s i+1 [ x ] is the i+ 1 sampling point x coordinate, s i [ y ] is the i Sampling points y coordinate, s i+1 [ y ] is the i +1 sampling point y coordinate, S Represents a collection of sampling points.

[0011] Optionally, the rate of change of the heading angle is calculated according to the following formula:

[0012] In the formula, ls i Indicates i The distance of the sampling points from the first sampling point along the basic road, ls i+1 Indicates i +1 sampling point is the distance from the first sampling point along the base road, hs i Indicates i The heading angle of the sampling points, hs i+1 Indicates i +1 sampling point heading angle, S Represents a collection of sampling points.

[0013] Optionally, the intersection nodes between the roads in the plurality of road libraries are extracted, and the intersection nodes are classified into simple intersections and complex intersections, including: Merge the nodes of the intersections in the OSM map and the edges related to the nodes to generate simple intersections, wherein the simple intersections include but are not limited to T-intersections and cross intersections with different intersection angles; Extract all intersection nodes in the OSM map, set the maximum interval distance between intersections, and use clustering methods to merge intersection nodes and edges related to intersection nodes to obtain complex intersections.

[0014] On the other hand, the present invention also provides a static map generation system, which is applied to the hardware-in-the-loop simulation test of the driving assistance system, comprising: An extraction unit, configured to select a target map area according to a test requirement of the driving assistance system, and extract basic roads in the target map area; A classification unit, used for classifying basic roads in the target map area to generate a plurality of road libraries of different types; The generation unit is used for extracting intersection nodes between roads in a plurality of road libraries and classifying the intersection nodes into simple intersections and complex intersections. On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for generating a static map when executing the program.

[0015] On the other hand, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the static map generation method described above are implemented.

[0016] Through the above technical solution, basic roads are extracted from the map, classified into different road libraries and different intersections are generated, and a static map is generated for the hardware-in-the-loop simulation test of the driving assistance system. By adding other road participants and road facilities on the static map to complete the hardware-in-the-loop simulation test, the efficiency of building the test map can be greatly improved. At the same time, the generated map is extracted from the real road environment, which can better reflect the real road conditions and has a higher coverage. Other features and advantages of the embodiments of the present invention will be described in detail in the subsequent detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the following specific implementations, they are used to explain the embodiments of the present invention, but do not constitute a limitation on the embodiments of the present invention. In the accompanying drawings: Figure 1 is an implementation flow chart of a method for generating a static map provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of an OSM map structure provided by an embodiment of the present invention; Figure 3 is a basic road extraction flow chart provided by an embodiment of the present invention; Figure 4 is a schematic diagram of a road heading angle provided by an embodiment of the present invention; Figure 5 is a flow chart for calculating the number of turns in a basic road provided by an embodiment of the invention; Figure 6It is a structural schematic diagram of a static map generation system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The specific implementation of the embodiment of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the embodiment of the present invention, and is not used to limit the embodiment of the present invention.

[0019] See also Figure 1 As shown, it is a flowchart of an implementation method of a static map generation method provided by an embodiment of the present invention, which is applied to a hardware-in-the-loop simulation test of a driving assistance system, and includes the following execution steps: Step 100: Select a target map area according to the test requirements of the driving assistance system, and extract basic roads in the target map area.

[0020] Specifically, when executing step 100, the following steps may be specifically performed: S1000: Select a target map area according to the test requirements of the driving assistance system, and download the corresponding OSM map from the OSM website.

[0021] In some embodiments, see Figure 2 As shown, it is a schematic diagram of the composition of an OSM map provided by an embodiment of the present invention. OSM is an online map writing project that constructs free content. Its goal is to create a world map with free content that can be edited by everyone. Users can obtain maps of areas of interest from the website, and can also upload and update maps. The OSM map uses a topological data structure, which includes three primitive components: points, roads, and relationships. Among them, the points in the map represent locations and can store longitude and latitude. Different points form roads and can characterize the shape of roads. In the OSM map, each road side can contain different numbers of lanes and intersections between lanes, and the driving directions of different lanes are marked.

[0022] S1001: The downloaded OSM map is read and processed by the simulation engine, and all lanes in the OSM map are extracted by using the ID information and road type labels in the OSM map. S1002: Traverse all lanes in the OSM map, classify lanes with the same starting point and the same end point as the same basic road, and store the basic road in the map template.

[0023] In some embodiments, see Figure 3 As shown in the figure, a basic road extraction flow chart provided by an embodiment of the present invention includes: based on the input OSM map, all lanes in the map are extracted to form a set Road (r1, ..., r i , r j,……,r n ), traverse all lanes R in the map i ∈Road, i≠j, judge r i , r j Are the starting point and end point the same? If not, then r i , r j Do not belong to the same basic road. If they are the same, then r i , r j Belongs to a basic road, saves the basic road, and outputs all basic roads.

[0024] First, the tester can select the map area of ​​interest according to the test requirements of the driving assistance function. Heavy commercial vehicles can focus on highways and national highways, or select some urban expressways. Secondly, the downloaded OSM map is read and processed through the simulation engine (SUMO), and all lanes in the map are extracted through the ID information and road type tags in the map. Finally, lanes with the same starting point (point coordinates of the lane starting point) and the same end point (point coordinates of the lane end point) are classified as the same basic road, and the basic road is stored in the map template. By repeating the above process, all basic roads in the original map can be extracted. The basic roads extracted through the above process include straight roads, right-angle curves, continuous curves (random curvature), etc., which provide a road foundation for the subsequent hardware-in-the-loop simulation test of the driving assistance function. However, the basic roads can only meet the test of simple working conditions, and cannot be tested for complex road working conditions (such as scenes requiring intersections). Therefore, it is necessary to classify the extracted basic roads to distinguish between straight roads, continuous curves, etc., so as to facilitate the rapid selection of appropriate roads for testing during testing. At the same time, it is also necessary to merge basic roads to form intersections to meet the testing of complex road conditions. Step 101: Classify the basic roads in the target map area to generate multiple road libraries of different types.

[0025] Specifically, when executing step 101, the following steps may be specifically performed: S1010: setting a sampling point at a preset distance on the basic road, and calculating the heading angle, the heading angle change rate, and the distance of each sampling point along the basic road relative to the first sampling point.

[0026] In some implementations, the heading angle of the i-th sampling point is calculated according to the following formula:

[0027] In the formula, s i [ x ] is the i Sampling pointsx coordinate, s i+1 [ x ] is the i+ 1 sampling point x coordinate, s i [ y ] is the i Sampling points y coordinate, s i+1 [ y ] is the i +1 sampling point y coordinate, S Represents a collection of sampling points.

[0028] In some embodiments, see Figure 4 As shown in the figure, it is a schematic diagram of a road heading angle provided by an embodiment of the present invention, in which sampling points are set every 0.2 meters on the basic road ( Figure 4 The heading angle of the point on lane 2 is the angle between the point on lane 2 and the point parallel to lane 1. The heading angle change rate formula shows that for Figure 4 In the straight basic road similar to lane 1, the heading angle change rate is 0. For the right-angle curve, | | is approximately equal to 90. For other more complex curved roads, Figure 5 The process shown obtains the number of turns on the underlying road.

[0029] It should be understood that the interval between sampling points can be set according to specific application scenarios. For example, when high precision is required, the distance between sampling points can be reduced. This is not limited here.

[0030] In some implementations, the rate of change of the heading angle is calculated according to the following formula:

[0031] In the formula, ls i Indicates i The distance of the sampling points from the first sampling point along the basic road, ls i+1 Indicates i +1 sampling point is the distance from the first sampling point along the base road, hs i Indicates i The heading angle of the sampling points, hs i+1 Indicates i +1 sampling point heading angle, S Represents a collection of sampling points.

[0032] S1011: Divide the basic road whose heading angle change rate meets the preset threshold into a straight road and a right-angle curve road.

[0033] In some implementations, a basic road with all heading angle change rates of 0 is a straight road, and a basic road with all heading angle change rates of 90 is a right-angle curve.

[0034] S1012: For basic roads other than straight roads and right-angle curves, a clustering method is used to obtain the number of curves in the road.

[0035] Specifically, when executing step S1012, the following steps may be specifically performed: all sampling points are recorded as independent clusters using a clustering method, and a maximum distance between two sampling points on adjacent roads at a turn is set; if the distance between two sampling points on adjacent roads at a turn is greater than the maximum distance, it is determined that the two sampling points belong to two different turns; if the distance between two sampling points on adjacent roads at a turn is less than the maximum distance, it is determined that the two sampling points belong to the same turn; and the relationship between the distance between two sampling points on adjacent roads at each turn and the maximum distance is traversed to obtain the number of turns in the road.

[0036] S1013: Classify the basic roads into straight roads, right-angle curves, and curves of different numbers to generate different types of road libraries.

[0037] In some embodiments, see Figure 5 As shown, it is a flow chart for calculating the number of turns in a basic road provided by an embodiment of the invention, including setting a sampling point every 0.2 meters on the basic road to obtain a sampling point set S{s1, s2, ..., si, ..., sn}; taking the heading angle in the vertical upward direction as 0, respectively calculating the heading angles of n sampling points; calculating the distance of each point from the 0th sampling point along the original road according to the distance of each point from the 0th sampling point l si and heading angle h si , calculate the change rate of all sampling points respectively ; Initialize each sampling point as an independent cluster C ( l si ,h si ), determine whether the number of clusters is greater than 1. If so, merge the two closest clusters into one cluster, update cluster set C, and set the maximum distance D between the two points at the turn. max When the distance between two points is greater than D max When the distance between the two points is less than D maxWhen , the two sampling points are considered to belong to the same curve. This method can return the number of curves in the original road; through the above steps, the basic road can be classified into different types of road libraries. If not, the maximum distance threshold D between the two points at the turn is set. max , classify C and get the number of curves.

[0038] Step 102: extracting intersection nodes between roads in a plurality of road libraries, and classifying the intersection nodes into simple intersections and complex intersections.

[0039] Specifically, when executing step 102, the following steps may be specifically performed: S1020: Merge the nodes of the intersections in the OSM map and the edges related to the nodes to generate simple intersections, where the simple intersections include but are not limited to T-junctions and cross intersections with different intersection angles.

[0040] S1021: Extract all intersection nodes in the OSM map, set the maximum interval distance between intersections, and use a clustering method to merge intersection nodes and edges related to the intersection nodes to obtain a complex intersection.

[0041] Through the above steps, basic roads can be extracted from the OSM map, classified into different road libraries and different intersections, and static maps can be generated for the hardware-in-the-loop simulation test of the driving assistance system. The hardware-in-the-loop simulation test can be completed by adding other road participants and road facilities on the static map. Generating static maps through this method can greatly improve the efficiency of building test maps. At the same time, the generated maps are extracted from the real road environment, which can better reflect the real road conditions and have higher coverage. See also Figure 6 FIG. 1 is a schematic diagram of a static map generation system provided by an embodiment of the present invention, which is applied to hardware-in-the-loop simulation testing of a driving assistance system, and includes: An extraction unit 60, configured to select a target map area according to a test requirement of the driving assistance system, and extract basic roads in the target map area; A classification unit 61, used for classifying basic roads in the target map area to generate a plurality of road libraries of different types; The generating unit 62 is used to extract the intersection nodes between the roads in the plurality of road libraries, and classify the intersection nodes into simple intersections and complex intersections. On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for generating a static map when executing the program.

[0042] On the other hand, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the static map generation method described above are implemented.

[0043] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0044] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0045] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0046] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0047] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0048] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0049] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0050] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0051] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

Claims

1. A method for generating a static map, applied to a hardware-in-the-loop simulation test of a driving assistance system, characterized in that: include: Selecting a target map area according to the test requirements of the driving assistance system, and extracting basic roads in the target map area; Classifying basic roads in the target map area to generate multiple road libraries of different types; The intersection nodes between roads in multiple road libraries are extracted, and the intersection nodes are classified into simple intersections and complex intersections.

2. The method for generating a static map according to claim 1, characterized in that: A target map area is selected according to the test requirements of the driving assistance system, and basic roads in the target map area are extracted, including: Select the target map area according to the test requirements of the driving assistance system and download the corresponding OSM map from the OSM website; The downloaded OSM map is read and processed through the simulation engine, and all lanes in the OSM map are extracted through the ID information and road type tags in the OSM map; All lanes in the OSM map are traversed, lanes with the same starting point and the same end point are classified as the same basic road, and the basic road is stored in the map template.

3. The method for generating a static map according to claim 1, characterized in that: The basic roads in the target map area are classified to generate multiple road libraries of different types, including: A sampling point is set at a preset distance on the basic road, and the heading angle, the heading angle change rate and the distance of each sampling point along the basic road relative to the first sampling point are calculated; Divide the basic road whose heading angle change rate meets the preset threshold into a straight road and a right-angle curve; For basic roads other than straight roads and right-angle curves, a clustering method is used to obtain the number of curves in the road; The basic roads are classified into straight roads, right-angle roads and different numbers of curves to generate different types of road libraries.

4. The method for generating a static map according to claim 3, characterized in that: For basic roads other than straight roads and right-angle curves, the number of curves in the road is obtained by clustering method, including: All sampling points are recorded as independent clusters by clustering method, and the maximum distance between two sampling points on the adjacent roads at the turn is set. If the distance between two sampling points on the adjacent roads at the turn is greater than the maximum distance, it is determined that the two sampling points belong to two different turns. If the distance between two sampling points on the adjacent roads at the turn is less than the maximum distance, it is determined that the two sampling points belong to the same turn. The relationship between the distance between two sampling points on the adjacent roads at each turn and the maximum distance is traversed to obtain the number of turns in the road.

5. The method for generating a static map according to claim 3, characterized in that: The heading angle of the i-th sampling point is calculated according to the following formula: In the formula, s i [ x ] is the i Sampling points x coordinate, s i+1 [ x ] is the i+ 1 sampling point x coordinate, s i [ y ] is the i Sampling points y coordinate, s i+1 [ y ] is the i +1 sampling point y coordinate, S Represents a collection of sampling points.

6. The method for generating a static map according to claim 3, characterized in that: The rate of change of heading angle is calculated according to the following formula: In the formula, ls i Indicates i The distance of the sampling points from the first sampling point along the basic road, ls i+1 Indicates i +1 sampling point distance from the first sampling point along the base road, hs i Indicates i The heading angle of the sampling points, hs i+1 Indicates i +1 sampling point heading angle, S Represents a collection of sampling points.

7. The method for generating a static map according to claim 2, characterized in that: Extract the intersection nodes between roads in multiple road libraries and classify the intersection nodes into simple intersections and complex intersections, including: Merge the nodes of the intersections in the OSM map and the edges related to the nodes to generate simple intersections, wherein the simple intersections include but are not limited to T-intersections and cross intersections with different intersection angles; Extract all intersection nodes in the OSM map, set the maximum interval distance between intersections, and use clustering methods to merge intersection nodes and edges related to intersection nodes to obtain complex intersections.

8. A static map generation system, applied to hardware-in-the-loop simulation testing of a driving assistance system, characterized in that: include: An extraction unit, configured to select a target map area according to a test requirement of the driving assistance system, and extract basic roads in the target map area; A classification unit, used for classifying basic roads in the target map area to generate a plurality of road libraries of different types; The generation unit is used for extracting intersection nodes between roads in a plurality of road libraries and classifying the intersection nodes into simple intersections and complex intersections.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method for generating a static map as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for generating a static map according to any one of claims 1 to 7 are implemented.

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