CN110502676B - Airport scene operation simulation method based on visual tool modeling and storage medium - Google Patents
Airport scene operation simulation method based on visual tool modeling and storage medium Download PDFInfo
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Abstract
The invention discloses an airport scene operation simulation method and a storage medium based on visual tool modeling, wherein the method comprises the following steps: 1) carrying out visual preprocessing on the airport scene element data based on a GlobalMapper tool to form a formatted data file; 2) extracting scene elements from the formatted data file, constructing a topological relation among the scene elements, and establishing an airport scene model; 3) reading airport planning data, and calculating flight motion trail according to the airport scene model and time sequence; 4) and performing conflict detection on the flights based on the public road sections in the airport scene model, and solving the flights with conflicts. The invention realizes the visualization of the modeling of the airport scene model, improves the modeling efficiency, realizes the real-time accurate simulation, is convenient for flexible loading and unloading of the modeling mode processing of the operation strategy, can also dynamically access the external strategy, improves the expansibility and is convenient to be applied to the scene of external algorithm verification.
Description
Technical Field
The invention relates to an airport scene operation simulation method and a storage medium, in particular to an airport scene operation simulation method and a storage medium based on visual tool modeling.
Background
With the rapid development of the air transportation industry, the scale and the operation complexity of an airport rapidly rise, the operation efficiency of the airport is evaluated in a modeling simulation mode, and the planning of a control strategy and a basic environment of the airport is verified to be a necessary means. The traditional airport scene modeling simulation method is lack of a visual modeling means in the static scene modeling aspect, the modeling efficiency is low, the scene operation rule cannot be effectively expressed in the static modeling stage, the description of the taxiway turning part is simplified and deviates from the actual situation, or broken line description is adopted, the data storage capacity is large, an off-line deduction mode is generally adopted in the simulation aspect, the real-time simulation requirement is difficult to meet, and the expansibility problem of dynamically accessing an external strategy is not considered.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the invention is to provide an airport scene operation simulation method based on visual tool modeling and a storage medium, which solve the defects that the existing method cannot realize visual modeling and has low modeling efficiency and inflexibility, realize the visualization of the airport scene model modeling by means of a GlobalMapper tool by combining the structural characteristics of the airport scene and scene operation rules, improve the modeling efficiency, realize real-time accurate simulation, facilitate flexible loading and unloading of the modeling mode processing of the operation strategy, dynamically access an external strategy, improve the expansibility and facilitate the application to scenes verified by external algorithms.
The technical scheme is as follows: the invention relates to an airport scene operation simulation method based on visual tool modeling, which comprises the following steps:
(1) carrying out visual preprocessing on the airport scene element data based on a GlobalMapper tool to form a formatted data file;
(2) extracting scene elements from the formatted data file, constructing a topological relation among the scene elements, and establishing an airport scene model;
(3) reading airport planning data, and calculating flight motion trail according to the airport scene model and time sequence;
(4) and performing conflict detection on the flights based on the public road sections in the airport scene model, and solving the flights with conflicts.
Further, the step (1) is specifically as follows:
(11) extracting the airport scene element data in a layered mode by using a Globalmapper tool, storing stop bit data by using a shp file in a point format, storing taxiway data by using a shp file in a line format, and storing runway data and building data by using a shp file in a surface format;
(12) editing taxiway data, breaking a taxiway broken line segment at a road intersection, splitting the taxiway broken line segment into at least one broken line segment, and generating meta-taxiway data;
(13) setting the attribute and rule information of the shutdown bit data and the taxiway data;
(14) setting an arc turning mark for the taxiway with the arc turning;
(15) marking the sliding waiting position point and the takeoff waiting point as special attribute points, and adding point type data to a GlobalMapper tool interface;
(16) and outputting the data into a shp file and a dbf file corresponding to the shp file.
Further, the step (13) further comprises: and setting the running rule attribute of the taxiway data, including setting a one-way passing taxiway and a passing angle range.
Further, the step (2) is specifically as follows:
(21) extracting scene elements and attributes thereof from the formatted data file, wherein the scene elements comprise a stand, a taxiway, a runway and a building;
(22) traversing the end point positions of the taxiways, merging two corresponding taxiway data into a meta taxiway data for the point with the end point position coincidence frequency of 2, and extracting the point with the end point position coincidence frequency not equal to 2 as a key point; associating the meta-taxiways with two corresponding key points, wherein each key point is associated with all meta-taxiways connected with the key points;
(23) establishing a corresponding relation between the stand and the key points, and further establishing an incidence relation between the stand and the taxiways through the incidence relation between the key points and the meta-taxiways;
(24) establishing an association relation between the taxiways and the taxiways through key points associated with the meta-taxiways and other meta-taxiways associated with the key points;
(25) judging the meta-taxiway to which the special attribute points belong according to the position relationship, inserting the special attribute points into a meta-taxiway data broken line point sequence, and establishing an association relationship between the special attribute points and the taxiway data;
(26) the position data is converted from the local coordinate system to the global coordinate system.
Further, an arc section fitting step is included, specifically, a broken line section set in the taxiway is traversed, if the arc section turning mark in the step (14) is found, arc section fitting is carried out, and the broken line section is represented by an arc section after fitting;
the arc segment fitting step is positioned between the step (21) and the step (26).
Further, the step (3) is specifically as follows:
(31) reading airport planning data, and allocating a stand and a runway for a flight;
(32) performing taxi path allocation on the flights, wherein the taxi path comprises an aircraft stop, a runway and a taxiway;
(33) and calculating the flight position according to the sliding path and driving the flight position to be updated.
Further, the step (4) is specifically as follows:
(41) obtaining the taxiing paths of all flights on the airport scene, comparing the taxiing paths of every two flights, extracting the overlapped part in the taxiing paths of the flights as a public road section, and predicting the arrival time of the flights using the public road section;
(42) judging whether the flights conflict or not according to the arrival time;
(43) and when the conflict exists, adopting a time waiting strategy to sequentially solve the conflict according to the sequence of the flight priorities.
Further, the judging method in the step (42) is as follows: the condition for a conflict between two flights is that,
(t1st-t2start)*(t1end-t2end)<0，
wherein the content of the first and second substances,t1stfor the moment when the first flight reaches the beginning of the public road section, t1endFor the moment when the first flight reaches the end of the public road section, t2starFor the moment when the second flight reaches the beginning of the public road section, t2endFor the moment the second flight reaches the end of the common segment.
Further, the solving method in the step (43) is as follows: and sequencing the priorities of the flights, taking out one flight from the flight queue according to the priority, traversing each flight with the priority lower than that of the flight in the queue to judge the conflict, if the conflict occurs, adding a waiting time slot to the previous key point of the flight with the low priority on the public road section, and traversing and processing the flights with the second priority in sequence until all the flights are processed.
The computer storage medium of the invention stores thereon a computer program which, when executed by a computer processor, implements the above-described method for simulating airport scene operation based on visualization tool modeling.
Has the advantages that: (1) the visualization of the modeling of the airport static model is realized by means of a GlobalMapper visualization tool; (2) the invention integrates the operation rule into the static model modeling process, and provides a visual extensible rule setting method; (3) in the simulation operation process, a conflict detection and resolution strategy based on a public road section is adopted, backtracking is avoided, the algorithm is converged, and the real-time performance is high; (4) the operation strategy in the simulation operation process can be dynamically accessed from the outside, and the expansibility is strong; (5) the optimal mode of the invention adopts an arc section fitting mode to model the turning section of the taxiway, so that the model is more fit with the reality of the airport, and the storage amount of data is reduced.
Drawings
FIG. 1 is a flowchart of the entire method of the present embodiment;
fig. 2 is a flow chart of data visualization preprocessing in the present embodiment;
fig. 3 is a schematic view of setting of an operation rule attribute in the present embodiment;
FIG. 4 is a flowchart of fast extraction of static model data in the present embodiment;
FIG. 5 is a flow chart of a scene operation simulation in the present embodiment;
fig. 6 is a schematic diagram of collision detection based on a common link in the present embodiment. (ii) a
Detailed Description
The method flow of the embodiment of the invention is shown in fig. 1, and comprises the following steps:
step 1, visually preprocessing airport scene element data based on a GlobalMapper tool to form formatted data; the method specifically comprises the following steps:
step 1-1, as shown in FIG. 2, pre-process the raw data. The specific method comprises the following steps: reading original data, wherein the format of the original data can be an AutoCAD format, a shp format, a mif format and the like, uniformly converting various data into shp data for processing, carrying out layered processing on the original data according to the types of parking places, taxiways, runways, buildings and the like, and storing the parking places in shp files in a point format, the taxiways in shp files in a line format, and the runways and the buildings in shp files in a surface format;
and 1-2, performing visual editing processing on the shp-format taxiway data through a Globalmapper tool under a visual interface to generate meta-taxiway data. The specific method comprises the following steps: breaking the taxiway broken line segment at the intersection point, namely splitting the broken line segment into a plurality of broken line segments at the intersection point, wherein the plurality of broken line segments share the same end point, and the split broken line segments are called meta-taxiway data;
and 1-3, setting the attribute and rule information of the data in a visual environment through a Globalmapper tool. The attributes of the stand include the code of the stand, the length and the width of the stand, the direction angle of the stand and the airplane type suitable for parking of the stand; the attributes of the taxiways comprise the names of the taxiways and the types of the taxiways, such as a main taxiway, an entering taxiway, an exiting taxiway, a stand taxiway and the like, and meanwhile, some related attributes of operation rules, such as a one-way passing taxiway, a passing angle range and the like, can be set. Taking the taxiway passing direction as an example, the taxiway D5 shown in fig. 3 is a quick exit, and the usage rule of the quick exit is as follows: only the exit from the rapid exit lane is allowed, and the entry from the rapid exit lane to the runway is not allowed, so that the EN _ DIRECTION field can be added to represent the DIRECTION range of the taxiway allowing to pass, and the passing angle range is set to be 180-360 degrees, thereby limiting the use DIRECTION of the taxiway;
step 1-4, setting an arc turning mark for a sliding road section turning at an arc section, so as to facilitate the subsequent arc fitting treatment of the sliding road section;
step 1-5, point type data are added on a visual interface in an interactive mode, and data attributes are marked as special attribute points, wherein the special attribute points comprise a sliding waiting position point, a takeoff waiting point and other special position points;
and 1-6, outputting the data after the visual editing and attribute labeling, and storing the data as a shp file in a standard point, line and plane format and a corresponding attribute file in a dbf format.
step 2-1, as shown in fig. 4, reading data of scene elements such as a parking space, a taxiway, a runway, a building and the like and corresponding attribute information from formatted shp and dbf files, storing the data into a memory, traversing the data in the memory, executing step 2-2 and step 2-3 if the data are the data of the taxiway, executing step 2-4 if the data are point type data, and executing step 2-5 if the data are plane type data;
and 2-2, reading taxiway attribute data, including taxiway names, taxiway types, relevant attributes of operation rules, arc turning marks and the like. Traversing the broken line set, if the curved section is a curved section turning taxiway, performing arc section fitting treatment, and representing the broken line section formed by a large number of points by the arc section after fitting so as to reduce the storage capacity of data; the arc segment fitting is that the broken line composed of a plurality of points is represented by an arc line, and the method has the advantages that the broken line points are very many if the broken line points are represented by the broken line at the turning place, the storage and calculation amount is large, and the data amount is reduced when the arc line is represented by the arc line.
And 2-3, extracting airport scene key points (the key points refer to intersections of taxiways and taxiways on the scene or the taxiways and the runways and end points of the taxiways which do not intersect with other taxiways) and meta-taxiway data (the taxiway data between two adjacent key points). The specific method comprises the following steps: and traversing the end point positions of the sliding track data to judge, recording the overlapping times of the end points of the broken line segments, extracting the points with the overlapping times of the end point positions being 1 or more than 2 as key points, and combining two corresponding sliding track data into one element sliding track data for the points with the overlapping times of the end point positions being 2. Associating the meta-taxiway data with two corresponding key points, wherein each key point is associated with a plurality of meta-taxiway data connected with the key point;
and 2-4, extracting the parking positions and the data of the special attribute points. The specific method comprises the following steps: judging whether the point type data is shutdown data, extracting the position of the central point of the stand from the position data, and extracting attribute information of the stand from the attribute file, wherein the attribute information comprises the code number of the stand, the length and the width of the stand, the direction angle of the stand, the airplane type suitable for parking of the stand and the like; if the point type data is a special attribute point, reading the position information of the special attribute point and the attribute information of the special attribute point, including a taxi waiting point, a takeoff waiting point and the like.
And 2-5, extracting surface type data of buildings, runways and the like. The specific method comprises the following steps: and extracting polygon position data from the surface type data, and extracting attribute information of the surface data from the attribute file, wherein the attribute information comprises names of buildings, runways and the like.
And 2-6, establishing the relation between the stand and the taxiway. The specific method comprises the following steps: comparing the point coordinates of the stand with the positions of the key points, if the positions are matched, establishing a corresponding relation between the stand and the key points, and further establishing an incidence relation between the stand and the taxiways through the relation between the key points and the meta-taxiways;
and 2-7, establishing a relationship between the taxiways. The specific method comprises the following steps: establishing an association relation between the taxiways and the taxiways through key points associated with the meta-taxiways and other related meta-taxiways associated with the key points;
and 2-8, establishing the relation between the special attribute point and the taxiway. The specific method comprises the following steps: judging the meta-taxiway where the special attribute points are located according to the position relationship, inserting the special attribute points into a meta-taxiway data broken line point sequence, and establishing a bidirectional association relationship between the special attribute points and the taxiway data;
and 2-9, converting the position data from the local coordinate system to the global coordinate system. The specific method comprises the following steps: and carrying out coordinate conversion processing according to the longitude and latitude coordinates and the rotation angle corresponding to the original data reference point, and converting to the global longitude and latitude coordinates. Suppose a local coordinate point (x)0,y0) With global latitude and longitude coordinate points (lon)0,lat0) Correspondingly, and the rotation angle is theta, firstly, global longitude and latitude coordinate points (lon) are determined0,lat0) The coordinate in the projection coordinate system is (X)0,Y0) Then, the coordinate position of any point under the local coordinate under the global projection coordinate system is:
transforming to global longitude and latitude coordinates (Lon, Lat) through projection coordinate (X, Y) projection transformation under the global coordinates;
step 3, reading airport plan data, and calculating the motion trail of the aircraft according to time sequence; the method specifically comprises the following steps:
step 3-1, as shown in fig. 5, reading flight plan information, according to the advance of time sequence, if all flight plan simulations are finished, exiting, otherwise, judging whether a new flight is added into the simulation queue, if so, allocating a flight seat and a runway to the flight, and allocating the flight seat and the runway according to different simulation purposes by selectively using a built-in seat allocation model (allocating the used seat and runway by using the principles of conflict-free and model matching) or directly and dynamically accessing an external seat and the result allocated by a runway allocation system to allocate the seat and the runway (verifying an external allocation algorithm by adopting the simulation mode);
step 3-2, performing real-time dynamic taxi path allocation according to the airplane stand, the runway information and the taxiway rule attribute;
and 3-3, carrying out target position calculation according to the sliding path, carrying out real-time position calculation in a relative time sequence advancing mode, and driving the target position to update so as to realize the updating of the simulation situation.
Step 4, real-time conflict detection and resolution processing based on public road sections is adopted; the method specifically comprises the following steps:
and 4-1, detecting conflicts based on the public road. The specific method comprises the following steps: predicting the flight path, obtaining the taxiing path of each flight on the airport surface, comparing the taxiing paths of two flights, extracting the overlapping part of the taxiing paths of two flights as the public road section (which may be a meta-taxiway or a combination of a plurality of meta-taxiways, and the problem of non-convergence of backtracking easily caused by the processing of the first conflict by using the processing mode of taking the meta-taxiway and the key point as the conflict judgment object, but the problem can be better processed by conflict detection and resolution based on the public road section) in the prediction path, as shown in fig. 5, the public road section is the road section between p1 and p2, predicting the arrival time of two flights using the public road section, and assuming that the time when the first flight arrives at the starting point of the public section is t1starThe time of reaching the end point of the common segment is t1endThe moment when the second flight arrives at the starting point of the common segment is t2staThe moment when the second flight arrives at the starting point of the common segment is t2endThen, the condition that two flights conflict is as follows:
(t1start-t2start)*(t1end-t2end)<0
as shown in FIG. 6, F1 flight position-time curve is F1As shown, the F2 flight can be represented as a set of curves shifted in the time axis direction according to the time of entering the common segment, and the curves are denoted by F2、f2' and f2"three curves indicate, for the case of left-hand fly-to-head f1And f2For the case of the same direction flight on the right side f1And f2Is of the same sign, but whether in-line or head-to-head flight, the position-time curve of the F2 flight is at F2Left side or f2' No conflict will occur in the right case, f2"the condition is conflict, and the common point of the co-directional flight and the head-to-head flight in the conflict condition is the difference sign of the time difference between the entering public section and the time difference between the exiting public section, that is, the above judgment condition is satisfied, so the rear-end collision of the co-directional flight and the head-to-head collision of the head-to-head flight can be represented by the above formula of the collision condition.
And 4-2, adopting a time waiting strategy to carry out conflict resolution by a flight dynamic priority method. The specific method comprises the following steps: and (3) carrying out priority sequencing on the simulated flights, taking out one flight from the flight queue in sequence according to the priority, traversing each flight with the priority lower than that of the flight in the queue in sequence, carrying out conflict judgment by adopting the method in the step 4-1, increasing a waiting time slot on the flight with the low priority at a key point in the front of a public road section when the conflict condition is met, and traversing and processing flights with the second priority in sequence until all flights are processed and finished.
The embodiments of the present invention, if implemented in the form of software functional modules and sold or used as independent products, may also be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present invention may be essentially implemented or a part contributing to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present invention. The storage medium includes various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read Only Memory (ROM), a magnetic disk, or an optical disk. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.
Accordingly, the embodiment of the invention also provides a computer storage medium on which the computer program is stored. The computer program, when executed by a processor, may implement the aforementioned method of simulating an airport scene run based on modeling by a visualization tool. For example, the computer storage medium is a computer-readable storage medium.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Claims (9)
1. An airport scene operation simulation method based on visualization tool modeling is characterized by comprising the following steps:
(1) carrying out visual preprocessing on the airport scene element data based on a GlobalMapper tool to form a formatted data file; the method comprises the following specific steps:
(11) extracting the airport scene element data in a layered mode by using a Globalmapper tool, storing stop bit data by using a shp file in a point format, storing taxiway data by using a shp file in a line format, and storing runway data and building data by using a shp file in a surface format;
(12) editing taxiway data, breaking a taxiway broken line segment at a road intersection, splitting the taxiway broken line segment into at least one broken line segment, and generating meta-taxiway data;
(13) setting the attribute and rule information of the shutdown bit data and the taxiway data;
(14) setting an arc turning mark for the taxiway with the arc turning;
(15) marking the sliding waiting position point and the takeoff waiting point as special attribute points, and adding point type data to a GlobalMapper tool interface;
(16) outputting the data into a shp file and a dbf file corresponding to the shp file;
(2) extracting scene elements from the formatted data file, constructing a topological relation among the scene elements, and establishing an airport scene model;
(3) reading airport planning data, and calculating flight motion trail according to the airport scene model and time sequence;
(4) and performing conflict detection on the flights based on the public road sections in the airport scene model, and solving the flights with conflicts.
2. The method for simulating airport surface operation based on visualization tool modeling according to claim 1, wherein step (13) further comprises: and setting the running rule attribute of the taxiway data, including setting a one-way passing taxiway and a passing angle range.
3. The method for simulating airport surface operation based on visualization tool modeling according to claim 1, wherein the step (2) is specifically as follows:
(21) extracting scene elements and attributes thereof from the formatted data file, wherein the scene elements comprise a stand, a taxiway, a runway and a building;
(22) traversing the end point positions of the taxiways, merging two corresponding taxiway data into a meta taxiway data for the point with the end point position coincidence frequency of 2, and extracting the point with the end point position coincidence frequency not equal to 2 as a key point; associating the meta-taxiways with two corresponding key points, wherein each key point is associated with all meta-taxiways connected with the key points;
(23) establishing a corresponding relation between the stand and the key points, and further establishing an incidence relation between the stand and the taxiways through the incidence relation between the key points and the meta-taxiways;
(24) establishing an association relation between the taxiways and the taxiways through key points associated with the meta-taxiways and other meta-taxiways associated with the key points;
(25) judging the meta-taxiway to which the special attribute points belong according to the position relationship, inserting the special attribute points into a meta-taxiway data broken line point sequence, and establishing an association relationship between the special attribute points and the taxiway data;
(26) the position data is converted from the local coordinate system to the global coordinate system.
4. The method of claim 3, wherein the method comprises: the method also comprises an arc segment fitting step, specifically, a broken line segment set in the taxiway is traversed, if the arc segment turning mark in the step (14) is found, arc segment fitting is carried out, and the broken line segment is represented by an arc segment after fitting;
the arc segment fitting step is positioned between the step (21) and the step (26).
5. The method for simulating airport surface operation based on visualization tool modeling according to claim 1, wherein the step (3) is specifically as follows:
(31) reading airport planning data, and allocating a stand and a runway for a flight;
(32) performing taxi path allocation on the flights, wherein the taxi path comprises an aircraft stop, a runway and a taxiway;
(33) and calculating the flight position according to the sliding path and driving the flight position to be updated.
6. The method for simulating airport surface operation based on visualization tool modeling according to claim 1, wherein the step (4) is specifically as follows:
(41) obtaining the taxiing paths of all flights on the airport scene, comparing the taxiing paths of every two flights, extracting the overlapped part in the taxiing paths of the flights as a public road section, and predicting the arrival time of the flights using the public road section;
(42) judging whether the flights conflict or not according to the arrival time;
(43) and when the conflict exists, adopting a time waiting strategy to sequentially solve the conflict according to the sequence of the flight priorities.
7. The method for simulating airport surface operation based on visualization tool modeling according to claim 6, wherein the determination method in step (42) is: the condition for a conflict between two flights is that,
(t1start-t2start)*(t1end-t2end)<0，
wherein, t1startFor the moment when the first flight reaches the beginning of the public road section, t1endFor the moment when the first flight reaches the end of the public road section, t2startFor the moment when the second flight reaches the beginning of the public road section, t2endFor the moment the second flight reaches the end of the common segment.
8. The visualization tool modeling based airport scene operation simulation method of claim 6, wherein the solution method in step (43) is: and sequencing the priorities of the flights, taking out one flight from the flight queue according to the priority, traversing each flight with the priority lower than that of the flight in the queue to judge the conflict, if the conflict occurs, adding a waiting time slot to the previous key point of the flight with the low priority on the public road section, and traversing and processing the flights with the second priority in sequence until all the flights are processed.
9. A computer storage medium having a computer program stored thereon, characterized in that: the computer program, when executed by a computer processor, implements the method of any one of claims 1 to 8.
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