CN104899360A - Method for drawing macroscopic fundamental diagram - Google Patents

Abstract

The invention discloses a method for drawing a macroscopic fundamental diagram, which comprises the following steps: 1) selecting a road network research range, and performing pertinent acquiring on basic data, comprising data in three aspects in total: road network geometric information, a node releasing strategy and a road network traffic organization; 2) drawing a macroscopic fundamental diagram (MFD) of a researched region, firstly setting a detector based on a reality environment, acquiring traffic data and drawing, after drawing of a scatter diagram is finished, judging whether the macroscopic fundamental diagram (MFD) meets the demands or not and directly transiting to step 3 if yes, and if not, adopting microscopic simulation for supplement drawing and entering step 3 after completely drawing; 3) dividing the scatter diagram into three intervals, removing data at inflection points, adopting a least square method to draw a fitting segment of the whole interval section, prolonging the three segments, forming a trapezoid with a cross coordinate axis, and drawing to finish the final macroscopic fundamental diagram. The invention simplifies a data collection means and has higher feasibility while ensuring the drawing accuracy of the macroscopic fundamental diagram.

Description

A kind of method of drawing macroscopical parent map

Technical field

The present invention relates to urban road traffic network planning and the technical field of management, refer in particular to a kind of method of drawing macroscopical parent map.

Background technology

Along with the development of society and the propelling of urbanization paces, urban district plan construction trend is more obvious, the traffic programme of Regional Road Network and the requirement of ladder of management are improved constantly, based on above demand, inventor better can reflect the base attribute of the running status of road network for the macroscopical parent map (Macroscopic Fundamental Diagram, MFD) describing relation between each key element in road network by research.Macroscopic view parent map (MFD) may be defined as the general relationship described in network between moving vehicle number and network operation level.By site test and data acquisition, demonstrate the existence of macroscopical parent map, can with reference to the parent map drawn according to the measured data of Japanese Yokohama and area, U.S. Amsterdam express network.But, due to the restriction of technology and the high request of detector arrangement on the spot, for a specific region, macroscopic view parent map drafting and be not easy realize, traditional macroscopical parent map mainly with road network average density and road network average discharge for transverse and longitudinal coordinate is drawn, the related content of " Macroscopic relations of urban traffic variables Bifurcations " that " existence based on Simulation experiments validate macroscopic view parent map " delivered as domestic scholars Ji Yang bud bud and foreign scholar Daganzo etc. deliver, need to lay loaded down with trivial details detecting device and process mass data in the method actual environment and simulated environment process, comparatively loaded down with trivial details, workload is large, in addition, some scholars using road network vehicle number and network power flow as transverse and longitudinal coordinate, as the related ends of " traffic management measure is to the impact analysis of road network macroscopic view parent map " that scholar Xu Feifei delivers, scholar Du Yiman then adopts network macroscopic view net flow and the clean truck kilometer number in key area to be transverse and longitudinal coordinate in " the regional traffic total amount dynamic regulation technology based on macroscopical parent map " literary composition, above method all needs to follow the tracks of the attribute in bar section every in vehicle and road network and add up, its accuracy and operability difficulty higher.For above deficiency, inventor proposes the method for a kind of novel drafting macroscopic view parent map, with vehicle fleet (the Net Volume of certain hour interval in network (Δ t), N) be horizontal ordinate, the vehicle fleet of road network is sailed out of for ordinate with certain hour interval in network (Δ t), be designated as G, draw macroscopical parent map, by the method that actual environment and simulated environment combine, the method can draw macroscopical parent map in scientific and efficient ground, greatly reduces the complexity of data processing.

Summary of the invention

The object of the invention is to overcome the shortcoming of prior art and deficiency, a kind of method of drawing macroscopical parent map is provided, break through conventional drafting macroscopic view parent map mode.

For achieving the above object, technical scheme provided by the present invention is: a kind of method of drawing macroscopical parent map, comprises the following steps:

1) selected road network research range, carries out specific aim acquisition to basic data, altogether comprises the data of three aspects, is respectively road network geological information, node lets pass strategy and road grid traffic tissue;

2) macroscopical parent map MFD of survey region is drawn, first detecting device is set based on actual environment, obtain traffic data to draw, after completing scatter diagram drafting, judge whether macroscopical parent map MFD meets the demands, satisfied then directly transit to step 3), if imperfect, adopt microscopic simulation carry out supplement draw, draw complete after enter step 3 again);

3) 3 intervals are divided into scatter diagram, reject flex point place data, adopt least square method to draw a segment matching line segment, 3 line segments are extended, and abscissa axis is formed trapezoidal, final macroscopical parent map of completing.

In step (1), described road network geological information comprises link length, road width and number of track-lines and arranges, described node strategy of letting pass comprises and allows line mode and signal Controlling vertex phase-relate without Controlling vertex, described road grid traffic tissue comprises one-way road and arranges, turns to restriction, and car type restriction and special lane are arranged.

In step (2), based on the scatter diagram of macroscopical parent map that actual environment is drawn, comprise the following steps:

2.1) with the vehicle fleet (Net Volume, N) of time interval Δ t preset in network for horizontal ordinate; Sail out of the vehicle fleet of road network for ordinate with the time interval Δ t preset in network, be designated as G;

2.2) according to road network flow view in region, image data from wagon flow low peak period, obtains main thoroughfare vehicle number in region and can meet the condition of drawing macroscopical parent map, adopt section video detector camera function, at t ₀moment takes pictures to all main thoroughfares whole process in region, counts t ₀operational vehicle number in moment road network region is N ₀;

2.3) determine all imports and the outlet on selection area road network border, and flow detector is set in each import and export, sum up all imports and set up import numbering set R-Entrance{R ₁, R ₂r _m, all outlet ports sets up exit numbers S set-Exit{S ₁, S ₂s _n, R _mrepresent m import, S _nrepresent the n-th outlet;

2.4) flow monitoring and statistics, determines Fixed Time Interval Δ t, sums up all timing node node set T-interval{t Time Created ₀, t ₁, t ₂t _j, wherein t _j=t _j-1+ Δ t; The flow volume change values of the import and export corresponding with each timing node is corresponding gather as follows:

R _j-Entrance{R _1j，R _2j···R _mj···}

S _j-Exit{S _1j，S _2j···S _nj···}

Wherein, R _mjrepresent that m import is at t _j-1to t _jthe vehicle number of statistics in time period, S _njrepresent that the n-th outlet is at t _j-1to t _jthe vehicle number of statistics in time period;

2.5) data processing stage, obtains effective macroscopical parent map sample value, is recorded as O _j(N _j, G _j), wherein N _jrepresent the vehicle number in j time point road network, G _jrepresent j time point, as follows:

$N_j=N_{j-1}+(\underset{m=1}{\Σ}{R}_{mj}-\underset{n=1}{\Σ}{S}_{nj})$

$G_j=\underset{n=1}{\Σ}{S}_{nj}$

Wherein, initial value N ₀at previous step 2.2) middle acquisition, according to above-mentioned relation, obtain the effective sample value of j group;

2.6) according to the sample data after process, scatter diagram is drawn;

In step (2), based on macroscopical parent map that microscopic simulation is drawn, comprise the following steps:

2.1) road network builds early-stage preparations, obtains road grid traffic data characteristics, investigates and analyses the region chosen, and corrects, arrange traffic components ratio to the parameter of emulation;

2.2) according to real road length and width, the attribute of different road is set; Build road network and node, turn to setting according to actual node, added turning lane, crossing inlet queue area are set;

2.3) according to actual crossing release manner, No-shell culture arranges and allows line discipline, signal-control crossing arrange corresponding phase-relate or adaptive control program;

2.4) all setup of entrances and exits flow detectors of road network, and corresponding assay intervals is set, guarantee to export the complete and orderly of data;

2.5) simulated environment can be directly emulation 0 from Road network traffic, and exports the traffic data detection limit of prefixed time interval Δ t, obtains the O of sufficient amount _j(N _j, G _j);

2.6) according to the sample data after process, scatter diagram is drawn.

In step (3), scatter diagram is carried out to the method for matching, comprises the following steps:

3.1) scatter diagram being divided into three intervals, is ascent stage, sustained segment and descending branch respectively;

3.2) carry out the matching of least square method respectively for three intervals, place, simulate three line segments;

3.3) three good for matching line segments are extended, in conjunction with abscissa axis formed one trapezoidal, complete the drafting of macroscopical parent map MFD.

Compared with prior art, tool has the following advantages and beneficial effect in the present invention:

The present invention takes full advantage of reality environment data and simulated environment data, ensures the integrality of drawing macroscopical parent map.Invention provides the step and method of detailed drafting macroscopic view parent map, and data processing amount is few relative to classic method, workable, and effect of publishing picture is good.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the present invention's macroscopic view parent map.

Fig. 2 is that flow process of the present invention is always schemed.

Fig. 3 is that the present invention adopts historical data to draw the process flow diagram of MFD scatter diagram.

Fig. 4 is that the present invention adopts microscopic simulation to draw the process flow diagram of MFD scatter diagram.

Fig. 5 is embodiment of the present invention Regional Road Network and gateway schematic diagram.

Fig. 6 is the MFD scatter diagram drawn based on actual environment.

Fig. 7 is the MFD be depicted as based on actual environment and simulated environment.

Embodiment

Below in conjunction with specific embodiment, the invention will be further described.

The method of the drafting macroscopic view parent map described in the present embodiment, basic ideas are by conjunction with site environment and simulated environment, draw macroscopical parent map to selected road network, and according to macroscopical parent map determination Regional Road Network bearing capacity.As shown in Figures 1 to 4, its situation is as follows:

1) selected road network research range, carries out specific aim acquisition to basic data, altogether comprises the data of three aspects, is respectively road network geological information, node lets pass strategy and road grid traffic tissue;

2) macroscopical parent map MFD of survey region is drawn, first detecting device is set based on actual environment, obtain traffic data to draw, after completing scatter diagram drafting, judge whether macroscopical parent map MFD meets the demands, satisfied then directly transit to step 3), if imperfect, adopt microscopic simulation carry out supplement draw, draw complete after enter step 3 again);

3) 3 intervals are divided into scatter diagram, reject flex point place data, adopt least square method to draw a segment matching line segment, 3 line segments are extended, and abscissa axis is formed trapezoidal, final macroscopical parent map of completing.

In step (1), described road network geological information comprises link length, road width and number of track-lines and arranges, described node strategy of letting pass comprises and allows line mode and signal Controlling vertex phase-relate without Controlling vertex, described road grid traffic tissue comprises one-way road and arranges, turns to restriction, and car type restriction and special lane are arranged.

In step (2), based on the scatter diagram of macroscopical parent map that actual environment is drawn, comprise the following steps:

2.1) with the vehicle fleet (Net Volume, N) of time interval Δ t preset in network for horizontal ordinate; Sail out of the vehicle fleet of road network for ordinate with the time interval Δ t preset in network, be designated as G;

2.2) according to road network flow view in region, image data from wagon flow low peak period, obtains main thoroughfare vehicle number in region and can meet the condition of drawing macroscopical parent map, adopt section video detector camera function, at t ₀moment takes pictures to all main thoroughfares whole process in region, counts t ₀operational vehicle number in moment road network region is N ₀;

2.3) determine all imports and the outlet on selection area road network border, and flow detector is set in each import and export, sum up all imports and set up import numbering set R-Entrance{R ₁, R ₂r _m, all outlet ports sets up exit numbers S set-Exit{S ₁, S ₂s _n, R _mrepresent m import, S _nrepresent the n-th outlet;

2.4) flow monitoring and statistics, determines Fixed Time Interval Δ t, sums up all timing node node set T-interval{t Time Created ₀, t ₁, t ₂t _j, wherein t _j=t _j-1+ Δ t; The flow volume change values of the import and export corresponding with each timing node is corresponding gather as follows:

R _j-Entrance{R _1j，R _2j···R _mj···}

S _j-Exit{S _1j，S _2j···S _nj···}

Wherein, R _mjrepresent that m import is at t _j-1to t _jthe vehicle number of statistics in time period, S _njrepresent that the n-th outlet is at t _j-1to t _jthe vehicle number of statistics in time period;

2.5) data processing stage, obtains effective macroscopical parent map sample value, is recorded as O _j(N _j, G _j), wherein N _jrepresent the vehicle number in j time point road network, G _jrepresent j time point, as follows:

$N_j=N_{j-1}+(\underset{m=1}{\Σ}{R}_{mj}-\underset{n=1}{\Σ}{S}_{nj})$

$G_j=\underset{n=1}{\Σ}{S}_{nj}$

Wherein, initial value N ₀at previous step 2.2) middle acquisition, according to above-mentioned relation, obtain the effective sample value of j group;

2.6) according to the sample data after process, scatter diagram is drawn.

In step (2), based on macroscopical parent map that microscopic simulation is drawn, comprise the following steps:

2.1) road network builds early-stage preparations, obtains road grid traffic data characteristics, investigates and analyses the region chosen, and corrects, arrange traffic components ratio to the parameter of emulation;

2.2) according to real road length and width, the attribute of different road is set; Build road network and node, turn to setting according to actual node, added turning lane, crossing inlet queue area are set;

2.3) according to actual crossing release manner, No-shell culture arranges and allows line discipline, signal-control crossing arrange corresponding phase-relate or adaptive control program;

2.4) all setup of entrances and exits flow detectors of road network, and corresponding assay intervals is set, guarantee to export the complete and orderly of data;

2.5) simulated environment can be directly emulation 0 from Road network traffic, and exports the traffic data detection limit of prefixed time interval Δ t, obtains the O of sufficient amount _j(N _j, G _j);

2.6) according to the sample data after process, scatter diagram is drawn.

In step (3), scatter diagram is carried out to the method for matching, comprises the following steps:

3.1) scatter diagram being divided into three intervals, is ascent stage, sustained segment and descending branch respectively;

3.2) carry out the matching of least square method respectively for three intervals, place, simulate three line segments;

3.3) three good for matching line segments are extended, in conjunction with abscissa axis formed one trapezoidal, complete the drafting of macroscopical parent map MFD.

Be specifically described below in conjunction with accompanying drawing 5 to accompanying drawing 7 pairs of the inventive method:

1) choose certain Regional Road Network, obtain basic data, comprise Regional Road Network geological information (length of each grade road, road width, number of track-lines); Node lets pass tactful (phase-relate that signal controls); Regional traffic organizational form (one-way road arranges, turns to restriction, and car type restriction and special lane are arranged).As shown in Figure 5, this network East and West direction length more than 3000 rice, north-south length more than 2000 rice, total cross junction 16,2, T-shaped crossing, five 2, crossings, tunnel.Section is unidirectional two tracks, and it is 3 tracks that crossing is widened.Cross junction is Four-phase control, and T-shaped crossing is three phase control, and five crossings, tunnel are five phase control.And setting out entrance in each section, vehicle enters network by gateway or reaches home.

2) macroscopical parent map scatter diagram is drawn

2.1) the present invention draw macroscopical parent map with the vehicle fleet of certain hour interval of delta t in network (Net Volume, N) for horizontal ordinate; Sail out of the vehicle fleet of road network for ordinate with certain hour interval of delta t in network, be designated as G.

2.2) according to road network flow view in region, image data from wagon flow low peak period (choosing the time in morning), research shows, obtains main thoroughfare vehicle number in region and can meet the condition of drawing macroscopical parent map, adopt section video detector camera function, at t ₀moment takes pictures to all main thoroughfares whole process in region, counts t ₀operational vehicle number in moment road network region is N ₀equal 365.

2.3) determine all imports and the outlet on selection area road network border, and arrange flow detector in each import and export, this example arranges 18 import and export altogether, and numbering as shown in Figure 5, is summed up all imports and set up import numbering set R-Entrance{R ₁, R ₂r _mr ₁₈, all outlet ports sets up exit numbers S set-Exit{S ₁, S ₂s _ns ₁₈.R _mrepresent m import, S _nrepresent the n-th outlet.

2.4) flow monitoring and statistics, determines Fixed Time Interval Δ t, and this routine Δ t value is 15 minutes, can adjust as the case may be.Time Created node set T-interval{t ₀, t ₁, t ₂t _j, wherein t _j=t _j-1+ Δ t.The flow value of the import and export corresponding with each timing node is corresponding gather as follows:

R _j-Entrance{R _1j，R _2j···R _mj···}

S _j-Exit{S _1j，S _2j···S _nj···}

Wherein, R _mjrepresent that m import is at t _j-1to t _jthe vehicle number of statistics in time period.S _njrepresent that the n-th outlet is at t _j-1to t _jthe vehicle number of statistics in time period.For ensureing number of samples, advise from t ₀moment, 7 working days of follow-up continuous collecting data.

2.5) data processing stage, obtains effective macroscopical parent map sample value, is recorded as O _j(N _j, G _j).Wherein N _jrepresent the vehicle number in j time point road network, G _jrepresent that j time point sails out of network vehicle number.

$N_j=N_{j-1}+(\underset{m=1}{\Σ}{R}_{mj}-\underset{n=1}{\Σ}{S}_{nj})$

$G_j=\underset{n=1}{\Σ}{S}_{nj}$

Wherein, initial value N ₀2.2) middle acquisition, according to above-mentioned relation, the effective sample value of j group can be obtained.

2.6) according to the sample data after process, draw scatter diagram, as shown in Figure 6, carrying out observation to scatter diagram and find, there is not complete rising and downward trend in scatter diagram, needs to perform step 2.7 below) carry out emulating supplementing and draw; If the scatter diagram drawn has complete rising and decline to be tending towards, directly can perform step 3).

2.7) MFD completed based on actual environment is generally imperfect, and transport need is subject to present situation traffic quantitative limitation, can not complete reaction on MFD figure.Solution builds road network simulated environment, and adopt microscopic simulation to solve the problem, and possess following advantage: the first, the macroscopical parent map drawn by emulation is more complete; The second, do not reach transport need in actual road network, as low need state, congestion status is blocked state even, can obtain corresponding data by microscopic simulation; 3rd, the output data acquisition of emulation is comparatively simple and accurate, improves the drafting efficiency of MFD.Concrete operation step is as follows:

2.7.1) road network builds early-stage preparations, obtains road grid traffic data characteristics.The region chosen is investigated and analysed, the parameter of emulation is corrected, traffic components ratio etc. is set.

2.7.2) according to real road length and width, the attribute of different road is set; Build road network and node, turn to setting according to actual node, added turning lane, crossing inlet queue area etc. are set.

2.7.3) according to actual crossing release manner, No-shell culture arranges and allows line discipline, signal-control crossing arrange corresponding phase-relate or adaptive control program.

2.7.4) all setup of entrances and exits flow detectors of road network, and corresponding assay intervals is set, guarantee to export the complete and orderly of data.

2.7.5) simulated environment can be directly emulation 0 from Road network traffic, and exports the traffic data detection limit of certain hour interval of delta t, obtains the O of sufficient amount _j(N _j, G _j), return step 2.6).

3) according to the scatter diagram drawn, as shown in Figure 7, the Trendline of fitting data, concrete operation step is as follows:

3.1) scatter diagram being divided into three intervals, is that ascendant trend is interval respectively, between meadow and downtrending interval.

3.2) carry out the matching of least square method respectively for three intervals, place, simulate three line segments.

3.3) three good for matching line segments are carried out proper extension, in conjunction with abscissa axis formed one trapezoidal, complete the drafting of MFD, as shown in Figure 7.

In sum, actual environment of the present invention and simulated environment combine, with the vehicle fleet of certain hour interval in network (Δ t) for horizontal ordinate, the vehicle fleet of road network is sailed out of for ordinate with certain hour interval in network (Δ t), overcome heavy dependence in the past lay detecting device in a large number and gather many multidata methods, while ensureing that macroscopical parent map draws accuracy, simplify the acquisition means of data, propose to adopt segmentation method matching to draw the combined type method for drafting of macroscopical parent map.Obtain macroscopical parent map more fast and exactly.From technological means, there is higher feasibility, be worthy to be popularized.

The examples of implementation of the above are only the preferred embodiment of the present invention, not limit practical range of the present invention with this, therefore the change that all shapes according to the present invention, principle are done, all should be encompassed in protection scope of the present invention.

Claims (4)

1. draw a method for macroscopical parent map, it is characterized in that, comprise the following steps:

1) selected road network research range, carries out specific aim acquisition to basic data, altogether comprises the data of three aspects, is respectively road network geological information, node lets pass strategy and road grid traffic tissue;

2) macroscopical parent map MFD of survey region is drawn, first detecting device is set based on actual environment, obtain traffic data to draw, after completing scatter diagram drafting, judge whether macroscopical parent map MFD meets the demands, satisfied then directly transit to step 3), if imperfect, adopt microscopic simulation carry out supplement draw, draw complete after enter step 3 again);

3) 3 intervals are divided into scatter diagram, reject flex point place data, adopt least square method to draw a segment matching line segment, 3 line segments are extended, and abscissa axis is formed trapezoidal, final macroscopical parent map of completing.

2. a kind of method of drawing macroscopical parent map according to claim 1, it is characterized in that: in step (1), described road network geological information comprises link length, road width and number of track-lines and arranges, described node strategy of letting pass comprises and allows line mode and signal Controlling vertex phase-relate without Controlling vertex, described road grid traffic tissue comprises one-way road and arranges, turns to restriction, and car type restriction and special lane are arranged.

3. a kind of method of drawing macroscopical parent map according to claim 1, is characterized in that: in step (2), based on the scatter diagram of macroscopical parent map that actual environment is drawn, comprises the following steps:

2.1) with the vehicle fleet (Net Volume, N) of time interval Δ t preset in network for horizontal ordinate; Sail out of the vehicle fleet of road network for ordinate with the time interval Δ t preset in network, be designated as G;

2.2) according to road network flow view in region, image data from wagon flow low peak period, obtains main thoroughfare vehicle number in region and can meet the condition of drawing macroscopical parent map, adopt section video detector camera function, at t ₀moment takes pictures to all main thoroughfares whole process in region, counts t ₀operational vehicle number in moment road network region is N ₀;

2.3) determine all imports and the outlet on selection area road network border, and flow detector is set in each import and export, sum up all imports and set up import numbering set R-Entrance{R ₁, R ₂r _m, all outlet ports sets up exit numbers S set-Exit{S ₁, S ₂s _n, R _mrepresent m import, S _nrepresent the n-th outlet;

2.4) flow monitoring and statistics, determines Fixed Time Interval Δ t, sums up all timing node node set T-interval{t Time Created ₀, t ₁, t ₂t _j, wherein t _j=t _j-1+ Δ t; The flow volume change values of the import and export corresponding with each timing node is corresponding gather as follows:

R _j-Entrance{R _1j，R _2j···R _mj···}

S _j-Exit{S _1j，S _2j···S _nj···}

Wherein, R _mjrepresent that m import is at t _j-1to t _jthe vehicle number of statistics in time period, S _njrepresent that the n-th outlet is at t _j-1to t _jthe vehicle number of statistics in time period;

2.5) data processing stage, obtains effective macroscopical parent map sample value, is recorded as O _j(N _j, G _j), wherein N _jrepresent the vehicle number in j time point road network, G _jrepresent j time point, as follows:

$N_j=N_{j-1}+(\underset{m=1}{\mathrm{\Σ}}{R}_{\mathrm{mj}}-\underset{n=1}{\mathrm{\Σ}}{S}_{\mathrm{nj}})$

$G_j=\underset{n=1}{\mathrm{\Σ}}{S}_{\mathrm{nj}}$

Wherein, initial value N ₀at previous step 2.2) middle acquisition, according to above-mentioned relation, obtain the effective sample value of j group;

2.6) according to the sample data after process, scatter diagram is drawn;

In step (2), based on macroscopical parent map that microscopic simulation is drawn, comprise the following steps:

2.1) road network builds early-stage preparations, obtains road grid traffic data characteristics, investigates and analyses the region chosen, and corrects, arrange traffic components ratio to the parameter of emulation;

2.2) according to real road length and width, the attribute of different road is set; Build road network and node, turn to setting according to actual node, added turning lane, crossing inlet queue area are set;

2.3) according to actual crossing release manner, No-shell culture arranges and allows line discipline, signal-control crossing arrange corresponding phase-relate or adaptive control program;

2.4) all setup of entrances and exits flow detectors of road network, and corresponding assay intervals is set, guarantee to export the complete and orderly of data;

2.5) simulated environment can be directly emulation 0 from Road network traffic, and exports the traffic data detection limit of prefixed time interval Δ t, obtains the O of sufficient amount _j(N _j, G _j);

2.6) according to the sample data after process, scatter diagram is drawn.

4. a kind of method of drawing macroscopical parent map according to claim 1, is characterized in that: in step (3), scatter diagram is carried out to the method for matching, comprise the following steps:

3.1) scatter diagram being divided into three intervals, is ascent stage, sustained segment and descending branch respectively;

3.2) carry out the matching of least square method respectively for three intervals, place, simulate three line segments;

3.3) three good for matching line segments are extended, in conjunction with abscissa axis formed one trapezoidal, complete the drafting of macroscopical parent map MFD.