CN103813377B - Method for obtaining total cover area of multiple circular regions - Google Patents
Method for obtaining total cover area of multiple circular regions Download PDFInfo
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- CN103813377B CN103813377B CN201410026228.8A CN201410026228A CN103813377B CN 103813377 B CN103813377 B CN 103813377B CN 201410026228 A CN201410026228 A CN 201410026228A CN 103813377 B CN103813377 B CN 103813377B
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- circular areas
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Abstract
The invention provides a method for obtaining total cover area of multiple circular regions. The method comprises the steps of 1, setting a to-be-detected region which is not smaller than the total cover area of the multiple circular regions, 2, dividing the to-be-detected region into a plurality of subregions, 3, determining whether each subregion is completely covered with one circular region or does not intersect with any circle, and if so, ending the step, otherwise, taking the subregion which is completely covered with one circular region or does not intersect with any circle as a fixed region and turning to step 4, step 4, continuously dividing the unfixed subregions of each non-fixed region into a plurality of subregions and returning to the step 3. The method is based on the idea of dividing and ruling and only the unfixed regions are divided continuously, and therefore, compared with the existing algorithm, the calculation complexity can be reduced while the calculation precision is not reduced.
Description
Technical field
The present invention relates to the circular ripple coverage technical field of the equipment such as sensor network, wireless communication base station, especially
Refer to a kind of acquisition methods of the total area coverage of many border circular areas.
Background technology
The coverage of many equipment such as sensor network (or referred to as wireless sensor network), wireless communication base station exists
Two dimensional surface is circle, is spherical in three-dimensional planar.System of the prior art all includes multiple equipment with collaborative work realization
Seamless coverage, therefore the just total area coverage of many border circular areas of necessary computing system.Calculate total coverage for it is existing this
A little systems are most important, can know the uncovered area of system by calculating total coverage or carry out other application.
By taking sensor network as an example, existing sensor network includes substantial amounts of sensor node, these sensor nodes
It is deployed in region to be monitored, and total area coverage of whole network is exactly the union of these border circular areas.Meanwhile, wireless telecommunications
In base station and chemistry, materialogy, optics, the mode of operation of the substantial amounts of small units such as molecule, micronic dust all thus, here not
Repeat again.
The method of the union of these many border circular areas is calculated in prior art following several classes：
(1) gridding method：It is many small area grid by region division to be monitored, then counts the lattice being completely covered by circle
The quantity of son, and the grid for generally covering part is according to 0.5 calculating.Then the sum of all pigeons is multiplied by into each grid
Area just can be approximate calculate total area coverage.The accuracy of this algorithm is controllable, but accuracy places one's entire reliance upon
The area of grid, but reducing grid area can improve precision cause the increase of computation complexity exponentially property.
(2) monte carlo method：A point is randomly selected in the zone, detects the point whether covering in certain circle
Under lid.After substantial amounts of random experiments, circle is just close to by the ratio of the written and total experiment number of the circular point for covering and is always covered
The ratio of area and the region gross area.The problem of monte carlo method is to be difficult to obtain higher precision, with the increasing of experiment number
Plus, precision is only increased with the subduplicate ratio of experiment number.
(3) the computational geometry method of approximate polygon：
Polygonal intersecting and merging, the calculating of difference are the ripe algorithms in computational geometry.Each circle is approximately into polygon
Shape, then can be solved using computational geometry.With the increase of side number, regular polygon Jing becomes closer to circle.For meat
For eye, positive 32 side shape and circle are closely.The side number that circle is approximately into regular polygon is more, and computational accuracy is got over
Height, but amount of calculation is also bigger.Hypothesis has N number of circle, and each circle is approximately positive M polygons, then the amount of calculation is in O
(N2M2) magnitude.Therefore it is more effective when circular negligible amounts.
Because existing system includes multiple equipment mostly, so if wanting to calculate multiple on the premise of precision is guaranteed
Circular total overlay area, the performance of these above-mentioned algorithms is all poor.
The content of the invention
The technical problem to be solved in the present invention be to provide one kind can either guarantee arithmetic accuracy again can more than enough border circular areas it is total
The acquisition methods of area coverage.
In order to solve the above problems, the embodiment of the present invention proposes a kind of acquisition side of the total area coverage of many border circular areas
Method, including：
Step 1, setting can cover the region to be monitored of each border circular areas；
Step 2, by the region division to be monitored be many sub-regions；
Step 3, judge each subregion whether all completely by a border circular areas cover or with it is arbitrary it is circular not
Intersecting, if it is step terminates；If otherwise will completely by a border circular areas cover or with arbitrary circular not phases
The region of friendship jumps to step 4 as determining region；
Step 4, each non-uncertainty area for having determined region is continued respectively to be divided into many sub-regions, and return to step 3.
As the preferred of above-mentioned technical proposal, also include between the step 3 and step 4：Judge each subregion
Area whether be both greater than predetermined threshold value, then step will terminate if not.
As the preferred of above-mentioned technical proposal, also include after the step 4：
Step 5, total area coverage is exported, total area coverage includes each being covered by a border circular areas completely
The area summation in region has been determined, and the area of each uncertainty area is multiplied by 0.5.
Used as the preferred of above-mentioned technical proposal, the region to be monitored is square.
Used as the preferred of above-mentioned technical proposal, the step 2 is specially：It is by the foursquare region division to be monitored
Multiple foursquare subregions.
Used as the preferred of above-mentioned technical proposal, the step 2 is specially：By the foursquare region quartering to be monitored
For four foursquare subregions.
Used as the preferred of above-mentioned technical proposal, the step 3 is specially：
Step 31, judge four summits of the square subregion whether all in a border circular areas, if it is
The subregion is covered completely by a border circular areas；
Step 32, judge on the four edges of the square subregion each point whether not in a border circular areas
Interior, if it is the subregion and arbitrary circle are all non-intersect；
Step 33, judge each subregion whether all completely by a border circular areas cover or with it is arbitrary it is circular not
Intersecting, if it is step terminates；If otherwise will completely by a border circular areas cover or with arbitrary circular not phases
The region of friendship jumps to step 4 as determining region.
The above-mentioned technical proposal of the present invention has the beneficial effect that：
A kind of acquisition methods of the total area coverage of many border circular areas are embodiments provided, based on the thought divided and ruled,
Only uncertainty area is continued to divide, so comparing more existing algorithm can reduce calculating multiple on the premise of computational accuracy is not reduced
Miscellaneous degree.
Description of the drawings
Fig. 1 is the schematic flow sheet of the acquisition methods of the total area coverage of many border circular areas of the embodiment of the present invention；
Fig. 2 is using square region to be monitored and using structural representation during quartering model split subregion；
Fig. 3 is the structural representation of border circular areas and subregion all standing；
Fig. 4 is the structural representation that border circular areas are contacted with subregion；
Fig. 5 be border circular areas and subregion from structural representation.
Specific embodiment
To make the technical problem to be solved in the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and tool
Body embodiment is described in detail.
The embodiment of the present invention proposes a kind of acquisition methods of the total area coverage of many border circular areas, including：
Step 1, setting can cover the region to be monitored of each border circular areas；
Step 2, by the region division to be monitored be many sub-regions；
Step 3, judge each subregion whether all completely by a border circular areas cover or with it is arbitrary it is circular not
Intersecting, if it is step terminates；If otherwise will completely by a border circular areas cover or with arbitrary circular not phases
The region of friendship jumps to step 4 as determining region；
Step 4, each non-uncertainty area for having determined region is continued respectively to be divided into many sub-regions, and return to step 3.
Such scheme only continues to divide based on the thought divided and ruled to uncertainty area, and so comparing more existing algorithm can be
Computation complexity is reduced on the premise of not reducing computational accuracy.By delimiting a fully big area to be monitored in such scheme
Domain, and the region to be monitored can include the border circular areas of all of equipment.This mode is very simple, a large amount of without the need for carrying out in advance
Preparation, only need to delimit a sufficiently large region.Due to carrying out division subregion by the way of recurrence, therefore
Even if the increase of inappropriate series rank for being also not result in amount of calculation greatly that the region to be monitored at initial stage divides.And it is existing
Gridding method is all constantly to be finely divided each subregion, once the region division to be monitored at initial stage is inappropriate big, why
A large amount of useless calculating can be caused, and cause amount of calculation to be increased sharply.
Wherein, the region to be monitored can be square.It is easy to using foursquare region to be monitored enterprising in map
Rower is noted, and the subregion of multiple positive directions can also be divided into when subregion is divided.So also may be used in sub-zone dividing
To reduce operand.In an embodiment of the invention, the region to be monitored can be divided into four sub-regions, and often
One subregion can also again be divided into four sub-regions when continuing and dividing.
When multiple foursquare subregions are divided into, the coordinate on four summits of each square subregion can be passed through
To determine the position relationship of the subregion and each border circular areas.That is, described step 3 can be specially：
Step 31, judge four summits of the square subregion whether all in a border circular areas, if it is
The subregion is covered completely by a border circular areas；
Step 32, judge on the four edges of the square subregion each point whether not in a border circular areas
Interior, if it is the subregion and arbitrary circle are all non-intersect；
Step 33, judge each subregion whether all completely by a border circular areas cover or with it is arbitrary it is circular not
Intersecting, if it is step terminates；If otherwise will completely by a border circular areas cover or with arbitrary circular not phases
The region of friendship jumps to step 4 as determining region.
Wherein, in embodiments of the present invention can be by way of the minimum subregion area of setting come the precision of control algolithm
And computing cost.That is, also include between described step 3 and step 4：Judge whether the area of each subregion is both greater than pre-
If threshold value, then step will terminate if not.So can first determine minimum subregion whether more than pre- before subregion is divided
If threshold value；If it is continue to divide subregion, if otherwise exported current result of calculation as end product.Due to this
When and not all subregion be all determined region, therefore can using the area of uncertainty area therein as 0.5 calculate.Now
Total area coverage of output, including each area summation for determining region for being covered by a border circular areas completely, and often
The area of one uncertainty area is multiplied by 0.5.
The present invention is introduced below by an example：
In an embodiment of the invention, it can be assumed that have N number of equipment, therefore N number of equipment in region to be monitored
There are N number of border circular areas that can be serviced.The service can be the coverage of wireless base station, or the sensing range of sensor etc.
Deng.It is assumed that the home position of each border circular areas i is (Xi,Yi), and per unit covering radius is all r.Certainly, due to setting
It is standby can be with difference, therefore per unit covering radius is probably different, now has no effect on the enforcement of the embodiment of the present invention,
The increase of algorithm complex is not resulted in yet.
Now, a sufficiently large region foursquare to be monitored is divided so that the region to be monitored can cover all
Border circular areas.The center in the region to be monitored is (A, B) and its length of side is a.Now N number of border circular areas certainly all with the pros
There is the part of overlap in the region to be monitored of shape, and these circles are called the impact circle in the region to be monitored in the embodiment of the present invention, and
Aggregated label by these impact circles is C.
Subsequently the region fourth class to be monitored is divided into into four foursquare subregions.As shown in Figure 2, this four sub-regions
It is respectively labeled as S1, S2, S3, S4.Now judge each border circular areas in impact circle set C and each subregion S1,
Position relationship between S2, S3, S4.As shown in Fig. 3, Fig. 4, Fig. 5, the relation between each subregion and border circular areas only can
There are three kinds：All standing, contact, from.As shown in Figure 3, when four summits of a sub-regions are all located at a border circular areas
Interior, then the subregion is by the border circular areas all standing.As shown in Figure 4, exist when there is a point on the four edges of a sub-regions
In one border circular areas, then the subregion is contacted with the border circular areas.As shown in Figure 5, when on the four edges of a sub-regions
Each point not in a border circular areas, then the subregion and arbitrary border circular areas all from.In the embodiment of the present invention
In, by all standing with from subregion referred to as determined region, and the subregion of contact is referred to as into uncertainty area.
Now need to continue to proceed these uncertainty areas subdivision, and then need not make further for region is determined
Operation, therefore can reduce the initial stage of algorithm and prepare expense, and reduce algorithm expense, reduce the amount of calculation of algorithm.Continue thin
After point, judge whether each subregion after segmenting can become and determined region, and the carrying out of recurrence calculates.It is thin each time
/ front, need the area of the subregion for first judging current minimum whether more than preset value, if it is proceed subdivision, such as
Fruit otherwise exports current result as final result.The now son of the entire area+contact of the subregion of all standings
The area in region is multiplied by 0.5, exports as final total area coverage.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, on the premise of without departing from principle of the present invention, some improvements and modifications can also be made, these improvements and modifications
Should be regarded as protection scope of the present invention.
Claims (7)
1. acquisition methods of the total area coverage of a kind of many border circular areas, it is characterised in that include：
Step 1, setting can cover the region to be monitored of each border circular areas；
Step 2, by the region division to be monitored be many sub-regions；
Step 3, judge whether each subregion is all covered or all non-intersect with arbitrary circle completely by a border circular areas,
If it is step terminates；If otherwise will completely by a border circular areas cover or with all disjoint area of arbitrary circle
Domain jumps to step 4 as determining region；
Step 4, each non-uncertainty area for having determined region is continued respectively to be divided into many sub-regions, and return to step 3.
2. acquisition methods of the total area coverage of many border circular areas according to claim 1, it is characterised in that the step 3
Also include and step 4 between：
Whether the area for judging each subregion is both greater than predetermined threshold value, then step will terminate if not.
3. acquisition methods of the total area coverage of many border circular areas according to claim 2, it is characterised in that the step 4
Also include afterwards：
Step 5, the total area coverage of output, total area coverage is determined completely including each by what a border circular areas were covered
The area summation in region, and the area of each uncertainty area is multiplied by 0.5.
4. acquisition methods of the total area coverage of many border circular areas according to claim 1 or 2 or 3, it is characterised in that described
Region to be monitored is square.
5. acquisition methods of the total area coverage of many border circular areas according to claim 4, it is characterised in that the step 2
Specially：It is multiple foursquare subregions by the foursquare region division to be monitored.
6. acquisition methods of the total area coverage of many border circular areas according to claim 5, it is characterised in that the step 2
Specially：The foursquare region fourth class to be monitored is divided into into four foursquare subregions.
7. acquisition methods of the total area coverage of many border circular areas according to claim 5, it is characterised in that the step 3
Specially：
Step 31, judge four summits of the square subregion whether all in a border circular areas, it is if it is described
Subregion is covered completely by a border circular areas；
Step 32, judge on the four edges of the square subregion each point whether not in a border circular areas,
If it is the subregion and arbitrary circle are all non-intersect；
Step 33, judge each subregion whether all completely by a border circular areas cover or with arbitrary circular not phases
Hand over, if it is step terminates；If otherwise will be covered or all non-intersect with arbitrary circle by a border circular areas completely
Region as determining region, and jump to step 4.
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| CN104853363B (en) * | 2015-04-07 | 2018-06-26 | 浙江工业大学 | The method for monitoring wireless sensing net node monitoring area coverage rate |
| CN115994442B (en) * | 2022-11-18 | 2024-03-19 | 湖南科大天河通信股份有限公司 | Alarm ringing sound coverage area and coverage rate calculation method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101431442A (en) * | 2008-10-19 | 2009-05-13 | 傅城 | Node movement distributed planning method for wireless sensor network |
| CN102291739A (en) * | 2011-08-16 | 2011-12-21 | 哈尔滨工业大学 | Method for detecting wireless sensor network sparse events based on compressed sensing and game theory |
| CN103338507A (en) * | 2013-06-26 | 2013-10-02 | 北京工业大学 | Synchronization method for wireless sensor network clock based on movable reference nodes |
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| US7359836B2 (en) * | 2006-01-27 | 2008-04-15 | Mitsubishi Electric Research Laboratories, Inc. | Hierarchical processing in scalable and portable sensor networks for activity recognition |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101431442A (en) * | 2008-10-19 | 2009-05-13 | 傅城 | Node movement distributed planning method for wireless sensor network |
| CN102291739A (en) * | 2011-08-16 | 2011-12-21 | 哈尔滨工业大学 | Method for detecting wireless sensor network sparse events based on compressed sensing and game theory |
| CN103338507A (en) * | 2013-06-26 | 2013-10-02 | 北京工业大学 | Synchronization method for wireless sensor network clock based on movable reference nodes |
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