CN103116593B - A kind of parallel method of the calculating convex hull based on multicore architecture - Google Patents
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Abstract
The present invention is directed to the deficiency that above-mentioned existing convex hull algorithm exists, provide a kind of parallel algorithm of the calculating convex hull based on multicore architecture, comprise the following steps: (1) finds the initial not exclusively convex hull of initial point set, and its anticlockwise directed edge in each limit represents; (2) according to initial not exclusively convex hull, a set is classified, find out all exterior points of each bar directed edge; (3) each directed edge in initial not exclusively convex hull is grown iteratively concurrently; (4) the non-convex hull summit on final gained convex hull is deleted.The present invention is effectively optimized former algorithm thus fully saves calculation resources.And parallel-expansion has been carried out to former algorithm Point Set assorting process and iterative process, take full advantage of the concurrent computation resource of polycaryon processor; Further by the adaptively selected parallel task granularity that controls of parallel, serial to control parallel speedup ratio, and eliminate issuable bottleneck.
Description
Technical field
The present invention relates to computational geometry field, especially relate to a kind of parallel method of the calculating convex hull based on multicore architecture.
Background technology
Convex hull be in computational geometry the most generally, the most basic a kind of structure, in computational geometry, occupy important position.Convex hull not only has numerous characteristics, but also is the effective tool of other geometrical bodies of structure.Convex hull also claims Minimum Convex Closure, is the minimum convex set comprising all objects in S set.Wherein, convex hull of planar point set is most important, most basic problem, and the Convex Problem of plane line-segment set peace face polygon set can be converted to the Convex Problem of plane point set.The Convex Problem of plane point set is widely used in computer graphics, image procossing and the various fields such as pattern-recognition, Geographic Information System.
Namely the convex hull solving plane point set is the minimum convex set that requirement obtains point set, and the border of convex hull is a convex polygon.About the serial algorithm calculating convex hull, in earlier work both domestic and external, mainly contain wraparound pack, grahame method, divided conquer, delta algorithm, real time algorithm, fast algorithm etc.Along with the development of parallel computing, many researchists both domestic and external attempt concurrent technique to be applied in the calculating of convex hull.In these parallel algorithms, the overwhelming majority employs divide-and-conquer strategy, is some subproblems by former PROBLEM DECOMPOSITION, parallelly independently solves these subproblems, and the solution then merging all subproblems obtains the solution of former problem.At present, also there are two subject matters in these parallel algorithms.The first, parallel granularity is uncontrolled, and load balance problem is considered not enough, likely occurs bottleneck; The second, introducing a large amount of extra computation task for realizing parallel computation, during as decomposed former problem, usually will sort etc. to initial point set.
With the Z solving convex hull of planar point set with divide and conquer that Zhou Peide proposes
3-2algorithm is example, its basic thought first obtains a little to concentrate x, y coordinate maximal value, minimum value, then the some quadrangularly be linked in sequence corresponding to maximal value, minimum value, this quadrilateral partition point set is 5 subsets, do not consider the subset being positioned at quadrilateral, deleting iteratively other 4 subsets is not the point on convex hull summit.In this algorithm, first judging point is positioned at which side (i.e. positive and negative division) of directed line segment, and re-use Euclidean distance and find out from directed line segment point farthest, algorithm is loaded down with trivial details, occupies a large amount of computational resources.
Summary of the invention
The present invention is directed to the deficiency that above-mentioned existing convex hull algorithm exists, on the basis of traditional planar convex hull algorithm, according to the application request of the real-time of planar convex hull and the calculating of mass data, propose a kind of parallel algorithm of Calculation Plane point set convex hull under multicore architecture, provide a kind of parallel method of the calculating convex hull based on multicore architecture, division when having abandoned compute euclidian distances and extracting operation, and whole computation process is resolved into some separate subtasks, make full use of the concurrent computation resource of polycaryon processor as far as possible, improve the execution efficiency of algorithm.
The present invention, after the extreme point finding point set on x direction, y direction, obtains an initial not exclusively convex hull.The all points concentrated point are classified according to its outside at this initial not exclusively each bar directed edge of convex hull, make every bar directed edge all comprise the data of its all exterior point, meanwhile, delete institute in this initial not exclusively convex hull inside a little.Iteration grows all directed edges concurrently, and continue the larger growth task of task resolution granularity according to threshold condition in an iterative process, carry out the intelligent selection of serial and concurrent operation, constantly insert new convex hull point to the assigned address in initial not exclusively convex hull, generate new directed edge, and according to newly-generated directed edge, the point in the set of former directed edge exterior point is classified, iteration like this, until the exterior point set of all directed edges is sky.Finally also will delete the non-salient point in all convex hull polygons, these points are on this polygonal limit, instead of its summit.
In order to achieve the above object, the invention provides following technical scheme:
Based on a parallel method for the calculating convex hull of multicore architecture, comprise the following steps:
(1) find the initial not exclusively convex hull of initial point set, its anticlockwise directed edge in each limit represents;
(2) according to initial not exclusively convex hull, a set is classified, find out all exterior points of each bar directed edge;
(3) each directed edge in initial not exclusively convex hull is grown iteratively concurrently;
(4) the non-convex hull summit on final gained convex hull is deleted.
As a kind of preferred version, the implementation method of described step (1) is: find four extreme points along x coordinate, y coordinate direction, delete point identical in these four points, the remaining convex polygon counterclockwise surrounded of pressing is initial not exclusively convex hull, is designated as LPBCH (S).
As a kind of preferred version, the implementation method of described step (2) is: definition line column
As a kind of preferred version, the implementation method of described step (3) is: for each directed edge P in incomplete convex hull side chain
ip
i+1carry out iteration growth concurrently, the process of described iteration growth is:
If (a) directed edge P
ip
i+1exterior point set be empty, then return ignore row;
B () is from directed edge P
ip
i+1exterior point set in find this directed edge Yan Shi must be the convex hull point of point set apart from maximum some P, this P;
(c) tie point P
iwith a P, some P and some P
i+1, generate two new directed edge P
ip and PP
i+1, to former directed edge P
ip
i+1exterior point set press directed edge P
ip and PP
i+1reclassify, obtain directed edge P respectively
ip and directed edge PP
i+1respective exterior point set;
If (d) directed edge P
ip
i+1the quantity of exterior point set mid point be not more than 2 times of MAXGROW, then go to step (f);
E () be iteration growth directed edge P concurrently
ip and PP
i+1obtain point range L respectively
1and L
2, make point range L={P
i∪ L
1∪ { P} ∪ L
2∪ { P
i+1, go to step (j);
F () definition chained list E stores some directed edges, by P
ip and PP
i+1insert E;
G () is for the every bar directed edge e in E, if its exterior point set is not empty, then obtain two new directed edge e according to the method for (b) (c) two step
1and e
2, and e
1and e
2exterior point set; From E, delete e, and insert e in the position of original e
1and e
2, wherein e
1identical with the starting point of e;
If h the exterior point set of any newly-generated directed edge is not empty in () (g), then go to step (g);
I () deletes Article 1 directed edge in E, and make L be the point range arranged by the starting point of directed edge each in E;
J point range L returns by () as a result;
Wherein, the MAXGROW in (d) is the threshold value of carrying out walking abreast, serial is selected.
As a kind of preferred version, the implementation method of step (4) is: the every bit of convex polygon that obtains of traversal step (3) successively, if P is current traversal point, R is forerunner's (upper namely by counterclockwise arrangement) of P, and Q is follow-up (more lower namely by counterclockwise arrangement) of P; If R, P, Q three point on a straight line, from LPBCH (S), just delete some P; Through the once traversal to LPBCH (S), delete the point on all non-convex hull summits, just can obtain the convex hull vertex sequence of point set, surround by these summits the convex hull that convex polygon just constitutes point set.
The present invention Yan Shi distance carrys out the position relationship of judging point and directed line segment, has abandoned former Z
3-2the division of the employing in algorithm during compute euclidian distances and extracting operation, reduce computational complexity, is effectively optimized former algorithm thus fully saves calculation resources.Secondly, parallel-expansion has been carried out to former algorithm Point Set assorting process and iterative process, by more Task-decomposing consuming time be some can the subtask of executed in parallel, the coupling eliminated between subtask makes separate execution between each parallel subtasks, make use of the concurrent computation resource of polycaryon processor fully; In addition, the process of Task-decomposing can complete in the time complexity of O (1), and parallel overhead is little.Finally, by the adaptively selected parallel task granularity that controls of parallel, serial to control parallel speedup ratio, and eliminate issuable bottleneck, in the Real-time solution of convex hull of planar point set and mass data solve, play the effect more outstanding than the parallel computation that simple serial calculates or coupling is higher.
Accompanying drawing explanation
Fig. 1 is the parallel method schematic flow sheet of the calculating convex hull based on multicore architecture provided by the invention;
Fig. 2 is Algorithm for Solving design sketch;
Fig. 3 is former Z
3-2algorithm, the Z after optimization
3-2the parallel algorithm execution time comparison diagram that algorithm and the present invention adopt;
Fig. 4 is the algorithm speed-up ratio schematic diagram that the present invention adopts.
Embodiment
Below with reference to specific embodiment, technical scheme provided by the invention is described in detail, following embodiment should be understood and be only not used in for illustration of the present invention and limit the scope of the invention.
Based on the calculating convex hull of multicore architecture parallel method flow process as shown in Figure 1, detailed process is described below:
(1) the initial not exclusively convex hull of initial point set is first found, its anticlockwise directed edge in each limit represents: find four extreme points along x coordinate, y coordinate direction, delete point identical in these four points, the remaining convex polygon counterclockwise surrounded of pressing is initial not exclusively convex hull, is designated as LPBCH (S).
LPBCH (S) comprises NCP (S) and NCE (S); Summit row in incomplete convex hull are designated as NCP (S), each summit P
i(x
i, y
i) represent, wherein 1≤i≤n, i is integer, and n is a little concentrated counting, and therefore has n summit in NCP (S).The anticlockwise oriented side chain formed between every two summits is designated as NCE (S), each directed edge P
ip
i+1(P
i(x
i, y
i), P
i+1(x
i+1, y
i+1)) represent; Wherein 1≤i≤n, i is integer, n be a little concentrate count; As i=n, P
i+1=P
n+1=P
1, therefore also have n element in NCE (S), wherein n-th directed edge is P
np
n+1, i.e. P
np
1, n bar directed edge surrounds a closed convex polygon.
(2) classified in the right side of initial not exclusively which bar directed edge of convex hull that all points in a set find according to it in step (1), find out all exterior points of each bar directed edge:
Point in some set represents with P (x, y), the vectorial P of directed edge in initial not exclusively convex hull
1p
2(P
1(x
1, y
1), P
2(x
2, y
2)) represent;
Definition line column
Value for some P (x, y) to vectorial P
1p
2(P
1(x
1, y
1), P
2(x
2, y
2)) Yan Shi distance, be designated as YD (P, P
1p
2).Classify to the right side of the initial not exclusively each bar directed edge of the convex hull whether all points in a set find according to it in step (1), wherein, the Yan Shi distance to this directed edge is greater than the point of 0 on the right side of this directed edge.By joining a little in the exterior point set of this directed edge on the right side of directed edge.Deleting all points not on the right side of any directed edge in some set, because they are in the inside of initial not exclusively convex hull, is the point on final convex hull scarcely.
(3) for each directed edge P in incomplete convex hull side chain
ip
i+1carry out iteration growth concurrently.The process of iteration growth is:
If (a) directed edge P
ip
i+1exterior point set be empty, then return ignore row;
B () is from directed edge P
ip
i+1exterior point set in find this directed edge Yan Shi must be the convex hull point of point set apart from maximum some P, this P;
(c) tie point P
iwith a P, some P and some P
i+1, generate two new directed edge P
ip and PP
i+1, to former directed edge P
ip
i+1exterior point set press directed edge P
ip and PP
i+1reclassify, obtain directed edge P respectively
ip and directed edge PP
i+1respective exterior point set;
If (d) directed edge P
ip
i+1the quantity of exterior point set mid point be not more than 2 times of MAXGROW, then go to step (f);
E () be iteration growth directed edge P concurrently
ip and PP
i+1obtain point range L respectively
1and L
2, make point range L={P
i∪ L
1∪ { P} ∪ L
2∪ { P
i+1, go to step (j);
F () definition chained list E stores some directed edges, by P
ip and PP
i+1insert E;
G () is for the every bar directed edge e in E, if its exterior point set is not empty, then obtain two new directed edge e according to the method for (b) (c) two step
1and e
2, and e
1and e
2exterior point set; From E, delete e, and insert e in the position of original e
1and e
2, wherein e
1identical with the starting point of e;
If h the exterior point set of any newly-generated directed edge is not empty in () (g), then go to step (g);
I () deletes Article 1 directed edge in E, and make L be the point range arranged by the starting point of directed edge each in E;
J point range L returns by () as a result.
Wherein, the MAXGROW in (d) is the threshold value of carrying out walking abreast, serial is selected, and only when the exterior point quantity of the directed edge grown is abundant, just selects parallel algorithm.Along with going deep into of iteration, the quantity of exterior point constantly reduces, and time below the twice that exterior point quantity is down to threshold value, parallel algorithm no longer will have superiority, now selection serial strategy is carried out finishing iteration, and obtains a result in limited number of time circulation.This step to control parallel speedup ratio, and eliminates issuable bottleneck by the adaptively selected parallel task granularity that controls of parallel, serial.
(4) every bit successively in the convex polygon that obtains of traversal step (3), if P is current traversal point, R is forerunner's (upper namely by counterclockwise arrangement) of P, and Q is follow-up (more lower namely by counterclockwise arrangement) of P.If R, P, Q three point on a straight line, from LPBCH (S), just delete some P.Through the once traversal to LPBCH (S), delete the point on all non-convex hull summits, just can obtain the convex hull vertex sequence of point set, surround by these summits the convex hull that convex polygon just constitutes point set.
Utilize convex hull parallel algorithm provided by the invention to carry out test for fusion, what fusion experiment adopted is the meteorological sampling number certificate representing province of China, and as shown in Figure 2, intensive point set is the sample distribution of weather data, and this is distributed as the website of all precipitation in this region.Polygonal region in Fig. 2 is the convex hull of this point set utilizing parallel algorithm provided by the invention to try to achieve.
As shown in Figure 3, algorithm the present invention adopted and former Z
3-2the execution efficiency of algorithm has carried out comparative analysis.For testing the parallel performance of algorithm of the present invention further, the present invention is to former Z
3-2algorithm is optimized and makes itself and algorithm of the present invention have comparability.To former Z
3-2the optimal way of algorithm is: with the class of algorithms of the present invention seemingly, instead of Euclidean distance by Yan Shi distance, eliminate former Z by stack architexture
3-2recurrence in algorithm, makes the Z optimized
3-2performance when algorithm and the serial of this algorithm perform is close.Fig. 3 is algorithm, the former Z that the present invention adopts
3-2the Z of algorithm and optimization
3-2the execution time comparison diagram of algorithm, to distinguish optimization and the performance boost that produces respectively of concurrent operation.
As shown in Figure 3: algorithm of the present invention is to 10
6the convex hull of the point set of the order of magnitude solve 200 milliseconds around, absolutely proved the high efficiency of this algorithm; After optimization, the performance of algorithm is greatly improved; Computing time is further reduced by parallel computation.When processor number is more, algorithm execution time is shorter.
Fig. 4 is algorithm improvement of the present invention and the speed-up ratio after optimizing, wherein, optimize speed-up ratio refer to optimize before and after the execution time ratio of algorithm, parallel speedup ratio refers to optimize the execution time ratio of rear algorithm and algorithm of the present invention, and total speed-up ratio refers to the execution time ratio of former algorithm and algorithm of the present invention.Experiment show that the average parallel speedup ratio of algorithm is about 1.55, and overall speed-up ratio is about 3.89.Wherein parallel speedup ratio converges on 2 when counting larger, and the parallel overhead which illustrating algorithm is less.It can also be seen that parallel speedup ratio has comparatively stable trend along with the increase that computing is counted from Fig. 4, and it is larger to optimize speed-up ratio shake.This is because the optimizing process of algorithm changes the Data Structures of algorithm and performs flow process, and the process of parallelization does not change algorithm self structure.As shown in Figure 4, this algorithm has stronger accelerating effect to former Z3-2 algorithm, thus has significantly saved calculation resources, promotes overall performance.
Technological means disclosed in the present invention program is not limited only to the technological means disclosed in above-mentioned technological means, also comprises the technical scheme be made up of above technical characteristic combination in any.
Claims (4)
1., based on a parallel method for the calculating convex hull of multicore architecture, it is characterized in that comprising the following steps:
(1) find the initial not exclusively convex hull of initial point set, its anticlockwise directed edge in each limit represents;
(2) according to initial not exclusively convex hull, a set is classified, finds out all exterior points of each bar directed edge:
Definition line column
Value for some P (x, y) to vectorial P
1p
2(P
1(x
1, y
1), P
2(x
2, y
2)) Yan Shi distance, the Yan Shi distance with initial not exclusively each bar directed edge of convex hull is greater than 0 join a little in the exterior point set of this directed edge, delete point gather in those points not on the right side of any directed edge;
(3) each directed edge in initial not exclusively convex hull is grown iteratively concurrently;
(4) the non-convex hull summit on final gained convex hull is deleted.
2. the parallel method of the calculating convex hull based on multicore architecture according to claim 1, it is characterized in that, the implementation method of described step (1) is: find four extreme points along x coordinate, y coordinate direction, delete point identical in these four points, the remaining convex polygon counterclockwise surrounded of pressing is initial not exclusively convex hull, is designated as LPBCH (S).
3. the parallel method of the calculating convex hull based on multicore architecture according to claim 1 and 2, is characterized in that, the implementation method of described step (3) is: for each directed edge P in incomplete convex hull side chain
ip
i+1carry out iteration growth concurrently, the process of described iteration growth is:
If (a) directed edge P
ip
i+1exterior point set be empty, then return ignore row;
B () is from directed edge P
ip
i+1exterior point set in find this directed edge Yan Shi must be the convex hull point of point set apart from maximum some P, this P;
(c) tie point P
iwith a P, some P and some P
i+1, generate two new directed edge P
ip and PP
i+1, to former directed edge P
ip
i+1exterior point set press directed edge P
ip and PP
i+1reclassify, obtain directed edge P respectively
ip and directed edge PP
i+1respective exterior point set;
If (d) directed edge P
ip
i+1the quantity of exterior point set mid point be not more than 2 times of MAXGROW, then go to step (f);
E () be iteration growth directed edge P concurrently
ip and PP
i+1obtain point range L respectively
1and L
2, make point range L={P
i∪ L
1∪ { P} ∪ L
2∪ { P
i+1, go to step (j);
F () definition chained list E stores some directed edges, by P
ip and PP
i+1insert E;
G () is for the every bar directed edge e in E, if its exterior point set is not empty, then obtain two new directed edge e according to the method for (b) (c) two step
1and e
2, and e
1and e
2exterior point set; From E, delete e, and insert e in the position of original e
1and e
2, wherein e
1identical with the starting point of e;
If h the exterior point set of any newly-generated directed edge is not empty in () (g), then go to step (g);
I () deletes Article 1 directed edge in E, and make L be the point range arranged by the starting point of directed edge each in E;
J point range L returns by () as a result;
Wherein, the MAXGROW in (d) is the threshold value of carrying out walking abreast, serial is selected.
4. the parallel method of the calculating convex hull based on multicore architecture according to claim 1, it is characterized in that, the implementation method of described step (4) is: the every bit successively in the convex polygon point range that obtains of traversal step (3), if P is current traversal point, R is the forerunner of P, Q is the follow-up of P, if R, P, Q three point on a straight line, from convex polygon point range, just deletes some P; Through the once traversal to convex polygon point range, delete the point on all non-convex hull summits.
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| US20020050990A1 (en) * | 1998-02-17 | 2002-05-02 | Henry Sowizral | Visible-object determination for interactive visualization |
| CN101377857A (en) * | 2008-07-30 | 2009-03-04 | 电子科技大学 | Method for simplifying three-dimensional model based on octree space division and culmination deletion |
| CN102200962A (en) * | 2011-07-25 | 2011-09-28 | 杭州电子科技大学 | Finite difference stencil parallelizing method based on iteration space sticks |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020050990A1 (en) * | 1998-02-17 | 2002-05-02 | Henry Sowizral | Visible-object determination for interactive visualization |
| CN101377857A (en) * | 2008-07-30 | 2009-03-04 | 电子科技大学 | Method for simplifying three-dimensional model based on octree space division and culmination deletion |
| CN102200962A (en) * | 2011-07-25 | 2011-09-28 | 杭州电子科技大学 | Finite difference stencil parallelizing method based on iteration space sticks |
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