CN105654552B - A kind of quick Delaunay network construction methods towards Arbitrary distribution large-scale point cloud data - Google Patents
A kind of quick Delaunay network construction methods towards Arbitrary distribution large-scale point cloud data Download PDFInfo
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Abstract
The present invention provides a kind of quick Delaunay network construction methods towards Arbitrary distribution large-scale point cloud data, includes the following steps：Multi grid is divided, the initial triangulation network is created；Incremental insertion；The triangulation network updates；Delete the structure that auxiliary triangle shape completes Delaunay triangulation network.The present invention is divided by multi grid and the sort method of Hilbert curve order traversal grids, reduce point location process step-size in search and network forming during generate the long-narrow triangular mesh quantity finally to be deleted, and during to point location, using new algorithm, the process for asking triangle core and intersection edges is avoided, calculation amount is reduced.Substantially increase the efficiency that a cloud builds Delaunay triangulation network in the case where data volume is larger and is unevenly distributed.
Description
Technical field
The present invention relates to technical field of information processing more particularly to a kind of towards the fast of Arbitrary distribution large-scale point cloud data
Fast Delaunay network construction methods.
Background technology
Triangulation is one of the important research content in computational geometry field, and wherein Delaunay Triangulation is due to tool
There are many advantageous properties, and in GIS-Geographic Information System, digital elevation interpolation, finite element analysis, the fields such as geometry reconstruction have extensively
Application.
The construction method of Delaunay triangulation network can be mainly divided into incremental algorithm, divide and rule algorithm and triangle terrain model
Three kinds.Wherein for triangle terrain model due to wanting frequent ergodic data point, time efficiency is low and algorithm is complicated, seldom adopts at present
With.Divide and rule algorithm the advantages of be time efficiency height, but occupied space is big, and algorithm is complicated.Although algorithm of dividing and ruling can be by parallel
The method of calculating makes efficiency of algorithm be greatly improved, but parallel computation is higher to hardware requirement, does not have generality.Point by point
Insertion due to its algorithm is simple, occupy little space the features such as become a kind of current most popular algorithm.In recent years, and have perhaps
More scholars are improved on the basis of traditional incremental algorithm.Xu Minghai etc. utilizes the side of the syntople of storage triangle
Method is improved incremental algorithm on the basis of Bowyer and Watson, keeps the number that insertion point carries out circumscribed circle judgement big
Big to reduce, efficiency of algorithm has large increase, and efficiency of algorithm is also made to depend on the sequence that point is inserted into the triangulation network to a greater extent.Slowly
Road column etc. propose it is a kind of uniform grid is divided to point set, the method added some points by grid can be such that the time further decreases.
Liu and Snoeyink, Zhou and Jones, Hornus and Boissonnat, Buchin are proposed on the basis of dividing uniform grid
According to the side at different space filling curve (such as Hilbert curves, Peano curves) order traversal interpenetration network midpoint
Method, further improves and divides the efficiency that uniform grid is added some points, and the Delaunay network formings to being uniformly distributed point set have preferable effect
Fruit.
Although existing method comparative maturity, but still many shortcomings of generally existing, such as：
First：Process object is of less demanding to the treatment effeciency of algorithm for a small amount of discrete point cloud, but when the number of point cloud
When larger, algorithm process efficiency is generally relatively low, is influenced on network forming very big；
Second：Due to the distribution of point cloud data and uneven, regular grid method can be formed very during mesh generation
Multiple spot collection is distributed overstocked or excessively thin grid, makes mesh generation degree that can not unify, affects subsequent treatment effeciency；
Third：Barycentric coodinates are calculated during current point location asks the process of intersection edges to considerably increase calculation amount, drops
The low speed to mass cloud data Delaunay network formings.
Invention content
For above-mentioned problem existing in the prior art, the present invention proposes one kind towards Arbitrary distribution large-scale point cloud number
According to quick Delaunay network construction methods, existing algorithm is improved and optimizated, network forming efficiency is substantially increased, it is specific
Technical solution is as follows：A kind of quick Delaunay network construction methods towards Arbitrary distribution large-scale point cloud data, including following step
Suddenly：Step 1：Multi grid is divided, and in such a way that Hilbert curves traverse grid, the sequence of insertion point is ranked up：
A：Control point array and non-controlling point array are established, for storing point sorting data；
B：Level-one grid is established according to the number of data point, and point is assigned in grid；
C：Ready-portioned level-one grid is ranked up according to sequence of the Hilbert curves from the lower left corner to the lower right corner；
D：To the level-one grid after sequence, the extraction at control point and non-controlling point is carried out to each grid in order；
E：The upper limit threshold of the points in grid is set, if the points in current grid are more than the threshold value, according to step
Rapid B is adjusted mesh openings direction, but without control point during Loop partition to step D grid Loop partitions
Extraction；
Step 2：Create the initial triangulation network：
Data point coordinates maximum value is added a smaller number, minimum value subtracts an one smaller number by selection；It finds
The diagonal line that the initial rectangular convex hull connection initial rectangular convex hull of all data points can be surrounded, is classified as two triangles
Shape adds syntople as the initial triangulation network, and for the initial triangulation network；
Step 3：Incremental insertion：According to control point array is first inserted into, insertion sequence is the backward of former storage order, inserts afterwards
Enter non-controlling point array, insertion sequence is identical as former storage order, proceeds as follows point by point：
A：Insertion point is positioned；
B：Structure includes the cavity for being currently inserted into a little all domains of influence；Make a place three sides of a triangle are currently inserted into
For cavity sides, external loop truss is done to the adjoining triangle of cavity sides respectively；If being currently inserted into point Mr. Yu's triangle circumscribed circle
The another both sides of the triangle are added in cavity sides, continue to cavity then by the corresponding cavity edge contract of the triangle by inside
While being judged, it is currently inserted into a little until the circumscribed circle of the adjoining triangle of all cavity sides does not all include；
C：The triangulation network updates：A little be connected being currently inserted into obtained cavity node, form new triangle, and update by
The syntople of new triangle and its adjacent triangle that cavity is formed；Step 4：Delete auxiliary triangle shape：Whole point sets are inserted into
Afterwards, the triangle containing four vertex of rectangle convex hull in vertex is deleted, that is, completes the structure of Delaunay triangulation network.
Further, establish level-one grid in the step B in step 1, and by point be assigned in grid as follows into
Row：
S1：The average each Grid dimension of setting is the number of grid with total points divided by averagely counting；
S2：The number of grid is adjusted to the form of 4 integral number power, and keeps the grid number of row and column identical；
S3：With x in point cloud data, the maximin of y-coordinate is boundary, grid division, and according to each data point
Point is assigned in level-one grid by position.
Further, the extraction in the step D in step 1 for control point and non-controlling point carries out as follows：
s1：If current grid is a little, first point is put into control point array；
s2：The upper limit threshold of the points in grid is set, if the points in current grid are less than or equal to set threshold
Value, then be put into non-controlling point array by other points in addition to control point.
Further, the Loop partition of grid is carried out as follows in the step E in step 1：
St1：If points in current grid are more than threshold value, to the net region operated at present, according to level-one grid
Identical division rule carries out the Loop partition of inferior grid；
St2：During Loop partition, the extraction at control point is no longer carried out, the point in ordering grid is all put into
Non-controlling point array；
St3：When carrying out Hilbert sequences to current grid, is adjusted, ensured by the opening direction of Hilbert curves
Hilbert is formed by all grids according to being linked in sequence for non-controlling point set is put into for overall traversal order
Curve does not intersect.
Further, in the step A of step 3, insertion point is positioned and is carried out as follows：
a：Last updated triangle is found, i.e., the last one in the triangulation network is newborn when handling a upper insertion point
At triangle, if the triangular apex be A, B, C, along arranged counterclockwise；
b：If it is P to be currently inserted into point coordinates, P is respectively with Atria side AB, BC, CA triangle area constitutedCalculate SA, SB, SC, judge wherein to be less than 0
Number；If SA, SB, SCIt is all higher than and is equal to 0, then Δ ABC is triangle where current point P to be inserted, and point location process terminates；
Work as SA, SB, SCWhen there are one being less than 0, step c is carried out, S is worked asA, SB, SCWhen there are two being less than 0, step d is carried out；
c：Find mutually should be less than 0 S, at this time P should be located at this less than 0 S corresponding to side outside；This while when facing
Triangle continues to judge as Δ ABC, return to step b；
d：Find S minimum in two S for mutually should be less than 0, at this time corresponding to minimum S while triangle when facing make
Continue to judge for Δ ABC, return to step b.
Beneficial effects of the present invention are embodied in：
First：In the present invention in such a way that Hilbert curves traverse grid, and adjusts curve in ergodic process and open
Mouth direction, reduces the step-size in search of point location process；By the way of adding control point, institute in disposable interpenetration network is avoided
When having insertion point and initial rectangular convex hull vertex and be completed Delaunay network formings zone boundary formed it is a large amount of long and narrow
Triangle reduces structure and deletes the extra time of these triangles occupancy, to improve network forming efficiency；
Second：During to point location, using new algorithm, the mistake for asking triangle core and intersection edges is avoided
Journey reduces calculation amount.The Delaunay triangulation network rapid build for realizing large-scale point cloud data substantially increases a cloud and exists
Data volume is larger and the speed of Delaunay triangulation network is built in the case of being unevenly distributed, and algorithm of the invention is imitated in network forming
In rate, have a clear superiority.
Description of the drawings
Fig. 1 is Delaunay entirety network forming process flow diagram flow chart of the present invention；
Fig. 2 is present invention point sequencer procedure flow chart；
Fig. 3 is point location process flow diagram flow chart of the present invention；
Fig. 4 is the final trellis traversal precedence diagram that point cloud data of the embodiment of the present invention is partially formed；
Fig. 5 is the schematic diagram that point location step of the present invention midpoint P is located in the triangle currently judged；
Fig. 6 is the schematic diagram that point location step of the present invention midpoint P is located on the outside of the triangle a line currently judged；
Fig. 7 is the schematic diagram that point location step of the present invention midpoint P is located on the outside of two sides of triangle currently judged；
Fig. 8 is partial points cloud data point position fixing process schematic diagram in the embodiment of the present invention；
Fig. 9 is the final Delaunay network formings result schematic diagram of point cloud data of the embodiment of the present invention (vacuating 10 times).
Specific implementation mode
With reference to the accompanying drawings and embodiments to a kind of towards the quick of Arbitrary distribution large-scale point cloud data of the present invention
Delaunay network construction methods are described further.
The implementation case towards distribution more uniformly, the point cloud data of 27013896 points, according to Fig. 1's of the present invention
Step in Delaunay entirety network forming process flows diagram flow chart carries out network forming:
The first step：Dividing multi grid and in such a way that Hilbert curves traverse grid, to the sequence of insertion point into
Row sequence, to improve the processing speed of subsequent process.
Wherein Hilbert curves are that Germany mathematics man DavidHilbert is found that a kind of curve：First a pros
Shape is divided into four small squares, successively from the square center of southwest corner toward north to northwest square center, then past east
To the square center of northeast corner, then southeast corner square center is southward arrived, this is an iteration, if to four small squares
It proceeds as described above, divides down, be repeated, finally just obtain a curve that can fill up entire square.
According to the distributing position of the points of present case and data point, specific sequencer procedure is as follows：
(1) control point array and non-controlling point array are established, for storing point sorting data.
(2) level-one grid is established according to the number of data point, and point is assigned in grid, it is specific as follows：
A. the maximin for finding out abscissa in data point, ordinate obtains MinX=3685.13, MaxX=
4030.06, MinY=4441.82, MaxY=4803.90, and as boundary demarcation level-one grid.
B. it is 10 that rough points in average each grid, which are arranged,.The number for the level-one grid then to be divided is substantiallyThe number of grid is adjusted to 4 integral number power, i.e. 4194304 grids, often row and each column
2048 grids.
C. line width is acquired according to grid number and col width is：
And then it can be according to the coordinate (x of each data pointi, yi) grid that obtains where it is horizontally-arranged theVertical setting of typesEach data point is assigned in its corresponding grid by a grid.
(3) ready-portioned level-one grid is ranked up according to sequence of the Hilbert curves from the lower left corner to the lower right corner.
(4) to the grid after sequence, each grid is proceeded as follows in order：
A. if current grid a little, by first point is put into control point array；Such as the level-one grid in attached drawing four
G0、G1、G2、G3In a little, then first point in these grids will be put into the array of control point.
B. if the points in current grid are less than or equal to 100, other points in addition to control point are put into non-controlling point
Array.Such as the level-one grid G in attached drawing four0、G1Middle points are less than 100, then by G0、G1In all the points in addition to control point
It is put into non-controlling point array.
C. if the points in current grid are more than 100, to the net region operated at present, according to step (2)~(4)
Process carry out next stage grid Loop partition.During Loop partition, it should be noted that the processing of following process：
(i) extraction at control point is no longer carried out；
(ii) it when carrying out Hilbert sequences to current grid, to be adjusted, be protected by the opening direction of Hilbert curves
It demonstrate,proves and overall traversal order is formed by all grids according to being linked in sequence for non-controlling point set is put into
Hilbert curves do not intersect.
Such as level-one grid, G in attached drawing 43Middle points are more than or equal to 100, then in G2Continue under Loop partition region
Grade grid has 16 according to division rule next stage grid, and the start-stop direction of adjustment Hilbert curves makes it from the lower left corner to a left side
Upper angle is traversed this 16 grids, judged simultaneously in ergodic process in sequence so that entirety Hilbert curves do not intersect
It does not count still above 100 in this 16 grids, then need not continue grid division, the point in 16 grids is sequentially placed into
Non-controlling point set, at this time to level-one grid G2It is disposed.Later G is handled according to same division rule3.And so on, until
All level-one grids are disposed.
The opening direction adjustment process of Hilbert curves is carried out with reference to following table, wherein：" previous grid and current net in table
The "-" of the position relationship of lattice " represents the grid that current grid is first, superior grid region traversal, " current grid with it is latter
The "-" of the position relationship of grid " represents the grid that current grid is the last one traversal of superior grid region.
Table 1：The opening direction of Hilbert curves adjusts the table of comparisons
Second step：It enables(MinX-
tx, MinY-ty)、(MaxX-tx, MinY-ty)、(MaxX+tx, MaxY+ty)、(MinX-tx, MaxY+ty) convex as initial rectangular
Four vertex of shell.Connect (MaxX+tx, MinY-ty) and (MinX-tx, MaxY+ty) two vertex, by initial rectangular convex hull point
For two triangles, syntople is added as the initial triangulation network, and for the initial triangulation network.
Third walks：According to control point array, the rear sequence for being inserted into non-controlling points class mid point is first inserted into, carry out point by point as follows
Operation：
(1) point location
A. last updated triangle is found, i.e., the last one in the triangulation network is newborn when handling a upper insertion point
At triangle.If the triangular apex is A, B, C, along arranged counterclockwise.
B. it sets and is currently inserted into point coordinates as P, P is respectively with Atria side AB, BC, CA triangle area constitutedIf legend five is that P points are in different location
When schematic diagram.Calculate SA, SB, SC, judge wherein to be less than 0 number.If SA, SB, SCIt is all higher than and is equal to 0, then Δ ABC is and works as
Triangle where preceding point P to be inserted, point location process terminate；Work as SA, SB, SCWhen there are one being less than 0, step c is carried out, S is worked asA, SB, SC
When there are two being less than 0, step d is carried out.
C. find mutually should be less than 0 S, at this time P should be located at this less than 0 S corresponding to side outside.This while when facing
Triangle continues to judge as Δ ABC, return to step b.
D. find S minimum in two S for mutually should be less than 0, at this time corresponding to minimum S while triangle when facing make
Continue to judge for Δ ABC, return to step b.
Such as attached drawing 8 is the local triangulation networks formed by point cloud data when P points to be inserted into, T1 is the three of first judgement
It is angular.Ask the triangle of P and T1 at the size of area first, obtain next triangle judged as T3, then continue to judge P with
T3 triangles at triangle area size, obtain next triangle judged as T6.And so on, until find P points with
T13 triangles at triangle area be all higher than equal to 0, obtain P and be located in T13, the point location process of P terminates.
(2) cavity is established
Structure includes the cavity for being currently inserted into a little all domains of influence.
First using a three sides of a triangle where being currently inserted into as cavity sides, respectively to the adjoining triangle of cavity sides
Do external loop truss.If being currently inserted into inside point Mr. Yu's triangle circumscribed circle, by the corresponding cavity edge contract of the triangle,
The another both sides of the triangle are added in cavity sides, continue to judge cavity sides, until the adjoining three of all cavity sides
Angular circumscribed circle, which does not all include, to be currently inserted into a little.
(3) triangulation network updates
A little be connected being currently inserted into obtained cavity node, form new triangle, and update formed by cavity it is new
The syntople of triangle and its adjacent triangle.
4th step：After whole point sets are inserted into, the triangle containing four vertex of rectangle convex hull in vertex is deleted, that is, is completed
The structure of Delaunay triangulation network.
The network forming efficiency of the present invention is detected below.
Vacuate 100 times, 10 times and original point set as test data set using examples detailed above point set, using it is existing at present, compared with
Common serial D elaunay constructor algorithms are inserted into the time to a sorting time, point and operation compare total time, test wrapper
Border is portable notebook computer, Intel (R) Core (TM) i7-4700HQ2.40GHz, 8GB memory, win8,64 bit manipulation systems
System.Testing result see the table below：
Table 2：The different network construction method times compare
Wherein, CGAL is computational geometry algorithms library, it provides a kind of faster Delaunay network formings of ratio generally acknowledged at present
Method；RG is regular grid partitioning algorithm, and MG is multi grid partitioning algorithm, and HG is algorithm of the present invention.From comparing result
As can be seen that efficiency of algorithm of the present invention is higher than other three kinds of algorithms.The present invention is easy to use, is not depending on Parallel Hardware
On the basis of structure, the Delaunay network forming efficiency of large-scale point cloud data is improved, through experiment test, speed highest can reach
To about 900,000 points of processing per second, hence it is evident that be higher than existing serial D elaunay constructor algorithms, improve large-scale point cloud data
Efficiency of post treatment.In addition, verified, the present invention is for line style distribution, round distribution, chiasma type distribution, screw type distribution etc.
On a large scale, the point set of uneven distribution also has apparent advantage in Delaunay network forming efficiency, disclosure satisfy that Arbitrary distribution
Large-scale point cloud data efficient Delaunay network formings requirement.
Example the above is only the implementation of the present invention is not intended to limit the scope of the invention, every to utilize this hair
Equivalent structure or equivalent flow shift made by bright specification and accompanying drawing content is applied directly or indirectly in other relevant skills
Art field, is included within the scope of the present invention.
Claims (5)
1. a kind of quick Delaunay network construction methods towards Arbitrary distribution large-scale point cloud data, it is characterised in that：Including with
Lower step：
Step 1：Multi grid is divided, and in such a way that Hilbert curves traverse grid, the sequence of insertion point is ranked up：
A：Control point array and non-controlling point array are established, for storing point sorting data；
B：Level-one grid is established according to the number of data point, and point is assigned in grid；
C：Ready-portioned level-one grid is ranked up according to sequence of the Hilbert curves from the lower left corner to the lower right corner；
D：To the level-one grid after sequence, the extraction at control point and non-controlling point is carried out to each grid in order；
E：The upper limit threshold of the points in grid is set, if the points in current grid are more than the threshold value, extremely according to step B
Step D grid Loop partitions are adjusted mesh openings direction during Loop partition, but carrying without control point
It takes；
Step 2：Create the initial triangulation network：
Data point coordinates maximum value is added a smaller number, minimum value subtracts an one smaller number by selection；Finding can
A diagonal line for surrounding the initial rectangular convex hull connection initial rectangular convex hull of all data points, is classified as two triangles,
Syntople is added as the initial triangulation network, and for the initial triangulation network；
Step 3：Incremental insertion：According to control point array is first inserted into, insertion sequence is the backward of former storage order, it is non-to be inserted into afterwards
Control point array, insertion sequence is identical as former storage order, proceeds as follows point by point：
A：Insertion point is positioned；
B：Structure includes the cavity for being currently inserted into a little all domains of influence；Using a three sides of a triangle where being currently inserted into as empty
External loop truss is done in chamber side to the adjoining triangle of cavity sides respectively；If being currently inserted into inside point Mr. Yu's triangle circumscribed circle,
Then by the corresponding cavity edge contract of the triangle, the another both sides of the triangle are added in cavity sides, continue to cavity sides into
Row judges, is currently inserted into a little until the circumscribed circle of the adjoining triangle of all cavity sides does not all include；
C：The triangulation network updates：A little it is connected being currently inserted into obtained cavity node, forms new triangle, and update by cavity
The syntople of the new triangle and its adjacent triangle that are formed；
Step 4：Delete auxiliary triangle shape：After whole point sets are inserted into, by the triangle containing four vertex of rectangle convex hull in vertex
It deletes, that is, completes the structure of Delaunay triangulation network.
2. a kind of quick network forming sides Delaunay towards Arbitrary distribution large-scale point cloud data according to claim 1
Method,
It is characterized in that：Establish level-one grid in step B in step 1, and by point be assigned in grid as follows into
Row：
S1：The average each Grid dimension of setting is the number of grid with total points divided by averagely counting；
S2：The number of grid is adjusted to the form of 4 integral number power, and keeps the grid number of row and column identical；
S3：With x in point cloud data, the maximin of y-coordinate is boundary, grid division, and according to the position of each data point
Point is assigned in level-one grid.
3. a kind of quick network forming sides Delaunay towards Arbitrary distribution large-scale point cloud data according to claim 1
Method,
It is characterized in that：The step D in step 1 of extraction in to(for) control point and non-controlling point carries out as follows：
s1：If current grid is a little, first point is put into control point array；
s2：The upper limit threshold of the points in grid is set, if the points in current grid are less than or equal to set threshold value,
Other points in addition to control point are put into non-controlling point array.
4. a kind of quick network forming sides Delaunay towards Arbitrary distribution large-scale point cloud data according to claim 1
Method, it is characterised in that：The Loop partition of grid is carried out as follows in step E in step 1：
St1：If the points in current grid are more than threshold value, to the net region operated at present, according to identical as level-one grid
Division rule, carry out the Loop partition of inferior grid；
St2：During Loop partition, the extraction at control point is no longer carried out, the point in ordering grid is all put into non-control
System point array；
St3：When carrying out Hilbert sequences to current grid, adjusted by the opening directions of Hilbert curves, ensure for
Overall traversal order is formed by Hilbert curves all grids according to being linked in sequence for non-controlling point set is put into
Do not intersect.
5. a kind of quick network forming sides Delaunay towards Arbitrary distribution large-scale point cloud data according to claim 1
Method, it is characterised in that：In the step A of step 3, insertion point is positioned and is carried out as follows：
a：Last updated triangle is found, i.e., the last one in the triangulation network is newly-generated when handling a upper insertion point
Triangle, if the triangular apex is A, B, C, along arranged counterclockwise；
b：If it is P to be currently inserted into point coordinates, P is respectively with Atria side AB, BC, CA triangle area constitutedCalculate SA, SB, SC, judge wherein to be less than 0
Number；If SA, SB, SCIt is all higher than and is equal to 0, then △ ABC are triangle where current point P to be inserted, and point location process terminates；
Work as SA, SB, SCWhen there are one being less than 0, step c is carried out, S is worked asA, SB, SCWhen there are two being less than 0, step d is carried out；
c：Find mutually should be less than 0 S, at this time P should be located at this less than 0 S corresponding to side outside；This while triangle when facing
Shape continues to judge as △ ABC, return to step b；
d：Find S minimum in two S for mutually should be less than 0, at this time using corresponding to minimum S while triangle when facing as △
ABC, return to step b continue to judge.
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| CN106294985B (en) * | 2016-08-08 | 2019-06-11 | 福建农林大学 | A kind of efficient distributed and parallel Delaunay triangular construction method |
| CN108717352B (en) * | 2018-05-28 | 2021-07-06 | 武汉大学 | Concurrent screening insertion ordering method for improving computer operation speed |
| CN108898659B (en) * | 2018-05-31 | 2022-04-22 | 中南大学 | Triangulation method and system for three-dimensional reconstruction |
| CN109949420B (en) * | 2019-02-15 | 2023-03-14 | 山东师范大学 | Delaunay triangulation grid refining method suitable for GPU, GPU and system |
| US11467584B2 (en) * | 2019-12-27 | 2022-10-11 | Baidu Usa Llc | Multi-layer grid based open space planner |
| CN112530017B (en) * | 2020-11-18 | 2024-05-17 | 上海应用技术大学 | Method for constructing Delaunay triangle network |
| CN112669463B (en) * | 2020-12-25 | 2022-02-15 | 河南信大融通信息科技有限公司 | Method for reconstructing curved surface of three-dimensional point cloud, computer device and computer-readable storage medium |
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