CN104850712B - Surface sampled data topology Region Queries method in kind - Google Patents
Surface sampled data topology Region Queries method in kind Download PDFInfo
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Abstract
The present invention provides a kind of surface in kind sampled data topology Region Queries method, belongs to product reverse Engineering Technology field, it is characterised in that：Dynamically spatial-data index is built to surface sampling point in kind using R* trees, R* trees are indexed and carry out depth-first traversal quick obtaining target sampling pointkNeighbour's point set, the regularity of distribution of sampling point is described using Density Estimator according to the relationship of Region Queries and sampling point distribution as the initial reference data of target sampling point topology neighborhood, sampling point in initial reference data is sorted by its probability density size, it is maximum to choose wherein probability densityA sampling point defines local probability density maximum point, the direction of search is determined using portion's probability density maximum point, initial reference data is set moderately to be extended to rarefaction, degree is lacked to reduce its neighborhood information, it is iterated calculating according to this, can finally obtain more complete target sampling point topology adjacent region data.Using this method can quick obtaining complex profile uniformly or the topological adjacent region data of non-uniform sampling data, query result includeskNeighborhood, Voronoi neighborhoods and other effective adjacent region datas, can preferably reflect the local profile feature of surface sampled data in kind.
Description
Technical field
The present invention provides a kind of surface in kind sampled data topology Region Queries method, belongs to product reverse Engineering Technology neck
Domain.
Background technology
The surface-type feature analytical technology of widely used material object surface sampled data is to expressed by sampled data in reverse-engineering
Type face information carry out characteristic area analysis, and using analysis result as the feature reference data of curved surface modeling, sample neighborhood of a point
Data have great influence to surface-type feature precision of analysis, and its inquiry velocity directly determines that surface-type feature is analyzed
Efficiency.
Currently used adjacent region data querying method has k Region Queries, Delaunay Region Queries and Voronoi neighborhoods
Inquiry etc..K Region Queries are current most widely used Region Queries methods, and distance objective sample is obtained based on Euclidean distance inquiry
K nearest sampling point of point, X Li et al. is in academic journal《Proceedings of the Institution of Mechanical
Engineers》2007,221 (9), scientific paper " the Algorithm for finding all k- delivered on P1467-1472
nearest neighbors in three-dimensional scattered points and its application
In reverse engineering " and Xiong Bangshu etc. are in academic journal《CAD and graphics journal》2004,
16 (7), in the scientific paper " k nearest-neighbor fast search algorithm of three-dimensional scattered data being " delivered on P909-911, to reality
Object surface sampled data carries out grid division and establishes Static-state Space index, and is searched in grid where target sampling point and neighbouring grid
K nearest neighborhood sampling point of rope.K Region Queries algorithm principles are simply easy to implement, but for non-uniform sampling data, by Euclidean
Usually there is the restriction k adjacent region datas of distance serious skewed popularity, query result easily to be limited by sampled data distribution situation.
Delaunay Region Queries and Voronoi Region Queries belong to topological Region Queries, overcome k Region Queries easily by hits
The defects of being restricted according to distribution, query result can relatively accurately reflect the topological adjacency relationship of sampling point, and Sun Dianzhu etc. is in academic journal《It is military
Chinese college journal (information science version)》2011,36 (1), the scientific paper delivered on P86-91 be " three-dimensional dispersion point cloud
In Voronoi topology neighborhood point sets search algorithm ", expanded with adaptive using eccentric extension based on sampled data dynamically spatial-data index
It opens up algorithm and obtains sampling point topology neighborhood reference data, generate the Voronoi diagram of local point set, inquire the Voronoi neighborhoods of sampling point
The topological adjacent region data of sampling point can be accurately obtained, but the algorithm increases calculation amount when constructing Voronoi diagram, improves calculation
The space complexity and time complexity of method, affect Region Queries efficiency.
Invention content
The technical problem to be solved by the present invention is to：Overcome existing Region Queries method existing suitable to non-uniform sampling data
The problems such as answering property is not high, search efficiency is relatively low provides a kind of surface in kind sampled data topology Region Queries method, quick, accurate
Really inquiry obtains the topological adjacent region data of arbitrarily complicated surface in kind sampled data.
1. a kind of material object surface sampled data topology Region Queries method, it is characterised in that step is followed successively by：(1) material object is set
Surface sampled data set is combined into S, and sampling point data dynamically spatial-data index is built to S using R* trees；(2) R* trees are indexed and carries out depth
First traversal obtains the k neighbours of target sampling point, as the initial reference data collection of target sampling point topology neighborhood；(3) it is based on
Density Estimator makes initial reference data collection be extended to the neighbouring sampled data sparse region of target sampling point, to the initial ginseng of abatement
The neighborhood information missing for examining data set, the specific steps are：1. enabling λi(p) it is the point set of iteration variation, wherein i desirable 0,1,2,
3...n, as i=0, λ0(p) k neighbour's point sets of p are indicated；2. can determine λ based on Density Estimatori(p) probability density is very big
It is worth point Q (λi(p))：Its step is right firstIts k neighbour's point set { x is inquired successively1,x2,x3,...,xk, ηe
The calculation formula of the Multilayer networks value at place is：
Wherein, h is bandwidth, value ηeTo its k neighbour's point set { x1,x2,x3,...,xkIn each point distance maximum
Value, G (x) are kernel function, take the gaussian kernel function, form to beThen by λi(p) it is close that its probability is respectively pressed in
It spends size descending and arranges { η1,η2,...,ηm, finally take λi(p) maximum ω sampling point defines λ ini(p) probability density is very big
It is worth point, calculation formula is：
Wherein ω can be considered that for sensitive factor, the value range of the propagation direction for adjusting initial reference data, ω is3. calculating Q (λi(p)) the symmetric points Q&apos about target sampling point p;(λi(p))；4. being looked into surface sampled data in kind
Ask Q'(λi(p)) k neighbour's point sets λi'(p)；5. from λi'(p) selection can reduce λ ini(p) the subset T of neighborhood information missing；
6. 9. if T=Φ, go to step；⑦λi+1(p)=λi(p) ∪ T, i=i+1；8. repeating step 2. to 7.；9. λ (p)=λi
(p), expansion process terminates, and λ (p) is approximately the topological neighborhood at target sampling point p at this time；The step of above process 5. in, from
λi'(p) selection can reduce λ ini(p) the subset T of neighborhood information missing, specific method are：1. couple λi'(p) sampling point in is according to it
Distance progress ascending order arrangement to p makes ordered set { q1,q2,...,qk}；2. enabling j=1, T=Φ, d (x, y) are that point x is arrived
The Euclidean distance of point y；3.T=T ∪ { qj}；4. can reflect the sampling point distribution of sampled data part using the calculating of Density Estimator method
The mode point of feature, λi(p) mode point M (λi(p)) calculation formula is：
Wherein, n λi(p) quantity of sampling point, η ine∈λi(p), it is target sampling point p to λ that h, which is bandwidth its value,i(p) in
The maximum value of all sampling point distances, G (x) take the gaussian kernel function, form to beIt can similarly be counted according to formula (c)
Calculate λi(p) the mode point M (λ of ∪ Ti(p)∪T)；5. if d (p, M (λi(p) ∪ T)) > d (p, M (λi(p)) q, is then deleted from Tj,
Go to step 8；6. enabling j=j+1；7. repeating step 3 to 6；8. returning to T.
Compared with prior art, the present invention haing the following advantages：
(1) surface in kind sampled data dynamically spatial-data index R* trees are based on, it can be fast using depth-priority-searching method traversal R* trees
Speed obtains the initial reference data of target sampling point topology neighborhood, and for uniform sampling data, k neighborhoods have usually included target sample
The all topological adjacent region data of point without continuing iterative query, and for non-uniform sampling data, also can by k neighborhoods
Include most of topological adjacent region data of target sampling point, it is only necessary to which it is O (log to carry out time complexity for several times based on Density Estimator
N) expanding query operation can obtain the topological adjacent region data of more complete target sampling point, due to without time complexity
Degree is O (n2) Voronoi diagram or the supplementary means such as Delaunay Triangulation, in practical applications search efficiency improve about
10%~40%；
(2) adaptive iteration extension is carried out to the initial reference data of target sampling point topology neighborhood based on Density Estimator to look into
It askes, influence of the sampled data distribution situation in surface in kind to query result can be reduced to a certain extent, avoid because of sampling point point
Neighborhood information caused by cloth unevenness lacks, and effectively increases topological Region Queries process to arbitrarily complicated surface in kind sampled data
Adaptability；
(3) the topological adjacent region data finally obtained includes not only k neighborhoods and part Voronoi neighborhoods, also include on a small quantity its
He can embody effective neighborhood sampling point of sampling point topological adjacency relationship, and query result can preferably reflect original surface target sampling point institute
Local profile feature in position.
Description of the drawings
Fig. 1 is the program implementation flow chart of surface in kind sampled data topology Region Queries method of the invention；
Fig. 2 is the k neighborhoods of arbitrary target sampling point p in surface sampled data in kind；
Fig. 3 is the Voronoi neighborhoods of arbitrary target sampling point p in surface sampled data in kind；
Fig. 4~Fig. 8 is the building process schematic diagram of surface sampled data dynamically spatial-data index R* trees in kind；
Fig. 9 is target sampling point topology neighborhood initial reference data query process schematic diagram；
Figure 10 is the initial reference data collection and its mode point schematic diagram of target sampling point p topology neighborhoods；
Figure 11 is to take the maximum ω sampling point of probability density in initial reference data concentration and calculate local probability density pole
Big value point Q；
Figure 12 is the schematic diagram that k neighbour's point sets are inquired centered on symmetric points Q ' of the Q about target sampling point p；
Figure 13 is the mode point distribution schematic diagram after one extension is inquired；
Figure 14 is subjects motorcycle seat uniform sampling data and target sampling point p in embodiment one；
Figure 15 is the topological Region Queries result of the target sampling point p in embodiment one；
Figure 16 is subjects Micky Mouse toy sampled data and target sampling point p in embodiment two；
Figure 17 is the topological Region Queries result of the target sampling point p in embodiment two.
Specific implementation mode
The invention will be further described with reference to the accompanying drawings and embodiments.
Fig. 1 is the program implementation flow chart of surface in kind sampled data topology Region Queries method of the invention, surface in kind
Sampled data topology Region Queries method program includes mainly structure, the mesh of surface in kind sampled data dynamically spatial-data index R* trees
The acquisition of standard specimen point initial topology neighborhood reference data, topological neighborhood reference data pattern point and local probability density maximum point
Calculating and adjacent region data adaptive iteration expanding query.
Fig. 2 and Fig. 3 is the k neighborhoods of arbitrary target sampling point p and Voronoi neighborhood schematic diagrames, k in surface sampled data in kind
Region Queries have many advantages, such as that principle is simply easy to implement, but for the sampled data of non-uniform Distribution, k neighborhoods have serious
Skewed popularity, cause to cannot get enough neighborhood sampling points in sampled data sparse region.Voronoi neighborhoods have with target sampling point
Stringent Voronoi topological adjacency relationships, because being limited without being distributed by sampled data, but when building Voronoi diagram
It is computationally intensive, influence Region Queries efficiency.Therefore, the present invention will combine a kind of search efficiency height of the advantage invention of the two, adapt to
Property strong topological Region Queries method.
Fig. 4~Fig. 8 is the building process schematic diagram of surface in kind sampled data dynamically spatial-data index R* trees, empty in view of dynamic
Between index R* trees using node minimum bounding box (minimum bounding rectangle, MBR) tissue data object sky
Between proximity relations, there is good spatial index performance for multidimensional data, and can preferably support the dynamic of sampled data
State is safeguarded, therefore can effectively improve efficiency data query using R* trees as the spatial index of sampled data.Build the correlation of R* trees
Parameter is node minimum child node number m=8, maximum child node number M=30, and node reinserts number R=13.Fig. 4 is material object
Surface sampled data, Fig. 5 are the root node of R* trees, and Fig. 6 and Fig. 7 are internal node, and Fig. 8 is leaf node.
Fig. 9 is target sampling point topology neighborhood initial reference data query process schematic diagram, and dynamic expansion is used based on R* trees
Hollow ball algorithm quick search obtains the k neighborhoods of target sampling point, and as the initial reference number of target sampling point topology neighborhood
According to specific querying method is：The leaf node for including target sampling point p in R* trees is searched using depth-first traversal algorithm, calculates it
MBR bounding polygons r1, using p as the centre of sphere, it is radius, determines hollow ball region, obtain the data sample in the hollow ball region,
If it, which is counted, is more than k, therefrom search with p apart from k nearest sampling point, otherwise using the present hollow radius of a ball as internal diameter,(l is acquired neighbour's number of samples) is outer diameter, dynamic expansion hollow ball region, until the point for including in ball
Number is more than or equal to k, then therefrom searches with p apart from k nearest point, the final k adjacent region datas for obtaining p, the suggestion value model of k
Enclose Wei [8,25]Interior integer, generally takes 15.
Figure 10 is the initial reference data and its mode point schematic diagram of target sampling point p topology neighborhoods, if λ (p) is the topology of p
Neighborhood reference data set can calculate mode point M (λ (p)) according to formula (1)；The Gaussian kernel, form is selected to be when calculatingBandwidth h values are the maximum value of all sampling point distances in p to λ (p), and h is an adaptive bandwidth value；
The distance of reference data pattern point to target sampling point is closer, and the reflection of reference data set pair target sampling point circumferential shape is better, more
Close to the topological neighborhood of target sampling point, and in Figure 10 reference data set be biased to close quarters, cause mode point according to target sampling point compared with
Far, therefore the topological neighborhood at the reference data set and non-targeted sampling point, it need to be extended inquiry, increasing being capable of reduction mode point
With the rarefaction sampling point of target sampling point distance.
Figure 11 is to reference data set λ shown in Figure 10i(p), the wherein maximum preceding ω sampling point (solid line of probability density is obtained
Enclose the sampling point of choosing) and calculate local probability density maximum point Q (λi(p)), the specific steps are：1. rightIt looks into successively
Ask its k neighbour's point set { x1, x2... xk, η is calculated according to formula (2)eIt is η that the probability density at place, wherein bandwidth, which take h values,eArrive it
K neighbour's point sets { x1, x2... xkIn each point distance maximum value, h is an adaptive bandwidth value, and kernel function G (x) takes Gaussian kernel
Function, form are2. by λi(p) its probability density size descending arrangement { η is respectively pressed in1, η2...
ηm}；3. taking λi(p) maximum ω sampling point calculates λ according to formula (3) ini(p) probability density maximum point Q (λi(p)),
Middle ω can be considered that for sensitive factor, the optimum valuing range of the propagation direction for finely tuning initial reference data, ω isM=10 in Figure 11, ω desirable 3.
Figure 12 is the schematic diagram that inquiry is extended to the topological neighborhood reference data of target sampling point p shown in Fig. 10, tool
Body process is：1. i=0 enables λ0(p) the k neighbour's point sets for being target sampling point p；2. it is true to be based on Density Estimator by way in Figure 11
Determine λi(p) probability density maximum point Q (λi(p))；3. calculating Q (λi(p)) about the symmetric points Q ' (λ of target sampling point pi
(p))；4. inquiring Q ' (λ in surface sampled data in kindi(p)) k neighbour point set λ 'i(p)；5. from λ 'i(p) selection can subtract in
Few λi(p) the subset T of neighborhood information missing；6. 9. if T=Φ, go to step；⑦λi+1(p)=λi(p) ∪ T, i=i+1；
8. repeating step 2. to 7.；9. λ (p)=λi(p), expansion process terminates, and λ (p) is approximately the topology at target sampling point p at this time
Neighborhood；The step of above process 5. in, from λ 'i(p) selection can reduce λ ini(p) the subset T of neighborhood information missing, specific side
Method is：1. to λ 'i(p) sampling point in makes ordered set { q according to its distance progress ascending order arrangement to p1, q2..., qm}；②
J=1, T=Φ, d (x, y) are the Euclidean distance of point x to point y；3. T=T ∪ { qj}；4. calculating can reflect sampled data part sample
The mode point of point distribution characteristics calculates λ according to formula (1)i(p) mode point M (λi(p)) method λ similarly, can be calculated accordinglyi
(p) the mode point M (λ of ∪ Ti(p)∪T)；If 5. d (p, M (λi(p) ∪ T)) > d (p, M (λi(p)) q, is then deleted from Tj, jump
Go to step 8.；6. j=j+1；7. repeating step 3. to 6.；8. returning to T.
Figure 13 is the mode point distribution schematic diagram after one extension is inquired, due to Q (λi(p)) it is close to be in sampled data
Spend larger region, thus its symmetric points Q ' (λ about target sampling point piIt (p)) will be positioned at the smaller area of sampled data density
Domain, therefore Region Queries process is always extended towards the sparse region of sampled data, and it is newest that acquisition can be inquired in expansion process
Neighborhood sampling point so that new adjacent region data is continuously added in topological neighborhood reference data in this region, to make pattern
Point position also change, and it is always close towards target sampling point and finally tend to converge on target sampling point, when mode point with
When target sampling point is close enough, above-mentioned expanding query will be unable to obtain more new neighborhood sampling points, so that iterative query
Journey restrains.At this point, topological neighborhood reference data will be distributed evenly in around target sampling point, it can preferably reflect sampled data
Neighborhood topology relationship and local surface-type feature.
Embodiment one：Topological neighborhood is carried out to the target sampling point p in motorcycle seat's uniform sampling data shown in Figure 14
Inquiry, sampling point quantity are 20055, k Region Queries points k=8, and the time of structure R* trees is 10.6259s, topological Region Queries
Time is 11.3246s, and query result is as shown in figure 15.
Embodiment two：Topological Region Queries are carried out to the target sampling point p in Micky Mouse toy sampled data shown in Figure 16,
The sampled data is the non-uniform sampling data for including Curvature varying large area, and sampling point quantity is counted for 8427, k Region Queries
The time of k=15, structure R* trees are 4.0125s, and the topological Region Queries time is 3.9613s, and query result is as shown in figure 17.
Can be obtained by embodiment, the present invention is applicable not only to uniform sampling data, for non-uniform sampling data with
And the larger local sampling data of Curvature varying equally can effective query arbitrary target sampling point topological adjacent region data, have relatively strong
Adaptability, query result includes not only k neighborhoods and Voronoi neighborhoods, while also including that other more multipotencys embody sampling point topology
Effective adjacent region data of syntople so that the topological adjacent region data of sampling point does not depend on the spatial distribution of sampled data, avoid because
Adjacent region data caused by sampling point is unevenly distributed lacks, therefore query result can preferably reflect that original surface target sampling point institute is in place
The local profile feature set.
The above described is only a preferred embodiment of the present invention, being not that the invention has other forms of limitations, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
Imitate embodiment.But it is every without departing from technical solution of the present invention content, according to the technical essence of the invention to above example institute
Any simple modification, equivalent variations and the remodeling made, still fall within the protection domain of technical solution of the present invention.
Claims (1)
1. a kind of material object surface sampled data topology Region Queries method, it is characterised in that step is followed successively by：(1) surface in kind is set
Sampled data set is combined into S, and sampling point data dynamically spatial-data index is built to S using R* trees；(2) R* trees are indexed and carries out depth-first
Traversal obtains the k neighbours of target sampling point, as the initial reference data collection of target sampling point topology neighborhood；(3) it is close to be based on core
Degree estimation makes initial reference data collection be extended to the neighbouring sampled data sparse region of target sampling point, to cut down initial reference number
It is lacked according to the neighborhood information of collection, the specific steps are：1. enabling λi(p) it is the point set of iteration variation, λ0(p) k neighbour's point sets of p are indicated；
2. can determine λ based on Density Estimatori(p) probability density maximum point Q (λi(p))：Its step is right firstIts k neighbour's point set { x is inquired successively1,x2,x3,...,xk, ηeThe calculating of the Multilayer networks value at place is public
Formula is：
Wherein, h is bandwidth, value ηeTo its k neighbour's point set { x1,x2,x3,...,xkIn each point distance maximum value, G
(x) it is kernel function, takes the gaussian kernel function, form to beThen by λi(p) it is big that its probability density is respectively pressed in
Small descending arranges { η1,η2,...,ηm, finally take λi(p) maximum ω sampling point defines λ ini(p) probability density maximum
Point, calculation formula are：
Wherein ω can be considered that for sensitive factor, the value range of the propagation direction for adjusting initial reference data, ω is3. calculating Q (λi(p)) the symmetric points Q&apos about target sampling point p;(λi(p))；4. being looked into surface sampled data in kind
Ask Q'(λi(p)) k neighbour's point sets λi'(p)；5. from λi'(p) selection can reduce λ ini(p) the subset T of neighborhood information missing；
6. 9. if T=Φ, go to step；⑦λi+1(p)=λi(p) ∪ T, i=i+1；8. repeating step 2. to 7.；9. λ (p)=λi
(p), expansion process terminates, and λ (p) is approximately the topological neighborhood at target sampling point p at this time；The step of above process 5. in, from
λi'(p) selection can reduce λ ini(p) the subset T of neighborhood information missing, specific method are：1. couple λi'(p) sampling point in is according to it
Distance progress ascending order arrangement to p makes ordered set { q1,q2,...,qk}；2. enabling j=1, T=Φ, d (x, y) are that point x is arrived
The Euclidean distance of point y；3.T=T ∪ { qj}；4. can reflect the sampling point distribution of sampled data part using the calculating of Density Estimator method
The mode point of feature, λi(p) mode point M (λi(p)) calculation formula is：
Wherein, n λi(p) quantity of sampling point, η ine∈λi(p), it is target sampling point p to λ that h, which is bandwidth its value,i(p) all samples in
The maximum value of point distance, G (x) take the gaussian kernel function, form to beSimilarly λ can be calculated according to formula (c)i(p)
Mode point M (the λ of ∪ Ti(p)∪T)；5. if d (p, M (λi(p) ∪ T)) > d (p, M (λi(p)) q), is then deleted from Tj, redirect
To step 8；6. enabling j=j+1；7. repeating step 3 to 6；8. returning to T.
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| CN106127677B (en) * | 2016-06-22 | 2019-07-12 | 山东理工大学 | The point cloud boundary characteristics recognition methods of fractional sample projected outline constraint |
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