CN109636913A - Triangle gridding increment topology joining method based on Delaunay subdivision - Google Patents
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Abstract
The purpose of the present invention is to provide a kind of triangle gridding increment topology joining method based on Delaunay subdivision.This method deletes the lopsided dough sheet in net boundary to be spliced by edge cleaning；Based on the vertex set of grid and deleted dough sheet after edge cleaning, the seam area between grid to be spliced is constructed, and adds boundary protection point for the area data point set；Partial reconstruction is carried out to suture area data point set using Delaunay surface interpolation algorithm for reconstructing, and propagates this partial reconstruction process in seam area by wavefront expansion strategy, obtains interpolation in the suture curved surface of grid stitching portion data point.The algorithm can realize the topologically correct splicing of triangle gridding, splicing efficiency with higher, and suture curved surface generated can relatively accurately reflect archetype in the local detail feature of grid stitching portion.
Description
Technical field
The present invention provides a kind of triangle gridding increment topology joining method based on Delaunay subdivision, it can be achieved that net surfaces
Topologically correct splicing between lattice belongs to product reverse-engineering field.
Background technique
Curve reestablishing technology based on surface sampled data in kind is widely used in CAD/CAM, machine vision, virtually shows
The numerous areas such as real.The development of 3-D scanning technology is so that the scale of Points Sample data is increasingly huge, such as laser scanner
Point cloud data obtained is up to even hundred million grades of millions.Curve reestablishing is directly carried out for such large-scale point cloud data,
The time complexity and space complexity of algorithm are usually higher, it is difficult to guarantee splicing result just while improving and splicing efficiency
True property.If carrying out piecemeal reconstruction to point cloud data, each piece of reconstruction grid of gained is then spliced into integral grid, then can significantly be dropped
The Space-time Complexity of low algorithm promotes the reconstruction efficiency of large-scale point cloud data.How correctly to splice each piece of weight in this process
Networking lattice are that restriction large-scale point cloud data reconstruction efficiency and reconstructed results are opened up to restore the topological adjacency relationship of whole curved surface
Flutter the critical issue of correctness.
To realize grid splicing, Turk etc. is at " Zippered polygon meshes from range images "
It is based in (Conference on Computer Graphics&Interactive Techniques.1994:311-318.)
The thought of cutting proposes a kind of Zipper algorithm, that is, utilizes the edge triangles of another piece of grid of border cuts of one piece of grid,
Boundary sampling point based on remaining grid and the vertex for being deleted tri patch generate the suture curved surface between grid to be spliced；Jin
Deng in " Mesh fusion using functional blending on topologically incompatible
Sections " be fitted first using radial basis function in (Visual Computer, 2006,22 (4): 266-275.) it is to be spliced
The boundary of model, the method for being then based on Hermite surface interpolation obtain the continuous curve surface in region to be spliced, realize the nothing of grid
Stitch smooth linking；Lin etc. is in " Mesh composition on models with arbitrary boundary
topology》(IEEE Transactions on Visualization&Computer Graphics,2008,14(3):
653.) discrete grid block is converted for the implicit fitting surface of seam area based on the method for marching cube in, obtains having spliced
At whole curved surface；Qin etc. is in " Efficient Smoothness-Preserving Fusion Modelling Method
for Mesh Models》(International Journal of Simulation Modelling,2017,16(3):
The boundary profile of grid to be spliced is projected into two-dimensional surface in 527-540.), triangulation is carried out to the vertex set of profile
And the profile vertex subdivision result by subdivision is carried out smoothly, to obtain smooth suture based on the method for Implicit Function Interpolation
Curved surface.The suture curved surface that the above method generates can be by the seamless smooth linking of grid to be spliced, but has ignored grid stitching portion
Topological adjacency relationship between sampling point, the local detail that suture curved surface generated is generally difficult to accurately reflect grid stitching portion are special
Sign.
Dey etc. " Localized Cocone surface reconstruction " (Computers&Graphics,
2011,35 (3): 483-491.) in the method based on Delaunay subdivision propose Localized Cocone algorithm.The algorithm
The correct splicing that Dividing Curve Surface is rebuild between grid can be achieved, and suture curved surface generated can relatively accurately reflect that grid is spelled
Connect the topological adjacency relationship between place's sampling point.But Localized Cocone algorithm needs in realizing grid splicing to grid
Vertex set carries out multiple Delaunay subdivision, and the time complexity and space complexity of algorithm are excessively high, reduces grid splicing
Efficiency.
Summary of the invention
The purpose of the present invention is to provide a kind of triangle gridding increment topology joining method based on Delaunay subdivision, can
Take into account the efficiency of grid splicing and the topologically correct property of splicing result.Its technical solution are as follows:
A kind of triangle gridding increment topology joining method based on Delaunay subdivision, it is characterised in that step is successively are as follows: (1) structure
Make list L={ D (Si) | i=1,2 ..., n }, either element D (S in listi) it is triangle gridding to be spliced, SiFor grid top
Point set, enabling S is S1∪S2∪...∪Sn；(2) to each piece of triangle gridding D (S to be splicedi) carry out edge cleaning, it may be assumed that it is right
D(Si) in outermost layer there is the incident dough sheet on complete topology disc structure dough sheet vertex to be deleted, and will be deleted patch
Vertex is stored in set Oi, until D (Si) in the Voronoi Neighbor Points that are located in S of remaining dough sheet vertex be both contained in SiIn；(3) will
D(Si) in be deleted dough sheet vertex set OiMerge, obtains seam area data point set O；(4) point to guarantee O borderline region
With complete Voronoi Neighbor Points, by D (Si) in outermost layer have complete topology disc structure dough sheet vertex Voronoi
Neighbor Points are added in O as the boundary protection point of O；(5) a point p is chosen from O0, and obtain distance p0K nearest point group
At point set λ (p0), to point set { p0}∪λ(p0) reconstruction of Delaunay surface interpolation is carried out, and it is initial using reconstructed results as curved surface
Region constructs interpolation in the suture curved surface Q of O by wavefront expansion algorithm；(6)Q∪D(S1)∪D(S2)∪...∪D(Sn) it is net
Lattice splicing result.
To realize goal of the invention, the triangle gridding increment topology joining method based on Delaunay subdivision is special
Sign is: in step (2), to each piece of triangle gridding D (Si) carry out edge cleaning the step of be specifically: (1) obtain D (Si)
Point in boundary edge incidence dough sheet in non-boundary edge is stored in set P by boundary edgeiIn；(2) enabling j is 1, k PiIn number of vertex
Amount；(3) from P (λi) in extract point pj, calculate pjPositioned at D (Si) in incident triangle maximum circumradius rj；(4) with pjFor
The centre of sphere,Make ball for radius, the point being contained in the ball in S is stored in empty setIn；(5) ifNot exclusively it is contained in D
(Si) corresponding to grid vertex set Si, then by PiThe incident dough sheet of middle each point is from D (Si) in delete, and by PiIt empties, then
It executes (1)；(6) it enables j increase 1, if j≤k, executes (3), otherwise scale removal process terminates.
To realize goal of the invention, the triangle gridding increment topology joining method based on Delaunay subdivision is special
Sign is: in step (4), from D (Si) in obtain O boundary protection point the step of be specifically: (1) inquire D (Si) boundary edge,
Point in boundary edge incidence dough sheet in non-boundary edge is stored in set Mi；(2) for MiIn each vertex pl, calculate plPositioned at D
(Si) in incident triangle maximum circumradius rl, then using pl as the centre of sphere,Make ball for radius, will not belong in the ball
Point in point set O is added in O labeled as protection point.
To realize goal of the invention, the triangle gridding increment topology joining method based on Delaunay subdivision is special
Sign is: in step (5), to { p0}∪λ(p0) Delaunay surface interpolation reconstructed results using described in claim 2
Method carries out edge cleaning, using acquired results as curved surface prime area, constructs interpolation in the suture of O by wavefront expansion algorithm
Curved surface Q.
To realize goal of the invention, the triangle gridding increment topology joining method based on Delaunay subdivision is special
Sign is: interpolation is constructed during the suture curved surface Q of O passing through wavefront expansion algorithm, for having constructed in curved surface area
Either boundary point pr, with prWith the point set λ (p formed in O away from k nearest pointr) target divided region is constituted, to λ
(pr) reconstruction of Delaunay surface interpolation is carried out, and edge cleaning is carried out using method described in claim 2 to reconstructed results,
Then dough sheet Chong Die with building completion region in edge cleaning result is deleted, and makees incremental expansion to curved surface has been constructed.
Compared with prior art, the present invention having the advantage that
(1) lopsided dough sheet on net boundary region to be spliced is deleted by edge cleaning；Based on the addition of protection point, use
Delaunay surface interpolation algorithm for reconstructing to suture area data point set carry out partial reconstruction, and by wavefront expansion algorithm by this
Partial reconstruction process is propagated in seam area, obtains interpolation in the suture curved surface of grid stitching portion data point set, it can be achieved that phase
Topologically correct splicing between adjacent grid.
(2) suture curved surface is that point of the modes such as expansion, division based on partial reconstruction and wavefront ring in grid stitching portion is concentrated
Gradually extend；Whole process relies only on the Delaunay mesh generation of a small amount of point set as a result, grid with higher splices
Efficiency.
(3) this method is suitable for the splicing that massive point cloud piecemeal rebuilds grid, it is ensured that the topologically correct property of final reconstructed results is simultaneously
It is obviously improved the reconstruction efficiency of mass cloud data.
Detailed description of the invention
Fig. 1 is the Voronoi Neighbor Points distribution of arbitrary point p on net boundary region to be spliced；
Fig. 2~Fig. 3 is the effect picture after the preceding cleaning with edge of adjacent mesh edge cleaning；
Fig. 4 is boundary point and the extended boundary point of seam area between adjacent mesh；
Fig. 5 is the wavefront expansion process schematic for suturing curved surface；
Fig. 6 is that the piecemeal of Happy Buddha model in embodiment one rebuilds grid；
Happy Buddha block model rebuilds grid splicing result figure in Fig. 7~Fig. 9 embodiment one；
The piecemeal of Venus model rebuilds grid in Figure 10 embodiment two；
Venus block model rebuilds grid splicing result figure in Figure 11 embodiment two.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
If the obtained each piece of subset of cut-point cloud S is { S1,S2,...,Sn, curve reestablishing is carried out to every piece of subset, is obtained
To each piece of triangle gridding to be spliced { D (S1),D(S2),...,D(Sn)}.In any grid D (S to be splicedi) independently generated
Cheng Zhong, due to D (Si) borderline region sampling point part Voronoi Neighbor Points be present in D (Si) in adjacent grid (such as Fig. 1 institute
Show), lead to D (Si) borderline region dough sheet be generally difficult to accurately reflect the topological adjacency relationship between the sampling point of grid stitching portion.Cause
This is the topologically correct splicing realized between each piece of grid, need to carry out edge cleaning to every piece of grid to be spliced, i.e., to its boundary
Point on region carries out Voronoi Neighbor Points integrity detection, and Voronoi Neighbor Points are not respectively positioned on the vertex in the block grid
Incident dough sheet delete.
To carry out accurate edge cleaning, it is necessary first to obtain the net boundary region to be spliced complete Voronoi of sampling point
Neighbor Points.For grid D (S to be splicedi) in for any sampling point p with complete topology disc structure, complete topology
Neighbor Points must be contained inIn, wherein B (p；R) refer to centered on p, r is the ball of radius, and r is D (Si) in
The maximum circumradius of point p incidence triangle.It therefore, can be to D (Si) in complete topology disc structure sampling point p, with p
For the centre of sphere,Make ball for radius, the point approximation for being included in the ball is regarded as to the complete Voronoi Neighbor Points of point p.But due to
The boundary point of grid to be spliced does not have complete topological disc structure, therefore in edge scale removal process, each piece of net to be spliced
The integrity detection of lattice borderline region sampling point Voronoi Neighbor Points needs to have complete topology disc structure from the block grid
Outermost layer sampling point starts to carry out.To the subset S of whole point cloud SiIt is independent to rebuild grid D (S to be spliced generatedi) carry out edge
The step of cleaning, is as follows: (1) obtaining D (Si) boundary edge, by boundary edge incidence dough sheet in non-boundary edge point be stored in set Pi
In；(2) enabling j is 1, k PiIn vertex quantity；(3) from P (λi) in extract point pj, calculate pjThe maximum of incident triangle is external
Radius of circle rj；(4) with pjFor the centre of sphere,Make ball for radius, the point being contained in the ball in S is stored in empty setIn；(5) ifNot exclusively it is contained in Si, then by PiThe incident dough sheet of middle each point is from D (Si) in delete, by the vertex to be deleted patch be stored in collect
Close Oi, and by PiIt empties, then executes (1)；(6) it enables j increase 1, if j≤k, executes (3), otherwise scale removal process terminates.It is adjacent to
Effect difference before the cleaning of splicing operator edge and after edge cleaning is as shown in Figures 2 and 3.
After the completion of each piece of grid edge is cleared up, the seam area between adjacent mesh is by being deleted dough sheet in each piece of grid
Vertex set constitute.Therefore, the suture between grid to be spliced can be constructed by merging the vertex set of deleted dough sheet
Region.As long as can be realized the correct reconstruction of data point set in seam area, suture curved surface can be generated between adjacent mesh,
Complete the process of grid splicing.
Correct rebuild of data point set also needs to guarantee that the point of its borderline region has completely in seam area
Voronoi Neighbor Points.As shown in figure 4, the boundary point of seam area is also the boundary point of the grid to be spliced after edge is cleared up,
Therefore the complete Voronoi Neighbor Points of every piece of net boundary point to be spliced can be added in seam area, to guarantee the area
The integrality of domain boundary point Voronoi Neighbor Points.But since the boundary point of grid to be spliced does not have complete topological disk knot
Structure, thus its complete Voronoi neighbour point set can not be inquired based on the maximum circumradius of its incident triangle.This
When, can there will be complete topology disk knot in grid to be spliced by the boundary point of seam area to grid internal extended to be spliced
Extended boundary point of the outermost layer sampling point of structure as seam area, and by the inquiry of the complete Voronoi Neighbor Points of extended boundary point
As a result it is added in seam area, to guarantee the integrality of seam area boundary point Voronoi Neighbor Points.Herein, will newly add
The point in seam area is added to as protection point.If seam area data point is O, then the construction and its boundary protection of seam area
Steps are as follows for the addition of point: (1) by each piece of grid D (S to be splicedi) vertex set of dough sheet is deleted in edge scale removal process
Close OiMerge, obtains seam area data point set O；(2) D (S is obtainedi) in outermost layer have complete topology disc structure dough sheet top
The Voronoi Neighbor Points of point, and be marked as protection point and be added in O；In above-mentioned steps (2), from any block grid D
(Si) in obtain O boundary protection point the step of be specifically: 1. inquire D (Si) boundary edge, by non-side in boundary edge incidence dough sheet
Point on boundary side is stored in set Mi；2. for MiIn each vertex pl, calculate plPositioned at D (Si) in incident triangle maximum it is outer
Meet radius of circle rl, then with plFor the centre of sphere,Make ball for radius, by the point being not belonging in point set O in the ball labeled as protection
Point is added in O.
Since seam area data point set belongs to the long strip type point cloud of non-close, directly it is carried out interpolation curved surface rebuild it is past
Toward a large amount of trans-regional dough sheet can be generated, the correctness of final reconstructed results is influenced.To solve this problem, it can be used
There is reconstructed results the theoretical Cocone algorithm guaranteed to rebuild seam area data point in Delaunay surface interpolation algorithm for reconstructing
The fractional sample of collection, and it is incomplete by Voronoi Neighbor Points in above-mentioned edge method for cleaning deletion partial reconstruction result
Vertex incidence dough sheet；It is then based on wavefront expansion algorithm and extends above-mentioned partial reconstruction process to entire seam area, to obtain
Interpolation is obtained in the suture curved surface of grid stitching portion data point set, completes the splicing of grid.
Using in seam area specific sampling point p and the point set λ (p) that forms of the nearest k point of distance p as partial reconstruction sample
This, and the suture curved surface of generation is set as Q.For promoted fractional sample acquisition efficiency, using R* tree as data directory.To each
Block triangle gridding to be spliced { D (S1),D(S2),...,D(Sn) carry out increment topology splicing the step of it is as follows: (1) construction column
Table L={ D (Si) | i=1,2 ..., n }, either element D (S in listi) it is triangle gridding to be spliced, SiFor grid vertex collection
It closes, enabling S is S1∪S2∪...∪Sn；(2) to each piece in L triangle gridding D (S to be splicedi) carry out edge cleaning, then base
The vertex set construction suture area data point set O of grid and deleted dough sheet after edge cleaning, and boundary is added for O
Protection point；(3) spatial index of R* tree construction point set O is used, while choosing the smallest point of Z coordinate in O as initial point p0, with
p0And distance p0Point set λ (the p of nearest k point composition0) it is used as initial local reconstruction sample；(4) using Cocone algorithm to λ
(p0) curve reestablishing is carried out, it obtains initial local and rebuilds grid D (λ (p0)), and to D (λ (p0)) carry out edge cleaning；(5) by D
(λ(p0)) be added in Q, and by D (λ (p0)) in point be labeled as saturation point；(6) boundary edge of Q is obtained, and from boundary edge
Obtain the first point p without containing boundary point labelrIf prIt is not present, executes step (9)；(7) by prAnd distance prNearest k
Point set λ (the p of point compositionr) it is used as fractional sample, if λ (p at this timer) in point be saturation point, then by prLabeled as boundary point,
It executes step (6), otherwise to λ (pr) curve reestablishing is carried out, obtain partial reconstruction grid D (λ (pr))；(8) to D (λ (pr)) carry out
Edge cleaning, and delete D (λ (pr)) in the dough sheet be overlapped in Q, remaining grid is added in Q, and will be in new addition Q
Grid vertex is labeled as saturation point, then executes (6)；(9) the incident dough sheet of protection point is deleted from Q, Q ∪ D (S1)∪D
(S2)...∪D(Sn) it is grid splicing result.
As shown in figure 5, the suture surface mesh generated through wavefront expansion can be seamless the boundary for being connected grid to be spliced,
So that adjacent Mesh Fusion to be spliced is at one piece of integral grid.
Major parameter used herein is that the fractional sample during suturing surface forming obtains quantity k, can be according to suture zone
The distribution density of data point set is chosen in domain, is distributed more uniform seam area data point set for sampling point, it is proposed that k value
It is 50, and for the seam area data point set of sampling point non-uniform Distribution, it can suitably increase fractional sample quantity, it is proposed that k value
It is 80.
Embodiment one: to the point cloud model piecemeal of Happy Buddha shown in Fig. 6 rebuild grid, using methods described herein into
Row splicing.The sampling point distribution of model meshes stitching portion shown in Fig. 6 is more uniform, but Curvature varying large area is locally present.From
Fig. 7~Fig. 9 can be seen that this paper algorithm being capable of the more uniform grid model of correct splicing boundary region sampling point distribution；Simultaneously
In the biggish aspect of model region of Curvature varying, the suture curved surface that this paper algorithm generates can accurately reflect archetype
Local detail feature at this.
Embodiment two: grid is rebuild to the piecemeal of Venus point cloud model shown in Figure 10, is spelled using methods described herein
It connects.There are sampling point characteristic areas unevenly distributed in grid stitching portion for Figure 10 institute's representation model.As shown in figure 11, this paper algorithm can
Correct splicing boundary region sampling point grid model unevenly distributed.
The above described is only a preferred embodiment of the present invention, being not the limitation for making other forms to the present invention, 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 without departing from the technical solutions of the present invention, according to the technical essence of the invention to above embodiments institute
Any simple modification, equivalent variations and the remodeling made, still falls within the protection scope of technical solution of the present invention.
Claims (5)
1. a kind of triangle gridding increment topology joining method based on Delaunay subdivision, which is characterized in that step is successively are as follows:
(1) list L={ D (S is constructedi) | i=1,2 ..., n }, either element D (S in listi) it is triangle gridding to be spliced, SiFor
Grid vertex set, enabling S is S1∪S2∪...∪Sn；(2) to each piece of triangle gridding D (S to be splicedi) carry out edge it is clear
Reason, it may be assumed that D (Si) in outermost layer there is the incident dough sheet on complete topology disc structure dough sheet vertex to be deleted, and will be deleted
Except the vertex of dough sheet is stored in set Oi, until D (Si) in the Voronoi Neighbor Points that are located in S of remaining dough sheet vertex be both contained in Si
In；(3) by D (Si) in be deleted dough sheet vertex set OiMerge, obtains seam area data point set O；It (4) is the guarantee boundary O
The point in region has complete Voronoi Neighbor Points, by D (Si) in outermost layer there is complete topology disc structure dough sheet vertex
Voronoi Neighbor Points are added in O as the boundary protection point of O；(5) a point p is chosen from O0, and obtain distance p0Nearest k
A point forms point set λ (p0), to point set { p0}∪λ(p0) reconstruction of Delaunay surface interpolation is carried out, and using reconstructed results as song
Face prime area constructs interpolation in the suture curved surface Q of O by wavefront expansion algorithm；(6)Q∪D(S1)∪D(S2)∪...∪D
(Sn) it is grid splicing result.
2. the triangle gridding increment topology joining method based on Delaunay subdivision as described in claim 1, it is characterised in that:
In step (2), to each piece of triangle gridding D (Si) carry out edge cleaning the step of be specifically: (1) obtain D (Si) boundary edge,
Point in boundary edge incidence dough sheet in non-boundary edge is stored in set PiIn；(2) enabling j is 1, k PiIn vertex quantity；(3) from
P(λi) in extract point pj, calculate pjPositioned at D (Si) in incident triangle maximum circumradius rj；(4) with pjFor the centre of sphere,Make ball for radius, the point being contained in the ball in S is stored in empty setIn；(5) ifNot exclusively it is contained in D (Si) institute
Corresponding grid vertex set Si, then by PiThe incident dough sheet of middle each point is from D (Si) in delete, and by PiIt empties, then executes
(1)；(6) it enables j increase 1, if j≤k, executes (3), otherwise scale removal process terminates.
3. the triangle gridding increment topology joining method based on Delaunay subdivision as described in claim 1, it is characterised in that:
In step (4), from D (Si) in obtain O boundary protection point the step of be specifically: (1) inquire D (Si) boundary edge, by boundary edge
Point in incident dough sheet in non-boundary edge is stored in set Mi；(2) for MiIn each vertex pl, calculate plPositioned at D (Si) in enter
Penetrate the maximum circumradius r of trianglel, then with plFor the centre of sphere,Make ball for radius, point set O will be not belonging in the ball
In point labeled as protection point be added in O.
4. the triangle gridding increment topology joining method based on Delaunay subdivision as described in claim 1, it is characterised in that:
To { p in step (5)0}∪λ(p0) Delaunay surface interpolation reconstructed results carried out using method described in claim 2
Edge cleaning constructs interpolation in the suture curved surface Q of O by wavefront expansion algorithm using acquired results as curved surface prime area.
5. the triangle gridding increment topology joining method based on Delaunay subdivision as claimed in claim 4, it is characterised in that:
Interpolation is constructed during the suture curved surface Q of O passing through wavefront expansion algorithm, for having constructed any side in curved surface area
Boundary point pr, with prWith the point set λ (p formed in O away from k nearest pointr) target divided region is constituted, to λ (pr) carry out
Delaunay surface interpolation is rebuild, and carries out edge cleaning using method described in claim 2 to reconstructed results, is then deleted
Dough sheet Chong Die with building completion region in result is cleared up at edge, and makees incremental expansion to curved surface has been constructed.
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| CN110111397A (en) * | 2019-05-16 | 2019-08-09 | 长江水利委员会长江科学院 | A kind of complex water areas Remeshing method method sutured based on boundary with expansion |
| CN111045090A (en) * | 2019-12-31 | 2020-04-21 | 核工业北京地质研究院 | Magnetic anomaly grid rapid stitching method |
| CN112669463A (en) * | 2020-12-25 | 2021-04-16 | 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 |
| CN113838212A (en) * | 2021-09-22 | 2021-12-24 | 杭州趣村游文旅集团有限公司 | A block splicing method for digital village 3D model |
| CN114510775A (en) * | 2021-12-30 | 2022-05-17 | 电子科技大学 | A 3D Space Curved Meshing Method for Complex Models |
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