CN1835021A - Curve triangle section structure method of 3-D scattered point set in 3-D scanning system - Google Patents
Curve triangle section structure method of 3-D scattered point set in 3-D scanning system Download PDFInfo
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- CN1835021A CN1835021A CN 200610039550 CN200610039550A CN1835021A CN 1835021 A CN1835021 A CN 1835021A CN 200610039550 CN200610039550 CN 200610039550 CN 200610039550 A CN200610039550 A CN 200610039550A CN 1835021 A CN1835021 A CN 1835021A
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Abstract
The invention advances a method for constructing curve triangulation of 3D scattered point set in a 3D scanning system, obtaining sea of point clouds with respect to fast measuring system, and making triangulation on filtered and spliced point clouds, comprising the steps as follows of: preprocessing 3D scattered points; making initial triangulation; then in increment mode, adding in new points point by point and forming new split until the whole point set has been processed; and finally making optimization on the formed basic grids by curvature least optimization rule and obtaining the final triangulation of the point set, where the optimization method as follows: in the basic grids, estimating curvaturesk1 and k2 of two splits T1 and T2 of a spacial convex quadrangle (A, B, C, D), and if ||ki||=min(||kj||), using the split T1 as the optimum split of this quadrangle; and for a plane convex quadrangle (A, B, C, D), determining its optimum split by Lawson side exchange rule.
Description
Technical field
The present invention relates to the surface triangulation building method of 3 d discrete point collection in a kind of 3 D scanning system.
Background technology
Reverse-engineering (Reverse Engineering, RE) technology is the later stage eighties 20th century to appear at the new technology in advanced manufacture field, it generally comprises four basic links: three-dimensional body detects and conversion (acquisition of physical data), data pre-service (put cloud processing, identification, look splicing more), the foundation of cad model (surface reconstruction), the moulding of CAM product, its basic flow sheet as shown in Figure 1.In the process that detects and change at three-dimensional body, by three-dimensional digital scanner, three-dimensional rapid scanning measurement is carried out in mock-up surface, meeting under the prerequisite of discrete sampling speed and the quality of data, obtain the 3 d-dem data of product, it is the very crucial ring of forming a connecting link during reverse-engineering mean camber is rebuild that data are carried out to triangulation, directly affect the quality of reconstruct success or not and cad model, its follow-up link is played to very crucial restrictive function.In the digitized process of reverse-engineering, when the point cloud directly obtaining with 3 D scanning system (accompanying drawing 2) is reduced to curved surface, because the cloud data to all acquisitions exists scrambling, common curve reestablishing algorithm is not too applicable, need carry out triangulation to 3D scattered points, so triangulation is one of important step in curve reestablishing.At present few about the direct triangulation of 3D scattered point set, a kind of delta algorithm proposing in " Triangulation of scattered data in 3D space. (B.K.Choi; H.Y.Shin; Y.I.Yoon, et al.CAD, 1988; 20 (5): 239～248) " is a kind of good method, be used widely, but this algorithm requirement can find a bit all visible to all scattered points, find easily this vector remarkable.
Summary of the invention
The invention provides a kind of surface triangulation building method that can reduce 3 d discrete point collection in time complexity and succinct reasonably 3 D scanning system, triangle gridding that the present invention produces has high fairing characteristic, has good conformality simultaneously.
The present invention adopts following technical scheme:
The surface triangulation building method of 3 d discrete point collection in a kind of 3 D scanning system, with Fast measurement system, obtain mass data point cloud, then these cloud datas are carried out to filtration treatment and seamless spliced, and spliced some cloud carried out to triangulation, the above-mentioned step that spliced some cloud carried out to triangulation is as follows:
3 d discrete point is carried out to pre-service, carry out again initial triangulation, after this by incremental mode, beyond the delta-shaped region obtaining at initial subdivision, pointwise adds new point, form new subdivision, until point set is disposed, finally to the basic grid forming, use curvature minimum optimization criteria to be optimized processing to it, obtained the final triangulation of 3 d discrete point collection; Above-mentioned processing of using curvature minimum optimization criteria to be optimized it to basic grid is adopted with the following method:
For four convex quadrangles (A, B, C, D) that summit is not coplanar in basic grid, carry out respectively the existing two kinds of triangle subdivision T of convex quadrangle (A, B, C, D)
1, T
2, and carry out curvature κ
1, κ
2estimation, when
Time, with this triangle subdivision T
ias this tetragonal optimal division; For four convex quadrangles (A, B, C, D) that summit is coplanar in basic grid, by Lawson limit exchange criterion, determine this tetragonal optimal division.
Compared with prior art, tool of the present invention has the following advantages:
The triangulation that the present invention proposes is mainly used in the triangulation aspect of the 3D scattered point set of all open surfaces, this simplify of arithmetic the data structure extensively adopting at present, make it more rationally succinct, reduced the space complexity of algorithm; Propose a kind of new Optimality Criteria based on curvature of curved surface, make the triangle gridding producing can have high fairing characteristic, there is good conformality simultaneously.Improve simultaneously and revised partial data structure, having reduced algorithm time and the space complexity of Choi, having improved greatly the quality of formation speed and the triangulation of grid.Can better be applied to the surface reconstruction of the scattered point set in 3 D scanning system.
Different from plane projection method, directly subdivision algorithm is directly according to 3D scattered points structure triangulation.Practical direct subdivision algorithm is few, a kind of delta algorithm that " Triangulation of scattered data in 3D space. (B.K.Choi; H.Y.Shin; Y.I.Yoon; et al.CAD; 1988,20 (5): 239～248) " proposes is a kind of good method, is used widely.But this algorithm is when the pre-service to point set, must find one can see vector a little, to all single-valued surfaces, can accomplish in theory, and when in the face of a scattered point set, find easily this vector remarkable.Though this algorithm provides good data structure, in order to reduce algorithm space complexity, can also remake simplification.The improvement of the present invention to Choi data structure, has proposed minimum curvature Optimality Criteria, has reduced the Space-time Complexity of algorithm, has accelerated the structure speed of triangle gridding, has guaranteed fairness and the shape-retaining ability of subsequent builds curved surface simultaneously.
The present invention inquires into triangulation, proposes the minimum minimum optimization criteria of curvature.Input is the unknown surface sampling point set that does not need additional structure and tissue order, and output is the triangulation of this point set, i.e. unknown curved surface linear proximity.Algorithm must meet: monodrome open surface.Concrete advantage is as follows:
(1) data structure is one of importance in surface triangulation, and this patent improves and revised partial data structure, has reduced algorithm space complexity.
(2) in surface triangulation algorithm, another important aspect is Optimality Criteria, and this patent is estimated to start with from curvature of curved surface, proposes curvature minimum optimization criteria, makes subdivision have good conformality.Spatial form Optimality Criteria is mainly conceived to conformality, and fairing criterion is mainly conceived to the fairness of curved surface.
(3) subdivision result is better: owing to having adopted curvature minimum optimization criteria, its starting point is that the intrinsic characteristic of curved surface is curvature, thereby on the 3D curved surface obtaining, the triangulation conformality of scattered point set is good, can meet the requirement of reconstruct.The tetragonal curvature of subdivision convexity is minimum guarantees that there is good fairing degree at former surface smoothing place, is combined and can obtains desirable subdivision result with the method for sampling of dividing and ruling.
(4) algorithm has good Space-time Complexity, more succinct reasonably data structure.Compare with Choi algorithm, the data structure LTL that this algorithm changes subdivision is TL, and it has been become to three-dimensional by 6 DOF, greatly reduces space complexity.Revise TBL simultaneously, be able to immediate updating TL and EL in subdivision easily, simplified the search of subdivision process.Adopt this data structure to reduce the time complexity of algorithm.
(5) widely applicable: the pre-service of this algorithm point set is simple and reliable, to single-valued surface arbitrarily, all can implement.Although pre-service projects on two dimensional surface, carry out, optimize and directly at 3d space, carry out, therefore this algorithm is still a kind of direct subdivision algorithm.
Accompanying drawing explanation
Fig. 1 is reverse-engineering process flow diagram.
Fig. 2 is grating style three-dimension scanning system composition diagram.
Fig. 3 is the graph of a relation on summit, limit, triangle and method arrow thereof, point and limit.
Fig. 4 is interim border table (TBL).
Fig. 5 is border table BL.
Fig. 6 is algorithm overall flow figure.
Fig. 7 is the formation of initial TL, EL and TBL.
Fig. 8 is the renewal that new point adds fashionable TL, EL and TBL.
Fig. 9 is four semi-cylindricals and the crossing subdivision result of a ball.
Figure 10 is a faceform's subdivision result.
Embodiment
The surface triangulation building method of 3 d discrete point collection in a kind of 3 D scanning system, with Fast measurement system, obtain mass data point cloud, then these cloud datas are carried out to filtration treatment and seamless spliced, and spliced some cloud carried out to triangulation, the above-mentioned step that spliced some cloud carried out to triangulation is as follows:
3 d discrete point is carried out to pre-service, carry out again initial triangulation, after this by incremental mode, beyond the delta-shaped region obtaining at initial subdivision, pointwise adds new point, form new subdivision, until point set is disposed, finally to the basic grid forming, use curvature minimum optimization criteria to be optimized processing to it, obtained the final triangulation of 3 d discrete point collection; Above-mentioned processing of using curvature minimum optimization criteria to be optimized it to basic grid is adopted with the following method:
For four convex quadrangles (A, B, C, D) that summit is not coplanar in basic grid, carry out respectively the existing two kinds of triangle subdivision T of convex quadrangle (A, B, C, D)
1, T
2, and carry out curvature κ
1, κ
2estimation, when
Time, with this triangle subdivision T
ias this tetragonal optimal division; For four convex quadrangles (A, B, C, D) that summit is coplanar in basic grid, by Lawson limit exchange criterion, determine this tetragonal optimal division.
Above-mentioned 3 d discrete point is carried out to pre-service employing and will in scattered point set P, have a P
i(x
i, y
i, z
i) (i=1,2 ..., m) project on X-Y plane, obtain in scattered point set P, there is a P
i(x
i, y
i, z
i) (i=1,2 ..., subpoint m), usings the mean value of X coordinate figure of each subpoint as the center P on X-Y plane
cx coordinate figure on X-Y plane, usings the mean value of Y coordinate figure of each subpoint as the center P on X-Y plane
cy coordinate figure on X-Y plane, according to all each point P in scattered point set P
i(x
i, y
i, z
i) (i=1,2 ..., m) to center P
cdistance, to all each point P in scattered point set P
i(x
i, y
i, z
i) (i=1,2 ..., m) in ascending order mode, resequence, to arriving center P
cdistance is identical respectively presses counterclockwise sequence, obtains pretreated point set V.
Below in conjunction with accompanying drawing example, the specific embodiment of the present invention is further described.According to said method, under the Matlab platform on the PC based on x86, move, CPU is P41.8Ghz, carries out internal memory 64Mb and has realized the triangulation to 3D scattered point set.Mainly comprise the following steps:
1) initial triangulation
A) point set pre-service
In scattered point set P, there is a P
i(x
i, y
i, z
i) (i=1,2 ..., m), obtain X-Y plane Shang center (x
c, y
c)=(∑ x
i/ m, ∑ y
i/ m), P
ion X-Y plane with (x
c, y
c) distance be d
i=‖ (x
i, y
i)-(x
c-y
c) ‖, with d
iascending order by P
irearrangement, then obtain V to thering is the counterclockwise arrangement of pressing of identical d value, later processing is all carried out V.
B) initial TBL
From V, take out V
1, V
2be assigned to TBL (for the sake of simplicity, below with array representation), TBL=[1 now, 2].In TBL, increase by 1 V
i, judge it and limit V
1v
2relation, if V
i.O.V
1v
2: the first point apart from TBL is nearer, insert head, otherwise insert afterbody; If V
i.R.V
1v
2, that TBL is reverse, then by V
iinsert TBL head; If V
i.L.V
1v
2, directly by V
iinsert TBL head.If V
i.O.V
1v
2, then take off any and add TBL, otherwise just formed initial TBL.Now TBL only has period, and border bark mark is temporarily empty.By initial TBL, can determine initial TL, EL.
If the length of TBL is k, there is k summit, there are k-2 triangle and 2k-3 bar limit.These triangles are (V
h, V
i, V
i+1) (i=2,3 ..., k-1), they have formed initial TL; According to TL, be just easy to obtain EL, adjacent two summits in TL are formed to ，Jiang Qi summit, a limit and deposit EL in, this is a directed edge, its direction is to point to second summit by the first summit.According to this direction, by the triangle number of its left and right relevant position in EL of restoring.Then by EL, gone again TBL.Process as shown in Figure 7.
By above step, just obtained the initial subdivision of point set.
2) main subdivision
A) add new point
From initial subdivision, one by one point is joined in subdivision in order, constantly form new subdivision, until point set is disposed, this process is called main subdivision.Through main subdivision, just obtain the basic subdivision of point set, the subdivision before optimizing.
When newly putting V by one
nwhile joining subdivision, mainly contain two steps: the convex polygon first forming from TBL, find all from V
nv is found on visible limit in TBL
nthe most left some V
lthe rightest some V
r, then upgrade all data structures, below narration respectively.
For V
n, search TBL, if 1 V wherein
imeet: V
n.L.V
i-1v
iand V
n.R.V
iv
i+1, stop search, V
ibe V
nv
l; On the contrary, if having: V
n.R.V
i-1v
iand V
n.L.V
iv
i+1, stop search, V
ibe V
nv
r.
If V
l, V
rbetween have j point, due to the insertion of new point, will generate j+1 newly triangle.First the new triangle increasing in existing k leg-of-mutton TL is tr
k+1=(V
l, V
n, V
l+1), k+1 is this leg-of-mutton call number.Tr
k+1there are two new limit V
lv
nand V
nv
l+1an and existing limit V
l+1v
l, in TBL by node V
lthe right value is composed as e
l, this right, limit triangle number in EL is composed for k+1, then by V
ninsert TBL in V
lafterwards, now two new limits all become boundary edge.New limit is directly joined to EL, and deposit their call number in TBL relevant position, so new three sides of a triangle are all disposed.Continue to process next new triangle tr
k+2=(V
l+1, V
n, V
l+2), it only has a new limit V
nv
l+2, all the other two is existing limit, equally, and V in TBL
nand V
l+1the limit call number on the right is composed this right, two limits triangle number for k+2 in EL, and new limit directly joins EL.Then by V
l+1from TBL, leave out, and node V
nthe right value should change to the call number on new limit.So constantly carry out, until last new triangle tr
k+i+1=(V
r-1, V
n, V
r).Because new triangle generates, TL and EL are upgraded like this, and correspondingly, TBL has also been updated, V
lwith V
rbetween institute a little all from TBL, leave out, generation be V
n.During to the new point of concrete insertion one, process as shown in Figure 8.
Above-mentioned procedure declaration a new point add fashionable EL, TL, the TBL of how upgrading to form new subdivision.
By above step, just obtained the subdivision of point set V, for correct reflection point set topology, at boundary, should remove illegal triangle, cut out on border.
B) cut out on border
Border is cut out exactly and is left out illegal triangle according to actual boundary.
Actual boundary point is inputted by counterclockwise order, sets up first accordingly initial BL, and its each joint form is V
i| 0, next in EL, search for limit V
iv
i+1if, V
iv
i+1∈ E, inserts respective nodes position tr in BL by the triangle number on its right
i; Otherwise need to carry out track, generate, until V
iv
i+1∈ E.PATH GENERATION is herein searched for the convex quadrangle being passed by track limit successively, carries out limit exchange, until complete.Through said process, just set up BL, just can cut out accordingly.While cutting out, search for BL, if in abutting connection with two boundary edge V
iv
i+1, V
i+1v
i+2there is identical the right triangle tr
i=(V
i, V
i+1, V
i+2), from TL, leave out tr
i, and upgrade immediately BL, leave out V
i+1this node upgrades EL simultaneously.Within ten minutes, simply in EL, there is leg-of-mutton boundary edge on search the right to renewal EL, and the triangle number on this right, limit is set to 0 to (representing that this triangle is left out).
3) optimize
Because one of curvature intrinsic characteristic that to be curved surface constant, is also one of criterion of geometric smoothness, therefore consider that the optimization of subdivision just starts with from curvature.To convex quadrangle (A, B, C, D), there are two kinds of subdivision T
1, T
2, estimate respectively its curvature κ
1, κ
2, when
Time, with T
ias this tetragonal optimal division, and claim that this criterion is curvature minimum optimization criteria.Concrete optimization method is that curvature minimum criteria is combined with Delaunay criterion, and method is as follows:
If it is coplanar to form two adjacent triangles of convex quadrangle, press the exchange of Lawson limit criterion, i.e. Minimum Internal Angle maximal criterion; Otherwise by formula (1), estimate the curvature of two kinds of subdivisions of convex quadrangle, then by curvature minimum criteria, optimize.
Here the Optimality Criteria proposing, just optimizes time consumption, is slightly larger than scalar product maximum, JND criterion, and much smaller than minimum average B configuration curvature, minimal Gaussian curvature, fairing criterion, space optimization criterion etc.
Two of left and right, ，Ruo Mou limit, the limit triangle of searching in order during optimization in EL forms convex quadrangle, optimizes as stated above, once certain Q is optimized to Q
atime, there is variation in two triangles originally, and TL is upgraded, and also there is variation in the left and right triangle on 4 limits of Q simultaneously, and EL is also upgraded, and while obviously upgrading, will search for 4 times EL.Travel through an EL and carried out a suboptimization, until the limit that need not optimize again in EL completes the optimization of whole subdivision.
Be positioned at the convex quadrangle Q=(V on a curved surface ∑
1, V
2, V
3, V
4), diagonal line is V
2v
4, (V
2, V
3, V
4) and (V
1, V
2, V
4) center of gravity C
1, C
2and method is vowed n
1, n
2.
After optimizing, just obtain the final subdivision of V.A large amount of experimental results shows that application this paper algorithm can obtain conformal subdivision.Accompanying drawing 9 and accompanying drawing 10, the former shows four semi-cylindricals and the crossing subdivision result of a ball, totally 248 points, its inner and outer boundary point is respectively 8 and 72,13.5 seconds consuming time of whole subdivision; The latter is a faceform, totally 5000 points, wherein outer boundary point is 196,5960 seconds consuming time altogether, due to Figure 10 not only count more but also curvature change more violent, therefore the optimization time is longer.
Claims (2)
1, the surface triangulation building method of 3 d discrete point collection in a kind of 3 D scanning system, with Fast measurement system, obtain mass data point cloud, then these cloud datas are carried out to filtration treatment and seamless spliced, and spliced some cloud carried out to triangulation, it is characterized in that the step that spliced some cloud carried out to triangulation is as follows:
3 d discrete point is carried out to pre-service, carry out again initial triangulation, after this by incremental mode, beyond the delta-shaped region obtaining at initial subdivision, pointwise adds new point, form new subdivision, until point set is disposed, finally to the basic grid forming, use curvature minimum optimization criteria to be optimized processing to it, obtained the final triangulation of 3 d discrete point collection; Above-mentioned processing of using curvature minimum optimization criteria to be optimized it to basic grid is adopted with the following method:
For four convex quadrangles (A, B, C, D) that summit is not coplanar in basic grid, carry out respectively the existing two kinds of triangle subdivision T of convex quadrangle (A, B, C, D)
1, T
2, and carry out curvature κ
1, κ
2estimation, when
Time, with this triangle subdivision T
ias this tetragonal optimal division; For four convex quadrangles (A, B, C, D) that summit is coplanar in basic grid, by Lawson limit exchange criterion, determine this tetragonal optimal division.
2,, according to the surface triangulation building method of 3 d discrete point collection in the above-mentioned 3 D scanning system of claim 1, it is characterized in that 3 d discrete point is carried out to pre-service employing will have a P in scattered point set P
i(x
i, y
i, z
i) (i=1,2 ..., m) project on X-Y plane, obtain in scattered point set P, there is a P
i(x
i, y
i, z
i) (i=1,2 ..., subpoint m), usings the mean value of X coordinate figure of each subpoint as the center P on X-Y plane
cx coordinate figure on X-Y plane, usings the mean value of Y coordinate figure of each subpoint as the center P on X-Y plane
cy coordinate figure on X-Y plane, according to all each point P in scattered point set P
i(x
i, y
i, z
i) (i=1,2 ..., m) to center P
cdistance, to all each point Pi (x in scattered point set P
i, y
i, z
i) (i=1,2 ..., m) in ascending order mode, resequence, to arriving center P
cdistance is identical respectively presses counterclockwise sequence, obtains pretreated point set V.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101510226B (en) * | 2009-03-26 | 2012-07-18 | 山东理工大学 | STL model rapid self-adapting subdividing method of products |
| CN104318622A (en) * | 2014-10-25 | 2015-01-28 | 大连理工大学 | Triangular mesh modeling method of indoor scene inhomogeneous three dimension point cloud data |
| CN106447613A (en) * | 2016-09-27 | 2017-02-22 | 西安蒜泥电子科技有限责任公司 | Image local registration based method and system for removing blur shadow of panorama |
| CN107507267A (en) * | 2017-07-28 | 2017-12-22 | 电子科技大学 | Human body back three-dimensional reconstruction method |
| CN110675502A (en) * | 2019-11-26 | 2020-01-10 | 北京唯智佳辰科技发展有限责任公司 | Multi-layer integrated circuit layout polygon alignment and simplification processing method and device |
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2006
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101510226B (en) * | 2009-03-26 | 2012-07-18 | 山东理工大学 | STL model rapid self-adapting subdividing method of products |
| CN104318622A (en) * | 2014-10-25 | 2015-01-28 | 大连理工大学 | Triangular mesh modeling method of indoor scene inhomogeneous three dimension point cloud data |
| CN104318622B (en) * | 2014-10-25 | 2017-02-22 | 大连理工大学 | Triangular mesh modeling method of indoor scene inhomogeneous three dimension point cloud data |
| CN106447613A (en) * | 2016-09-27 | 2017-02-22 | 西安蒜泥电子科技有限责任公司 | Image local registration based method and system for removing blur shadow of panorama |
| CN107507267A (en) * | 2017-07-28 | 2017-12-22 | 电子科技大学 | Human body back three-dimensional reconstruction method |
| CN110675502A (en) * | 2019-11-26 | 2020-01-10 | 北京唯智佳辰科技发展有限责任公司 | Multi-layer integrated circuit layout polygon alignment and simplification processing method and device |
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