CN106504328A - A kind of complex geological structure modeling method reconstructed based on sparse point cloud surface - Google Patents
A kind of complex geological structure modeling method reconstructed based on sparse point cloud surface Download PDFInfo
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Abstract
The present invention discloses a kind of complicated geological construction method reconstructed based on sparse point cloud surface, and the geologic horizon that the application consideration is reversed in geological structure has the situation of multiple value in subregion, it is impossible to the problem processed using traditional grid method；Propose the thought of projection plane, will primordial seed point data upright projection in certain plane, Delaunay triangulation network connection is carried out in the plane, then the one-to-one relationship by seed point with subpoint recovers space triangular net, so as to complete complicated geological surface reconstruction, the selection of projection plane is converted to mathematical model of optimization wherein, and is converted into convex optimization problem again and is carried out rapid solving.
Description
Technical field
The invention belongs to geological technique field, and in particular to a kind of complex geological structure modeling method.
Background technology
With continually developing for oil-gas reservoir, three-dimensional geological modeling plays more and more important role, and it is used as oil-gas reservoir
During exploration and development, most basic most important research work, not only can provide capsule information for developing of reservoirs,
Geological personnel can be allowed to have subsurface geological structure more accurately cognitive, therefore, for the research of three-dimensional geological modeling technology shows
Obtain ever more important.Three-dimensional geological modeling is that foundation can be accurately reflected out based on the initial data such as borehole data, profile
The digital model of subsurface geological structure, used as most important part in three-dimensional geological modeling, i.e. construction modeling, it is mainly logical
Crossing carries out seismic interpretation to initial data and obtains series of discrete point data, is then processed by interpolation, surface reconstruction etc. and is obtained
The closing block model of description subsurface geological structure, i.e. geological structure model.With the continuous progress of geological exploration techniques, people
Need to become apparent from underground geological condition, comprehensively cognitive, and traditional exploration engineering and modeling method can not meet people
Higher requirement, therefore, for the research of three-dimensional geologic structure modeling technique is also to seem more and more important.
In three-dimensional geologic structure modeling, the research work of complex geological structure modeling is necessary, and which is complicated
Property is mainly reflected in：Geologic body is subject to the tectonic stress effect of some strength and deforms upon, and has eventually formed tomography or fold,
The two is the main representative of complex geological structure.They destroy original geologic structure, and wherein, tomography is presented as geology not
Continuous modification, is divided into normal fault, offlap, vertical fault and reversed fault according to its trend for deforming, and fold is presented as ground
The continuous modification of matter.
Although numerous scholars both domestic and external are more and more to the research of the three-dimensional construction modeling method of complex geologic body, people
For the construction Modeling Method of the research mainly based on tomography of complex geological structure modeling, i.e. normal fault, translation
Tomography, vertical fault and reversed fault.Now, for the method for the complex geological structure modeling containing tomography is also relatively ripe,
And for the research of the complex geological structure modeling method containing fold is relatively very few, so far, also there is no a kind of relative maturity
Method be applied to all containing fold complex geological structures modeling.
With geology and science and technology progress and development, three-dimensional geologic structure modeling have become digitlization with visual
Change important one side, now, a large amount of scholars both domestic and external have put into the further investigation work of complex geological structure modeling
Central.Its complexity is acted on by tectonic stress mainly due to geologic body so that geologic body is deformed upon, and is destroyed original
Topological structure and the continuity of geologic body, are divided into tomography and fold according to deformation tendency, and the two is the main of complex geological structure
Represent.
Complex geological structure modeling basic procedure be exactly：It is base according to the original point cloud data that geology scout obtains
Plinth, fits geological interface, such as layer position curved surface and tomography curved surface using related geological surface reconstructing method.Then according to geology
Topological relation and restriction relation between curved surface, carries out well-regulated cutting to geology FEM layer model, with tomography curved surface is finally
Construct the block geological model of closing in border.
Surface Reconstruction basic thought in geology field is exactly：Interpolation processing is carried out to seed point data, then is adopted
Traditional grid cutting algorithm：The process such as polygon, subdivision triangle is attached, geological surface reconstruct is finally completed.By
In the openness of geology initial data, if carrying out surface fitting only with original point cloud data, reconstructing geological surface may
Can be more uneven, coarse, in order to construct the geological surface of more fairing, need to carry out curved surface using the technology of mesh generation
Reconstruct, and mesh generation is needed first with spatial interpolation technology.The spatial interpolation methods that commonly uses in geology field mainly have instead
Than distance weighting method, Ke Lijin etc..Conventional space curved surface mesh generation technology is generally divided into rectangular mesh subdivision and the triangulation network
Lattice subdivision, in the case of going the form for describing plane and curved surface to go for any complexity by triangle, so,
Can more using the method for triangulation in geological surface fitting.
1989, Mallet et al. proposed discrete smooth interpolation method, and the method is applied to three-dimensional construction modeling
Central, this is a key technology in complex geological structure modeling.1992, Mallet was by the Technology application to geometrical model
Build.Lorensen et al. proposed Marching Cubes algorithms in 1987, and the method is obtained in construction contour surface
It is widely applied.2002, Marching Cubes algorithms were applied to Marching Cubes algorithms by Yuan Guodong et al.
In the middle of surface reconstruction algorithm.2008, Wei Jia et al. combined Marching Cubes algorithms and constraint Delaunay triangles are cutd open
Divide algorithm and apply to the reconstruction of geological surface, achieve preferable effect.After geological surface reconstruct is completed, in order to build most
Closing bulk geological model afterwards, needs to carry out at cutting curved surface according to the restriction relation between geological surface and topological relation
Restriction relation and topological relation that reason, Euler et al. go to determine space curved surface there is provided complete method.
For complex geological structure is modeled, the most complicated geological still based on tomography of lot of domestic and foreign scholar's research
Construction modeling, wherein most important most basic research work is exactly the successful structure of sectional model.2006, Xu Nengxiong et al. was carried
Go out the complex geological structure based on hexahedral mesh subdivision to model, and achieve preferable effect.2007, wait health et al.
The method for proposing wire frame component, the structure for closely matter block model provide new thinking.2012, stone was kindly helped secure the success of et al.
Proposing " point-line-face-body " four step rule carries out fault tectonic modeling.2014, Wang Wei et al. was by constraining Delaunay triangles
The method of subdivision reconstructs geological stratum and fault plane, and being finally stitched together using certain rule, it is block to define closing
Model of geological structure body.
For another kind of situation of complex geological structure, i.e. overfold, scholar both domestic and external to this research relatively very
Few, 2000, Wei Honggu et al. proposed the method for piecemeal modeling to carry out reversing construction modeling, will STRATIGRAPHIC DIVISION be three
Part, then to each part adopt no construction modeling method, finally by these three partially synthetic after be obtained many
The closing model of geological structure body of stratum fold building.But the shortcoming of the method is exactly last when three parts are synthesized, side
Boundary occurs problem.
So far, for the three-dimensional modeling of complex geological structure, the most complicated structure of numerous scholar's research both domestic and external
Makes all be often i.e. normal fault, offlap, vertical fault and reversed fault based on geological fault.And it is this multiple for reversing
The research of the three-dimensional construction modeling technique of miscellaneous geology is very few, once had scholar to propose in the case where geological structure is reversed, and adopted
With piecemeal model method, will stratum be divided into 3 parts so that situation of each part without multiple value, then to per
A part adopts different modeling methods, can obtain the closing block model for reversing construction after finally merge 3 parts.But
It is that border occurs problem, is defective in this approach due to last when 3 parts are merged in the method.
Content of the invention
The present invention is solution above-mentioned technical problem, it is proposed that a kind of complex geological structure reconstructed based on sparse point cloud surface
Modeling method, after successfully layer model is constructed, carries out Seal treatment according to certain rule to its side, finally obtains envelope
The inversely quality structure that closes makes block model, solves the problems, such as to reverse the three-dimensional construction modeling of geology.
The technical solution used in the present invention is：A kind of complex geological structure modeling side reconstructed based on sparse point cloud surface
Method, including：
S1, selection projection plane；
S2, step S1 choose projection plane on carry out Delaunay triangulation network connection obtain two dimension triangle net topology
Structure；
S3, the three-dimensional triangulation network is recovered by the one-to-one relationship of primordial seed point and subpoint, complete three
Dimension space reverses geology surface reconstruction.
Further, step S1 include following step by step：
S11, set up projection plane, for by primordial seed point data upright projection to the plane；
S12, optimal model is set up, by the Maximizing Minimum Distance between subpoint；
S13, the optimal model of step S12 is converted into minimization maximum problem；
S14, the minimization maximum problem obtained according to Definition of Convex Function solution procedure S13, obtain best projection plane.
Further, step S11 also includes：The projection plane meets：
(1) without weight values point；The distance of any two subpoint is all higher than 0；
(2) sequence constraint relation；Adjacent 3 primordial seed point corresponding 3 subpoint, first subpoint are traveled through successively
It is more than the distance of first subpoint and second subpoint, and first subpoint and the 3rd with the distance of the 3rd subpoint
The distance of individual subpoint is more than second subpoint and the distance of the 3rd subpoint.
Further, the optimal model of step S12 is specially：
Target variable：b
Object function：min(d(pi,pj)) → max, i=1,2 ..., n；J=1,2 ..., n；i≠j
Constraints：d(pi,pj)>0, i=1,2 ..., n；J=1,2 ..., n；i≠j
d(pj-1,pj+1)-d(pj-1,pj)>0, j=2,3 ..., ni-1；I=1,2 ..., m
d(pj-1,pj+1)-d(pj,pj+1)>0, j=2,3 ..., ni-1；I=1,2 ..., m
Wherein, b represents target variable, d (pi,pj) represent the distance between i-th subpoint and j-th subpoint, niTable
Show that the seed points of each section, m represent the number of section.
Further, step S13 specifically include following step by step：
The distance between S131, the characteristic according to the architectonic seed point data of reversing, the seed point on single section
Relatively intensive, and distance is relatively sparse between the seed point between section and section, by the optimization mould of step S12
Type is converted into the minimum problems of the distance between the corresponding subpoint of two neighboring seed point on single section；
S132, according to constraints：The distance of any two subpoint is all higher than 0, it is known that between two neighboring subpoint
Distance be more than 0, by the minimum of the distance between corresponding subpoint of two neighboring seed point on the single section of step S131
Value problem, the maximum for being converted into the inverse of the distance between the corresponding subpoint of two neighboring seed point on single section are minimum
Change problem；
S133, it is to be directly proportional according to the distance between any two subpoint to the difference of their ordinate, by step
The Min-Max problem of the inverse of the distance between corresponding subpoint of two neighboring seed point on the single section of S132,
It is converted into the maximum minimization problem of the distance between the corresponding subpoint of two neighboring seed point on single section.
Further, step S14 is specially：Increased based on ordinate successively, the corresponding projection of primordial seed point
The respective ordinate of point increases successively, obtains the effective range of projection plane, that is, obtains best projection plane.
Beneficial effects of the present invention：Present invention firstly provides for reversing architectonic processing method, it is considered to reverse
There is the situation of multiple value in the geologic horizon in geological structure, it is impossible at traditional grid method in subregion
Reason；It is therefore proposed that the thought of projection plane, will primordial seed point data upright projection in certain plane, enter in the plane
Row Delaunay triangulation network connects, and then the one-to-one relationship by seed point with subpoint recovers space triangular net, from
And complicated geological surface reconstruction is completed, the selection of projection plane is converted to mathematical model of optimization wherein, and is converted again
For convex optimization problem and carry out rapid solving；The method of the present invention.
Description of the drawings
Fig. 1 is that the embodiment of the present invention reverses geology surface reconstruction flow chart；
Fig. 2 implements to reverse projection weight values point schematic diagram for the present invention；
Fig. 3 implements to reverse projection sequence restriction relation schematic diagram for the present invention；
Fig. 4 implements multiple sections for the present invention and reverses primordial seed point data schematic diagram；
Fig. 5 is the subpoint schematic diagram data that the present invention implements each section；
Fig. 6 implements parallel projection floor map for the present invention.
Specific embodiment
For ease of skilled artisan understands that the technology contents of the present invention, enter one to present invention below in conjunction with the accompanying drawings
Step explaination.
The solution of the present invention flow chart is illustrated in figure 1, the present invention proposes a kind of based on answering that sparse point cloud surface is reconstructed
Miscellaneous geological structure modeling method, including：
S1, selection projection plane；And by primordial seed point data upright projection to the projection plane, the projection plane
It must is fulfilled for two constraintss：
(1) without multiple value point, i.e., two or more primordial seed point data upright projections can not be contained to projection
After in plane, its subpoint is completely superposed, i.e. projection point coordinates is just the same.As shown in Fig. 2 A, B, C, D, C1, B1, C2, D1,
Primordial seed point data of the discrete points data representated by E for inverted position, B ', C ', the discrete points data representated by D ' is throwing
Shadow point data, L are projection straight line (being exactly projection plane on two dimensional surface).Upright projection is being carried out to primordial seed point data
After out, the subpoint of B and B1 is all B ', and it is all D ' that the subpoint of C, C1 and C2 is all the subpoint of C ', D and D1, and this is not
Meet constraints (1), i.e., projection plane L (i.e. straight line in Fig. 2) is invalid.
Without multiple value point, the distance that mathematically can be expressed as any two subpoint is both greater than 0, i.e. d (pi,pj)>
0, i=1,2 ..., n；J=1,2 ..., n；I ≠ j, wherein, d (pi,pj) represent between i-th subpoint and j-th subpoint
Distance, n represent the number of subpoint.
(2) sequence constraint relation.That is the order of primordial seed point must must keep one with the order of corresponding subpoint
Cause.As shown in figure 3, point 1,2,3,4,5,6 puts 1 ', 2 ', 3 ', 4 ', 5 ', 6 ' for reversing architectonic primordial seed point data
For corresponding projection point data, L is projection straight line (being exactly projection plane in two dimension), and the order of primordial seed point is exactly 1,2,3,
4,5,6, and the order of subpoint is 1 ', 2 ', 5 ', 4 ', 3 ', 6 ', it is clear that inconsistent with the order of primordial seed point, it is not inconsistent contract
Beam condition (2), therefore, the projection plane (straight line) is invalid.
Sequence constraint relation, mathematically can be expressed as：For each section, adjacent 3 primordial seeds are traveled through successively
The distance of corresponding 3 subpoints of point, first point and the 3rd point is more than the distance of first point and second point, and first
The distance of individual point and the 3rd point is more than second point and the distance of the 3rd point；That is, d (pj-1,pj+1)-d(pj-1,pj)>0, d
(pj-1,pj+1)-d(pj,pj+1)>0, j=2,3 ..., ni- 1i=1,2 ..., m；pj-1,pj,pj+1For 3 adjacent primordial seeds
Corresponding 3 subpoints of point, niRepresent that the seed points of each section, m represent the number of section.
After meet the constraint condition (1) and (2), may there are multiple projection planes, and which projection plane selected
Relatively good is a difficult point.If separated between discrete points data on a projection plane as far as possible, i.e., between subpoint away from
From as far as possible greatly, the effect for so building Delaunay triangulation network topological structure on a projection plane is relatively good, according to original
Point is recovered after space triangular net with the one-to-one relationship of subpoint, and the effect of surface fitting is also relatively good.And project here
Separated between discrete points data as far as possible in plane, as on projection plane, between discrete point, that of Maximizing Minimum Distance is thrown
Shadow plane is optimal, and the effect of last surface fitting is optimum.
As shown in figure 4, the figure is the reversing primordial seed point data distribution map of multiple sections, 3 are only depicted in figure and is cutd open
The seed data in face, 3 planes are parallel to each other, and are the seed point data of section 1 from left to right respectively, the seed points of section 2
According to the seed point data of section 3.Wherein, the seed point data of each section has ordinal relation, according to primordial seed point
Order A, B, C, D, E, F, G；In section 1 order of subpoint be A1, B1, C1, D1, E1, F1, G1；In section 2, subpoint is suitable
Sequence is A2, B2, C2, D2, E2, F2, G2；In section 3 order of subpoint be A3, B3, C3, D3, E3, F3, G3.
Seen from the above description, the section for reversing the primordial seed point data place of construction is parallel to each other, it is assumed that all parallel
In xoy planes.For simple process, it is assumed that projection plane is ax+by+c=0 perpendicular to the equation of plane, i.e. projection plane.By
In primordial seed point data be located section each parallel to xoy planes, so the seed point data projection of each section is to plane
Projection point data afterwards is all on same straight line.As shown in figure 5, the figure is the subpoint schematic diagram data of each section, figure
In depict the corresponding projection point data of seed point data in 3 sections, the round dot of each row is the projection points of corresponding section
According to being successively from left to right：The subpoint of section 1, the subpoint of section 2, the subpoint of section 3；This it appears that each
The corresponding point data that projects of the seed point data of section is all on same straight line.
Therefore projection situation of the seed point data on single section to projection straight line, and each section can only be considered
Do similar process.If the data for projection of each section meets above-mentioned two constraints, all primordial seed points
Data for projection can all meet above-mentioned two constraints.Equivalent to the On The Projection of two dimensional surface is converted on one-dimensional straight line
On The Projection, can thus be more convenient for processing.
As shown in fig. 6, the figure is the corresponding diagram of the seed point data on single section and One Dimensional Projection straight line, L1 and L2 is
Two projection straight lines being parallel to each other (single section is actually projection straight line), the point on curve are primordial seed points
According to the point on L1 and L2 is subpoint.Assume that L1 meets above-mentioned two constraints, as primordial seed point is that upright projection is arrived
In plane, then L2 also necessarily meets above-mentioned two constraints, this is because between the projection point data in two projection straight lines
Relative position will not change.Process for convenience, it can be assumed that projection straight line is through origin, if the equation of projection straight line is ax
+ by=0, does to projection equation after normalized, as x+by=0.Again as projection plane is perpendicular to xoy planes, so
Assume that projection plane is π, its equation is x+by=0.
After normalized is done to projection equation, substantially it is exactly to eliminate this plane of y=0, i.e. xoz planes, such as
Shown in Fig. 6, according to the distribution characteristics of the seed point data for reversing construction, if choosing this projection plane of y=0, point data is projected
Above-mentioned two constraints will not necessarily be met, this situation for showing directly to exclude y=0 this projection plane is feasible.Institute
With it is assumed that the equation of projection plane π is feasible for y=0.
After projection plane is chosen, by primordial seed point data upright projection to the projection plane of the selection, in order that
The effect for obtaining space surface fitting is good as far as possible, it is necessary to which the effect of the Delaunay triangulation network connection on projection plane to the greatest extent may be used
Can good.If projection point data separates as far as possible, i.e., the distance between subpoint and subpoint are big as far as possible, also
It is to say the Maximizing Minimum Distance between subpoint and subpoint, that is, selects best projection plane, then the projection plane is enterprising
Topological structure best results after the connection of row Delaunay triangulation network, i.e., recover space triangular finally by one-to-one relationship
After net, the effect of triangulation network topological structure of curved surface is reversed preferably, the reversing geological surface best results for finally fitting.
In the application, the calculating process of specific selection best projection plane is：
Assume that primordial seed point data is a total of n, be distributed in m section, the seed of each section is counted out as nx,
Wherein, x represents the number of section, x=1,2, L, m.In order to find optimal projection plane π, the application sets up an optimization
Mathematical Modeling：
Target variable：b
Object function：min(d(pi,pj)) → max i=1,2 ..., n；J=1,2 ..., n；i≠j
Constraints：d(pi,pj)>0 i=1,2 ..., n；J=1,2 ..., n；i≠j
d(pj-1,pj+1)-d(pj-1,pj)>0 j=2,3 ..., ni- 1i=1,2 ..., m
d(pj-1,pj+1)-d(pj,pj+1)>0 j=2,3 ..., ni- 1i=1,2 ..., m
Wherein, target variable b is the coefficient in projection plane EQUATION x+by=0, d (pi,pj) represent any i-th projection
The distance between point and j-th subpoint.
In above-mentioned mathematical model of optimization, an object of the application function is the minimum range between subpoint and subpoint
Maximize, i.e.,：
min(d(pi,pj))→max (1)
Wherein, d (pi,pj) represent the distance between i-th subpoint and j-th projection.
Due to reversing the particularity of architectonic seed point data：The distance between seed point on single section is relative
Than comparatively dense, and the distance between section and section are relatively sparse.So, corresponding without the seed point for considering two sections
Subpoint between minimum range (because the distance between section and section are sufficiently large), and only consider seed on single section
Minimum range between the corresponding subpoint of point, i.e., the distance between corresponding subpoint of two neighboring seed point on single section
Minimum of a value.Then formula (1) can be converted to：
min(d(pi,pi+1))→max (2)
Wherein, d (pi,pi+1) represent the distance between two neighboring subpoint, due between two neighboring subpoint away from
From being greater than 0, so the maximum that formula (2) can be converted to the inverse of distance is minimized, i.e.,：
As the distance between two subpoints are directly proportional to the difference of their ordinate, so formula (3) can enter one
Step is expressed as：
Wherein, y 'i,i+1The difference of the ordinate of the two neighboring subpoint of each section is represented, i.e.,：
y′i,i+1=y 'i+1-y′i(5)
Can be drawn by formula (4), above-mentioned mathematical model of optimization is changed for maximum minimization problem.
According to subpoint coordinate formulaIt is taken in formula (5), obtains：
Continue abbreviation, obtain：
Wherein make：X=xi-xi+1, y=yi-yi+1
Then formula (7) with abbreviation can be：
Formula (8) is updated in object function, i.e., in formula (4), obtains new object function：
In the method for being increased based on ordinate successively, the corresponding subpoint of sequential primordial seed point ordinate according to
Secondary increase, i.e.,：
y′1<y′2<y′3<…<y′n-1<y′n(10)
According to the effective range that formula (10) can obtain projection plane, the i.e. effective range of b.
By object function is converted into convex optimization problem, best projection plane can be obtained with rapid solving；Described convex excellent
Change problem refers to that object function is convex function, and the domain of definition obtained by constraints is the optimization problem of convex set.Lead to below
The definition for crossing convex function proves object function for convex function, and detailed process is：
Can be obtained by formula (10), the coordinate mark of a subpoint is bigger than previous subpoint afterwards, i.e.,：
y′i,i+1=y 'i+1-y′i>0 (11)
Convolution (8) and formula (11) can be released
bx-y>0 (12)
There was only mono- independent variable of b in object function, it is possible to make：
Want to prove that object function is convex function, the second dervative for proving object function can be converted to more than or equal to 0,
Need first to prove the second dervative of the g (b) in object function more than or equal to 0, below, the first derivative of g (b) is calculated, i.e.,：
Continue abbreviation, obtain：
Below, the second dervative of g (b) is calculated, i.e.,：
Continue abbreviation, obtain：
Last abbreviation, obtains：
Can obtain in conjunction with formula (12)：
g”(b)>0 (19)
So, it was demonstrated that g (b) is strictly convex function.According to the definition of convex function, for the domain of definition of independent variable b
Middle any two points b1With b2With any real number θ, wherein 0<θ<1, have：
g(θb1+(1-θ)b2)≤θg(b1)+(1-θ)g(b2) (20)
For object function, i.e. formula (9), can be converted to：
max{g1(b),g2(b),…,gn(b)}→min (21)
Wherein giB (), i=1,2 ..., n represent the inverse of the distance of the corresponding subpoint of two neighboring primordial seed point,
And giB () has proven to the convex function with regard to variable b.Below, it was demonstrated that the object function in formula (21) is convex function, if target
Function is：
F (b)=max { g1(b),g2(b),…,gn(b)} (22)
Prove that the function is a convex function below according to definition, for any two points in the domain of definition of independent variable b
b1With b2With arbitrary real number θ, wherein 0<θ<1：
In conjunction with formula (20), have：
Common factor θ and 1- θ is extracted, can be obtained：
f(θb1+(1-θ)b2)≤θf(b1)+(1-θ)f(b2) (27)
So, according to the definition of convex function, it was demonstrated that object function (22) is convex function.According to being increased based on ordinate successively
Big method, can obtain the effective range of last b in a linearly interval, i.e., its domain of definition is convex set.
The present invention proposes a kind of new Surface Reconstruction, i.e., by the thought of projection plane：Spatially look for first
To a new plane, and in primordial seed point data upright projection to the plane, will wherein must be fulfilled for two constraint bars
Part：(1) without multiple value, (2) sequence constraint relation.Then carry out Delaunay triangulation network connection in the plane and obtain the three of two dimension
Angle net topology structure, recovers the three-dimensional triangulation network finally by one-to-one relationship of the original point with subpoint, i.e., complete
Geology surface reconstruction is reversed into three dimensions.Including：
S2, step S1 choose projection plane on carry out Delaunay triangulation network connection obtain two dimension triangle net topology
Structure；
S3, the three-dimensional triangulation network is recovered by the one-to-one relationship of primordial seed point and subpoint, complete three
Dimension space reverses geology surface reconstruction.
Triangulation network topological structure that Delaunay triangulation network connection obtain two dimension is carried out in the plane, finally by original point
The three-dimensional triangulation network is recovered with the one-to-one relationship of subpoint, that is, is completed three dimensions and is reversed geological surface weight
Structure, this part are existing routine techniques, are not the key contents of the application, do not elaborate.Detailed process can be joined
Examine documents below：
D.T.Lee,B.J.Schachter.Two algorithms for constructing a Delaunay
triangulation[J].International Journal of Computer and Information Sciences,
1980,2(9):219-242.
T.K.Dey,J.Giesen.Detecting undersampling in surface reconstruction
[M].Discrete and Computational Geometry.Springer Berlin Heidelberg,2003,329-
345
Xu Shouqian, Zhu Yanjuan. the surface reconstruction [J] of sparse cloud. Chinese manufacturing is information-based:Scholarly edition, 2011,40
(2):35-38
Wei Jia, Tang Jie, Yue Chengqi, etc. three-dimensional geologic structure Modeling Technique Research [J]. petroleum exploration, 2008,47 (4):
319-327
One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this
Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.For ability
For the technical staff in domain, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, made
Any modification, equivalent substitution and improvements etc., should be included within scope of the presently claimed invention.
Claims (6)
1. a kind of based on sparse point cloud surface reconstruct complex geological structure modeling method, it is characterised in that include：
S1, selection projection plane；
S2, step S1 choose projection plane on carry out Delaunay triangulation network connection obtain two dimension triangle net topology knot
Structure；
S3, the three-dimensional triangulation network is recovered by the one-to-one relationship of primordial seed point and subpoint, complete three-dimensional space
Between reverse geology surface reconstruction.
2. a kind of complex geological structure modeling method reconstructed based on sparse point cloud surface according to claim 1, which is special
Levy and be, step S1 include following step by step：
S11, set up projection plane, for by primordial seed point data upright projection to the plane；
S12, optimal model is set up, by the Maximizing Minimum Distance between subpoint；
S13, the optimal model of step S12 is converted into minimization maximum problem；
S14, the minimization maximum problem obtained according to Definition of Convex Function solution procedure S13, obtain best projection plane.
3. a kind of complex geological structure modeling method reconstructed based on sparse point cloud surface according to claim 2, which is special
Levy and be, step S11 also includes：The projection plane meets：
(1) without weight values point；The distance of any two subpoint is all higher than 0；
(2) sequence constraint relation；Adjacent 3 primordial seed point corresponding 3 subpoint, first subpoint and are traveled through successively
The distance of three subpoints is more than first subpoint and the distance of second subpoint, and first subpoint and the 3rd throwing
The distance of shadow point is more than second subpoint and the distance of the 3rd subpoint.
4. a kind of complex geological structure modeling method reconstructed based on sparse point cloud surface according to claim 3, which is special
Levy and be, the optimal model of step S12 is specially：
Target variable：b
Object function：min(d(pi,pj)) → max, i=1,2 ..., n；J=1,2 ..., n；i≠j
Constraints：d(pi,pj)>0, i=1,2 ..., n；J=1,2 ..., n；i≠j
d(pj-1,pj+1)-d(pj-1,pj)>0, j=2,3 ..., ni-1；I=1,2 ..., m
d(pj-1,pj+1)-d(pj,pj+1)>0, j=2,3 ..., ni-1；I=1,2 ..., m
Wherein, b represents target variable, d (pi,pj) represent the distance between i-th subpoint and j-th subpoint, niRepresent every
The seed points of individual section, m represent the number of section.
5. a kind of complex geological structure modeling method reconstructed based on sparse point cloud surface according to claim 4, which is special
Levy and be, step S13 specifically include following step by step：
The distance between S131, the characteristic according to the architectonic seed point data of reversing, the seed point on single section are relative
Than comparatively dense, and distance is relatively sparse between the seed point between section and section, and the optimal model of step S12 is turned
Turn to the minimum problems of the distance between the corresponding subpoint of two neighboring seed point on single section；
S132, according to constraints：The distance of any two subpoint is all higher than 0, it is known that between two neighboring subpoint away from
From more than 0, the minimum of a value of the distance between corresponding subpoint of two neighboring seed point on the single section of step S131 is asked
Topic, the maximum for being converted into the inverse of the distance between the corresponding subpoint of two neighboring seed point on single section are minimized and are asked
Topic；
S133, it is to be directly proportional according to the distance between any two subpoint to the difference of their ordinate, by step S132
On single section, the Min-Max problem of the inverse of the distance between corresponding subpoint of two neighboring seed point, is converted into
The maximum minimization problem of the distance between corresponding subpoint of two neighboring seed point on single section.
6. a kind of complex geological structure modeling method reconstructed based on sparse point cloud surface according to claim 5, which is special
Levy and be, step S14 is specially：Increased based on ordinate successively, the respective vertical seat of the corresponding subpoint of primordial seed point
Mark increases successively, obtains the effective range of projection plane, that is, obtains best projection plane.
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