CN108614939B - Underground working well facility modeling method considering three-dimensional topology - Google Patents
Underground working well facility modeling method considering three-dimensional topology Download PDFInfo
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Abstract
The invention provides an underground working well facility modeling method considering three-dimensional topology, which comprises the following steps: simplifying the point cloud; extracting a work well point cloud main shaft; rotating the original point cloud so that the original point cloud is erected in a three-dimensional space along the direction of the main shaft; the simplified modeling step for constructing the triangular patch to realize the working well model comprises the following steps: a) carrying out point cloud extraction on the top surface of the working well and carrying out plane fitting; b) carrying out point cloud extraction on the surface of the bottom of the work well and carrying out plane fitting; c) constructing a triangular patch according to the top surface boundary line, the bottom surface boundary line and the height between the top surface and the bottom surface to carry out simplified modeling of the attached point cloud data; and constructing a working well model component. The method can adapt to various point cloud types, and the algorithm adaptability is strong; the model is attached to the actual point cloud, and the constructed model has good quality; compared with a common curved surface reconstruction algorithm, the method has the advantages of high model building speed and strong practicability, realizes organic unification of the internal pipeline and the external point cloud, and well meets the reappearance of an actual scene.
Description
Technical Field
The invention belongs to the technical field of spatial information, and particularly relates to an underground working well facility modeling method considering three-dimensional topology.
Background
The three-dimensional laser scanning technology was originally developed in reverse engineering in the industrial field, is mainly used in the industrial manufacturing fields of artware design, automobiles, airplanes, ships and the like, and is gradually applied to the mapping industry field later. In the development of urban underground pipelines, along with the improvement of the information construction level of the urban underground pipelines, the information expression form of the urban underground pipelines is gradually improved into a three-dimensional space from a traditional two-dimensional symbol. The pipelines are distributed in the underground in a criss-cross mode, and the spatial relationship among the pipelines cannot be represented by a two-dimensional graph. Some pipelines fluctuate up and down, and a section of pipeline vertical to the ground can be represented by only one point and corresponding marks on a plane view, so that the visual effect is not intuitive. Therefore, under the atmosphere of competitive development of three-dimensional digital cities and three-dimensional digital communities at home and abroad, research on underground three-dimensional pipelines and underground working well models is imperative, so that the construction of the underground working well and cable models by using high-precision point cloud data information of the underground working well is well in line with the current research trend.
The underground pipeline has a complex structure and a large amount of information, and the three-dimensional visual expression of the pipeline has higher requirements on the efficiency and the precision of the three-dimensional modeling of the pipeline and the working well. Foreign scholars, Burger and remes, reconstruct three-dimensional pipeline models by close-range-photogrammetry (CSG) technique and structural entity (CSG). Their research is effective for displaying complex pipelines on the ground such as chemical plants, but it is difficult to reconstruct underground workwell models. The method comprises the following steps that a three-dimensional space data model facing to space structure information and space attribute information modeling and visualization is designed according to the characteristics and requirements of three-dimensional modeling and visual analysis of urban underground space information, such as Zhuliang, and the like; jujuan and the like research the underground space integrated modeling based on B.Rep and provide a city underground space object space index method based on a pre-blocking technology. However, most of underground space modeling researches are focused on underground pipeline three-dimensional modeling and stratum modeling at present, the topological relation of pipelines between underground working wells and working wells is considered a little, and the artificial earthquake and the like provides two three-dimensional simulation methods of pipe fitting facility curved surface dynamic registration and model dynamic transformation to construct an underground pipeline model, but the constructed model has certain error with the reality. The down frame realizes three-dimensional transformation of a two-dimensional model through interaction, but has certain limitation because of the need of two-dimensional data and interactive operation. The Liqingquan proposes a model calculation method of piecewise gradual calculation, but the article only introduces the generation of a circular pipeline and lacks the research on a working well model.
Disclosure of Invention
The invention aims to construct a three-dimensional model of an underground cable facility by utilizing the characteristics of three-dimensional laser point cloud data under the condition of fully considering the spatial topological relation of the three-dimensional laser point cloud data.
The invention provides an underground working well facility modeling method considering three-dimensional topology, which comprises the following steps:
1) simplifying the point cloud;
2) extracting a work well point cloud main shaft;
3) rotating the original point cloud so that the original point cloud is erected in a three-dimensional space along the direction of the main shaft;
4) simplified modeling for constructing triangular patch to realize working well model
a) Carrying out point cloud extraction on the top surface of the working well and carrying out plane fitting;
b) carrying out point cloud extraction on the surface of the bottom of the work well and carrying out plane fitting;
c) constructing a triangular patch according to the top surface boundary line, the bottom surface boundary line and the height between the top surface and the bottom surface to carry out simplified modeling of the attached point cloud data;
5) and constructing a working well model component.
The preferred scheme is as follows: the point cloud simplification step comprises the following steps:
1) carrying out space grid division on the point cloud model;
2) dividing the point cloud model into a plurality of small grids in three spatial directions according to a given distance threshold in each grid;
3) the small grids are arranged in ascending or descending order according to their corresponding code values.
The preferred scheme is as follows: and obtaining the axial direction by using an OBB bounding box method, taking the direction of the longest side as the main direction of the geometric body, and adjusting the main shaft according to the precision information when the main shaft is selected wrongly.
The preferred scheme is as follows: and rotating the original point cloud according to a quaternion rotating method so that the original point cloud is erected in a three-dimensional space along the direction of the main shaft.
The preferred scheme is as follows: by calculating the highest point z of the point cloudmaxAnd the lowest point zminSetting the number of layers N, the distance of each layer is (z)max-zmin) and/N, sequentially extracting the point clouds from the top layer downwards until a certain number of point clouds are met.
The preferred scheme is as follows: the method comprises the following steps of extracting top point cloud by adopting a mode of plane fitting for multiple times, wherein the specific method comprises the following steps:
1) performing plane fitting through a Ransac algorithm, and realizing optimization of plane fitting through barycentric point cloud coordinates during parameter extraction;
2) and extracting point clouds with a certain distance threshold value from the plane from the whole point cloud according to the fitting parameters, and gradually reducing the threshold value to carry out repeated iteration processing to obtain final top surface point cloud data without loss.
The preferred scheme is as follows: the step of building a refined simple model of the triangular patch for fitting point cloud data comprises the following steps:
1) firstly, finding a side with the quantity of 1 adjacent triangles in a side set, wherein two end points of the side are respectively used as a previous point and a current point of a polygon boundary;
2) searching for edges with the number of adjacent triangles being 1 in adjacent triangles of the current point, wherein two end points of the edges have one point which is overlapped with the current point or the previous point;
3) using a non-coincident end point in the end points as a subsequent point of the polygon boundary, sequentially searching other subsequent points of the boundary by a recursive method, and finishing the boundary extraction until the non-coincident end point coincides with the first point;
4) and entering the next cycle to extract the next boundary until all boundaries are extracted.
The preferred scheme is as follows: and performing space circle fitting by adopting a Ransac algorithm, and extracting wellhead parameters by setting a radius threshold value.
The preferred scheme is as follows: the construction of the work well model component comprises the construction of a work well pipe hole and the construction of a cable inside the work well, and the construction of the work well pipe hole comprises the following steps:
1) performing plane separation of the point cloud and the model according to the original point cloud data and the generated model parameters,
2) extracting a boundary line from the separated point cloud plane through rotating projection so as to fit the center and the radius of the pipe hole;
3) and constructing a ball according to the circle center and the radius extracted in the step, so that the ball and the model plane are subjected to topology reconstruction and subdivision to construct a model with pipe holes.
The preferred scheme is as follows: the construction method of the cable inside the work well is characterized in that three times of Hermite interpolation of two nodes is adopted to realize the interpolation of passing points of the cable, so that a cable model is optimized.
The invention has the following beneficial effects:
1) the algorithm provided by the invention fully considers the topological relation of the working well model, and is obviously improved compared with the common modeling;
2) the method can adapt to various point cloud types, and the algorithm adaptability is strong;
3) the model is attached to the actual point cloud, and the constructed model has good quality;
4) compared with a common curved surface reconstruction algorithm, the method has the advantages of high model building speed and strong practicability;
5) compared with the traditional pipeline modeling, the method realizes the organic unification of the internal pipeline and the external point cloud, and well meets the reappearance of an actual scene.
Drawings
FIG. 1 is a time-lapse graph of point cloud reduction consumption;
FIG. 2 is a diagram of the effect of extracting the cloud main shaft of the working well point;
FIG. 3 is a diagram of the effect of extracting the cloud main shaft of the working well point;
FIG. 4 is a diagram of a point cloud layering effect;
FIG. 5 is a top point cloud plane fit;
FIG. 6 illustrates point cloud boundary and key point extraction;
FIG. 7 is a diagram of a process for constructing a triangular patch generative model;
FIG. 8 is a process diagram of construction of a well tubular;
FIG. 9 is a diagram of a model pore generation process;
FIG. 10 is a flow chart of spatial entity intersection finding;
FIG. 11 is a diagram of a linear cable generation;
FIG. 12 is a cable model triangular patch construction diagram;
FIG. 13 is a cable model generation diagram;
FIG. 14 is a diagram illustrating the effects of different reduction methods;
FIG. 15 is a diagram of effects of different working well model constructions.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description.
It is to be understood that the terms "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
The invention provides an underground working well facility modeling method considering three-dimensional topology, which comprises the following steps:
1) simplification of point clouds
Because the point cloud data obtained by scanning has the characteristic of large redundancy, a large amount of time and resources are consumed when the original point cloud is directly used for modeling, and therefore point cloud data simplification and filtering work is generally carried out before point cloud data registration. The first methods for simplifying and filtering point cloud data are based on the principles of distance, curvature, normal direction and the like among points, and the current methods for simplifying point cloud data mainly focus on the following typical methods: bounding box method, geometric image simplification method, curvature simplification method and normal precision simplification method.
Based on the analysis summary of the existing algorithm, the invention adopts a point cloud simplification filtering algorithm of movable grid division, the algorithm mainly simplifies the point cloud through a space grid, the simplification speed has obvious advantage and can achieve the expected effect, and the simplification criterion of the algorithm can be included in the quadratic grid simplification criterion of the algorithm.
For the simplification of point clouds with large data volume, if the point cloud model is divided into a plurality of small grids according to a given distance threshold directly, the whole bounding box of the point cloud is divided into countless small grids along three spatial directions, and the point clouds are screened and simplified in the small grids respectively. As shown in fig. 1. Along with the gradual increase of the number of the original point clouds, the simplification consumes more and more time, and the simplification efficiency is greatly reduced. In order to solve the performance bottleneck, the invention adopts the mode that the grid division is carried out once before the small grid division is carried out, and the point cloud model is firstly processed in a blocking mode, so that the small grid is arranged in the grid once, and the time consumption of the dichotomy insertion of the small grid is greatly reduced.
2) Main shaft for extracting point cloud of work well
Three directions can be obtained by utilizing the OBB bounding box technology, and the initial value of the main direction of the geometric solid can be screened out according to the length of the side. The invention adopts an OBB bounding box method to obtain the axial direction, and takes the direction of the longest side length as the main direction of the geometric body, and the effect is shown in figures 2 and 3.
Let the original input point set be Cloud ═ P1,P2,P3K,PkGet a point P arbitrarilyiIs epsilon, let PCIs the centroid of the point cloud, i.e.:
and k is the number of point clouds, and then the covariance matrix is established as follows:
CV＝∑(Pi-PC)(Pi-PC)T (1)
wherein (P)i-PC) Is a column vector, (P)i-PC)TCV is a symmetric semi-positive 3 × 3 matrix for the corresponding transposed row vector.
Wherein X, Y and Z are coordinate values corresponding to each point. Assuming that the smallest one of the characteristic values of CV is λ, and the eigenvector corresponding to the smallest characteristic value is v, and unitizing the vector, that is, compressing the length to 1, the normal n is equal to v or n is equal to-v. The direction of the normal vector can be adjusted according to the viewpoint position.
Let the viewpoint be Vp(xp,yp,zp) For any sampling point P (x, y, z), if the following equation is satisfied, the direction of the normal vector needs to be adjusted.
n·(P-Vp)＜0 (3)
That is to take
n＝-v (4)
The above method is also called PCA (principal Component analysis) principal Component analysis method. The above method is improved by assigning different gaussian weights to each point P. Thus, the influence degrees of points with different distances on the normal are different, and the influence of points closer to the point P is larger, so that a more real estimation result is obtained.
CV＝∑ui(Pi-PC)(Pi-PC)T (5)
Wherein:
and finally extracting a working well point cloud main shaft.
3) Rotating the original point cloud to ensure that the original point cloud is erected along the main axis direction and is in a three-dimensional space
And (4) calculating an included angle value between n and the coordinate axis z by using a formula (7) according to the axial n obtained by the OBB in the formula (4).
cosθ＝n·n1 (7)
Wherein: n is1With (0,0,1), the symbol · represents the product of the quantities of the two vectors.
According to the quaternion rotation method, only one rotating shaft and one rotating angle are needed to complete arbitrary rotation (rotating by any angle around any shaft) in the space. The rotation angle is θ obtained in equation (7), and the rotation axis can be solved by equation (8).
dir＝n×n1 (8)
Where dir is the rotational axis, n1The symbol x represents the vector product of two vectors, and the result is a vector, similarly unitizing dir, as in equation (7). According toThe quaternion rotation formula (9) completes the rotation process.
P1＝uPu-1 (9)
Where P represents an arbitrary point in the original point cloud to be rotated, P1Represents the corresponding point after rotation by quaternion, and
the formula can complete from P to P1So that the original point cloud is erected in the Z-axis direction.
By using the quaternion rotation method, the rotating shaft of the rotating body is rotated to the Z-axis direction, the corresponding rotation matrix is calculated, and the point cloud data is multiplied by the rotation matrix respectively, so that the rotating body is erected in a three-dimensional space along the main shaft direction.
4) Simplified modeling for constructing triangular patch to realize working well model
a) Carrying out point cloud extraction on the top surface of the working well and carrying out plane fitting;
the invention extracts the top point cloud by a self-adaptive method, and calculates the highest point z of the point cloudmaxAnd the lowest point zminSetting the number of layers N, the distance of each layer is (z)max-zmin) and/N, sequentially extracting the point clouds from the top layer downwards until a certain number of point clouds are met, as shown in fig. 4 and 5. Because the distribution of different data is different in the separation process, partial top surface can be incompletely separated, the top point cloud extraction method adopts a mode of plane fitting for multiple times, and the specific method is as follows:
the method carries out plane fitting through a Ransac algorithm, and realizes optimization of plane fitting through barycentric point cloud coordinates during parameter extraction. Since the top point cloud may be missing, on the basis of plane fitting, the point cloud with a certain distance threshold from the plane is extracted from the whole point cloud according to the fitting parameters, and the threshold is gradually reduced to perform multiple iteration processing to obtain the final top point cloud data without missing, as shown in fig. 6.
And projecting the point cloud data to a specified plane. Based on the determined plane above, we project all data onto the plane. The plane equation is set to
Ax+By+Cz+D＝0 (10)
A, B, C and D are four parameters of a plane, and the distance D from each point to the plane is calculated as follows:
d＝(A,B,C,D)·(x,y,z,1) (11)
where (x, y, z) is the coordinate of each point, (a, B, C) has undergone unitization, and the corresponding projection point pro is:
pro＝(x,y,z,1)-(A,B,C,0)×d (12)
b) carrying out point cloud extraction on the surface of the bottom of the work well and carrying out plane fitting;
extracting the bottom surface of the point cloud data according to the same method, performing plane fitting, calculating the distance between the two planes according to the parameter information of the two planes, and realizing the projection of the boundary point of the upper bottom surface to the lower bottom surface by taking the boundary line of the upper bottom surface as the reference
c) Constructing a triangular patch according to the top surface boundary line, the bottom surface boundary line and the height between the top surface and the bottom surface to carry out simplified modeling of the attached point cloud data;
before the boundary is extracted, a topological relation among a triangle, an edge and a vertex needs to be established, and then the boundary is extracted through a recursion method. Using a cyclic process, firstly, find an edge with the number of 1 adjacent triangles in the edge set, and two end points of the edge are respectively used as a previous point and a current point of the polygon boundary. Then find the side with the number of 1 in the adjacent triangle of the current point, and the two end points of the side have and only one point is coincident with the current point or the previous point. And (4) taking a non-coincident end point in the end points as a subsequent point of the polygon boundary, sequentially searching other subsequent points of the boundary by a recursive method, and ending the boundary extraction when the non-coincident end point is coincident with the first point. And then, entering the next cycle to extract the next boundary until all boundaries are extracted. And calculating the distance between the two planes according to the parameter information of the two planes, and realizing the projection of the boundary point of the upper bottom surface to the lower bottom surface by taking the boundary line of the upper bottom surface as a reference. And constructing a triangular patch according to the boundary information and the model height so as to perform refined simple model modeling of the attached point cloud data. For the top wellhead boundary point, the center and the radius of the working well hole are extracted by adopting a Randac space circle fitting method, so that a triangular patch is constructed together with the integral boundary point to realize the construction of the working well model, and the construction process is shown in FIG. 7.
5) And constructing a working well model component.
A) Construction of well bore
The invention relates to a method for matching a pipe hole center, which is based on cable connection, and comprises the steps of carrying out plane separation of point cloud and a model according to original point cloud data and generated model parameters, extracting a boundary line for the separated point cloud plane through rotary projection, and fitting the pipe hole center, wherein the whole process is shown in fig. 8;
since the plane separated from the actual point cloud is a space arbitrary plane, the plane is rotated to the xoy plane by using the rodlike rotation matrix, and the initial normal of the space plane is set to be n ═ n (n ═ n)x,ny,nz) When the normal line after rotation is n' ═ 0,0,1, the rotation angle θ is:
the rotation axis omega (omega)x，ωy，ωz) Comprises the following steps:
ω＝n×n′ (14)
the rotation matrix is then:
and (3) projecting the point cloud on the xoy plane after rotation, and extracting boundary lines after projection, wherein the method also adopts a Ranac method to perform space circle fitting on all extracted boundary lines to set a circle radius threshold value, so that the center of the pipe hole is extracted, as shown in FIG. 9. And (3) obtaining a projection point of the circle center on the wall surface triangulation by adopting a ray projection method when the actually obtained circle center point has a certain error with the actual surface of the model. And performing topological shearing on the wall surface triangulation network by using the projection point as a reference and adopting a three-dimensional model sectioning algorithm to finish secondary shearing of the simple model. The existing three-dimensional model cutting methods have certain instability, and when complex target entities, such as curved wall surfaces, are cut to obtain doors, windows or pipeline holes, cutting errors can occur. And modifying the algorithm by combining the application of Opencascade and Cork in model sectioning to realize the stable topology sectioning algorithm suitable for architectural expression. A method for sectioning the triangular net by fusing Toptop is tried to solve the sectioning problem of the complex triangular net with unclosed surface, non-manifold side and self-cross. And finally generating a model with pipe holes.
Pipe holes in the work well model are the basis of cable connection, and in order to meet the requirement of reverse reconstruction, Boolean operation needs to be carried out on the work well model to complete topology reconstruction.
Boolean operations, which were invented in 1847 in the United kingdom and aimed at dealing with the relationship between two values[24]. The Boolean operation consists of two parts, wherein the first part is a Boolean operator and is divided into a quadrature operation (COMMON), a union operation (FUSE) and a difference operation (CUT); the second part is the two voxel parameters S1 target objects in space that need to be boolean operated on and the S2 boolean operated tool. The implementation of boolean operations depends on geometrical elements implicit in the parametric voxels, such as surface parametric equations of voxel parameters, etc. As shown in Table 1, several element parameter equations participating in the topology reconstruction of the working well model
The first voxel parameter S1 wall model of boolean operation and the projection position of the S2 boolean operation tool are obtained in the foregoing, and the pipe hole radius (side length) set by the user or the pipe hole radius (side length) fitted by the ranac may be used to generate the clipped element S2 of boolean operation, which performs topological reconstruction with the geometric model of the wall of the work well.
The algorithm requires the input A, B of two target spatial voxels. All edges in a are traversed (parametric curve representation) while all faces in B are traversed (parametric surface representation). And solving the intersection points of all the edges in the A and all the surfaces in the B to obtain a new edge divided by the intersection points. And performing intersection operation on all edges in the B and all surfaces in the A to obtain intersection points.
The edges obtained by the intersection point segmentation are classified, after the intersection point is obtained through the voxel, the edge intersected with the middle plane of the B in the A is segmented into a plurality of segments by the intersection point. At this time, it is determined whether the sides after division in A are inside, outside, or overlapped with each other in B. Similarly, B takes the same action with respect to A.
And solving a new intersection line. The valid intersection points need to be determined before solving for the new intersection. That is, if the solved intersection is satisfied on the boundary of a and within the boundary of B (including the boundary), the intersection is the valid point. And similarly, judging the effective point of B relative to A. And after all the effective points are judged, re-connecting the effective points to obtain a new intersection line.
A determination A, B is made regarding the removal of the original boundary. And completing Boolean operation according to the classification result of the edge classification processing and the connected new intersection line. When A and B are intersecting, then the edges in A are internal and bounded with respect to B as a reservation, leaving the edges outside with respect to B, while taking the same action with respect to B as with A. When A and B are either a union or a difference, the edges in A are external with respect to B, leaving the interior to be discarded. And constructing a ring from the edge according to the topology reconstruction idea, and constructing a shell and a body from the ring construction surface and the surface to obtain a result S after the Boolean operation A and B.
Through the processes, namely, the intersection points are calculated, new intersection lines are solved, the boundary is left, and topology recombination is carried out, so that the boundary topology reconstruction of the space model of the intersection relation is realized, and the redundancy of topology data is reduced. The algorithm is shown in fig. 10.
In the calculation of the intersection point in the algorithm process, all the parameter curves need to be uniformly expressed as:
C(t)＝(x(t),y(t),z(t)) (16)
all parametric surfaces are uniformly expressed as:
F(u,v)＝(x(u,v),y(u,v),z(u,v)) (17)
the intersection of the parametric curve and the parametric surface is determined by the following algorithm:
two space entities are expressed by adopting a parameter equation, and the parameter equation meets the requirement:
C(t)-F(u，v)＝0 (18)
order to
S(t，u，v)＝C(t)-F(u，v) (19)
Solving a parameter differential equation:
the parameters of the differential equation are displayed in a differential way and multiplied by points at two sides
Order to
An iterative equation can be obtained:
after obtaining an iterative equation, respectively constructing bounding box trees for the curve and the curved surface, when the leaves of the bounding box tree of the curve are intersected with the leaves of the bounding box tree of the curved surface, taking parameter values in the two leaves as initial values t0, u0 and v0 for iteration until a convergence condition is met, and finally obtaining an intersection point.
According to the algorithm, the topological relation among the models is regressed to the construction of the internal topological relation of the models and the access of the topological structure through Boolean operation among the models.
The algorithm can only cut a single hole on the phase surface, and in order to realize the complex wall with multiple holes on the wall surface, an iterative method is adopted, the wall surface finished in the previous step is taken as a new S1 to be brought into Boolean operation, and the operation is repeated for multiple times, so that the topological reconstruction of the wall surface is finished.
B) Construction of internal cable of work well
The cable is an important component of the underground electric power well, but the direct connection of the cable between the pipe holes is not beautiful and the crossing of the cable model and the well model inevitably occurs, as shown in fig. 11. Therefore, the invention adopts three times of Hermite interpolation [29] of two nodes to realize the interpolation of the cable passing points so as to optimize the cable model.
Before the cable model is built, a cable connection starting point is picked up in a three-dimensional interaction mode, and the cable starting point p can be obtained because the cable starting position is located on a work well model planea＝(xa,ya,za)， pb＝(xb,yb,zb) Normal to the plane na ═ nx,ny,nz)，nb＝(nx,ny,nz) If the surface normal dir is equal to na×nb. The symbol x represents the vector product of two vectors, the result being a vector, dir being similarly unitized. dir is the normal of the plane where the curve is located, and a Gaussian plane rectangular coordinate system x is constructed by taking the plane as the reference00y0With pa，pbThe midpoint is the coordinate origin.
Thus at point pa，pbThe coordinates after conversion are p'a＝(-dis/2,0,0)，p'b(dis/2,0,0), which is the distance between two points. Then let the rotation matrix be R and the translation vector be t (t)x,ty,tz) Then:
p′a＝R·pa+t (24)
p′b＝R·pb+t (25)
order:
p'c＝(0,0,1) (27)
the rotation matrix R30 can be solved backwards from the relationship of the three corresponding points.
Let the center of point set p be C, and the center of point set p 'be C'.
Center of gravity of point cloud
pci＝pi-C (28)
p'ci＝p'i-C' (29)
Calculating a matrix H:
finally, matrix H is subjected to SVD to obtain
H＝U∑VT (31)
U, V are decomposed matrices, and then the rotation matrix R of 3 × 3 is as follows:
R＝VUT (32)
then translate vector t (t)x,ty,tz) The following were used:
t＝C-RC' (33)
let dirx＝(1,0,0)，diry＝(0,1,0)，n'a＝(nx,ny,nz)，n'b＝(nx,ny,nz) The slope of the point a in the rectangular coordinate system of the gaussian plane is:
the slope of the point b in the rectangular coordinate system of the gaussian plane is:
the symbol · represents the product of the quantities of two vectors.
If the interpolation function is required to have the same value as the function at the node, and the same first-order, second-order or even higher-order derivative value as the function is required, the Hermite interpolation problem is solved.
The cubic Hermite interpolation polynomial for the two nodes is:
let x0＝-dis/2，x1＝dis/2，y′0＝ka，y′1＝kbThen at x0～x1Interpolation is carried out, if the interpolation number is m, the interpolation step length delta x is dis/m, and the interpolation point is:
p'i(xi,H(x0+iΔxi),0) (37)
the curve insertion point p in the three-dimensional spacei：
pi＝R-1p'i-t (38)
The radius of the cable is set, a cross section circle of the cable is generated on the starting point of the cable, a smooth cable is generated by interpolation points and a cross section circle Sweep method, and a triangular net is constructed according to curve interpolation points, as shown in fig. 12. Drawing a triangular patch through Direct3D according to the generated triangulation structure, and finally generating a cable model, as shown in fig. 13.
Effect of the experiment
Firstly, the mobile grid quadratic division algorithm is obtained through comparison of a plurality of simplified algorithms, the efficiency of the simplified algorithm is high, and the simplified effect is good.
The method uses the mobile grid for twice division and simplification, simultaneously uses the density-based adaptive simplification and percentage-based simplification for comparison, and the simplification effect of various methods is shown in figure 14. a is original point cloud, b is mobile grid quadratic division simplification, c is density adaptive simplification, d is percentage simplification. The results are reduced for a variety of algorithms and the results are compared as shown in table 2.
TABLE 2 multiple Algorithm reduction results comparison
The table can be used for obtaining the mobile grid secondary division, so that the reduction consumption time is short, and the reduction effect is good. In order to verify the generation effect of the underground cable model, the invention adopts various data to construct a work well model and an internal cable model, and verifies the applicability of the algorithm of the invention by modeling the various data.
The general point cloud modeling algorithm is based on three-dimensional Diloney triangulation network to carry out curved surface reconstruction, modeling comparison is carried out through various model generation calculation methods, and the method is high in modeling speed and high in modeling precision in underground working well model construction, and is shown in figure 15. The different model generation times and errors are shown in table 3.
TABLE 3 Generation times and errors of different models
Analysis of Experimental results
As can be known from the work well cable model generation experiment, the algorithm disclosed by the invention can be well applied to point cloud data of different types, has wide applicability and consumes little time for modeling each time. The error in the error between the model and the actual point cloud can be known, the fitting precision between the algorithm and the actual working well is high enough, and the requirement of actual production can be well met.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in a variety of fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.
Claims (8)
1. The underground working well facility modeling method considering the three-dimensional topology is characterized by comprising the following steps of:
1) obtaining an original point cloud through scanning, and simplifying the point cloud;
2) extracting a work well point cloud main shaft;
3) rotating the original point cloud so that the original point cloud erects in a three-dimensional space along the direction of the main shaft;
4) simplified modeling for constructing triangular patch to realize working well model
a) Carrying out point cloud extraction on the top surface of the working well and carrying out plane fitting;
b) carrying out point cloud extraction on the surface of the bottom of the work well and carrying out plane fitting;
c) constructing a triangular patch according to the top surface boundary line, the bottom surface boundary line and the height between the top surface and the bottom surface to carry out simplified modeling of the attached point cloud data;
5) constructing a work well model component, wherein the construction of the work well model component comprises construction of a work well pipe hole and construction of a cable inside the work well, and the construction of the work well pipe hole comprises the following steps:
a) performing plane separation of the point cloud and the model according to the original point cloud data and the generated model parameters,
b) extracting a boundary line from the separated point cloud plane through rotating projection so as to fit the center and the radius of the pipe hole;
c) constructing a ball according to the circle center and the radius extracted in the step b), carrying out topology reconstruction on the ball and a model plane, and subdividing to construct a model with pipe holes;
the construction method of the cable inside the working well is characterized in that three times of Hermite interpolation of two nodes is adopted to realize the interpolation of cable passing points, so that a cable model is optimized.
2. A method of modeling a subterranean well facility having three-dimensional topology considerations in accordance with claim 1, wherein said step of point cloud reduction comprises:
21) carrying out space grid division on the point cloud model;
22) dividing the point cloud model into a plurality of small grids in three spatial directions according to a given distance threshold in each grid;
23) the small grids are arranged in ascending or descending order according to their corresponding code values.
3. An underground working well facility modeling method considering three-dimensional topology according to claim 1, characterized in that in step 2), the axial direction is obtained by using an OBB bounding box method, the direction of the longest side is taken as the main direction of a geometric body, and spindle adjustment is performed according to precision information for the case of spindle selection error.
4. A method of modeling a subterranean well facility with three-dimensional topology as recited in claim 1, wherein in step 3), the original point cloud is rotated according to a quaternion rotation method so that the original point cloud is erected in a three-dimensional space along a main axis direction.
5. A method of modelling a subterranean well installation having regard to three-dimensional topology according to claim 1, wherein in step 4) the highest point z of the point cloud is calculatedmaxAnd the lowest point zminSetting the number of layers N, the distance of each layer is (z)max-zmin) and/N, sequentially extracting the point clouds from the top layer downwards until a certain number of point clouds are met.
6. A method for modeling an underground working well facility considering three-dimensional topology according to claim 1, characterized in that in step 4), a plurality of plane fitting manners are adopted for top point cloud extraction, and the specific method is as follows:
61) performing plane fitting through a Ransac algorithm, and realizing optimization of plane fitting through barycentric point cloud coordinates during parameter extraction;
62) and extracting point clouds with a certain distance threshold value from the plane from the whole point clouds according to the fitting parameters, and gradually reducing the threshold value to carry out repeated iteration processing to obtain final top surface point cloud data without loss.
7. The method for modeling a facility of an underground working well considering three-dimensional topology according to claim 1, wherein the step of constructing a triangular patch for performing a refined and simplified model modeling of fitting point cloud data comprises:
71) firstly, finding a side with the quantity of 1 adjacent triangles in a side set, wherein two end points of the side are respectively used as a previous point and a current point of a polygon boundary;
72) searching for edges with the number of adjacent triangles being 1 in adjacent triangles of the current point, wherein two end points of the edges have one point which is overlapped with the current point or the previous point;
73) using a non-coincident end point in the end points as a subsequent point of the polygon boundary, sequentially searching other subsequent points of the boundary by a recursive method, and ending the boundary extraction until the non-coincident end point coincides with the first point;
74) and entering the next cycle to extract the next boundary until all boundaries are extracted.
8. A three-dimensional topology-aware underground workwell facility modeling method according to claim 6, characterized in that a Ranpac algorithm is used for spatial circle fitting, and wellhead parameters are extracted by setting a radius threshold.
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| CN110717937A (en) * | 2019-09-29 | 2020-01-21 | 深圳市图郅创新科技有限公司 | Image correction method and system, electronic device and storable medium |
| CN111581776B (en) * | 2020-04-07 | 2023-09-26 | 华南理工大学 | Iso-geometric analysis method based on geometric reconstruction model |
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| CN112598781A (en) * | 2020-12-08 | 2021-04-02 | 上海欣能信息科技发展有限公司 | Modeling method for three-dimensional laser point cloud data of cable work well |
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