Three-dimensional rapid modeling method based on profile contour multi-feature constraint

Abstract

The invention relates to a three-dimensional rapid modeling method based on section contour multi-feature constraint, and the method comprises the steps: extracting preset key points based on the drilling space information data of a geologic body section, and constructing a discrete point set of the geologic body section; searching a starting point pair for the discrete point set, and unifying the bypassing direction of adjacent point sets; constructing an initial adjacent contour point set based on the starting point pair and the bypassing direction, performing multi-feature constrained auxiliary point interpolation on the initial adjacent contour point set, and constructing a one-to-one corresponding point set; carrying out interlayer interpolation on the contour point set after the auxiliary point interpolation; and based on the shortest diagonal constraint, carrying out triangulation network splicing on the contour point set after interlayer interpolation. According to the method, the property and the inlaying process of the basic triangular patch can be considered, reconstruction of sparse contour line discrete points with low shape similarity and different points is realized, and the problem of complex surface reconstruction under a sparse profile is effectively solved.

Description

Technical Field

[0001] The invention relates to the technical fields of geological engineering and surveying and mapping engineering, and in particular to a three-dimensional rapid modeling method based on multi-feature constraints of a profile. Background Art

[0002] Surface reconstruction based on the profile of an object is an important method of surface rendering. It generates a series of triangular facets between the vertices of adjacent contour lines to construct the surface of an object. It is widely used in three-dimensional modeling and numerical simulation in the fields of geological information science, geophysical exploration, and surveying and mapping engineering. Point set optimization and triangulation are the core contents of this method. The main research objects are feature measurement and constraint set. The key is to achieve effective expression of profile features and quantitative description of constraint conditions. Studies have shown that due to the limitations of geological environment and exploration technology, the contour vertex set based on reconstruction has problems such as sparse and scattered distribution, lacks a complete representation of the contour shape and strict constraints on the morphology between contour lines, and needs to be balanced and densely distributed through interpolation; in triangulation, a single constraint rule often appears unbalanced, and constraints need to be added to achieve smooth local transitions and consistent overall morphology.

[0003] There are many studies on point group optimization. For example, Liu Gang et al. used midpoint interpolation iteration to weaken the number of feature points of long edges and uniform contours; Sun Lishuang et al. used perimeter projection interpolation to enhance the distribution balance of feature points at the distance level; Meng Yaowei and Sun Yizhong proposed an adaptive interpolation algorithm, which was encrypted according to the consistency of the weaving ratio, enhanced the consistency of the distribution of feature points and the mosaic order, and improved the rigor of the synchronous advance method; Ma Hongbin and Guo Jiateng searched for control points based on the nearest neighbor rule, and used coordinate changes, scaling and translation to reconstruct the index and coordinates of the point set, weakening the spatial heterogeneity between point sets; Yang Yang et al. constructed a mapping relationship between points based on the synchronous advance rule. By interpolating the mapping function to generate transition contours, the effects of profile sparseness and large distribution differences are weakened; Hiroyuki and Yoichi provide contour optimization methods under sparse control points based on Cartesian coordinates and tangent angles, based on arc spline interpolation and cubic Hermite spline interpolation; Huang Jixian et al. improve the contour morphology through uniform interpolation to enhance the rationality of matching correspondence in view of the defects of the shortest diagonal constraint on concave contours and non-parallel contours; Jia Chao et al. use the curvature radius to extract contour key points, match corresponding points through key points, interpolate between matching points, and adjust the number of key points according to the fitting accuracy requirements. These methods focus on distance and its measurement in the selection of feature metrics, but lack effective representation of contour shape, lack discussion on key parameters such as the number of points used for interpolation and function index, and lack robustness in solving the two types of problems: sparse point set and sparse profile.

[0004] The optimization objectives and constraints of triangulated mesh splicing are mainly divided into those oriented to the overall properties of triangulated meshes and those based on the properties of single triangles. The former constructs an undirected graph of feature metrics and searches for the minimum spanning tree based on constraints such as the minimum surface area, maximum volume, and minimum total span length of the triangulated mesh. Related research has fully applied geometric, mathematical, and computational models such as ant colony optimization, genetic optimization, dynamic programming, neural networks, quadratic matching, and Hausdorff distance, significantly weakening the defects of non-adjacent span intersections and strong randomness of triangulated mesh degenerate regions. However, there are problems such as cumbersome processes, low modeling efficiency, and high computing power requirements. When applied to simple models, it causes a waste of computing resources, and is not as good as voxel-based surface rendering methods for complex surfaces, making it difficult to achieve real-time modeling and dynamic process simulation. The latter is widely used due to its significant advantages in time and space complexity. Its core is to construct the starting span and complete subsequent splicing. The rationality and global optimality of the former greatly affect the subsequent splicing, while the key to the latter is to control the generation and mosaic of basic triangles through feature metrics and constraints. Existing research focuses on subsequent splicing and pays insufficient attention to the starting span. The starting span is searched through the distance correlation matrix and the minimum distance method. Improvements are made around the shortest diagonal method that focuses on the generation of basic triangles and the synchronous forward method that focuses on the mosaic process. Feature metrics and constraints based on distance and its measurement are fully discussed, and attempts are made to introduce control lines to achieve a balance between the two. Literature analysis and case tests show that the sparsity of point sets will reduce the effectiveness of the distance correlation matrix and lead to a decrease in the rationality of the starting span. Single constraints are difficult to take into account, resulting in local span distortion, conical surfaces, many-to-one mapping relationships, and overall connection disorder. Artificially adding control lines reduces the adaptability of the algorithm. The distance metric cannot include the distribution characteristics of point sets and the similarity between sets into constraints due to the lack of effective representation of the shape. Summary of the invention

[0005] The purpose of the present invention is to propose a three-dimensional rapid modeling method based on multi-feature constraints of profile contours, focusing on two important components of contour reconstruction: reconstructing the three-dimensional surface of an object by contour splicing from the two-dimensional profile contour line data is an important surface drawing method, which includes three sub-problems of contour correspondence, splicing, and branching, and the optimization of feature point sets, corresponding point matching, and triangulation splicing is the core of the contour splicing problem. Existing methods are based on feature metrics such as distance and its measurement and single constraint conditions, without considering the shape of the contour line and the robustness of the constraint rules. When discrete feature points are sparse and unevenly distributed, the distance between adjacent contour lines is far, and the distribution of feature points is very different, problems such as span distortion, generation of a large number of degenerate triangles, and overlap and discontinuity of triangle pieces occur. The present invention uses the nearest neighbor iteration to generate the starting span as the basis for point pair matching; based on the quantification of contour shape features, auxiliary points are constructed through equi-angle projection interpolation and angle bisector interpolation to avoid the many-to-one problem in point pair matching; for angle failure in complex concave contours and flat distribution of feature points, the rationality of matching is enhanced by using distance equisection interpolation; for insufficient inter-layer constraints, contour encryption is performed using inverse distance weighted interpolation; the starting span is generated based on the nearest neighbor iteration and the control span is generated based on the equi-angle mapping to provide global constraints, and the remaining span is generated through the shortest diagonal rule to provide local constraints. Experimental results show that this algorithm can take into account the properties of basic triangular facets and the mosaic process, realize the reconstruction of sparse contour line discrete points with low shape similarity and different number of points, and effectively solve the problem of complex surface reconstruction under sparse sections.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A three-dimensional rapid modeling method based on multi-feature constraints of a cross-section profile, comprising:

[0008] Based on the borehole spatial information data of the geological body section, the preset key points are extracted to construct a discrete point set of the geological body section;

[0009] Searching for a starting point pair of the contour line for the discrete point set, and unifying the detour direction of the adjacent point set;

[0010] Constructing an initial adjacent contour point set based on the starting point pair and the detour direction, performing auxiliary point interpolation with multi-feature constraints on the initial adjacent contour point set, and constructing a one-to-one correspondence relationship between vertices of different contours;

[0011] Perform interlayer interpolation on the contour point set after auxiliary point interpolation to obtain a new contour;

[0012] Based on the shortest diagonal constraint, the contour point set after inter-layer interpolation is triangulated.

[0013] Optionally, extracting preset key points to construct a discrete point set of a geological body profile includes:

[0014] The polygon evolution method is used to calculate the influence weight of each point on the source polygon on the shape, and the points with weights lower than the preset threshold are removed, and the preset key points that affect the shape are extracted as the discrete point set of the geological body profile.

[0015] Optionally, searching for a starting point pair for the discrete point set and unifying the detour direction of the adjacent point set includes:

[0016] The similarity of three-dimensional Euclidean distance is used to search for the starting point pair, the discrete point set is copied to the auxiliary space, the auxiliary space is interpolated and encrypted, the index of the starting point pair is obtained using the maximum similarity and set as the initial point pair, the index of the discrete point set is readjusted with the set initial point pair as the starting point, two vectors are constructed using three adjacent points in a point set and the cross product is calculated to obtain the detour direction, and the detour direction of the adjacent point set is unified.

[0017] Optionally, the algorithm for performing interpolation encryption processing on the auxiliary space is:

[0018]

[0019] in, and Represents the contour i With l j The average side length of i The number of vertices in, h represents the parameter required to traverse the edge length set, Represents the contour i The element with index h in the edge set of , n represents the number of feature points of a contour, k represents the parameter required to traverse the edge length set, Represents the contour j The element with index k in the edge set of represents an endpoint of the span with the smallest calculated span length, Represents the parameters needed to traverse the distance between points, representing a vertex, Indicate point The sum of the distances to any set of adjacent points of the original point group, It represents the absolute value of the difference between the distance mentioned above and the distance to this set of neighboring points.

[0020] Optionally, performing multi-feature constrained auxiliary point interpolation on the initial adjacent contour point set includes: performing equi-angle projection interpolation, angle bisector interpolation, and minimum edge reference interpolation;

[0021] The equi-angle projection interpolation is:

[0022] S11, constructing a starting point pair of the contour line and adjusting the detour direction of the contour line;

[0023] S21, calculate contour line L i ,L i+1 Center i ,Center i+1 , translate the two contour lines to (0,0) as the geometric center;

[0024] S23. Calculate and fill the angle set Angle of two contour lines i With Angle i+1 ;

[0025] S24. Set IndexUp as the angle i The index of the angle set Angle is IndexDown i+1 Index to determine the angle Angle i [IndexUp] and angle Angle i+1 The size of [IndexDown] is interpolated on the contour line with a smaller angle according to the equal-angle projection rule;

[0026] S25. For the interpolated contour line, update its angle set Angle;

[0027] S26. Repeat steps S25 and S26, using Points i .Count indicates contour L i Angle collection Angle i Capacity, using Points i+1 .Count indicates contour L i+1 Angle collection Angle i+1 Capacity, when IndexUp = Points i .Count-1 or IndexDown=Points i+1 When .Count-1, the step ends;

[0028] S27. translating the interpolated point to the original position;

[0029] The angle bisector interpolation is:

[0030] S21. Calculate and fill the contour L i Angle collection Angle i ;

[0031] S22. Find the angle set Angle i The largest angle in imax , calculate the intersection points of the angle bisector and the corresponding side insert , insert into the point set Points i[] between the two endpoints of the edge;

[0032] S23, repeat steps S1 and S2 to the intersection point i [] The number of midpoints reaches the specified number, and the algorithm ends;

[0033] The minimum edge base interpolation is:

[0034] When the contour is concave, the contour line l i ={p i0 ,p i1 ,p i2 …p i35}, p iA Represents the vertices of the contour, A = 0, 1, ..., 35, calculates the adjacent point distance set D i ={d i0 ,d i1 ,d i2 …d i35}, d iA Represents the distance between adjacent points in the vertex set of the contour line, searching for the minimum distance d min , the number of interpolation points n is calculated by the first preset formula i , calculate the adjacent contour l in the same steps j The number of interpolation points n j , determine the number of interpolation points n according to the second preset formula, and calculate |p by the third preset formula i0 p i1 |Number of interpolation points in the interval According to point p i0 and p i1 The interpolation point {p i1′ ,p i2′ ,p i3′ ,p i4′ ,p i5′ ,p i6′}, traverse l i Interpolation is completed;

[0035] The first preset formula is:

[0036]

[0037] Among them, n i The contour line l i The number of interpolation points, The contour line l i The distance between adjacent points, m and h are necessary parameters, n j The contour line l j The number of interpolation points, The contour line l jThe distance between adjacent points, k and l are necessary parameters;

[0038] The second preset formula is:

[0039] n=max <n i ,n j >

[0040] Where n is the number of interpolation points, n i With n j l i With l j The number of interpolation points;

[0041] The third preset formula is:

[0042]

[0043] in, is the number of interpolation points between adjacent points, is the distance between adjacent points, Used to calculate the perimeter of the contour line;

[0044] The fourth preset formula is:

[0045]

[0046] in, and are the original adjacent point coordinates, is the number of interpolation points between adjacent points, p is the pth interpolation point, is the interpolation point's seat.

[0047] Optionally, performing inter-layer interpolation on the contour point set after the auxiliary point interpolation includes:

[0048] S61. Unify the detour directions of the two contour lines in the contour point set after the auxiliary point interpolation, and determine the similarity of the two contour lines. If the similarity is lower than a preset value, the algorithm terminates;

[0049] S62. Iteratively obtain the initial point pair according to the minimum distance method and unify the detour directions of the two contour lines;

[0050] S63. Adjust all contour lines to have the same number of points based on the angle bisector interpolation algorithm. Starting from the starting point pair, calculate the distance between it and the adjacent point and the next adjacent point, and determine the weight according to the inverse ratio of the distance;

[0051] S64. Calculate the coordinates of the insertion point based on the weights insert1 [IndexUp], repeat S63, traverse Points i [], you can generate a set of interpolation points with the same number of pointsinsert1 ;

[0052] S5. According to S3 and S4, Points i+1 [ ] Generate Points insert2 ;

[0053] S6. Points insert1 With Points insert2 Taking the average at the same index can get the final interpolation result Points insert [].

[0054] Optionally, performing triangulation on the contour point set after inter-layer interpolation includes:

[0055] S71, generating a control span at the same index in the contour point set after interpolation between layers according to the equal angle mapping rule, generating two triangles between the two control spans according to the shortest diagonal rule, and the winding direction of the triangle should comply with the counterclockwise direction to provide a correct normal direction for rendering;

[0056] S72, traverse the contour point set after interlayer interpolation, and repeat step S71;

[0057] S73, splicing the last point of the contour point set after interlayer interpolation with the first point, generating two triangles between the first and last control spans according to the shortest diagonal rule, and completing triangulation splicing.

[0058] Optionally, the drilling spatial information data includes drilling coordinates, hole depth, and inclination measurement.

[0059] The beneficial effects of the present invention are:

[0060] The starting point pair search method based on auxiliary space interpolation and nearest neighbor iterative search optimizes the rationality reduction defect of the optimal solution caused by the sparsity of the original point group.

[0061] The introduction of angle sets effectively incorporates the contour shape into the constraint conditions, which is applicable to convex contours and simple concave contours. The equal-division interpolation based on distance features can adapt to narrow and long contours and concave contours.

[0062] The inter-layer interpolation with inverse distance weighting weakens the spatial sparsity of the point group and strengthens the inter-layer constraints.

[0063] The control span is generated based on the equal-angle mapping constraint and the remaining span is generated based on the shortest span constraint, which takes into account the optimality of basic triangle faces and the optimality of the tessellation process, and maintains the overall consistency of the triangulated network and the local rationality. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0065] Figure 1 A schematic flow chart of a method for reconstructing a three-dimensional structure of a geological body surface according to an embodiment of the present invention;

[0066] Figure 2 Schematic diagram of the process of constructing a starting point pair based on auxiliary space interpolation and nearest neighbor iteration according to an embodiment of the present invention; wherein (a) is the replication of the original contour line, (b) is the point encryption based on midpoint interpolation, (c) is the iterative search using the minimum distance method, and (d) is the insertion of the starting point pair;

[0067] Figure 3 Schematic diagram of interpolation comparison based on angle and distance features according to an embodiment of the present invention; wherein (a) is interpolation based on distance, (b) is interpolation based on angle, (c) is the influence of the distance from the center and the edge direction, and (d) is the influence of a complex concave contour;

[0068] Figure 4 Schematic diagram of the measurement and interpolation method of the constrained contour shape according to an embodiment of the present invention; wherein (a) is the measurement Angle for measuring the contour shape; (b) is the equi-angle projection interpolation; (c) is the angle bisector interpolation; (d) is the point set after interpolation; (e) is the reconstruction of the original point set; (f) is the reconstruction of the point set after interpolation;

[0069] Figure 5 Schematic diagram of interlayer interpolation in an embodiment of the present invention; wherein (a) is feature point correspondence matching; (b) and (c) are interpolation point calculation and insertion;

[0070] Figure 6 Schematic diagram of the triangulated mesh stitching process with multi-feature constraints according to an embodiment of the present invention; wherein, (a) is the original contour line; (b) is the corresponding point matching; (c) is the interlayer interpolation; (d) is the control span generation; (e) is the residual span generation;

[0071] Figure 7 Schematic diagram of the reconstruction and comparison of adjacent contours in the case of low similarity according to an embodiment of the present invention; wherein, (a) is the search for a starting point pair (minimum distance method); (b) is the search for a starting point pair (algorithm of the present invention); (c) is the shortest diagonal line method (20 points); (d) is the algorithm of the present invention (20 points); (e) is the shortest diagonal line method (100 points); (f) is the algorithm of the present invention (100 points);

[0072] Figure 8Schematic diagrams of two complex concave contour reconstructions according to an embodiment of the present invention; (a) is a complex concave contour reconstruction with different directions in corresponding intervals; (b) is a complex concave contour reconstruction with the same directions in corresponding intervals;

[0073] Fig. 9 Schematic diagram of interlayer encryption based on corresponding point matching and inverse distance weighted interpolation of an embodiment of the present invention; wherein (a) is a contour shape; (b) is equi-angle projection interpolation and angle bisector interpolation; (c) is a point group after 5 iterations of interlayer interpolation; (d) is a reconstruction result of angle interpolation; (e)(f)(g)(h) are reconstruction results of 1 to 5 iterations of interlayer interpolation;

[0074] Fig.10 Schematic diagram of goaf reconstruction and triangulation comparison according to an embodiment of the present invention; wherein (a) is the original contour source; (b) is the first interlayer interpolation; (c) is the second interlayer interpolation; (d) is the contraction contour generated by deleting the interpolation; (e) is the reconstruction result of the first interlayer interpolation; (f) is the reconstruction result of the second interlayer interpolation;

[0075] Fig.11 Schematic diagram of the comparison of triangulated network span length and triangle similarity according to an embodiment of the present invention; wherein, (a) is the triangulated network span length distribution; (b) is the angle-based similarity distribution; (c) is the distance-based similarity distribution; and (d) is the cosine similarity distribution around the adjacent surface normal. DETAILED DESCRIPTION

[0076] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] This embodiment proposes a three-dimensional rapid modeling method based on multi-feature constraints of a cross-section profile, including:

[0079] Based on the borehole spatial information data of the geological body section, the preset key points are extracted to construct a discrete point set of the geological body section;

[0080] Search for the starting point pair for the discrete point set and unify the detour direction of the adjacent point set;

[0081] An initial adjacent contour point set is constructed based on the starting point pair and the detour direction, and auxiliary point interpolation with multi-feature constraints is performed on the initial adjacent contour point set to construct a one-to-one corresponding point set;

[0082] Perform inter-layer interpolation on the contour point set after auxiliary point interpolation;

[0083] Based on the shortest diagonal constraint, the contour point set after inter-layer interpolation is triangulated.

[0084] Furthermore, the discrete point set for extracting preset key points to construct the geological body profile includes:

[0085] The polygon evolution method is used to calculate the influence weight of each point on the source polygon on the shape, and the points with weights lower than the preset threshold are removed, and the preset key points that affect the shape are extracted as the discrete point set of the geological body profile.

[0086] Furthermore, searching for a starting point pair for a discrete point set and unifying the detour direction of an adjacent point set includes:

[0087] Use the similarity of three-dimensional Euclidean distance to search for starting point pairs (such as Figure 2 As shown, Figure 2 (a) is a copy of the original contour line. Figure 2 (b) is point encryption based on midpoint interpolation. Figure 2 (c) Minimum distance method iterative search, Figure 2 (d) is the starting point pair insertion), the discrete point set is copied to the auxiliary space, the auxiliary space is interpolated and encrypted, the maximum similarity is used to obtain the index of the starting point pair and set it as the initial point pair, the index of the discrete point set is readjusted with the set initial point pair as the starting point, two vectors are constructed using three adjacent points in a point set and the cross product is calculated to obtain their detour direction, and the detour direction of the adjacent point set is unified.

[0088] Furthermore, the initial adjacent contour point set is interpolated with auxiliary points constrained by multiple features (such as Figure 3 and Figure 4 As shown, Figure 3 (a) is the distance-based interpolation. Figure 3 (b) is the interpolation based on the angle, Figure 3 (c) is the distance from the center and the influence of the edge direction, Figure 3 (d) is the influence of complex concave contour, Figure 4 (a) is the Angle which measures the contour shape; Figure 4 (b) is the equi-angle projection interpolation; Figure 4 (c) is the angle bisector interpolation; Figure 4 (d) is the point set after interpolation; Figure 4 (e) is the reconstruction of the original point set; Figure 4 (f) is the point set reconstruction after interpolation), specifically including:

[0089] S51. Calculate and fill L i Angle collection Angle i ;

[0090] S52. Find the angle set Angle i The largest angle in imax , calculate the intersection points of the angle bisector and the corresponding side insert , insert into Points i [] between the two endpoints of the edge;

[0091] S53, repeat steps S1 and S2 to Points i [] When the number of midpoints reaches the specified number, the algorithm ends.

[0092] Furthermore, the contour point set after the auxiliary point interpolation is interpolated is interpolated between layers (such as Figure 5 As shown, Figure 5 (a) is the feature point correspondence matching; Figure 5 (b) and Figure 5 (c) is the calculation and insertion of interpolation points), which specifically includes:

[0093] S61. Unify the detour directions of two contour lines (because contour reconstruction occurs between two contour lines, here refers to these two contour lines) in the contour point set after auxiliary point interpolation, and judge the similarity of the two contour lines. If the similarity is lower than a preset value, the algorithm terminates;

[0094] S62. Iteratively obtain the initial point pair according to the minimum distance method and unify the detour directions of the two contour lines;

[0095] S63. Adjust all contour lines to have the same number of points based on the angle bisector interpolation algorithm. Starting from the starting point pair, calculate the distance between it and the adjacent point and the next adjacent point, and determine the weight according to the inverse ratio of the distance;

[0096] S64. Calculate the coordinates of the insertion point based on the weights insert1 [IndexUp], repeat S63, traverse Points i [], you can generate a set of interpolation points with the same number of points insert1 ;

[0097] S5. According to S3 and S4, Points i+1 [ ] Generate Points insert2 ;

[0098] S6. Pointsinsert1 With Points insert2 Taking the average at the same index can get the final interpolation result Points insert [].

[0099] Furthermore, the contour point set after interpolation between layers is triangulated (e.g. Figure 6 As shown, Figure 6 (a) is the original contour line; Figure 6 (b) is the corresponding point matching; Figure 6 (c) is interlayer interpolation; Figure 6 (d) is the control span generation; Figure 6 (e) is the remaining span generation), specifically including:

[0100] S71, generating a control span at the same index in the contour point set after interpolation between layers according to the equal angle mapping rule, generating two triangles between the two control spans according to the shortest diagonal rule, and the winding direction of the triangle should comply with the counterclockwise direction to provide a correct normal direction for rendering;

[0101] S72, traverse the contour point set after interlayer interpolation, and repeat step S71;

[0102] S73, splicing the last point of the contour point set after interlayer interpolation with the first point, generating two triangles between the first and last control spans according to the shortest diagonal rule, and completing triangulation splicing.

[0103] Specifically, the present embodiment proposes a three-dimensional rapid modeling method based on multi-feature constraints of a cross-section profile, such as Figure 1 As shown in the figure, the starting point pairs of adjacent point sets are searched in the auxiliary space to establish the basis for matching, one-to-one point matching is established by inserting auxiliary points, and the heterogeneity and sparsity of the point group are weakened by interlayer interpolation. The original interval is divided by the control span generated based on the matching result, and the angle constraint and the shortest diagonal constraint are used to generate the remaining span within the control interval to complete the reconstruction. The method flow is as follows Figure 1 shown.

[0104] S1. Obtaining the borehole spatial information data of the geological body section, using polygon evolution technology to calculate the influence weight of each point on the source polygon on the shape, removing the points with weights lower than the threshold, and extracting the key points that affect the shape as the discrete point set of the geological body section;

[0105] S2. Use the similarity of three-dimensional Euclidean distance to search for the starting point pair, copy the discrete point set to the auxiliary space, perform interpolation encryption on the auxiliary space to increase the global optimality of the starting point pair solution, use the maximum similarity to obtain the index of the starting point pair and set it as the initial point pair, readjust the index of the discrete point set with this point pair as the starting point, use three adjacent points in a point set to construct two vectors and calculate the cross product to obtain their detour direction, and unify the detour direction of the adjacent point set.

[0106] S3, starting point pairs and detour directions can only construct basic matches of adjacent contour point sets. Due to the difference in the number of adjacent contour vertices, it is impossible to construct a one-to-one vertex matching correspondence. Inserting an appropriate amount of auxiliary points without changing the contour shape can weaken the heterogeneity of the original point sets of adjacent contours and achieve better matching correspondence. This method uses the polygonal approximate skeleton and the polygonal adjacent point triangle combination to calculate the similarity of the global and local combinations of contours, and uses the angle and distance constraint features according to the similarity threshold to construct the objective function of auxiliary point interpolation.

[0107] S4. After constructing a one-to-one correspondence of the point set by inserting auxiliary points, the first-order inverse distance weighted interpolation based on the corresponding relationship of the vertices is used to perform interlayer encryption to achieve the deformation between adjacent contours. A series of contours are inserted between the source contour and the target contour to achieve a smooth interlayer transition, thereby weakening the impact of sparse geological profiles and missing partial boundaries.

[0108] S5. Based on the vertex correspondence and inter-layer deformation mentioned above, use the equal-angle mapping constraint to connect the vertices with the same index to generate the control span for global constraint, and use the shortest diagonal constraint to generate the common span to provide local constraint, and obtain the reconstructed triangulated network.

[0109] Specifically, the drilling spatial information data includes drilling coordinates, hole depth, and inclination measurement.

[0110] Specifically, in step S2, the method for constructing a starting point pair based on auxiliary space interpolation and nearest neighbor iterative search includes the following steps:

[0111] Input. The original point set of adjacent contour lines Points i [],Points i+1 [];

[0112] Output. Correct the starting point to the point set Points i [],Points i+1 [];

[0113] S1. Points i [] and Points i+1 The point information of [] is copied to CoppyPoints i [ ] with CoppyPointsi+1 [];

[0114] S2. CopyPoints i [ ] with CoppyPoints i+1 [] Iterate according to the midpoint interpolation algorithm until the number of points is N;

[0115] S3. Calculate CoppyPoints i [0] to CoppyPoints i+1 [] The distance of all points on the surface, store the minimum distance in the distance set D;

[0116] S4. Calculate CoppyPoints i [1] to CoppyPoints i+1 [] The distance of all points on the surface, store the minimum distance in the distance set D;

[0117] S5. Repeat steps S3 and S4 to CoppyPoints i [N];

[0118] S6. Return the two endpoints with the smallest distance in D as the starting points of the two contour lines Points start0 ,Points start1 , insert it into Points i [],Points i+1 [].

[0119] Specifically, the steps of the algorithm for searching the position of any point on the contour line are as follows:

[0120] Input: Any point on the contour line random , the original point set of the contour line Points i [];

[0121] Output: Search Points random Position in the contour and interpolate Points i [];

[0122] S1. Traversing Points i [], to determine whether there is a point with Points random If there is overlap, the algorithm ends;

[0123] S2. Calculate Points random To Points i [j] and Points i The distance of [j+1] is stored in set D;

[0124] S3. Repeat step S2 to traverse Pointsi [ ] all points;

[0125] S4. Fill L i The side length set Side i ;

[0126] S5. Calculation | D j -Side i |, stored in the set Δ;

[0127] S6. Repeat step S4 to traverse Points i [], returns the j corresponding to the minimum value in Δ, and Points random Insert Points i [j] and Points i [j+1], the algorithm ends.

[0128] In this embodiment, the starting point pair is constructed, and the basis for matching adjacent contour feature points is to determine the starting point and unify the detour direction. The detour direction can be determined by calculating the cross product of the contour adjacent edge direction vectors by the feature point set. In order to construct the starting point pair, this embodiment, based on the existing method, encrypts the feature point set of the original contour by midpoint interpolation to enhance the integrity of the point set representation of the contour. The bounding box technology and translation method are introduced to weaken the distribution range differences of the original point group. The three-dimensional Euclidean distance of the corresponding points is calculated to establish a correlation matrix, and the global nearest neighbor search is used to calculate the optimal solution. The bounding box technology can describe the spatial distribution characteristics of discrete point sets. The directed bounding box OBB can reduce range redundancy and adapt to flat concave contours. It is not affected by the geometric center inside or outside the contour line. Unifying the bounding box centers of adjacent contours by coordinate translation can effectively weaken the impact of point group distribution differences on the distance of corresponding points. It is widely used in contour feature point matching. After unifying the bounding box centers of the contours, the distances of corresponding points can be calculated to construct a correlation matrix. represents adjacent contour lines, then the correlation matrix can be expressed by formula (1):

[0129]

[0130] Increasing the number of feature points of the contour by interpolation encryption can improve the diversity of the matrix and weaken the impact of the sparseness of the original point set of the contour on the rationality of the optimal solution. Since the long side of the contour is more likely to cause unreasonable matching of corresponding points than the short side, the encryption method here is based on splitting the long side and inserting the midpoint at the longest adjacent distance in the search point set. When the number of feature points of a contour is n, the adjacent points and Distance is Then the contour l i With l j The average side length of and Determine the smaller value and calculate the interpolation number N by the formula. After interpolation, calculate the new Correlation Matrix and calculate the minimum distance corresponding point calculate To i Adjacent point pairs The distance and calculate and The absolute value of the difference Traverse all points to get the set Calculated by Insert it into l at index position h i And adjust to the collection starting point, point Follow the same steps. The algorithm flow is as follows Figure 2 shown.

[0131]

[0132] Specifically, the auxiliary point interpolation method in this embodiment includes equi-angle projection interpolation, angle bisector interpolation, and minimum edge reference interpolation.

[0133] Auxiliary point interpolation is to insert some points without affecting the shape of the contour to weaken the differences in the distribution and quantity of the vertex set, as well as the sparsity of the original point group. Traditional views mostly use the re-vertex method or the midpoint interpolation method to implement this step, and the effectiveness of these two methods is fully explained. This patent conducts a new analysis of the constraints of auxiliary point interpolation, incorporates more effective shape constraints, and uses different interpolation constraints for contours in different situations.

[0134] The steps of interpolation based on equiangular projection are as follows:

[0135] Input: Points of the contour line i [] and Points i+1 [];

[0136] Output: a balanced set of points i [] and Points i+1 [];

[0137] S1. Construct the starting point pair of the contour line and adjust the detour direction of the contour line;

[0138] S2. Calculate L i ,L i+1 Center i ,Center i+1 , translate the two contour lines to (0,0) as the geometric center;

[0139] S3. Calculate and fill the angle of the two lines i With Angle i+1 ;

[0140] S4. Determine Angle i [IndexUp] and Angle i+1 The size of [IndexDown] is interpolated on the contour line with a smaller angle according to the equal-angle projection rule;

[0141] S5. For the interpolated contour line, update its Angle;

[0142] S6. Repeat steps S5 and S6, when IndexUp = Points i .Count-1 or IndexDown=Points i+ 1. When Count-1, the step ends;

[0143] S7. Move the interpolated points to their original positions.

[0144] The steps for interpolation based on the angle bisector are as follows:

[0145] Input: Points of the contour line to be interpolated i [];

[0146] Output: The encrypted contour point set Points i [];

[0147] S1. Calculate and fill L i Angle collection Angle i ;

[0148] S2. Find Angle i The largest angle imax, , calculate the intersection points of the angle bisector and the corresponding side insert , insert into Points i [] between the two endpoints of the edge;

[0149] S3. Repeat steps S1 and S2 to Points i [] When the number of midpoints reaches the specified number, the algorithm ends.

[0150] The steps of interpolation based on the minimum edge criterion are as follows:

[0151] When the contour is concave and has a complex shape, such as Figure 3As shown in (d): The winding direction of the contour is clockwise, but the winding direction of each contour interval is not uniform and varies. At this time, the concave contour needs to be divided into several convex intervals in advance using the interpolation method mentioned above. When the concavity and convexity of the corresponding intervals of adjacent contours are inconsistent, the matching difficulty will be increased. Since the spacing between contour feature points is not affected by the contour convexity, the uniformity and density of the point set can be enhanced by inserting auxiliary points to weaken the distance difference between adjacent points. Contour line l i ={p i0 ,p i1 ,p i2 …p i35}, calculate the adjacent point distance set D i ={d i0 ,d i1 ,d i2 …d i35}, search for the minimum distance d min , the number of interpolation points n is calculated by formula (6) i , calculate the adjacent contour l in the same steps j The number of interpolation points n j , determine the number of interpolation points n according to formula (7), and calculate |p by formula (8) i0 p i1 |Number of interpolation points in the interval According to point p i0 and p i1 The interpolation point {p i1′ ,p i2′ ,p i3′ ,p i4′ ,p i5′ ,p i6′}, traverse l i Interpolation is completed.

[0152]

[0153] n=max <n i ,n j > (7)

[0154]

[0155] Specifically, in this embodiment, the inverse distance weighted interlayer interpolation method in S4 includes the following steps:

[0156] Input: Points of two adjacent contour lines i [],Points i+1 [];

[0157] Output: The new contour vertex set Points at the same distance from the plane where the two adjacent contours are located insert [];

[0158] S1. Unify the detour directions of the two contour lines and determine the similarity of the two contour lines. If the similarity is low, the algorithm terminates.

[0159] S2. Iterate the minimum distance method to obtain the initial point pair and unify the detour directions of the two contour lines;

[0160] S3. Adjust all contour lines to have the same number of points based on the angle bisector interpolation algorithm. Starting from the starting point pair, calculate the distance between it and the adjacent point and the next adjacent point, and determine the weight according to the inverse ratio of the distance;

[0161] Points i [IndexUp] and Points i [IndexUp+1] distance D1,Points i [IndexUp] and Points i [IndexUp+2] distance D2, Points i [IndexUp] and Points i [IndexUp-1] distance D3, Points i [IndexUp] and Points i [IndexUp-2] distance D4. Points i [IndexUp+1,Points i [IndexUp+2],Points i [IndexUp-1],Points i The corresponding weights of [IndexUp-2] are P1, P2, P3, P4, P1 / P2 / P3 / P4=(1 / d1)(1 / d2)(1 / d3)(1 / d4)

[0162] S4. Calculate the coordinates of the insertion point based on the weights insert1 [IndexUp], repeat S3, traverse Points i [], you can generate a set of interpolation points with the same number of points insert1 ;

[0163] S5. According to S3 and S4, Points i+1 [ ] Generate Points insert2 ;

[0164] S6. Points insert1 With Points insert2 Taking the average at the same index can get the final interpolation result Points insert [].

[0165] The method based on inverse distance weighted interpolation is used to encrypt the contour lines, generate new contour lines between adjacent contour lines, and solve the sparseness problem of the section; it is characterized in that when the section is sparse and the distance between adjacent contour lines is too large, the weight of the influence of the contour line spacing on the span length will be much greater than the side length of the contour line, resulting in a decrease in the correlation of adjacent point sets, resulting in rough transitions between layers and a decrease in constraint effectiveness. On the basis of the matching in the previous article, this embodiment introduces a nonlinear interpolation method for interlayer encryption. Since the coupling degree between the interpolated points and the sample points is relatively high, this embodiment uses the inverse distance rule to determine the weights. The point set has achieved similarity, balance, and density through equi-angle projection interpolation and angle bisector interpolation. In order to avoid the large power value resulting in excessive weights of adjacent points and tending to linear interpolation, resulting in a decrease in the smoothness of the surface and an increase in the risk of cross-section misalignment, and to avoid the lack of effective distinction between adjacent point and sub-adjacent point information due to too low a power value, after a large number of modeling example tests, this embodiment sets the power value p to 1. Figure 2 As shown, {p i0 ,p i1 ,p i2 ,p i3 ,p i4} and {p j0 ,p j1 ,p j2 ,p j3 ,p j4}, p is calculated by formula (10) i2 The adjacent and sub-adjacent distances {d i0 ,d i1 ,d i2 ,d i3}, according to formula (11) calculate {p i0 ,p i1 ,p i3 ,p i4 The weight of {w i0 ,w i1 ,w i2 ,w i3}, and finally the interpolation point p is calculated by formula (12): k2′ . Follow the same steps {p j0 ,p j1 ,p j3 ,p j4}Calculate the interpolation point p k2″ , calculate the interpolation point p by formula (13) k2 . By traversing the feature point set of the contour, {p k0 ,p k1 ,p k2 ,p k3 ,p k4 …}.

[0166]

[0167] Specifically, in this embodiment, the steps of the triangulated mesh stitching algorithm with multiple feature constraints in S5 are as follows:

[0168] Input: A set of contour points after equalization and encryption;

[0169] Output: a set of triangular facets formed by contour vertices;

[0170] S1. Generate control spans at the same index in the feature point set of adjacent contour lines according to the equal angle mapping rule, and generate two triangles between the two control spans according to the shortest diagonal rule. The winding direction of the triangle should be counterclockwise to provide the correct normal for rendering;

[0171] S2. Traverse the feature point set of the contour line and repeat step S1;

[0172] S3. The contour line is a closed curve. It is necessary to connect the last point of the point set with the first point. Two triangles are generated between the first and last control spans according to the shortest diagonal rule. The algorithm ends.

[0173] The reconstruction result of this embodiment is as follows Figure 7 , Figure 8 , Fig. 9 , Fig.10 , Fig.11 As shown, Figure 7 (a) is the starting point pair search (minimum distance method); Figure 7 (b) is the starting point pair search (algorithm of the present invention); Figure 7 (c) is the shortest diagonal method (20 points); Figure 7 (d) is the algorithm of the present invention (20 points); Figure 7 (e) is the shortest diagonal method (100 points); Figure 7 (f) is the algorithm of the present invention (100 points); Figure 8 (a) is the reconstruction of the complex concave contour with directional differences in the corresponding intervals; Figure 8 (b) is the reconstruction of the complex concave contour with the same direction in the corresponding interval; Fig. 9 (a) is the outline shape; Fig. 9 (b) is the equi-angle projection interpolation and angle bisector interpolation; Fig. 9 (c) is the point group after 5 iterations of interlayer interpolation; Fig. 9 (d) is the reconstruction result of angle interpolation; Fig. 9 (e)(f)(g)(h) are the reconstruction results after 1 to 5 iterations of interlayer interpolation; Fig.10 (a) is the original contour source; Fig.10 (b) is the first interlayer interpolation; Fig.10(c) is the second interlayer interpolation; Fig.10 (d) is the contraction contour produced by deleting the interpolation; Fig.10 (e) is the reconstruction result of the first interlayer interpolation; Fig.10 (f) is the reconstruction result of the second interlayer interpolation; Fig.11 (a) is the distribution of span length of triangulated network; Fig.11 (b) is the similarity distribution based on angle; Fig.11 (c) is the similarity distribution based on distance; Fig.11 (d) is the cosine similarity distribution of the normal of the adjacent surface; the comparison of the first and second order center distances of the triangulated network features is shown in Table 1:

[0174] Table 1 Comparison of first and second order center distances of reconstructed triangulated network features

[0175]

[0176] The above-mentioned geological body three-dimensional surface reconstruction method based on profile provided in this embodiment has the following main beneficial effects:

[0177] ① The starting point pair search method based on auxiliary space interpolation and nearest neighbor iterative search optimizes the rationality reduction defect of the optimal solution caused by the sparsity of the original point group.

[0178] ②The introduction of angle sets effectively incorporates the contour shape into the constraint conditions, which is applicable to convex contours and simple concave contours. The equal-division interpolation based on distance features can adapt to narrow and long contours and concave contours.

[0179] ③ The inter-layer interpolation with inverse distance weighting weakens the spatial sparsity of the point group and strengthens the inter-layer constraints.

[0180] ④ Based on the equal-angle mapping constraint, the control span is generated and the shortest span constraint is used to generate the remaining span, which takes into account the optimal basic triangle facets and the optimal tessellation process, maintaining the overall consistency of the triangulated network and the local rationality.

[0181] The above embodiments are only descriptions of the preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the protection scope determined by the claims of the present invention.

Claims

1. A three-dimensional rapid modeling method based on multi-feature constraints of profile, characterized in that: include: Based on the borehole spatial information data of the geological body section, the preset key points are extracted to construct a discrete point set of the geological body section; Searching for a starting point pair of the contour line for the discrete point set, and unifying the detour direction of the adjacent point set; Constructing an initial adjacent contour point set based on the starting point pair and the detour direction, performing auxiliary point interpolation with multi-feature constraints on the initial adjacent contour point set, and constructing a one-to-one correspondence relationship between vertices of different contours; Perform interlayer interpolation on the contour point set after auxiliary point interpolation to obtain a new contour; Based on the shortest diagonal constraint, the contour point set after inter-layer interpolation is triangulated.

2. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: The discrete point set for extracting preset key points to construct the geological body profile includes: The polygon evolution method is used to calculate the influence weight of each point on the source polygon on the shape, and the points with weights lower than the preset threshold are removed, and the preset key points that affect the shape are extracted as the discrete point set of the geological body profile.

3. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: Searching for a starting point pair for the discrete point set and unifying the detour direction of the adjacent point set includes: The similarity of three-dimensional Euclidean distance is used to search for the starting point pair, the discrete point set is copied to the auxiliary space, the auxiliary space is interpolated and encrypted, the index of the starting point pair is obtained using the maximum similarity and set as the initial point pair, the index of the discrete point set is readjusted with the set initial point pair as the starting point, two vectors are constructed using three adjacent points in a point set and the cross product is calculated to obtain the detour direction, and the detour direction of the adjacent point set is unified.

4. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 3 is characterized in that: The algorithm for interpolation encryption of auxiliary space is: in, and Represents the contour i With l j The average side length of m represents l i The number of vertices in, h represents the parameter required to traverse the edge length set, Represents the contour i The element with index h in the edge set of , n represents the number of feature points of a contour, k represents the parameter required to traverse the edge length set, Represents the contour j The element with index k in the edge set of represents an endpoint of the span with the smallest calculated span length, Represents the parameters needed to traverse the distance between points, representing a vertex, Indicate point The sum of the distances to any set of adjacent points of the original point group, It represents the absolute value of the difference between the distance mentioned above and the distance to this set of neighboring points.

5. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: The auxiliary point interpolation with multiple feature constraints on the initial adjacent contour point set includes: performing equal angle projection interpolation, angle bisector interpolation, and minimum edge reference interpolation; The equi-angle projection interpolation is: S11, constructing a starting point pair of the contour line and adjusting the detour direction of the contour line; S21, calculate contour line L i ,L i+1 Center i ,Center i+1 , translate the two contour lines to (0,0) as the geometric center; S23. Calculate and fill the angle set Angle of two contour lines i With Angle i+1 ; S24. Set IndexUp as the angle i The index of the angle set Angle is IndexDown i+1 Index to determine the angle Angle i [IndexUp] and angle Angle i+1 The size of [IndexDown] is interpolated on the contour line with a smaller angle according to the equal-angle projection rule; S25. For the interpolated contour line, update its angle set Angle; S26. Repeat steps S25 and S26, using Points i .Count indicates contour L i Angle collection Angle i Capacity, using Points i+1 .Count indicates contour L i+1 Angle collection Angle i+1 Capacity, when IndexUp = Points i .Count-1 or IndexDown=Points i+1 When .Count-1, the step ends; S27. translating the interpolated point to the original position; The angle bisector interpolation is: S21. Calculate and fill the contour L i Angle collection Angle i ; S22. Find the angle set Angle i The largest angle in imax , calculate the intersection points of the angle bisector and the corresponding side insert , insert into the point set Points i [ ] between the two endpoints of the edge; S23, repeat steps S1 and S2 to the intersection point i [ ] When the number of midpoints reaches the specified number, the algorithm ends; The minimum edge base interpolation is: When the contour is concave, the contour line l i ={p i0 ,p i1 ,p i2 …p i35 }, p iA Represents the vertices of the contour, A = 0, 1, ..., 35, calculates the adjacent point distance set D i ={d i0 ,d i1 ,d i2 …d i35 }, d iA Represents the distance between adjacent points in the vertex set of the contour line, searching for the minimum distance d min , the number of interpolation points n is calculated by the first preset formula i , calculate the adjacent contour l in the same steps j The number of interpolation points n j , determine the number of interpolation points n according to the second preset formula, and calculate |p by the third preset formula i0 p i1 |Number of interpolation points in the interval According to point p i0 and p i1 The interpolation point {p i1′ ,p i2′ ,p i3′ ,p i4′ ,p i5′ ,p i6′ }, traverse l i Interpolation is completed; The first preset formula is: Among them, n i The contour line l i The number of interpolation points, The contour line l i The distance between adjacent points, m and h are necessary parameters, n j The contour line l j The number of interpolation points, The contour line l j The distance between adjacent points, k and l are necessary parameters; The second preset formula is: n=max <n i ,n j > Where n is the number of interpolation points, n i With n j l i With l j The number of interpolation points; The third preset formula is: in, is the number of interpolation points between adjacent points, is the distance between adjacent points, Used to calculate the perimeter of the contour line; The fourth preset formula is: in, and are the original adjacent point coordinates, is the number of interpolation points between adjacent points, p is the pth interpolation point, is the interpolation point's seat.

6. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: Interlayer interpolation of the contour point set after auxiliary point interpolation includes: S61. Unify the detour directions of the two contour lines in the contour point set after the auxiliary point interpolation, and determine the similarity of the two contour lines. If the similarity is lower than a preset value, the algorithm terminates; S62. Iteratively obtain the initial point pair according to the minimum distance method and unify the detour directions of the two contour lines; S63. Adjust all contour lines to have the same number of points based on the angle bisector interpolation algorithm. Starting from the starting point pair, calculate the distance between it and the adjacent point and the next adjacent point, and determine the weight according to the inverse ratio of the distance; S64. Calculate the coordinates of the insertion point based on the weights insert1 [IndexUp], repeat S63, traverse Points i [], you can generate a set of interpolation points with the same number of points insert1 ; S5. According to S3 and S4, Points i+1 [ ] Generate Points insert2 ; S6. Points insert1 With Points insert2 Taking the average at the same index can get the final interpolation result Points insert [ ].

7. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: The triangulation of the contour point set after interpolation between layers includes: S71, generating a control span at the same index in the contour point set after interpolation between layers according to the equal angle mapping rule, generating two triangles between the two control spans according to the shortest diagonal rule, and the winding direction of the triangle should comply with the counterclockwise direction to provide a correct normal direction for rendering; S72, traverse the contour point set after interlayer interpolation, and repeat step S71; S73, splicing the last point of the contour point set after interlayer interpolation with the first point, generating two triangles between the first and last control spans according to the shortest diagonal rule, and completing triangulation splicing.

8. The three-dimensional rapid modeling method based on multi-feature constraints of cross-section profile according to claim 1 is characterized in that: The drilling spatial information data includes drilling coordinates, hole depth, and inclination measurement.

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