Line-plane boundary constraint promotion modeling method and device, electronic equipment and storage medium

Abstract

The invention belongs to the technical field of geological three-dimensional modeling, and provides a line-plane boundary constraint promotion modeling method and device, electronic equipment and a storage medium, and the method comprises the steps: carrying out the modeling through employing a line-plane boundary constraint promotion model, and obtaining a three-dimensional geologic body model; the modeling method comprises the steps that a point set of a three-dimensional geologic body is obtained, optimization is conducted through a minimization energy function when radial basis function implicit modeling processing is conducted according to the point set, and a normal vector and an implicit function are obtained; the method comprises the following steps: introducing information of a planar geologic structure into an implicit modeling framework in an integral form, performing line-plane constraint on an implicit function, processing the line-plane constrained implicit function through a solution matrix to obtain an implicit function parameter, and determining a line-plane boundary constraint promotion model according to the implicit function and the implicit function parameter. The planar feature information of a geologic body can be effectively utilized, accurate constraint and continuous expression of a geological interface or a stratigraphic structure are achieved, and the spatial precision and reliability of three-dimensional geological modeling are improved.

Description

Technical Field

[0001] This invention relates to the field of 3D implicit modeling technology, and in particular to a method, apparatus, electronic device and storage medium for generalizing line-surface boundary constraints. Background Technology

[0002] Current 3D implicit modeling methods, whether the basic radial basis method or the Hermite radial basis method, are all point constraint methods. Point constraint methods typically require a large amount of geological point data. In actual geological exploration, obtaining complete and high-density geological point data often places very high demands on technology and cost. At the same time, the accuracy and precision of point constraint methods depend on the input geological point data, but this data may contain errors or inaccuracies, including positional deviations, uneven sampling density, and data noise, all of which can lead to deviations in the modeling results. Summary of the Invention

[0003] Aimed at at least in solving one of the technical problems existing in the prior art, the present invention provides a method, apparatus, electronic device and storage medium for generalizing line-surface boundary constraints, thereby improving the modeling accuracy of three-dimensional geological bodies.

[0004] One aspect of the present invention provides a method for generalizing line-surface boundary constraints, comprising:

[0005] The three-dimensional geological body of the target area is obtained, and a line-surface boundary constraint generalization model is used for modeling to obtain a three-dimensional geological body model.

[0006] The line-surface boundary constraint generalization model is obtained through the following steps:

[0007] When obtaining the point set of a three-dimensional geological body and performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function;

[0008] Line-surface constraints are applied to the implicit functions. The implicit functions of the line-surface constraints are processed by solving the matrix to obtain the implicit function parameters. Based on the implicit functions and their parameters, a generalized model of line-surface boundary constraints is determined.

[0009] The line-surface boundary constraint generalization modeling method, wherein a point set of a 3D geological body is obtained, and when performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function, including:

[0010] Obtain the discretized point set of the sampling contour line of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit functions;

[0011] By using the energy function and preset adjustment parameters, a first objective function to be minimized is determined as the optimization objective. for:

[0012]

[0013] The constraint for minimizing the first objective function is: Among them, the central sampling points ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. It is an energy function, and

[0014]

[0015] Based on the implicit function, the function value and gradient value of each sampling point in the point set are calculated. Hermite data is determined based on the function value and gradient value. The first objective function to be minimized is optimized using the Hermite data to obtain the second objective function to be minimized. for:

[0016]

[0017] The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ;

[0018] Based on the minimization of the second objective function and its constraints, the third objective function is determined to be:

[0019]

[0020] The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration.

[0021] The line-surface boundary constraint generalization modeling method described above includes area integral constraints and line constraints of the line segments constituting the surface.

[0022] Area integral constraints are used to characterize any known triangular patch on an implicit surface. The integral is treated as zero, and the area integral constraint is expressed as:

[0023]

[0024] in, Let $\mathbf{a}$ represent any point inside any given triangle in space, and its calculation formula is: , and Both are constants and , Represents the three vertices of a triangle;

[0025] The line constraints of the line segments constituting the surface include line integral constraints and endpoint derivative constraints. The line integral constraints are used to characterize any known triangular patch on the implicit surface. The three sides All integrals are treated as zero, and the line integral constraint is expressed as:

[0026]

[0027] in, The formula for calculating any point on any known line segment in space is: t is a constant and , , representing the start and end points of a line segment;

[0028] The endpoint derivative constraint is used to characterize the gradient at the endpoint of a line segment that is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is as follows: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

[0029] According to the aforementioned line-surface boundary constraint generalization modeling method, the implicit function is subjected to line-surface constraints. The implicit function parameters are obtained by processing the implicit function through matrix solving. The line-surface boundary constraint generalization model is then determined based on the implicit function and its parameters, including:

[0030] The implicit function of the line-surface constraint is:

[0031]

[0032] Among them, the implicit function of line-surface constraints Used to constrain special geological units of three-dimensional geological bodies; These are the weighting coefficients of the line integral constraint terms. Let be the index of the line constraint, and =1,2,… , (Total number of line constraints); These are the weighting coefficients of the area integral constraint term. Let be the index of the surface constraint, and =1,2,… m is the total number of surface constraints; These are the weighting coefficients of the directional gradient constraint term at the endpoints of the line segment. =1,2,… , This represents the total number of gradient constraint points, with header annotations. Represents the coordinates of the endpoints of the line segment, and ; , Implicit functions used for line-surface constraints Provides a highly smooth base surface shape; It is a radial basis function. This indicates the second variable in the kernel function. gradient at; in, ; It is a radial basis function. This indicates the second variable in the kernel function. The gradient at; where, , , , , , and Let be the scalar coefficients to be solved. Let be the three-dimensional vector to be solved. Indicates the number of line segments and sampling points. The system of linear equations satisfied is expressed as:

[0033]

[0034] in, The system of linear equations corresponding to the constraints of minimizing the third objective function. The unknown vector to be solved Here are the constraints, where for:

[0035]

[0036]

[0037]

[0038]

[0039] Among them, matrix The The elements are ,and For scalars, matrices , It is a symmetric matrix. Both represent a point in three-dimensional space; The first in The element is ;matrix The The element is , for The Hessian matrix; Transpose; matrix In For gradient calculation;

[0040] matrix The The elements are , Given a line segment in three-dimensional space. As a scalar, For line segments The equation, ;matrix The The elements are , Given a triangle in three-dimensional space, The equations of three given triangles are: ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are ;

[0041] matrix The The elements are , For line segments The equation, For line segments Equations; matrices The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are ;

[0042] Applying the Gaussian integral method to the linear equation system The implicit function parameters are obtained through calculation:

[0043]

[0044] The line-surface boundary constraint generalization model is determined based on the implicit function and its parameters.

[0045] The modeling method based on the line-surface boundary constraints is extended, wherein the Gaussian integral method is used for the linear equation system. The calculations include:

[0046] matrix The element The calculation method is as follows:

[0047]

[0048] in, , Representing line segments respectively The two endpoints of the line segment The equation is , , , , All are coordinate components of the integral term, and , , , , , , , , It is a point The three coordinate components;

[0049] matrix The element The calculation method is as follows:

[0050]

[0051] in, ;

[0052] When applying surface integral constraints to implicit functions, the integral of the implicit function over triangular elements is introduced as a constraint term. A kernel function in the form of radial basis functions is used as the integration term, and numerical integration is performed over the parameter domain using the Gaussian integration method. The kernel function in the form of radial basis functions is... ; Parameter domain The three vertices of the triangular element are respectively The parametric form of any point on the triangular face is: ;

[0053] matrix The The elements are ,in This indicates that the derivative with respect to the second parameter is taken, and the matrix is... The composition is as follows:

[0054]

[0055] Among them, point This represents a control point, a point. These represent the endpoints of a line segment. Indicates the direction vector at the endpoint of the line segment;

[0056]

[0057] matrix The The elements are ,symbol This indicates taking the derivative with respect to the first parameter, and the matrix... The composition is as follows:

[0058]

[0059] matrix The The elements are ,matrix The composition is as follows:

[0060]

[0061] matrix The The element is The calculation method is as follows:

[0062]

[0063] in, , , , and , They are line segments and line segments The starting point and the ending point, , , , , , Let be the coordinate components of the integral term, where and It is a scalar;

[0064] matrix The The elements are ;matrix The The elements are ;

[0065] matrix The The elements are:

[0066] .

[0067] The modeling method based on the described line-surface boundary constraints further includes:

[0068] A GPU-accelerated dual-moving cube algorithm is used to visualize implicit function surfaces.

[0069] The modeling method based on the described line-surface boundary constraints further includes:

[0070] The effectiveness of the line-surface constraint is evaluated using the MAE loss function.

[0071] Another aspect of the embodiments of the present invention discloses a line-surface boundary constraint generalization modeling apparatus, comprising:

[0072] The first module is used to obtain the three-dimensional geological body of the target area. It uses a line-surface boundary constraint generalization model for modeling to obtain a three-dimensional geological body model.

[0073] The generalized model of line-surface boundary constraints is obtained through the following modules:

[0074] The second module is used to obtain the point set of the three-dimensional geological body. When performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function.

[0075] The third module is used to apply line-surface constraints to implicit functions. By solving the matrix, the implicit functions of the line-surface constraints are processed to obtain the implicit function parameters. Based on the implicit functions and their parameters, the generalized model of the line-surface boundary constraints is determined.

[0076] Another aspect of the present invention provides an electronic device, including a processor and a memory;

[0077] The memory is used to store programs;

[0078] The processor executes the program to implement the method as described above.

[0079] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the methods described above.

[0080] The beneficial effects of this invention are as follows: by introducing planar geological structure information into the implicit modeling framework in the form of integrals, the planar feature information of geological bodies can be effectively utilized to achieve precise constraints and continuous expression of geological interfaces or stratigraphic structures, thereby significantly improving the spatial accuracy and reliability of three-dimensional geological modeling. Attached Figure Description

[0081] Figure 1 This is a schematic diagram of the line-surface boundary constraint generalization modeling process according to an embodiment of the present invention.

[0082] Figure 2 This is a schematic diagram of the implicit modeling process of HRBF-type radial basis functions according to an embodiment of the present invention.

[0083] Figure 3 These are comparison diagrams of modeling using the HRBF method and modeling using line-surface constraints according to an embodiment of the present invention, wherein (a) is a modeling diagram of model I using the HRBF method; (b) is a modeling diagram of model I using line-surface constraints according to an embodiment of the present invention; (c) is a modeling diagram of model II using the HRBF method; and (d) is a modeling diagram of model II using line-surface constraints according to an embodiment of the present invention.

[0084] Figure 4These are comparison diagrams of the line-surface constraint modeling shapes obtained by the HRBF method and the embodiments of the present invention, wherein (a) is the modeling shape obtained by the HRBF method; (b) is the line-surface constraint modeling shape obtained by the embodiments of the present invention; (c) is the modeling shape obtained by the HRBF method including constraint lines; and (d) is the line-surface constraint modeling shape obtained by the embodiments of the present invention.

[0085] Figure 5 This is a schematic diagram of the line-surface boundary constraint generalization modeling device according to an embodiment of the present invention. Detailed Implementation

[0086] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings. Throughout the description, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions. In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the purpose of illustrative purposes and have no specific meaning in themselves. Therefore, "module," "part," or "unit" can be used interchangeably. Terms such as "first," "second," etc., are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the sequential relationship of the indicated technical features. In the following description, the consecutive reference numerals for method steps are for ease of review and understanding. Adjusting the implementation order of steps, in conjunction with the overall technical solution of the present invention and the logical relationship between the various steps, will not affect the technical effect achieved by the technical solution of the present invention. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0087] refer to Figure 1 A schematic diagram of the line-surface boundary constraint generalization modeling process, which includes, but is not limited to, steps S100~S300:

[0088] S100: Obtain the three-dimensional geological body of the target area, and use the line-surface boundary constraint generalization model for modeling to obtain the three-dimensional geological body model.

[0089] In some embodiments, the three-dimensional geological body is three-dimensional spatial data, which can be obtained by using geological profiles, geophysical exploration and remote sensing methods in the target area (mining area).

[0090] In some embodiments, the line-surface boundary constraint generalization model is obtained through steps S200~S300, wherein:

[0091] S200: Obtain the point set of the 3D geological body. When performing implicit modeling of radial basis functions based on the point set, optimize by minimizing the energy function to obtain the normal vector and implicit function.

[0092] In some embodiments, reference Figure 2 The schematic diagram of the implicit modeling process for HRBF-type radial basis functions shown includes, but is not limited to, steps S210~S230:

[0093] S210: Obtain the point set of the discretized sampling contour of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit function.

[0094] In some embodiments, HRBF is used in the following forms:

[0095]

[0096] S220 determines the first objective function to be minimized as the optimization objective by using the energy function and preset adjustment parameters.

[0097] The first objective function to be minimized for:

[0098]

[0099] The constraint for minimizing the first objective function is: , indicating that the magnitude of the gradient at each sampling point is 1; where the sampling points are in the point set. ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. It is an energy function, and

[0100]

[0101] S230: Based on the implicit function, calculate the function value and gradient value of each sampling point in the point set, determine the Hermite data based on the function value and gradient value, and optimize the minimized first objective function using the Hermite data to obtain the minimized second objective function.

[0102] In some embodiments, for each input point Its function value ,gradient ,in A set of Hermite data for the sampling points was obtained. Therefore, the first objective function can be transformed into the second objective function. for:

[0103]

[0104]

[0105] The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. .

[0106] S240, Based on the minimized second objective function and the constraints of the minimized second objective function, determine the minimized third objective function.

[0107] In some embodiments, the third objective function to be minimized is determined based on the minimized second objective function and the constraints of the minimized second objective function:

[0108]

[0109] It should be noted that in the implicit geological modeling of this invention, This is a smoothness penalty term in the normal vector space. Its core function is to achieve a global consistency constraint on the normal vector (attitude) of the geological surface by minimizing this quadratic form. In essence, it is to minimize the smoothness penalty term in the normal vector space under the geometric constraint that the normal vector is a unit vector. By minimizing the spatial variation of the normal vector field, a geological surface normal vector field that conforms to the attitude of the sampling points and is globally smooth and continuous is obtained, providing attitude support for the accurate construction of implicit surfaces.

[0110] The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration.

[0111] S300 applies line-surface constraints to the implicit function. By solving the matrix, the implicit function of the line-surface constraint is processed to obtain the implicit function parameters. Based on the implicit function and the implicit function parameters, the generalized model of the line-surface boundary constraint is determined.

[0112] In some embodiments, surface constraints include area integral constraints and line constraints on the line segments constituting the surface. The area integral constraint is used to characterize any known triangular facet on the implicit surface. The integral is treated as zero, and the area integral constraint is expressed as:

[0113]

[0114] Given that a triangular patch S is a local geometric unit of an implicit surface, this constraint is essentially a global property restriction that the integral of an implicit function f within the region of the patch must return to zero. It requires that within the local region of the surface corresponding to the triangular patch S, the implicit function f... The weighted cumulative effect is zero, ensuring that the function properties of the patch are consistent with the preset geometric / physical rules of the overall implicit surface (such as the continuity of isosurfaces and the balance of field distribution), thus avoiding surface distortion caused by excessive shift of function values ​​in local patches.

[0115] In some embodiments, the line constraints of the line segments constituting the surface include line integral constraints and endpoint derivative constraints. The line integral constraint is used to characterize any known triangular patch on the implicit surface. The three sides All integrals are treated as zero, and the line integral constraint is expressed as:

[0116]

[0117] The formula for calculating any point on any known line segment in space is: t is a constant and , , represents the starting and ending points of a line segment.

[0118] In some embodiments, the line constraints of the line segments constituting the surface include line integral constraints and endpoint derivative constraints. The line integral constraint is used to characterize any known triangular patch on the implicit surface. The three sides All integrals are treated as zero, and the line integral constraint is expressed as:

[0119]

[0120] The formula for calculating any point on any known line segment in space is: t is a constant and , , represents the starting and ending points of a line segment.

[0121] In some embodiments, the endpoint derivative constraint is used to characterize that the gradient at the endpoint of a line segment is perpendicular to the direction vector of the line segment, within the set of endpoints of the line segment. The endpoint derivative constraint is: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

[0122] It should be noted that, within the functional framework of the three-dimensional geological implicit modeling proposed in the method of this embodiment of the invention, It is the core basic fitting term, essentially a linear combination of Hermite radial basis functions (HRBF). Its function is to fuse function value constraints and gradient constraints to form the entire implicit function. Provides a highly smooth base surface shape. Subsequent line integrals, surface integrals, and directional gradient constraints are all in On the constructed basic surface, targeted constraints are applied to special geological units.

[0123] In some embodiments, the specific geological unit is the geological boundary, profile, endpoint orientation, etc. of a three-dimensional geological body.

[0124] In some embodiments, the implicit function of the line-surface boundary constraint is:

[0125]

[0126] Among them, the implicit function of line-surface constraints Used to constrain special geological units of three-dimensional geological bodies; These are the weighting coefficients of the line integral constraint terms. Let be the index of the line constraint, and =1,2,… , (Total number of line constraints); These are the weighting coefficients of the area integral constraint term. Let be the index of the surface constraint, and =1,2,… m is the total number of surface constraints; These are the weighting coefficients of the directional gradient constraint term at the endpoints of the line segment. =1,2,… , This represents the total number of gradient constraint points, with header annotations. Represents the coordinates of the endpoints of the line segment, and ; , Implicit functions used for line-surface constraints Provides a highly smooth base surface shape; It is a radial basis function. This indicates the second variable in the kernel function. gradient at; It is the area infinitesimal element of the surface, that is, the integral element in the surface integral; where, , , , , , and Let be the scalar coefficients to be solved. For the three-dimensional vector to be solved, the sampling points The system of linear equations satisfied is expressed as:

[0127]

[0128] in, The system of linear equations corresponding to the constraints of minimizing the third objective function. The unknown vector to be solved Here are the constraints, where for:

[0129]

[0130] in, ;

[0131] in, Representation matrix transpose of matrix The The elements are , It is a scalar, and the matrix It is a symmetric matrix. Both represent a point in three-dimensional space; The first in The element is , This indicates that the gradient is calculated with respect to the second element in the parentheses; Representation matrix transpose of matrix; It is also a symmetric matrix. The The element is , This indicates that the gradient of each of the two elements within the parentheses is calculated, and the result is a value of size . The Hessian matrix.

[0132] matrix The The elements are , Given a line segment in three-dimensional space. As a scalar, For line segments The equation, ;matrix The The elements are , Given a triangle in three-dimensional space, It is a triangle The equation, ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are .

[0133] matrix The The elements are , For line segments The equation, For line segments Equations; matrices The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are . , , Represent matrices respectively , , The transpose of .

[0134] This invention employs a Gaussian integral method for solving linear equation systems. The implicit function parameters are obtained through calculation:

[0135]

[0136] The line-surface boundary constraint generalization model is calculated based on the implicit function and its parameters. The matrix represents the implicit function parameters to be determined, where... That is This vector represents the constraint condition, where mean:

[0137] 1) The first part = 0, the implicit function is zero at the sampling point (the point is on the implicit surface);

[0138] 2) The second part = n, the gradient is equal to the normal vector constraint, that is, the gradient of HRBF must match the given normal vector;

[0139] 3) The third, fourth and fifth parts = 0, indicating some additional constraints, such as surface constraints, line segment constraints and line segment direction constraints in the embodiments of the present invention.

[0140] In some embodiments, the Gaussian integral method is used to solve the linear equation system. The calculations include:

[0141] matrix The element The calculation method is as follows:

[0142]

[0143] in, , Representing line segments respectively The two endpoints of the line segment The equation is , , , , All are coordinate components of the integral term, and , , , , , , , , It is a point The three coordinate components;

[0144] matrix The element The calculation method is as follows:

[0145]

[0146] in,

[0147]

[0148] When applying area constraints to the implicit function model, the integral of the implicit function over the triangular facet is introduced as a constraint term. For any triangular facet, its three vertices are... ( Any point on the triangular face can be represented by a parametric form. Represented. The integral term uses a kernel function in the form of radial basis functions. The parameter domain is determined by the Gaussian integral method. Numerical integration is performed to achieve an approximate calculation of the surface integral.

[0149] matrix The The elements are ,symbol This indicates that the derivative with respect to the second parameter is taken, and the matrix is... The composition is as follows:

[0150]

[0151] Among them, point This represents a control point, a point. These represent the endpoints of a line segment. This represents the direction vector at the endpoints of the line segment.

[0152]

[0153] matrix The The elements are ,symbol This indicates taking the derivative with respect to the first parameter, and the matrix... The composition is as follows:

[0154]

[0155] matrix The The elements are ,matrix The composition is as follows:

[0156]

[0157] matrix The The element is The calculation method is as follows

[0158]

[0159] in, , , , and , They are line segments and line segments The starting point and the ending point, , , , , , Let be the coordinate components of the integral term, where and It is a scalar.

[0160] matrix The The elements are Let the triangular face element (the s-th face) be △ABC, whose parametric representation is as follows:

[0161]

[0162] Let line segment The two endpoints are Its parameterized representation is

[0163]

[0164] Let the length of the line segment be...

[0165]

[0166] Given kernel function (For example The double integral, which involves first integrating the area of ​​the triangle with respect to y and then integrating along the line L, can be written as:

[0167]

[0168] matrix The The elements are The specific derivation process is as follows:

[0169] Let the two triangular face elements be Parameterize each point as follows:

[0170]

[0171]

[0172] Given kernel function (For example Then the matrix The The elements are double area integrals (integrated over each of the two triangular faces):

[0173]

[0174] By parameterizing the triangle and substituting it into the Jacobian factor (area scale), we obtain an equivalent parameter domain expression:

[0175]

[0176] in,

[0177]

[0178]

[0179] These are the Jacobian factors of the areas of the two triangles, respectively.

[0180] In particular, when When the above formula is:

[0181]

[0182] matrix The The elements are:

[0183]

[0184] In some embodiments, an improved moving cube algorithm is used to visualize the implicit function surface.

[0185] refer to Figure 3 The diagrams show a comparison between the HRBF method modeling and the line-surface constraint modeling of the present invention, where (a) is the modeling diagram of Model I using the HRBF method; (b) is the modeling diagram of Model I using the line-surface constraints of the present invention; (c) is the modeling diagram of Model II using the HRBF method; and (d) is the modeling diagram of Model II using the line-surface constraints of the present invention. It can be determined that... Figure 3 The red triangle represents the applied surface constraint, and the boundary of the red triangle, i.e., the black line segment, represents the applied line constraint. For (a) and (c), it can be seen that without line-surface constraints, the model has a noticeable bulge in this area (the red triangle is obscured, leaving only three points). For (b) and (d), using the method of this embodiment, it can be seen that the bulge of the model is constrained and closely matches the triangle at the constraint point. The red triangle is clearly visible, and the black line segment of its boundary represents the applied line constraint. The shape of the model in this area is effectively constrained, closely matching the shape of the red triangle, and the original bulge is suppressed. This demonstrates that the method of this embodiment, through the combination of line-surface constraints, can precisely control the local shape, making the shape of the model in the constrained area more in line with design requirements.

[0186] To quantify the effect of line-surface constraints on the local shape constraints of curved surfaces, mean absolute error (MAE) is selected as the accuracy evaluation index. MAE refers to the target value... Compared with the predicted value The average of the absolute values ​​of the differences, where The MAE is the total number of midpoints of a line segment, calculated as follows:

[0187]

[0188] The specific implementation involves discretizing the red triangular facets into points, calculating the distance from each point to the implicit surface, obtaining this series of distance values, and then calculating the MAE, resulting in Table 1 below. It is easy to see from Table 1 that the addition of line-surface constraints effectively constrains the local shape of the surface. Using the method of this embodiment, the areas where triangle integral constraints are applied fit the implicit surface more closely.

[0189] Table 1. Comparison of MAE values ​​between the HRBF method and the method of this embodiment.

[0190] In some embodiments, a GPU-accelerated Dual Marching Cubes algorithm is used to visualize the implicit function surface, thereby achieving efficient reconstruction and rendering of the three-dimensional geological body surface.

[0191] The method of this invention can not only use a single triangular facet to constrain the local surface shape of the model, but also use the entire triangular mesh to constrain the global shape of the model. This method combines the core characteristics of explicit modeling (directly constraining the model shape through explicit geometric elements such as triangular faces and triangular meshes, reflecting explicit geometric control) and implicit modeling (using implicit functions or algorithms to fuse these explicit constraints, achieving smooth transitions and global coordination of the shape, reflecting "implicit" mathematical driving). It is an organic combination of the two in the modeling process, enabling both explicit and implicit modeling.

[0192] refer to Figure 4 The diagrams show a comparison of the HRBF method and the line-surface constraint modeling shapes of the embodiments of the present invention. (a) shows the modeling shape obtained by the HRBF method; (b) shows the line-surface constraint modeling shape of the embodiment of the present invention; (c) shows the modeling shape including constraint lines obtained by the HRBF method; and (d) shows the line-surface constraint modeling shape of the embodiment of the present invention. (a) and (c) show the results using the HRBF method. Without the line-surface boundary constraints of a triangular mesh, the model appears relatively blurry, lacking structural details, and exhibiting weak overall regularity. The model shapes (a) and (c) obtained by the HRBF method, lacking global constraints similar to a triangular mesh, have limited control over the global shape of the model, making it difficult to accurately preserve complex structural features. Consequently, the surface refinement and morphological integrity of the calculated results are not as high as those of the model shapes in the embodiments of the present invention.

[0193] (b) and (d) show the results of using the line-surface boundary constraints of this embodiment of the invention. The blue triangular mesh represents the constraint conditions, and the model surface exhibits clear structural details and a regular shape. For example, the vertical texture in the middle and the edge contours are relatively clear, and the overall model has the texture of an "explicit model." This is because the method of this embodiment of the invention applies global morphological constraints through the entire triangular mesh, which can accurately control the overall shape of the model, preserve structural details, and make the surface shape more in line with expectations.

[0194] Figure 5 This is a schematic diagram of a line-surface boundary constraint generalization modeling device according to an embodiment of the present invention. The device includes a first module 510, a second module 520, and a third module 530.

[0195] The first module is used to acquire the three-dimensional geological body of the target area and to model it using a line-surface boundary constraint generalization model to obtain the three-dimensional geological body model. The line-surface boundary constraint generalization model is obtained through the following modules: The second module is used to acquire the point set of the three-dimensional geological body. When performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function; The third module is used to apply line constraints to the implicit function. The implicit function with line constraints is processed by solving the matrix to obtain the implicit function parameters. The line-surface boundary constraint generalization model is determined based on the implicit function and the implicit function parameters.

[0196] Exemplarily, with the cooperation of the first, second, and third modules in the device, the embodiment device can implement any of the aforementioned line-surface boundary constraint generalization modeling methods, namely, acquiring the three-dimensional geological body of the target area, performing modeling processing using the line-surface boundary constraint generalization model, and obtaining a three-dimensional geological body model; the line-surface boundary constraint generalization model is obtained through the following steps: acquiring the point set of the three-dimensional geological body, optimizing by minimizing the energy function when performing implicit modeling processing based on the point set, obtaining the normal vector and implicit function; applying line-surface constraints to the implicit function, processing the implicit function of the line-surface constraint by solving the matrix, obtaining the implicit function parameters, and determining the line-surface boundary constraint generalization model based on the implicit function and the implicit function parameters. The beneficial effects of the present invention are: by introducing the planar geological structure information into the implicit modeling framework in integral form, the planar feature information of the geological body can be effectively utilized to achieve precise constraints and continuous expression of geological interfaces or stratigraphic structures, thereby significantly improving the spatial accuracy and reliability of three-dimensional geological modeling.

[0197] This invention also provides an electronic device, which includes a processor and a memory;

[0198] The memory stores the program;

[0199] The processor executes a program to perform the aforementioned line-surface boundary constraint generalization modeling method; the electronic device has the function of carrying and running the software system for line-surface boundary constraint generalization modeling provided in the embodiments of the present invention, such as a personal computer, minicomputer, mainframe, workstation, network or distributed computing environment, standalone or integrated computer platform, or communicating with charged particle tools or other imaging devices, etc.

[0200] This invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement the line-surface boundary constraint generalization modeling method described above.

[0201] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented in the embodiments of this invention. Alternative embodiments are contemplated, in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0202] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned line-surface boundary constraint generalization modeling method.

[0203] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, considering the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed in the embodiments of the invention, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0204] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0205] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can include, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0206] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0207] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0208] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0209] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0210] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A method for generalizing line-surface boundary constraints, characterized in that, include: The three-dimensional geological body of the target area is obtained, and a line-surface boundary constraint generalization model is used for modeling to obtain a three-dimensional geological body model. The line-surface boundary constraint generalization model is obtained through the following steps: When obtaining the point set of a three-dimensional geological body and performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function; Line-surface constraints are applied to the implicit functions. The implicit functions of the line-surface constraints are processed by solving the matrix to obtain the implicit function parameters. Based on the implicit functions and their parameters, a generalized model of line-surface boundary constraints is determined.

2. The line-surface boundary constraint generalization modeling method according to claim 1, characterized in that, When acquiring the point set of the three-dimensional geological body and performing implicit modeling of the radial basis function based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and implicit function, including: Obtain the discretized point set of the sampling contour line of the three-dimensional geological body, and use HRBF-type radial basis functions to determine the implicit functions; By using the energy function and preset adjustment parameters, a first objective function to be minimized is determined as the optimization objective. for: ； The constraint for minimizing the first objective function is: Among them, the central sampling points ,and , The total number of sampling points in the point set. Implicit function for preset adjustment parameters The zero-level set is an implicit surface of a three-dimensional geological body. It is an energy function, and ； Based on the implicit function, the function value and gradient value of each sampling point in the point set are calculated. Hermite data is determined based on the function value and gradient value. The first objective function to be minimized is optimized using the Hermite data to obtain the second objective function to be minimized. for: ； The constraint for minimizing the second objective function is: , The gradient value represents the gradient of a single sampling point; The function value vector of the sampling points. This indicates that the function value at each sampling point will be... The column vector formed by collecting them; This is the smooth implicit function approximation solution obtained based on Hermite data, i.e., the optimal solution obtained after optimization. ; Based on the minimization of the second objective function and its constraints, the third objective function is determined to be: ； The constraint for minimizing the third objective function is: ,in Let be the normal vector, where the normal vector is... By analyzing the gradient value The result is obtained by normalization and integration.

3. The line-surface boundary constraint generalization modeling method according to claim 2, characterized in that, The line-surface constraint includes area integral constraints and line constraints of the line segments constituting the surface, including: The area integral constraint is used to characterize any known triangular facet on the implicit surface. The integral is treated as zero, and the area integral constraint is expressed as: ； in, Let $\mathbf{a}$ represent any point inside any given triangle in space, and its calculation formula is: , and Both are constants and , Represents the three vertices of a triangle; The line constraints of the line segments constituting the surface include line integral constraints and endpoint derivative constraints. The line integral constraints are used to characterize any known triangular patch on the implicit surface. The three sides All integrals are treated as zero, and the line integral constraint is expressed as: ； in, The formula for calculating any point on any known line segment in space is: t is a constant and , , representing the start and end points of a line segment; The endpoint derivative constraint is used to characterize the gradient at the endpoint of a line segment that is perpendicular to the direction vector of the line segment. The endpoint derivative constraint is as follows: , This represents the direction vector of the line segment. It is calculated by the difference between the coordinates of the endpoint and the starting point of the line segment.

4. The line-surface boundary constraint generalization modeling method according to claim 3, characterized in that, The process of applying line-surface constraints to the implicit function involves processing the implicit function through matrix solving to obtain implicit function parameters. Based on the implicit function and its parameters, a generalized model for the line-surface boundary constraints is determined, including: The implicit function of the line-surface constraint is: ； Among them, the implicit function of line-surface constraints Used to constrain special geological units of three-dimensional geological bodies; These are the weighting coefficients of the line integral constraint terms. Let be the index of the line constraint, and =1,2,… , (Total number of line constraints); These are the weighting coefficients of the area integral constraint term. Let be the index of the surface constraint, and =1,2,… m is the total number of surface constraints; These are the weighting coefficients of the directional gradient constraint term at the endpoints of the line segment. =1,2,… , This represents the total number of gradient constraint points, with header annotations. Represents the coordinates of the endpoints of the line segment, and ; , Implicit functions used for line-surface constraints Provides a highly smooth base surface shape; It is a radial basis function. This indicates the second variable in the kernel function. The gradient at; where, , , , , , and Let be the scalar coefficients to be solved. For the three-dimensional vector to be solved, the sampling points The system of linear equations satisfied is expressed as: ； in, The system of linear equations corresponding to the constraints of minimizing the third objective function. The unknown vector to be solved Here are the constraints, where for: ； ； ； ； Among them, matrix The The elements are ,and For scalars, matrices , It is a symmetric matrix. Both represent a point in three-dimensional space; The first in The element is ;matrix The The element is , for The Hessian matrix; Transpose; matrix In For gradient calculation; matrix The The elements are , Given a line segment in three-dimensional space. As a scalar, For line segments The equation, ;matrix The The elements are , Given a triangle in three-dimensional space, The equations of three given triangles are: ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are ,matrix The The elements are ; matrix The The elements are , For line segments The equation, For line segments Equations; matrices The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are ;matrix The The elements are ; Applying the Gaussian integral method to the linear equation system The implicit function parameters are obtained through calculation: ； The line-surface boundary constraint generalization model is determined based on the implicit function and its parameters, whereby... These are constraints.

5. The line-surface boundary constraint generalization modeling method according to claim 1, characterized in that, The Gaussian integral method is used to solve the linear equation system. The calculations include: matrix The element The calculation method is as follows: ； in, , Representing line segments respectively The two endpoints of the line segment The equation is , , , , All are coordinate components of the integral term, and , , , , , , , , It is a point The three coordinate components; matrix The element The calculation method is as follows: ； in, ; When applying surface integral constraints to implicit functions, the integral of the implicit function over triangular elements is introduced as a constraint term. A kernel function in the form of radial basis functions is used as the integration term, and numerical integration is performed over the parameter domain using the Gaussian integration method. The kernel function in the form of radial basis functions is... ; Parameter domain The three vertices of the triangular element are respectively The parametric form of any point on the triangular face is: ; matrix The The elements are ,in This indicates that the derivative with respect to the second parameter is taken, and the matrix is... The composition is as follows: ； Among them, point This represents a control point, a point. These represent the endpoints of a line segment. Indicates the direction vector at the endpoint of the line segment; ； matrix The The elements are ,symbol This indicates taking the derivative with respect to the first parameter, and the matrix... The composition is as follows: ； matrix The The elements are ,matrix The composition is as follows: ； matrix The The element is The calculation method is as follows: ； in, , , , and , They are line segments and line segments The starting point and the ending point, , , , , , Let be the coordinate components of the integral term, where and It is a scalar; matrix The The elements are ;matrix The The elements are ; matrix The The elements are: 。 6. The implicit modeling method for three-dimensional geological bodies according to claim 1, characterized in that, The method further includes: A GPU-accelerated dual-moving cube algorithm is used to visualize implicit function surfaces.

7. The implicit modeling method for three-dimensional geological bodies according to claim 1, characterized in that, The method further includes: The effectiveness of the line-surface constraint is evaluated using the MAE loss function.

8. A line-surface boundary constraint generalization modeling device, characterized in that, include: The first module is used to obtain the three-dimensional geological body of the target area. It uses a line-surface boundary constraint generalization model for modeling to obtain a three-dimensional geological body model. The generalized model of line-surface boundary constraints is obtained through the following modules: The second module is used to obtain the point set of the three-dimensional geological body. When performing implicit modeling of radial basis functions based on the point set, optimization is performed by minimizing the energy function to obtain the normal vector and the implicit function. The third module is used to apply line-surface constraints to implicit functions. By solving the matrix, the implicit functions of the line-surface constraints are processed to obtain the implicit function parameters. Based on the implicit functions and their parameters, the generalized model of the line-surface boundary constraints is determined.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the line-surface boundary constraint generalization modeling method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that is executed by a processor to implement the line-surface boundary constraint generalization modeling method as described in any one of claims 1-7.

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