Non-euclidean distance field-based ore body three-dimensional modeling method, electronic device and storage medium

Abstract

The application discloses a non-Euclidean distance field-based ore body three-dimensional modeling method, an electronic device and a storage medium, and the method comprises the following steps: taking a first ore body contour line in adjacent ore body contour lines of an original ore body contour line as a reference layer, performing affine normalization processing on a second ore body contour line adjacent to the first ore body contour line, and generating a normalized ore body contour line; constructing a conformal circular distance field of a layer where the contour line is located in the second voxel; determining a distance field value corresponding to an intermediate layer between adjacent contour lines in the second voxel; inversely mapping the conformal circular distance field of the layer where the second voxel contour line is located and the conformal circular distance field of the intermediate layer in the second voxel to each first voxel vertex in the first voxel, and generating an original voxel distance field; and extracting a zero isosurface of the original voxel distance field based on a marching cubes algorithm, and generating an ore body surface triangular mesh model of a target ore body. In this way, the continuous smooth transition of the distance field between adjacent contour lines is realized, and the model surface is smooth.

Description

Technical Field

[0001] This application relates to the field of 3D modeling technology, and in particular to a 3D modeling method, electronic device and storage medium for ore bodies based on a non-Euclidean distance field. Background Technology

[0002] Contour-based 3D reconstruction of ore bodies is the mainstream technology for mine 3D modeling, typically employing either contour-based stitching or distance-field-based Marching Cubes (MC) isosurface methods. Among these, the distance-field-based MC isosurface method is widely used due to its high degree of automation and wide applicability. Currently, existing distance-field-based methods mainly include Euclidean distance fields and non-Euclidean scanline distance fields. Euclidean distance fields offer high computational accuracy and smooth field value distribution, but when the ore body dips significantly or there is spatial misalignment between adjacent contour lines, the distance field is prone to discontinuities in the interlayer transition region, resulting in poor continuity of the reconstructed model. Non-Euclidean scanline distance fields offer fast computation speed, but their accuracy is lower than that of Euclidean distance fields, and they also cannot resolve the model discontinuity problem under conditions of adjacent contour line misalignment, often resulting in 3D models that do not conform to geological understanding.

[0003] However, when the outlines of adjacent ore bodies are spatially misaligned, tilted, or non-parallel, the distance field is constructed independently only locally within each layer, with no continuous transition between layers. This results in poor continuity and distorted morphology of the ore body, contradicting actual geological understanding. Furthermore, traditional Euclidean distance fields and non-Euclidean distance fields using scan lines suffer from fundamental problems such as distorted distance representation and inconsistency with ore body morphology, failing to accurately describe the true proximity of spatial points to the ore body's outline boundary. Specifically, this manifests in the following aspects:

[0004] (1) The interlayer distance field lacks a continuous transition mechanism, resulting in poor model continuity. When there are complex geological conditions such as spatial misalignment, large dip angle, or non-parallel strike of adjacent ore body outlines, traditional distance field methods usually construct distance fields independently within each profile layer, lacking effective spatial correlation and smooth transition mechanisms between layers. This "independent calculation layer by layer" architecture leads to abrupt changes in the gradient of the interlayer distance field, which in turn causes problems such as local pinch-out, surface discontinuity, and morphological distortion in the 3D model extracted by the MC algorithm, seriously violating the basic geological understanding that geological bodies are continuously and gradually distributed in space.

[0005] (2) Distance representations are distorted in terms of physical meaning and cannot be adapted to the morphological characteristics of irregular ore bodies. Traditional distance fields generally use isotropic absolute straight-line distance (Euclidean distance) as the sole metric, which can only represent the straight-line distance in spatial geometry, while ignoring the influence of the ore body boundary morphology on the "effective proximity" of spatial points. Taking a typical elliptical ore body outline as an example, two spatial points with fixed distances (e.g., 1m) from the boundary in both the major and minor axis directions have equal absolute geometric distances. However, from the perspective of ore body morphological evolution and geological cognition, the points in the major axis direction are more constrained by the boundary curvature and have a closer actual effective distance. Traditional distance fields cannot distinguish such morphological differences, leading to a disconnect between distance measurement and the cognition of real geological morphology, and the distance representation loses its geological and physical meaning.

[0006] (3) Severe distortion in the modeling of irregular contours and low quality of isosurface extraction. The actual contours of ore bodies are mostly complex irregular polygons or closed curves. The isotropic linear distance measurement characteristics of traditional distance fields will lead to a severely uneven distribution of distance gradients in the surrounding areas of irregular contours. When using the MC algorithm to extract isosurfaces, this uneven gradient distribution will directly translate into unevenness, harsh transitions, local mesh distortion, and morphological distortion of the model surface. Especially in areas where the contour curvature changes drastically or where there are sharp corners, the model is prone to artifacts and distortions of non-geological origin, which greatly reduces the geometric accuracy and engineering usability of the ore body 3D model.

[0007] (4) Traditional algorithms struggle to balance computational efficiency and morphological fidelity. While Euclidean distance fields offer high accuracy and relatively smooth surfaces, their continuity drops sharply when contour misalignment is severe. Non-Euclidean scanline distance fields, though computationally fast, have low accuracy and also fail to address model discontinuities caused by interlayer misalignment. Existing methods struggle to achieve a balance between computational efficiency, interlayer continuity, and morphological fidelity, lacking a unified distance field construction system capable of adapting to arbitrary irregular closed contours and providing smooth interlayer transitions.

[0008] In summary, existing distance-field-based 3D reconstruction technologies for ore bodies are limited by the measurement limitations of absolute geometric distance and the architectural defects of independent calculation between layers, making it difficult to achieve morphological adaptation and continuous smooth transition of the distance field under complex dislocation and tilted geological conditions. Summary of the Invention

[0009] In view of this, the embodiments of this application provide a three-dimensional modeling method, electronic device and storage medium for ore bodies based on non-Euclidean distance fields. The aim is to provide a three-dimensional modeling method for ore bodies that provides continuous distance fields between adjacent complex contour lines, smooth model shape and consistent with geological understanding, and solves the technical problems of existing distance field method modeling results, such as local pinch-out, uneven surface, uneven transition, local distortion, shape distortion and inconsistency with geological understanding.

[0010] The technical solution of this application embodiment is implemented as follows:

[0011] In a first aspect, embodiments of this application provide a method for three-dimensional modeling of ore bodies based on a non-Euclidean distance field, the method comprising:

[0012] Obtain the original ore body outline and the first voxel of the target ore body, wherein the first voxel is the original regular grid in the three-dimensional space of the target ore body;

[0013] Using the first ore body contour line among the adjacent ore body contour lines of the original ore body contour line as the reference layer, the second ore body contour line adjacent to the first ore body contour line is subjected to affine normalization processing to generate a normalized ore body contour line. The affine normalization processing includes: orientation alignment processing based on rotation transformation of minimum bounding rectangle, centroid alignment processing based on translation transformation of centroid, and scale unification processing based on scaling transformation of area ratio. Based on the inter-layer voxel weighted affine transformation rule, the vertices of the first voxel located between the first ore body contour line and the second ore body contour line are transformed to construct the second voxel. The second voxel includes a planar mesh covering the first ore body contour line and the normalized ore body contour line.

[0014] Constructing a conformal circular distance field for the layer containing the contour line in the second voxel; the construction of the conformal circular distance field for the layer containing the contour line in the second voxel includes: performing conformal topological disk mapping on the ore body contour line in the second voxel to generate the mapped boundary vertex coordinates, and fixing the mapped boundary vertices on the unit circumference based on the mesh boundary constraint conditions; performing global conformal transformation on the planar mesh of the layer containing the contour line based on the global conformal distortion optimization objective function that satisfies the Cauchy-Riemann conformal constraint to generate the optimized inner and outer vertex coordinates of the inner and outer mesh vertices of the second voxel in the unit disk parameter domain; generating a conformal transformation mesh based on the mapped boundary vertex coordinates and the optimized inner and outer vertex coordinates; calculating the Euclidean distance from each vertex in the conformal transformation mesh to the unit circumference based on the Euclidean distance calculation rules; and inversely mapping the Euclidean distance back to the original regular planar mesh to construct the conformal circular distance field for the layer containing the contour line in the second voxel.

[0015] Determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel; the determination of the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel includes: obtaining the projection points of the second voxel vertices of the intermediate layer between adjacent contour lines in the second voxel, which are respectively vertically projected onto the intermediate layer projection points of the adjacent contour lines; the intermediate layer projection points include: the first intermediate layer projection point projected onto the first contour line in the adjacent contour lines and the second intermediate layer projection point projected onto the second contour line adjacent to the first contour line in the adjacent contour lines; based on the topological spatial relationship between the intermediate layer projection points and the contour line layer planar mesh and the conformal circular distance field value of the mesh cell of the contour line layer of the second voxel, solve for the conformal circular distance field value of the intermediate layer projection points; the topological spatial relationship includes: the first topological spatial relationship where the intermediate layer projection point falls on the mesh vertex, the second topological spatial relationship where the intermediate layer projection point falls on the mesh edge, and the third topological spatial relationship where the intermediate layer projection point falls inside the mesh cell; based on the conformal circular distance field weighted interpolation calculation rule and the conformal circular distance field value of the intermediate layer projection points, determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel.

[0016] The conformal circular distance field of the layer containing the second voxel contour and the conformal circular distance field of the middle layer of the second voxel are inversely mapped to each first voxel vertex in the first voxel to generate the original voxel distance field.

[0017] The zero isosurface is extracted from the original voxel distance field based on the moving cube algorithm, and a triangular mesh model of the ore body surface of the target ore body is generated.

[0018] In some embodiments, performing affine normalization on the contour line of the second ore body adjacent to the contour line of the first ore body to generate a normalized ore body contour line includes:

[0019] Based on the calculation rules for the area and centroid of the region enclosed by the outline of the first ore body, the outline centroid of the first ore body is determined.

[0020] Based on the two-dimensional minimum bounding rectangle of the first ore body outline and the two-dimensional minimum bounding rectangle of the second ore body outline, the long side vector of the rectangle is determined. The long side vector of the rectangle is the strike vector, which includes the reference strike, the strike to be transformed, and the strike angle between the reference strike and the strike to be transformed.

[0021] Based on the translation rule, the centroid of the second ore body outline is translated to the centroid of the first ore body outline for centroid alignment.

[0022] The translation rule is as follows:

[0023] ;

[0024] in, Let be the coordinates of the k-th vertex of the translated outline of the second ore body. The coordinates of the kth vertex of the original second ore body outline are given. The coordinates of the centroid of the first ore body outline are: These are the original centroid coordinates of the second ore body outline;

[0025] Based on a two-dimensional rotation transformation matrix and rotation rules, the outline of the second ore body after centroid alignment is rotated so that the direction of the second ore body outline is aligned with the direction of the first ore body outline; the two-dimensional rotation transformation matrix is ​​constructed based on the direction angle.

[0026] The rotation rule is as follows:

[0027] ;

[0028] in, Let be the coordinates of the k-th vertex of the rotated outline of the second ore body. Let be the coordinates of the k-th vertex of the translated outline of the second ore body. Based on the angle of approach Constructed two-dimensional rotation matrix;

[0029] Based on the scaling rules of the area scaling factor, the coordinates of the vertices of the outline of the second ore body after centroid alignment are scaled and transformed to perform scale unification processing and generate the normalized ore body outline.

[0030] The scaling rule is as follows:

[0031] ;

[0032] in, These are the coordinates of the vertices of the normalized ore body outline. This is the area scaling factor. These are the coordinates of the vertices of the rotated second ore body outline. The coordinates of the centroid of the first ore body outline are given.

[0033] In some embodiments, the centroid calculation rules include horizontal centroid coordinate calculation rules and vertical centroid calculation rules. Determining the centroid of the first ore body outline based on the area enclosed by the first ore body outline and the centroid calculation rules includes:

[0034] Based on the area of ​​the region enclosed by the first ore body outline and the calculation rules for the lateral centroid coordinates, the lateral coordinates of the centroid are determined.

[0035] Based on the area of ​​the region enclosed by the first ore body outline and the calculation rules for the longitudinal centroid coordinates, the longitudinal coordinates of the centroid are determined.

[0036] The outline centroid is generated based on the lateral coordinates of the centroid, the longitudinal coordinates of the centroid, and the height of the first ore body outline.

[0037] The calculation rule for the horizontal centroid coordinates is as follows:

[0038] ;

[0039] in, Let be the lateral coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline;

[0040] The rule for calculating the longitudinal centroid coordinates is as follows:

[0041] ;

[0042] in, Here is the longitudinal coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline.

[0043] In some embodiments, the interlayer voxel weighted affine transformation rule is as follows:

[0044]

[0045] ;

[0046] in, Let (i,j) be the coordinates of the vertex at index (i,j) in the k-th layer of the second voxel. The first weight value of the p-th layer of the baseline layer. For the affine transformation operator of the p-th layer of the baseline layer, For the affine transformation operator of the adjacent reference layer p+1, Let the coordinates be the vertex coordinates of the first voxel. This is the second weight value of the (p+1)th layer adjacent to the baseline layer. The height of the p-th layer of the reference layer. The height of the (p+1)th layer adjacent to the reference layer. Let k be the height of the intermediate layer.

[0047] In some embodiments, the Cauchy-Riemann conformal constraint is:

[0048] ;

[0049] in, For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk;

[0050] The objective function for global conformal distortion optimization is:

[0051] ;

[0052] in, The total energy of conformal distortion of the global mesh; To traverse all quadrilateral cells of the original mesh; For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the lateral deformation gradient. For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized within the parameter domain of the unit disk to determine their coordinates. For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the longitudinal deformation gradient.

[0053] In some embodiments, the Euclidean distance calculation rule is as follows:

[0054] ;

[0055] in, Let be the Euclidean distance from each vertex in the conformal transformation mesh to the unit circle. The layer number where the outline is located. These are the row and column numbers of the grid, respectively. : The inside of the disc; :circumference; : The outside of the disk, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk.

[0056] In some embodiments, solving for the conformal circular distance field value of the intermediate layer projection point based on the topological spatial relationship between the intermediate layer projection point and the contour layer planar mesh, and the conformal circular distance field value of the mesh cell of the contour layer of the second voxel, includes:

[0057] If the topological spatial relationship is the first topological relationship, then the conformal circular distance field value of the projection point is the conformal circular distance field value of the vertex of the quadrilateral mesh that coincides with the projection point of the intermediate layer.

[0058] If the topological spatial relationship is the second topological relationship, then obtain the two vertices of the target mesh edge of the intermediate projection point, and solve for the conformal circular distance field value of the projection point based on the first field value calculation rule; the first field value calculation rule is:

[0059] ;

[0060] in, The conformal circularized distance field value for the projection points of the intermediate layer. The starting vertex from the intermediate layer projection point to the edge of the target mesh. , The terminating vertex from the intermediate layer projection point to the edge of the target mesh. distance, Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value;

[0061] If the topological spatial relationship is a third topological relationship, then a bilinear interpolation rule is constructed based on the normalized local coordinates of the intermediate projection point; based on the bilinear interpolation rule, the conformal circular distance field value of the projection point is solved, and the bilinear interpolation rule includes: a horizontal linear interpolation rule and a vertical linear interpolation rule;

[0062] The bilinear interpolation rule is as follows:

[0063] ;

[0064] The horizontal linear interpolation rule is as follows:

[0065] ;

[0066] The vertical linear interpolation rule is as follows:

[0067] ;

[0068] in, The conformal circularized distance field value for the projection points of the intermediate layer. Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value, (u,v) is the normalized local coordinate of the intermediate projection point. For horizontally normalized coordinates, The coordinates are normalized vertically.

[0069] In some embodiments, the conformal circularized distance field weighted interpolation calculation rule is as follows:

[0070] ;

[0071] in, The final conformal circularized distance field value of the intermediate layer k of the second voxel. Let be the vertical distance from the intermediate voxel point of intermediate layer k to the p-th layer; Let be the vertical distance from the intermediate voxel point of intermediate layer k to the (p+1)th layer. The distance field value projected onto the p-th layer. This represents the distance field value projected onto the (p+1)th layer.

[0072] In a second aspect, embodiments of this application provide an electronic device, including: a processor and a memory for storing a computer program capable of running on the processor, wherein the processor, when running the computer program, performs the steps of the method described in the first aspect above.

[0073] Thirdly, embodiments of this application provide a computer storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of the method described in the first aspect above.

[0074] This application provides a method for 3D modeling of ore bodies based on a non-Euclidean distance field. The method includes: acquiring the original ore body contour line and a first voxel of the target ore body, where the first voxel is the original regular mesh of the target ore body in 3D space; using the first ore body contour line among the adjacent ore body contour lines of the original ore body contour line as a reference layer, performing affine normalization processing on the second ore body contour line adjacent to the first ore body contour line to generate a normalized ore body contour line. The affine normalization processing includes: orientation alignment processing based on rotation transformation of the minimum bounding rectangle, centroid alignment processing based on translation transformation of the centroid, and scale unification processing based on scaling transformation of area ratio; and applying a weighted affine transformation rule to the second ore body contour line based on the inter-layer voxel weighted affine transformation rule. The first voxel vertices located between the first and second ore body contour lines in a single voxel are transformed to construct the second voxel. The second voxel includes a planar mesh covering the first and normalized ore body contour lines. A conformal circular distance field is constructed for the layer containing the contour lines in the second voxel. The construction of the conformal circular distance field for the layer containing the contour lines in the second voxel includes: performing conformal topological disk mapping on the ore body contour lines in the second voxel to generate the mapped boundary vertex coordinates, and fixing the mapped boundary vertices on the unit circumference based on mesh boundary constraints; and optimizing the global conformal distortion based on a global conformal distortion optimization objective function that satisfies Cauchy-Riemann conformal constraints. A global conformal transformation is performed on the planar mesh of the layer to generate optimized vertex coordinates of the inner and outer mesh vertices of the second voxel within the unit disk parameter domain; a conformal transformation mesh is generated based on the mapped boundary vertex coordinates and the optimized inner and outer vertex coordinates; the Euclidean distance from each vertex in the conformal transformation mesh to the unit circumference is calculated based on the Euclidean distance calculation rules; the Euclidean distance is inversely mapped back to the original regular planar mesh to construct the conformal circular distance field of the layer containing the contour lines in the second voxel; the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel is determined; the determination of the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel includes: obtaining the distance field value between adjacent contour lines in the second voxel. The second voxel vertices of the intermediate layer are vertically projected onto the intermediate layer projection points of adjacent contour lines; the intermediate layer projection points include: a first intermediate layer projection point projected onto a first contour line in the adjacent contour lines and a second intermediate layer projection point projected onto a second contour line adjacent to the first contour line in the adjacent contour lines; based on the topological spatial relationship between the intermediate layer projection points and the contour line layer planar mesh, and the conformal circular distance field value of the mesh cell of the second voxel contour line layer, the conformal circular distance field value of the intermediate layer projection points is solved; the topological spatial relationship includes: a first topological spatial relationship where the intermediate layer projection point falls on a mesh vertex, a second topological spatial relationship where the intermediate layer projection point falls on a mesh edge, and a third topological spatial relationship where the intermediate layer projection point falls inside a mesh cell;Based on the conformal circularized distance field weighted interpolation calculation rule and the conformal circularized distance field value of the intermediate layer projection point, the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel is determined; the conformal circularized distance field of the layer where the second voxel contour line is located and the conformal circularized distance field of the intermediate layer of the second voxel are inversely mapped to each first voxel vertex in the first voxel to generate the original voxel distance field; the zero isosurface is extracted from the original voxel distance field based on the moving cube algorithm to generate the ore body surface triangular mesh model of the target ore body.

[0075] Thus, based on the Riemann conformal mapping theory, this application proposes the concept of conformal circular distance field to replace the traditional Euclidean distance field, and uses this as the basis for 3D modeling of ore bodies. Specifically: (1) At the single-layer distance field construction level, by replacing the traditional Euclidean distance field with a conformal circular distance field, the distance measurement deviation caused by the contour shape is eliminated, and the problems of distortion of the physical meaning of distance representation and severe distortion of irregular contour modeling in the traditional distance field are solved. The traditional Euclidean distance field uses absolute straight-line distance as the only measurement standard, which cannot distinguish the morphological differences of irregular contours in different directions. This application conformally maps the irregular ore body contour to a unit circle, calculates the Euclidean distance in the circular parameter domain, and then inversely maps it back to the original space, so that the distance measurement is transformed from isotropic straight-line distance to an adaptive measurement that fits the morphological characteristics of the ore body, thus solving the problem of distance representation distortion from the bottom layer; at the same time, the distance gradient distribution is uniform, avoiding the model surface being unsmooth, local distortion, and morphological distortion. (2) At the interlayer transition level, based on the above-mentioned conformal circularized distance field, the problems of discontinuity in the interlayer distance field and local pinch-out fractures in the model are solved by using interlayer affine normalization and weighted interpolation algorithms. Traditional methods construct distance fields independently for each layer, resulting in a lack of interlayer transition. This application performs affine normalization processing on adjacent contour lines to align their orientation, centroids, and scale, eliminating spatial misalignment; then, weighted interpolation is performed according to the vertical distance from the vertex of the intermediate layer to the upper and lower contour lines to achieve a continuous and smooth spatial transition of the distance field from the upper layer to the lower layer, fundamentally solving the problems of local pinch-out and discontinuity in the model. Thus, this application uses a conformal circularized distance field instead of the traditional Euclidean distance field as the core metric basis, fundamentally solving the problem of distance measurement distortion, while achieving a continuous and smooth transition of the distance field between layers. The final generated ore body 3D model has a smooth surface, continuous interlayers, and natural morphology, consistent with geological cognition. Attached Figure Description

[0076] Figure 1 A flowchart illustrating the 3D modeling method for ore bodies based on a non-Euclidean distance field provided in this application embodiment;

[0077] Figure 2 A schematic diagram of a first voxel provided for an embodiment of this application;

[0078] Figure 3A schematic diagram of a second voxel provided for an embodiment of this application;

[0079] Figure 4 The conformal circularized distance field grayscale cloud map provided in the embodiments of this application;

[0080] Figure 5 The traditional Euclidean distance field grayscale cloud map provided for the embodiments of this application;

[0081] Figure 6 A flowchart illustrating the 3D modeling method for ore bodies based on conformal circular distance fields provided for this application example;

[0082] Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0083] The present application will now be described in further detail with reference to the accompanying drawings and embodiments.

[0084] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0085] This application provides a method for three-dimensional modeling of ore bodies based on a non-Euclidean distance field, such as... Figure 1 As shown, the specific steps are as follows:

[0086] Step 110: Obtain the original ore body outline and the first voxel of the target ore body. The first voxel is the original regular mesh of the target ore body in three-dimensional space.

[0087] It is understandable that the original ore body outline is the boundary line of the ore body delineated on various horizontal profiles during geological exploration. In this embodiment, the ore body outline is a planar closed polyline, formed by connecting multiple vertices in sequence, closing at both ends. Here, there are multiple original ore body outlines, which are approximately parallel in space, constituting the cross-sectional boundaries of the ore body at different elevations. For example, suppose the input is N approximately parallel original ore body outlines: .

[0088] To unify the spatial transformation benchmark and standardize the alignment logic of the contour lines, this application establishes a local coordinate system for the ore body. The coordinate system definition rules are as follows:

[0089] Definition of reference plane: The plane containing the outline of the reference ore body is the local XY plane;

[0090] X-axis definition: The local X-axis is the direction of the long side of the smallest enclosing rectangle of the baseline ore body outline; the smallest enclosing rectangle is the rectangle with the smallest area that can completely enclose the outline, and its long side direction represents the main extension direction of the ore body, that is, the strike of the ore body.

[0091] Z-axis definition: The local Z-axis is perpendicular to the plane of the ore body outline and points in the direction of the ore body's interlayer extension.

[0092] Y-axis definition: Following the right-hand coordinate system rule, it is perpendicular to the X-axis and lies within the contour plane. Its parameters are defined as follows: : No. The outline of the ore body is a closed polyline in a plane. , These are three-dimensional vertices in the local coordinate system. Outline The elevation of the plane in which it is located.

[0093] Through this local coordinate system, all vertices of the ore body outline are converted from the original geographic coordinates to local coordinates, providing a unified geometric benchmark for subsequent operations such as affine normalization.

[0094] It is understandable that the first voxel refers to the original regular grid that divides the three-dimensional space of the target ore body. A voxel is the smallest solid unit in three-dimensional space, used to discretize a continuous three-dimensional space into a finite number of grid points.

[0095] For example, such as Figure 2 As shown in the figure, a three-dimensional regular mesh block is formed by a large number of equally sized cubic units arranged in a regular pattern. The closed outline of the top surface is used to indicate the scope of the target area; let the three-dimensional space be divided into first voxels (original regular mesh): ,in: The first voxel vertex, with coordinates as ; Voxel resolution (user setting).

[0096] It should be noted that the original regular mesh of the first voxel completely covers the three-dimensional spatial region where the target ore body is located. The significance of dividing the space into voxel meshes is that computers cannot directly process continuous spatial surfaces. Only by discretizing the continuous space into voxel meshes and storing the distance values ​​obtained from subsequent calculations at the mesh vertices can the surface model of the ore body be reconstructed through numerical calculations. Therefore, the first voxel is the data foundation of the entire modeling method.

[0097] Step 120: Using the first ore body contour line among the adjacent ore body contour lines of the original ore body contour line as the reference layer, perform affine normalization processing on the second ore body contour line adjacent to the first ore body contour line to generate a normalized ore body contour line. The affine normalization processing includes: orientation alignment processing based on rotation transformation of minimum bounding rectangle, centroid alignment processing based on translation transformation of centroid, and scale unification processing based on scaling transformation of area ratio. Based on the interlayer voxel weighted affine transformation rule, transform the vertices of the first voxel located between the first and second ore body contour lines in the first voxel to construct the second voxel. The second voxel includes a planar mesh covering the first ore body contour line and the normalized ore body contour line.

[0098] Here, adjacent orebody outlines refer to two orebody outlines that are spatially adjacent. For example, adjacent outlines include the outline of the first orebody. The outline of the second ore body adjacent to the outline of the first ore body. Here, the outline of the first ore body. This serves as the baseline layer.

[0099] It should be noted that in this application, the first ore body contour line refers to the contour line used as the reference between two adjacent contour lines, and the second ore body contour line refers to the contour line that needs to be transformed between two adjacent contour lines. This naming applies to any pair of adjacent contour lines. For example, when the p-th contour line is used as the reference and the (p+1)-th contour line is the layer to be transformed, the first ore body contour line is... The outline of the second ore body is... .

[0100] Here, the centroid is the geometric center of the region enclosed by the polygon, and its coordinates are determined by the positions of all vertices of the contour line. The minimum bounding rectangle of the ore body contour line is the rectangle with the smallest area that can completely enclose the contour line, and its long side represents the main extension direction of the ore body, i.e., the strike of the ore body. Since the areas enclosed by the contour lines of ore bodies at different strata may differ, an equal-area scaling transformation, i.e., scale unification processing, is required to ensure that adjacent contour lines are uniform in scale.

[0101] Here, affine normalization refers to aligning the second ore body contour line among adjacent contour lines with the first ore body contour line in terms of spatial orientation, position, and scale through strike alignment, centroid alignment, and scale unification. Specifically, strike alignment determines the strike angle based on the direction of the long side of the minimum bounding rectangle, and uses rotation to make the strike of the second ore body contour line consistent with that of the first ore body contour line; centroid alignment uses translation to make the centroid of the second ore body contour line coincide with that of the first ore body contour line; scale unification calculates the scaling factor based on the area ratio of the two contour lines, and uses scaling to make their areas equal. Through these three processes, the second ore body contour line is normalized into a normalized ore body contour line with consistent strike, coincident centroid, and equal area, providing a spatially aligned data basis for subsequent interlayer interpolation. In specific implementation, the execution order of the above three processes can be flexibly adjusted according to actual needs, and this application does not impose specific limitations on this.

[0102] Here, after the first and second ore body contour lines have undergone affine normalization, several untransformed interlayer first voxel vertices remain between the two layers. This application transforms these interlayer voxel vertices based on the interlayer voxel weighted affine transformation rule. Specifically: for any interlayer voxel vertex located between the two layers, the influence weights of the two contour lines on the vertex are calculated based on the vertical distances of the vertex from the plane containing the first and second ore body contour lines, with closer distances resulting in larger weights; then, the first orientation alignment transformation operator corresponding to the first ore body contour line and the second orientation alignment transformation operator corresponding to the second ore body contour line are obtained, and the interlayer voxel vertex is substituted into the two operators to obtain two transformed positions; finally, the two transformed positions are weighted and summed to obtain the final coordinates of the vertex in the second voxel. By performing the above weighted affine transformation on all interlayer first voxel vertices between the two layers, a spatially continuous second voxel is constructed.

[0103] For example, for any adjacent contour lines , ,by Using the baseline contour lines as a reference, the orientation of the two ore body contours is first extracted using the minimum bounding rectangle long side determination method. Rotation transformations are then applied to ensure that adjacent contour lines have the same orientation. Finally, translation and equal-area scaling transformations are combined to... Regularization to Normalized contour lines are obtained using references of the same orientation, scale, and plane. Finally, a distance-weighted affine transformation is performed on other voxel layers between two adjacent contour lines to construct a spatially continuous second voxel. .

[0104] Here, the second voxel is a new voxel space obtained by performing an affine transformation on the vertices of the interlayer voxels based on the first voxel. The second voxel includes a planar mesh covering the contour lines of the first ore body and the normalized ore body. This planar mesh is composed of the transformed voxel vertices. The topological structure of the mesh is consistent with the original regular mesh of the first voxel, that is, the connection relationship between vertices remains unchanged, but the spatial coordinates of each vertex have been adjusted according to the interlayer weighted affine transformation, so that the second voxel has a spatially continuous transition shape that matches the normalized contour line in the interlayer region. The second voxel constructed in step 120 will serve as the data basis for constructing the conformal circular distance field and determining the intermediate layer distance field value in subsequent steps 130 and 140. This step solves the prerequisite for the problem of discontinuous interlayer distance fields in traditional methods—only by first aligning adjacent contour lines in space and constructing a continuous second voxel can the interlayer interpolation obtain the correct correspondence, and the finally generated ore body model can achieve a smooth transition at the interlayer connection without producing breaks or pinch-outs.

[0105] For example, such as Figure 3 As shown in the figure, the second voxel mesh model is generated after interlayer weighted affine transformation. Compared with the original regular first voxel cube mesh in Figure 1, which is regular, orthogonal, and has uniform length, width, and height, the topological connection relationship of the mesh in this figure has not changed. However, the coordinates of all voxel vertices have been spatially offset after affine transformation. The overall geometry presents a continuous deformable curved surface shape that is wider at the top and bottom and narrower in the middle. The mesh unit is no longer a standard cube, and the side length of each unit is adaptively stretched and compressed according to the contour constraint. The transformed planar mesh completely covers the contour boundary of the ore body, and the smooth and continuous spatial transition between the contours of adjacent ore layers is achieved by relying on the deformation of vertex coordinates.

[0106] Step 130: Construct the conformal circular distance field of the layer containing the contour line in the second voxel; Constructing the conformal circular distance field of the layer containing the contour line in the second voxel includes: performing conformal topological disk mapping on the ore body contour line in the second voxel, generating the mapped boundary vertex coordinates, and fixing the mapped boundary vertices on the unit circumference based on the mesh boundary constraint conditions; performing global conformal transformation on the planar mesh of the layer containing the contour line based on the global conformal distortion optimization objective function that satisfies the Cauchy-Riemann conformal constraint, generating the optimized inner and outer vertex coordinates of the inner and outer mesh vertices of the second voxel in the unit disk parameter domain; generating a conformal transformation mesh based on the mapped boundary vertex coordinates and the optimized inner and outer vertex coordinates; calculating the Euclidean distance from each vertex in the conformal transformation mesh to the unit circumference based on the Euclidean distance calculation rules; inversely mapping the Euclidean distance back to the original regular planar mesh to construct the conformal circular distance field of the layer containing the contour line in the second voxel.

[0107] It should be noted that the layer containing the contour lines in the second voxel refers to the voxel layer containing the first ore body contour line and the normalized ore body contour line, respectively, within the second voxel constructed in step 120. The conformal circular distance field refers to the distance field obtained by transforming the irregular ore body contour into a standard circle through conformal mapping, calculating the distance field within the circular parameter domain, and then inversely mapping this distance field back to the original regular mesh. Compared to the traditional Euclidean distance field, this distance field can eliminate the distance measurement bias caused by the ore body contour shape, allowing the distance values ​​to reflect the true proximity of spatial points to the ore body boundary.

[0108] In this embodiment, the conformal circular distance field of the layer containing the contour line in the second voxel is constructed, specifically including the following: (1) Conformal topological disk mapping is performed on the ore body contour line in the second voxel to generate the coordinates of the mapped boundary vertices. It can be understood that conformal topological disk mapping refers to transforming the closed ore body contour line into points on the unit circle through conformal mapping based on the Riemann mapping theorem. That is, the boundary vertices of the contour line are mapped one-to-one to the unit circle in a way that the arc length is uniformly parameterized, thereby normalizing the ore body contour of any shape into a standard circular boundary. Based on the grid boundary constraint condition, the coordinates of the mapped boundary vertices are fixedly constrained on the unit circle. The grid boundary constraint condition means that in the subsequent grid transformation process, the boundary vertices that have been mapped to the unit circle remain unchanged as fixed boundary conditions for global conformal transformation, thereby ensuring that the original contour line boundary strictly corresponds to the standard circular boundary after transformation. (2) Based on the global conformal distortion optimization objective function that satisfies the Cauchy-Riemann conformal constraint, a global conformal transformation is performed on the planar mesh of the contour layer to generate the optimized internal and external vertex coordinates of the inner and outer mesh vertices of the second voxel within the parameter domain of the unit disk. The Cauchy-Riemann conformal constraint is the mathematical condition for conformal mapping, used to ensure that the local angles of the mesh remain unchanged before and after the transformation. The global conformal distortion optimization objective function is used to quantify the total angular distortion generated by the mesh during the transformation process. The globally optimal approximate conformal transformation is achieved by minimizing this objective function. Global conformal transformation refers to the coordinate transformation of all planar mesh vertices in the contour layer, so that the regular mesh inside the original irregular contour is smoothly mapped to the inside of the unit disk. The transformed mesh has no intersections, no folds, and no angular distortion. Based on the mapped boundary vertex coordinates and the optimized internal and external vertex coordinates, a conformal transformation mesh is generated. The conformal transformation mesh is a transformed mesh located within the parameter domain of the unit disk, composed of boundary vertices and inner and outer vertices. The topology of this mesh is consistent with the original regular mesh, but the spatial coordinates of each vertex have been adjusted according to the conformal transformation. (3) Calculate the Euclidean distance from each vertex in the conformal transformation mesh to the unit circle. Within the parameter domain of the unit disk, the center is at the origin, and the radius is 1. Therefore, the distance from vertex (u,v) to the unit circle is... -1, this value is the sign distance, a negative value indicates that the vertex is inside the disk, a positive value indicates that it is outside the disk, and a zero value indicates that it is on the circumference. (4) The above Euclidean distance is inversely mapped back to the original regular planar mesh to construct the conformal circular distance field of the layer where the contour line in the second voxel is located. Inverse mapping means mapping the distance values ​​of each vertex in the parameter domain of the unit disk back to the corresponding vertices of the original regular mesh according to the correspondence between the vertices before and after the conformal transformation, so as to obtain the conformal circular distance field values ​​of each mesh vertex in the layer where the original irregular contour is located. This distance field is the basic data for subsequent interlayer interpolation and model extraction.

[0109] For example, the layer containing the contour line in the second voxel ( The core logic involves constructing a conformal circular distance field. This is achieved through a closed-loop process of conformal topological disk mapping, conformal mesh transformation, Euclidean distance field calculation, and inverse mapping. This process normalizes the irregular ore body outline into a standard circle, enabling morphological adaptation of distance measurement, accurately matching geological morphological perception, and ultimately obtaining a high-precision, distortion-free single-layer conformal circular distance field.

[0110] Here, as Figure 4 and Figure 5 As shown in Figure 4, the grayscale cloud map of the conformal circularized distance field is shown. The black solid line in the figure represents the boundary of the original irregular ore body outline. The grayscale gradient of the image represents the numerical distribution of the distance field. The grayscale transition extends smoothly and uniformly in a radial pattern along the ore body outline. The grayscale levels inside the ore body are continuous and soft, without obvious sharp angles or abrupt changes. The distance gradient perfectly matches the geometric trend of the irregular ore body outline. After conformal transformation, isotropic and distortion-free distance representation is achieved. The grayscale gradient in the transition area outward from the boundary is uniform and continuous. Figure 5 shows the grayscale cloud map of the traditional Euclidean distance field. The same ore body outline is superimposed. Its grayscale gradient is calculated only based on the Euclidean distance of the plane straight line. Obvious sharp angles and abrupt grayscale changes appear at the corners and narrow neck areas of the ore body outline. The grayscale transition has abrupt angles. The distance gradient distribution in the far end and side areas of the outline is uneven, resulting in local distance field distortion.

[0111] Understandably, step 130 addresses the problem of distorted physical meaning of distance representation in traditional Euclidean distance fields under irregular ore body contours, as well as the resulting issues of uneven model surfaces, local distortion, and morphological distortion. By conformally transforming the irregular contour into a standard circle, measuring distance within the circular parameter domain, and then performing inverse mapping and regression, the distance metric is transformed from isotropic linear distance into an adaptive metric that fits the ore body's morphological characteristics. The conformal circularized distance field of the layer containing the contour line constructed in step 130 will serve as the input for interlayer interpolation in step 140, i.e., as the upper and lower bound reference values ​​for calculating the intermediate layer distance field between adjacent contour lines.

[0112] Step 140: Determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel; Determining the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel includes: obtaining the projection points of the second voxel vertices of the intermediate layer between adjacent contour lines in the second voxel, which are respectively vertically projected onto the intermediate layer projection points of the adjacent contour lines; the intermediate layer projection points include: the first intermediate layer projection point projected onto the first contour line in the adjacent contour lines and the second intermediate layer projection point projected onto the second contour line adjacent to the first contour line in the adjacent contour lines; Based on the topological spatial relationship between the intermediate layer projection points and the contour line layer planar mesh and the conformal circular distance field value of the mesh cell of the contour line layer of the second voxel, solve for the conformal circular distance field value of the intermediate layer projection points; the topological spatial relationship includes: the first topological spatial relationship where the intermediate layer projection points fall on the mesh vertices, the second topological spatial relationship where the intermediate layer projection points fall on the mesh edges, and the third topological spatial relationship where the intermediate layer projection points fall inside the mesh cells; Based on the conformal circular distance field weighted interpolation calculation rule and the conformal circular distance field value of the intermediate layer projection points, determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel.

[0113] It is understandable that the intermediate layer between adjacent contour lines refers to the voxel layer located between the layer containing the first ore body contour line and the layer containing the second ore body contour line in the second voxel constructed in step 120. Since step 130 only constructed the conformal circularized distance field of the contour line layers (i.e., the layer containing the first ore body contour line and the layer containing the normalized ore body contour line), and the vertices of the intermediate layer voxels between the two layers have not yet been assigned distance field values, it is necessary to determine the distance field values ​​of these intermediate layer vertices through this step in order to achieve a continuous transition of the interlayer distance field.

[0114] Here, determining the distance field value corresponding to the intermediate layer specifically includes the following: obtaining the vertices of the second voxel in the intermediate layer between adjacent contour lines in the second voxel and projecting them vertically to the intermediate layer projection points of the adjacent contour lines. Vertical projection means projecting the intermediate layer vertices along the Z-axis direction (i.e., the direction perpendicular to the plane where the contour lines are located) to the planes where the first ore body contour lines and the second ore body contour lines are located, respectively. The XY coordinates of the projection points are the same as the original vertices, and the Z coordinates are replaced with the elevation of the corresponding contour line planes. The intermediate layer projection points include: the first intermediate layer projection point projected onto the first ore body contour line, and the second intermediate layer projection point projected onto the second contour line adjacent to the first ore body contour line.

[0115] Here, the conformal circular distance field value of the intermediate layer projection point is solved based on the topological spatial relationship between the intermediate layer projection point and the contour layer planar mesh, and the conformal circular distance field value of the contour layer mesh cell of the second voxel. The topological spatial relationship describes the specific location of the projection point within the contour layer planar mesh, including three cases: the first topological spatial relationship is that the projection point falls on a mesh vertex; the second topological spatial relationship is that the projection point falls on a mesh edge; and the third topological spatial relationship is that the projection point falls inside a mesh cell. For each of these three different topological spatial relationships, a corresponding interpolation strategy is used to calculate the conformal circular distance field value of the projection point: for the first topological spatial relationship, the field value of the vertex is directly taken; for the second topological spatial relationship, linear weighted interpolation is performed based on the proportion of the distance from the projection point to the two vertices of the edge; and for the third topological spatial relationship, bilinear interpolation is performed based on the normalized local coordinates of the projection point within the mesh cell.

[0116] Here, based on the conformal circular distance field weighted interpolation calculation rule and the conformal circular distance field value of the intermediate layer projection points, the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel is determined. The weighted interpolation calculation rule refers to calculating weights based on the vertical distances of the intermediate layer vertex from the plane containing the first contour line and the vertical distance from the intermediate layer vertex to the plane containing the second contour line. The conformal circular distance field values ​​of the first and second intermediate layer projection points are then weighted and summed using these two weights to obtain the final distance field value of the intermediate layer vertex. The weights are inversely proportional to the vertical distance; that is, the closer the distance to a certain layer, the greater the influence of the field value of that layer on the intermediate layer vertex; the farther the distance, the smaller the influence.

[0117] Understandably, step 140 addresses the local pinch-out and breakage issues in the model caused by discontinuities in the interlayer distance field in traditional methods. By vertically projecting intermediate layer vertices onto the upper and lower contour layers, conformal circular distance field values ​​of the projected points in each layer are obtained. Then, weighted interpolation is performed using the vertical distance as the weight, achieving a smooth and continuous transition of the distance field from the upper to the lower layers. The distance field values ​​of the intermediate layers between adjacent contour lines in the second voxel determined in step 140, together with the conformal circular distance field of the contour layer constructed in step 130, constitute the conformal circular distance field of all voxel layers of the second voxel, which will serve as the data basis for the inverse mapping to the first voxel in step 150.

[0118] Step 150: Inversely map the conformal circular distance field of the layer containing the second voxel contour line and the conformal circular distance field of the intermediate layer of the second voxel to each first voxel vertex in the first voxel to generate the original voxel distance field.

[0119] Here, the conformal circular distance field of the layer containing the second voxel contour is constructed in step 130, and the conformal circular distance field of the middle layer of the second voxel is determined in step 140. Together, they constitute the conformal circular distance field D2 of all voxel layers of the second voxel.

[0120] In this embodiment, inverse mapping refers to the process of mapping the distance field values ​​of each vertex of the second voxel back from the second voxel space to the first voxel space according to the correspondence between the vertices in the first voxel and the second voxel. Since the second voxel is constructed based on the first voxel through affine transformation, there is a one-to-one correspondence between the vertices of the two, that is, any vertex in the second voxel... (i,j,k) and the first voxel (i,j,k) have the same index number, and the mapping relationship between them is bijective. Therefore, the inverse mapping can be directly accomplished by assigning the distance field value of each vertex in V2 to the vertex with the same index number in V1.

[0121] For example, the second voxel From the first voxel The topological isomorphism transformation yields a one-to-one correspondence between vertices. conformal circularized distance field Inverse mapping to The original voxel distance field is obtained. .

[0122] It should be noted that the reason why step 150 can perform the inverse mapping without data loss or misalignment is due to the topological isomorphic transformation relationship between the second voxel and the first voxel in step 120—the mesh connection relationship between the two has not changed, only the vertex position has undergone an affine transformation, so the distance field value can be returned along the same index path.

[0123] Step 160: Extract the zero isosurface from the original voxel distance field based on the moving cube algorithm to generate a triangular mesh model of the target ore body surface.

[0124] In this embodiment, the Moving Cubes (MC) algorithm is a three-dimensional discrete data field isosurface extraction algorithm. It processes each cube cell in the three-dimensional voxel mesh one by one, calculating the position where the isosurface passes through the cube by interpolation based on the positive and negative relationships of the distance field values ​​at the eight vertices of the cube relative to zero, and outputting the isosurface fragments as triangular patches. The zero isosurface refers to the set of all points in the original voxel distance field D1 where the distance value is equal to zero, i.e., the spatial position satisfying D1=0. In the signed distance field, the position of D1=0 corresponds precisely to the boundary surface of the ore body. Specifically, for each voxel cell, if there are vertices with distance values ​​greater than zero and less than zero among its eight vertices, it indicates that the zero isosurface passes through the voxel cell. The algorithm determines the connection method of the triangular patches within the voxel cell according to a preset lookup table and calculates the precise position of each triangular patch vertex through linear interpolation. After traversing all voxel cells, all triangular patches together constitute a complete triangular mesh model of the ore body surface.

[0125] For example, for the first voxel distance field The Marching Cubes algorithm is used to extract the zero isosurface ( Step 150 generates a triangular mesh model of the ore body surface. This triangular mesh model is the final 3D modeling result of the ore body output in this application, which can be used for subsequent applications such as reserve estimation, mining design, and digital mine management. Since the original voxel distance field generated in step 150 has already incorporated the morphological adaptive measurement characteristics brought by conformal circularization and the continuous smooth transition characteristics brought by interlayer weighted interpolation, the triangular mesh model of the ore body surface extracted in step 160 achieves the technical effects of smooth surface, interlayer continuity, and natural morphology.

[0126] Thus, based on the Riemann conformal mapping theory, this application proposes the concept of conformal circular distance field to replace the traditional Euclidean distance field, and uses this as the basis for 3D modeling of ore bodies. Specifically: (1) At the single-layer distance field construction level, by replacing the traditional Euclidean distance field with a conformal circular distance field, the distance measurement deviation caused by the contour shape is eliminated, and the problems of distortion of the physical meaning of distance representation and severe distortion of irregular contour modeling in the traditional distance field are solved. The traditional Euclidean distance field uses absolute straight-line distance as the only measurement standard, which cannot distinguish the morphological differences of irregular contours in different directions. This application conformally maps the irregular ore body contour to a unit circle, calculates the Euclidean distance in the circular parameter domain, and then inversely maps it back to the original space, so that the distance measurement is transformed from isotropic straight-line distance to an adaptive measurement that fits the morphological characteristics of the ore body, thus solving the problem of distance representation distortion from the bottom layer; at the same time, the distance gradient distribution is uniform, avoiding the model surface being unsmooth, local distortion, and morphological distortion. (2) At the interlayer transition level, based on the above-mentioned conformal circularized distance field, the problems of discontinuity in the interlayer distance field and local pinch-out fractures in the model are solved by using interlayer affine normalization and weighted interpolation algorithms. Traditional methods construct distance fields independently for each layer, resulting in a lack of interlayer transition. This application performs affine normalization processing on adjacent contour lines to align their orientation, centroids, and scale, eliminating spatial misalignment; then, weighted interpolation is performed according to the vertical distance from the vertex of the intermediate layer to the upper and lower contour lines to achieve a continuous and smooth spatial transition of the distance field from the upper layer to the lower layer, fundamentally solving the problems of local pinch-out and discontinuity in the model. Thus, this application uses a conformal circularized distance field instead of the traditional Euclidean distance field as the core metric basis, fundamentally solving the problem of distance measurement distortion, while achieving a continuous and smooth transition of the distance field between layers. The final generated ore body 3D model has a smooth surface, continuous interlayers, and natural morphology, consistent with geological cognition.

[0127] In some embodiments, the contour line of the second ore body adjacent to the contour line of the first ore body is subjected to affine normalization to generate a normalized ore body contour line, including:

[0128] Based on the calculation rules for the area and centroid of the region enclosed by the outline of the first ore body, the centroid of the outline of the first ore body is determined.

[0129] Based on the two-dimensional minimum bounding rectangle of the first ore body outline and the two-dimensional minimum bounding rectangle of the second ore body outline, the long side vector of the rectangle is determined. The long side vector of the rectangle is the strike vector, which includes the reference strike, the strike to be transformed, and the strike angle between the reference strike and the strike to be transformed.

[0130] Based on the translation rules, the centroid of the second ore body outline is translated to the centroid of the first ore body outline for centroid alignment.

[0131] The translation rules are as follows:

[0132] ;

[0133] in, Let be the coordinates of the k-th vertex of the translated outline of the second ore body. The coordinates of the kth vertex of the original second ore body outline are given. The coordinates of the centroid of the first ore body outline are: These are the original centroid coordinates of the second ore body outline;

[0134] Based on the two-dimensional rotation transformation matrix and rotation rules, the outline of the second ore body after centroid alignment is rotated so that the direction of the second ore body outline is aligned with the direction of the first ore body outline; the two-dimensional rotation transformation matrix is ​​constructed based on the direction angle.

[0135] The rotation rules are as follows:

[0136] ;

[0137] in, Let be the coordinates of the k-th vertex of the rotated outline of the second ore body. Let be the coordinates of the k-th vertex of the translated outline of the second ore body. Based on the angle of approach Constructed two-dimensional rotation matrix;

[0138] Based on the scaling rules of the area scaling factor, the coordinates of the vertices of the outline of the second ore body after centroid alignment are scaled and transformed to perform scale unification processing and generate a normalized ore body outline.

[0139] The scaling rules are as follows:

[0140] ;

[0141] in, These are the coordinates of the vertices of the normalized ore body outline. This is the area scaling factor. These are the coordinates of the vertices of the rotated second ore body outline. The coordinates of the centroid of the first ore body outline are given.

[0142] In this embodiment, centroid alignment is performed first. Based on the area enclosed by the first ore body outline and the centroid calculation rules, the centroid of the first ore body outline is determined. Similarly, the original centroid of the second ore body outline is determined in the same way. Subsequently, based on translation rules, the centroid of the second ore body outline is translated to the position of the centroid of the first ore body outline, so that the two coincide in spatial position. Through the above translation operation, each vertex of the second ore body outline moves the same distance in the same direction, and the shape and orientation of the outline do not change due to translation. Next, orientation alignment is performed. The two-dimensional minimum bounding rectangle is solved for the first and second ore body outlines respectively, and the long side vector of the rectangle is extracted as the orientation vector of the ore body outline, i.e., the reference orientation and the orientation to be transformed, and the orientation angle between the two is calculated. Subsequently, the second ore body outline after centroid alignment is rotated based on the two-dimensional rotation transformation matrix and rotation rules, so that its orientation is aligned with the orientation of the first ore body outline. Finally, scale unification is performed based on scaling rules.

[0143] For example, the alignment of the contour lines based on the minimum bounding rectangle and affine transformation ( The specific steps include:

[0144] (1) Extraction of contour line direction

[0145] For the reference contour line Contour lines to be transformed Solve for the minimum bounding rectangle in two dimensions, and extract the long side vector of the rectangle as the ore body outline direction vector: (Baseline trend) (Direction to be changed), the included angle of the direction is .

[0146] (2) Rotation transformation (alignment)

[0147] Constructing a two-dimensional rotation transformation matrix ,Will Overall rotation Make its long side align with the baseline outline. Their X-axis directions completely coincide, rotation formula: ;

[0148] In the formula: These are the coordinates of the vertices of the translated contour line. This is a rotation matrix constructed based on the ore body strike deviation angle.

[0149] (3) Translation transformation (centroid alignment) will Centroid Translate to the centroid of the reference profile line :

[0150] (4) Equal area scaling transformation

[0151] To ensure that adjacent contour lines have a uniform scale, the area scaling factor is calculated: Scaled vertex coordinates:

[0152] After the transformation, the normalized ore body outline is obtained. Outline of the first ore body By ensuring consistency in orientation, coincidence of centroids, equal area, and unified planar reference, problems such as spatial misalignment, angular deviation, and scale differences between adjacent contour lines are completely eliminated.

[0153] In some embodiments, the centroid calculation rules include horizontal centroid coordinate calculation rules and vertical centroid calculation rules. Based on the area of ​​the region enclosed by the first ore body outline and the centroid calculation rules, the outline centroid of the first ore body outline is determined, including:

[0154] Based on the area enclosed by the outline of the first ore body and the calculation rules for the lateral centroid coordinates, the lateral coordinates of the centroid are determined.

[0155] Based on the area enclosed by the outline of the first ore body and the calculation rules for the longitudinal centroid coordinates, the longitudinal coordinates of the centroid are determined.

[0156] Based on the horizontal coordinates of the centroid, the vertical coordinates of the centroid, and the height of the first ore body outline, the outline centroid is generated;

[0157] The rules for calculating the horizontal centroid coordinates are as follows:

[0158] ;

[0159] in, Let be the lateral coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline;

[0160] The rules for calculating the vertical centroid coordinates are as follows:

[0161] ;

[0162] in, Here is the longitudinal coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline.

[0163] In this embodiment, the centroid calculation rule is used to determine the geometric centroid position of the ore body contour line. The centroid is the geometric center of the region enclosed by the polygon, and its coordinates are determined by the positions of all vertices of the contour line. It is a key parameter for subsequent translation transformations to achieve centroid alignment. The centroid calculation rule includes two parts: the horizontal centroid coordinate calculation rule and the vertical centroid coordinate calculation rule. This is based on the area enclosed by the first ore body contour line. Based on the rules for calculating the horizontal centroid coordinates, determine the horizontal coordinates of the centroid. Area enclosed by the outline of the first ore body Based on the rules for calculating the vertical centroid coordinates, determine the vertical coordinates of the centroid. Finally, based on the lateral coordinates of the centroid. Vertical coordinates Elevation of the plane containing the outline of the first ore body Generate the centroid of the contour The elevation here is the z-coordinate of the plane containing the contour line defined in step 110.

[0164] For example, the calculation of the reference profile parameters ( This includes: (1) Calculation of the area of ​​the closed contour (shoelace formula): The area enclosed by the contour line of the ore body is calculated using the two-dimensional polygon shoelace formula, and the resulting area is... (2) Calculation of the centroid of the contour (polygon centroid formula): The centroid is calculated using the formula for calculating the centroid of a closed planar polygon. Let the sequence of vertices of the two-dimensional contour be... Closure condition The area of ​​the polygon is Centroid The calculation formula is: Here, the two-dimensional centroid is combined with the elevation of the plane containing the contour. The three-dimensional geometric centroid of the contour line is obtained: This serves as the reference center point for subsequent translation and alignment.

[0165] In some embodiments, the interlayer voxel weighted affine transformation rule is as follows:

[0166]

[0167] ;

[0168] in, Let (i,j) be the coordinates of the vertex at index (i,j) in the k-th layer of the second voxel. The first weight value of the p-th layer of the baseline layer. For the affine transformation operator of the p-th layer of the baseline layer, For the affine transformation operator of the adjacent reference layer p+1, Let the coordinates be the vertex coordinates of the first voxel. This is the second weight value of the (p+1)th layer adjacent to the baseline layer. The height of the p-th layer of the reference layer. The height of the (p+1)th layer adjacent to the reference layer. Let k be the height of the intermediate layer.

[0169] For example, interlayer voxel weighted affine transformation (constructing a second voxel) ) includes: Corresponding layer , Corresponding layer any intermediate layer :

[0170] (1) Calculate the layer weights: ;

[0171] (2) Affine transformation of voxel vertices: ;

[0172] in These are the translation, rotation, and scaling transformation operators for the corresponding layer.

[0173] In some embodiments, the Cauchy-Riemann conformal constraint is:

[0174] ;

[0175] in, For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk;

[0176] The objective function for global conformal distortion optimization is:

[0177] ;

[0178] in, The total energy of conformal distortion of the global mesh; To traverse all quadrilateral cells of the original mesh; For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the lateral deformation gradient. For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized within the parameter domain of the unit disk to determine their coordinates. For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the longitudinal deformation gradient.

[0179] In some embodiments, the Euclidean distance calculation rule is as follows:

[0180] ;

[0181] in, Let be the Euclidean distance from each vertex in the conformal transformation mesh to the unit circle. The layer number where the outline is located. These are the row and column numbers of the grid, respectively. : The inside of the disc; :circumference; : The outside of the disk, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk.

[0182] In some embodiments, the conformal circular distance field value of the intermediate layer projection point is solved based on the topological spatial relationship between the intermediate layer projection point and the contour layer planar mesh, and the conformal circular distance field value of the mesh cell of the contour layer of the second voxel, including:

[0183] If the topological spatial relationship is the first topological relationship, then the conformal circular distance field value of the projection point is the conformal circular distance field value of the vertices of the quadrilateral mesh that coincides with the projection point of the intermediate layer.

[0184] If the topological spatial relationship is the second topological relationship, then obtain the two vertices of the target mesh edge where the intermediate projection point lands, and solve for the conformal circular distance field value of the projection point based on the first field value calculation rule; the first field value calculation rule is:

[0185] ;

[0186] in, The conformal circularized distance field value for the projection points of the intermediate layer. The starting vertex from the intermediate layer projection point to the edge of the target mesh. , The terminating vertex from the intermediate layer projection point to the edge of the target mesh. distance, Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value;

[0187] If the topological spatial relationship is a third topological relationship, then a bilinear interpolation rule is constructed based on the normalized local coordinates of the intermediate projection point; based on the bilinear interpolation rule, the conformal circular distance field value of the projection point is solved. The bilinear interpolation rule includes: a horizontal linear interpolation rule and a vertical linear interpolation rule.

[0188] The bilinear interpolation rule is:

[0189] ;

[0190] The horizontal linear interpolation rule is:

[0191] ;

[0192] The vertical linear interpolation rule is as follows:

[0193] ;

[0194] in, The conformal circularized distance field value for the projection points of the intermediate layer. Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value, (u,v) is the normalized local coordinate of the intermediate projection point. For horizontally normalized coordinates, The coordinates are normalized vertically.

[0195] For example, the conformal circularized distance field weighted interpolation content between voxel layers containing adjacent contour lines specifically includes:

[0196] For any layer between adjacent contour lines in the second voxel The distance field value is calculated using vertical distance weighted interpolation.

[0197] (1) Calculation of projection distance.

[0198] Layer any vertex in ;

[0199] Vertical projection to layer( ), projection point ,distance: ;

[0200] Vertical projection to layer( ), projection point ,distance: .

[0201] (2) Accurate interpolation calculation of distance field based on the spatial relationship of quadrilateral grid

[0202] Based on the topological spatial relationship between the projection points of the intermediate layer and the quadrilateral mesh of the contour layer, a quadrilateral bilinear interpolation algorithm is used to accurately solve for the conformal circular distance field value of the projection points. The reference layers are defined as adjacent contour layers. , For example, for the projection points respectively , The complete judgment and calculation logic for performing refined field value calculations is as follows:

[0203] Let the two-dimensional regular quadrilateral mesh element of the contour layer be any element. The four vertices are arranged in clockwise order as follows: , , , The corresponding conformal circularized distance field values ​​are respectively , , , The coordinates of the projection point are Local coordinates within a cell are obtained through coordinate normalization. ,in For horizontally normalized coordinates, The coordinates are normalized vertically. Field values ​​are calculated accurately under three working conditions based on the projection point location:

[0204] Condition 1: The projection point falls on a grid vertex.

[0205] If the projection point Coordinates and arbitrary vertices of the grid Completely coincident, normalized coordinates satisfy Then the field value of the projection point is directly taken as the field value of the corresponding vertex: ;

[0206] In the formula: For the precise conformal circularization of the projection point, the distance field value is calculated. This represents the field value corresponding to the overlapping grid vertex.

[0207] Condition 2: The projected point falls on the edge of the grid.

[0208] If the projection point The projection point falls on any edge of the quadrilateral grid. Two vertices of that edge are selected, and linear weighted interpolation is performed based on the proportion of the straight-line distance from the projection point to the two vertices. This is done using the horizontal edge... For example, let the projection point be... The distance is ,arrive The distance is Total length of side The formula for calculating the field value is:

[0209] ;

[0210] The other three edges ( , , The field value calculation is adapted to this linear weighted formula, only replacing the field value and distance parameters of the vertices at both ends of the corresponding edge.

[0211] Condition 3: The projection point falls inside the grid cell.

[0212] If the projection point Located within quadrilateral mesh cells, and leveraging the uniform mesh shape and distortion-free angles after conformal transformation, standard bilinear interpolation is used to calculate the field values, fully conforming to the continuous gradient characteristics of the conformal circularized distance field. This is based on normalized local coordinates. The step-by-step calculation formula is as follows:

[0213] Step 1: Horizontal linear interpolation, calculate the transition field values ​​for the upper and lower edges respectively:

[0214] ;

[0215] Step 2: Vertical linear interpolation to obtain the final projected point field values:

[0216] ;

[0217] Simultaneous simplification yields the complete bilinear interpolation formula:

[0218] ;

[0219] (3) Assignment of layered field values

[0220] After calculating based on the above three working conditions, the precise field values ​​of the projection points corresponding to the two contour lines are obtained respectively: ( (layer projection point field value) ( The field values ​​of the layer projection points are used for subsequent interlayer weighted interpolation calculations.

[0221] In some embodiments, the conformal circularized distance field weighted interpolation calculation rule is as follows:

[0222] ;

[0223] in, The final conformal circularized distance field value of the intermediate layer k of the second voxel. Let be the vertical distance from the intermediate voxel point of intermediate layer k to the p-th (upper) layer; Let be the vertical distance from the voxel point of the intermediate layer k to the (p+1)th layer (the lower layer). The distance field value projected onto the p-th layer. This represents the distance field value projected onto the (p+1)th layer.

[0224] The embodiments of this application will now be described in detail with reference to an application example.

[0225] Addressing the numerous pain points of existing open-pit mine personnel positioning technologies, this application example breaks through the limitations of traditional absolute geometric distance measurement. Combining Riemannian conformal mapping theory, it proposes a core concept and modeling system for conformal circular distance fields. The core principle is as follows: for any irregular closed contour of an ore body, conformal mapping is used to topologically normalize the irregular contour into a standard circle, eliminating distance measurement biases caused by the contour shape. This ensures that the transformed distance gradient closely matches the ore body's morphological characteristics, solving the fundamental problem of distorted distance representation in traditional distance fields. Simultaneously, by combining interlayer affine normalization and weighted interpolation algorithms, a continuous and smooth transition of the interlayer distance field for inclined and misaligned contour lines is achieved. This fundamentally solves the technical challenges of local pinch-out, uneven surface, uneven transition, local distortion, morphological distortion, and inconsistencies with geological understanding in ore body modeling results.

[0226] Below, in conjunction with Figure 6 The technical solution of this application example is explained in detail, and the specific steps are as follows:

[0227] Step 601: Data definition and parameter description.

[0228] (1) Input data

[0229] Suppose the input consists of N approximately parallel ore body contour lines: To unify the spatial transformation benchmark and standardize the alignment logic of the contour lines, this application establishes a local coordinate system for the ore body. The coordinate system definition rules are as follows:

[0230] Definition of reference plane: The plane containing the outline of the reference ore body is the local XY plane;

[0231] X-axis definition: The local X-axis is defined by the direction of the longest side of the smallest bounding rectangle of the baseline ore body outline.

[0232] Z-axis definition: The local Z-axis is perpendicular to the plane of the ore body outline and points in the direction of the ore body's interlayer extension.

[0233] Y-axis definition: Following the right-hand coordinate system rule, it is perpendicular to the X-axis and lies within the contour plane.

[0234] The parameters are defined as follows:

[0235] : No. The outline of the ore body is a closed polyline in a plane.

[0236] , These are three-dimensional vertices in the local coordinate system.

[0237] Outline The elevation of the plane in which it is located.

[0238] (2) Definition of the first voxel (primordial voxel)

[0239] Let the three-dimensional space be divided into first voxels (original regular mesh): ;

[0240] in:

[0241] The first voxel vertex, with coordinates as ;

[0242] : Voxel resolution (user setting);

[0243] Step 602: Affine normalize the voxel layer containing the adjacent contour lines to construct the second voxel.

[0244] For any adjacent contour lines , ,by Using the baseline contour lines as a reference, the orientation of the two ore body contours is first extracted using the minimum bounding rectangle long side determination method. Rotation transformations are then applied to ensure that adjacent contour lines have the same orientation. Finally, translation and equal-area scaling transformations are combined to... Regularization to Normalized contour lines are obtained using references of the same orientation, scale, and plane. Finally, a distance-weighted affine transformation is performed on other voxel layers between two adjacent contour lines to construct a spatially continuous second voxel. .

[0245] 1. Calculation of baseline contour parameters ( )

[0246] (1) Calculation of the area of ​​the closed contour (shoelace formula): The area enclosed by the contour line of the ore body is calculated using the two-dimensional polygon shoelace formula. The resulting area is: .

[0247] (2) Calculation of the centroid of the contour (polygon centroid formula): The centroid is calculated using the formula for calculating the centroid of a closed planar polygon. Let the sequence of vertices of the two-dimensional contour be... Closure condition The area of ​​the polygon is Centroid The calculation formula is: ;

[0248] Combine the two-dimensional centroid with the elevation of the plane containing the contour. The three-dimensional geometric centroid of the contour line is obtained: This serves as the reference center point for subsequent translation and alignment.

[0249] 2. Contour alignment and affine transformation based on the minimum bounding rectangle ( );

[0250] (1) Extraction of contour line direction

[0251] For the reference contour line Contour lines to be transformed Solve for the minimum bounding rectangle in two dimensions, and extract the long side vector of the rectangle as the ore body outline direction vector: (Baseline trend) (Direction to be changed), the included angle of the direction is .

[0252] (2) Rotation transformation (alignment)

[0253] Constructing a two-dimensional rotation transformation matrix ,Will Overall rotation Make its long side align with the baseline outline. Their X-axis directions completely coincide, rotation formula:

[0254] In the formula: These are the coordinates of the vertices of the translated contour line; This is a rotation matrix constructed based on the ore body strike deviation angle.

[0255] (3) Translation transformation (centroid alignment): Transform the centroid into the centroid. Centroid Translate to the centroid of the reference profile line : ;

[0256] (4) To ensure that adjacent contour lines have the same scale, the area scaling factor is calculated for the equal area scaling transformation: Scaled vertex coordinates: ;

[0257] After the transformation is completed, and With consistent orientation, coincident centroids, equal areas, and unified planar references, the problems of spatial misalignment, angular deviation, and scale differences between adjacent contour lines are completely eliminated.

[0258] 3. Interlayer voxel weighted affine transformation (constructing the second voxel) )

[0259] set up Corresponding layer , Corresponding layer any intermediate layer :

[0260] Calculate layer weights:

[0261] ;

[0262] Affine transformation of voxel vertices:

[0263] in, These are the translation, rotation, and scaling transformation operators for the corresponding layer.

[0264] Step 603: Interlayer voxel weighted affine transformation (constructing the second voxel) ).

[0265] set up Corresponding layer , Corresponding layer any intermediate layer :

[0266] Calculate layer weights:

[0267] ;

[0268] Affine transformation of voxel vertices:

[0269] in, These are the translation, rotation, and scaling transformation operators for the corresponding layer.

[0270] 1. Contour line conformal topological disk mapping

[0271] Based on the Riemann mapping theorem, closed polylines Conformal mapping to the unit circle : Mapping rule: Boundary vertices are parameterized uniformly according to arc length, corresponding one-to-one with the unit circle.

[0272] 2. Conformal transformation of planar mesh

[0273] After completing the conformal topological disk boundary mapping of the ore body contour line, a global conformal transformation needs to be performed on the overall planar regular mesh of the contour line layer to achieve topological normalization with no internal mesh intersections, no folds, and no angular distortion. The Least Squares Conformal Maps (LSCM) algorithm is used to complete the mesh transformation, which weakens mesh scale distortion, strictly preserves local angular features, and adapts to arbitrary planar meshes, smoothly mapping the original irregular contour's planar regular mesh to the conformal transformed mesh under the unit disk.

[0274] (1) Variable definition and mesh constraint system

[0275] Let the original regular planar mesh to be transformed in the second voxel be... The mesh completely covers the planar region containing the ore body outline, defining the core variables and constraint set:

[0276] Original mesh The original two-dimensional coordinates of the vertex in the local XY plane;

[0277] The two-dimensional coordinates of the mesh vertices in the parameter domain of the unit disk after conformal transformation are the unknown variables to be solved in this step.

[0278] The grid boundary constraint set refers to the grid boundary points corresponding to the ore body contour. These points are fixedly constrained within a unit circle by the aforementioned contour arc length parameterization mapping rule. Above, forced topological circularization of irregular contours is achieved;

[0279] The grid consists of a set of free vertices inside and outside the grid, without fixed position constraints. The optimal coordinates are adaptively solved through conformal optimization to ensure continuous and uniform deformation inside the grid.

[0280] Conformal mapping satisfies Cauchy-Riemann conformal constraints, ensuring that the local angles and relative positions of the mesh remain unchanged before and after the transformation, with no angular distortion. Its two-dimensional constraint equations are:

[0281] ;

[0282] (2) Global conformal distortion optimization objective function

[0283] Employing the least squares fitting approach, a global mesh angle distortion energy function is constructed. By minimizing the overall cumulative distortion, a globally optimal approximate conformal transformation is achieved, avoiding local compression and stretching distortions. The global conformal energy function is defined as follows:

[0284] ;

[0285] Explanation of parameters in the formula:

[0286] : Total energy of global mesh conformal distortion. The smaller the value, the better the overall conformal performance and the lower the mesh deformation distortion.

[0287] : Traverse all quadrilateral cells of the original mesh to achieve global optimization;

[0288] : Parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the lateral deformation gradient;

[0289] : Parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the longitudinal deformation gradient.

[0290] (3) Constraint solution and conformal mesh reconstruction

[0291] By combining hard boundary constraints and energy minimization criteria to solve simultaneously, we can achieve synchronous conformal transformation between the mesh and the irregular contour:

[0292] Boundary fixed constraint: The grid boundary points corresponding to the ore body outline are strictly anchored on the unit circumference to ensure that the irregular outline is completely transformed into a standard circular boundary;

[0293] Global numerical optimization: By iteratively solving for the minimum value of the energy function, ... The optimal parameter coordinates of all internal and external mesh vertices are obtained by solving the problem. This ensures accurate internal and external grid angles and a uniform transition.

[0294] Mesh reconstruction output: Integrating the coordinates of boundary constraint vertices and internal and external optimized vertices, a conformal transformation mesh that is fully mapped to the original mesh is reconstructed. .

[0295] (3) Calculation of Euclidean distance field of the transformed grid

[0296] right any vertex in Calculate the Euclidean distance to the unit circle: ;

[0297] : The interior of the disk (within the original outline);

[0298] : Circumference (original outline boundary);

[0299] : Outside the disk (outside the original outline).

[0300] (4) Inverse mapping of the distance field (to obtain the conformal circularized distance field)

[0301] Will Map back to the original mesh one by one The conformal circular distance field of the voxel layer containing the contour line in the second voxel is obtained:

[0302] Step 604: Conformal circular distance field weighted interpolation between voxel layers containing adjacent contour lines.

[0303] For any layer between adjacent contour lines in the second voxel The distance field value is calculated using vertical distance weighted interpolation.

[0304] (1) Calculation of projection distance

[0305] Layer any vertex in ;

[0306] Vertical projection to layer( ), projection point ,distance: ;

[0307] Vertical projection to layer( ), projection point ,distance: .

[0308] (2) Accurate interpolation calculation of distance field based on the spatial relationship of quadrilateral grid

[0309] Based on the topological spatial relationship between the projection points of the intermediate layer and the quadrilateral mesh of the contour layer, a quadrilateral bilinear interpolation algorithm is used to accurately solve for the conformal circular distance field value of the projection points. The reference layers are defined as adjacent contour layers. , For example, for the projection points respectively , The complete judgment and calculation logic for performing refined field value calculations is as follows:

[0310] Let the two-dimensional regular quadrilateral mesh element of the contour layer be any element. The four vertices are arranged in clockwise order as follows: , , , The corresponding conformal circularized distance field values ​​are respectively , , , The coordinates of the projection point are Local coordinates within a cell are obtained through coordinate normalization. ,in For horizontally normalized coordinates, The coordinates are normalized vertically. Field values ​​are calculated accurately under three working conditions based on the projection point location:

[0311] Condition 1: The projection point falls on a grid vertex.

[0312] If the projection point Coordinates and arbitrary vertices of the grid Completely coincident, normalized coordinates satisfy Then the field value of the projection point is directly taken as the field value of the corresponding vertex:

[0313]

[0314] In the formula: For the precise conformal circularization of the projection point, the distance field value is calculated. This represents the field value corresponding to the overlapping grid vertex.

[0315] Condition 2: The projected point falls on the edge of the grid.

[0316] If the projection point The projection point falls on any edge of the quadrilateral grid. Two vertices of that edge are selected, and linear weighted interpolation is performed based on the proportion of the straight-line distance from the projection point to the two vertices. This is done using the horizontal edge... For example, let the projection point be... The distance is ,arrive The distance is Total length of side The formula for calculating the field value is:

[0317] ;

[0318] The other three edges ( , , The field value calculation is adapted to this linear weighted formula, only replacing the field value and distance parameters of the vertices at both ends of the corresponding edge.

[0319] Condition 3: The projection point falls inside the grid cell.

[0320] If the projection point Located within quadrilateral mesh cells, and leveraging the uniform mesh shape and distortion-free angles after conformal transformation, standard bilinear interpolation is used to calculate the field values, fully conforming to the continuous gradient characteristics of the conformal circularized distance field. This is based on normalized local coordinates. The step-by-step calculation formula is as follows:

[0321] Step 1: Horizontal linear interpolation, calculate the transition field values ​​for the upper and lower edges respectively:

[0322] ;

[0323] Step 2: Vertical linear interpolation to obtain the final projected point field values:

[0324]

[0325] Simultaneous simplification yields the complete bilinear interpolation formula:

[0326] ;

[0327] Layered field value assignment:

[0328] After calculating based on the above three working conditions, the precise field values ​​of the projection points corresponding to the two contour lines are obtained respectively: ( (layer projection point field value) ( The field values ​​of the layer projection points are used for subsequent interlayer weighted interpolation calculations.

[0329] (3) Weighted interpolation calculation layer Distance field value

[0330] ;

[0331] Step 605: Inverse map the distance field to the first voxel.

[0332] Here, the second voxel From the first voxel The topological isomorphism transformation yields a one-to-one correspondence between vertices. conformal circularized distance field Inverse mapping to The original voxel distance field is obtained. .

[0333] Step 606: Marching Cubes isosurface extraction to generate a 3D model of the ore body.

[0334] For the first voxel distance field The Marching Cubes algorithm is used to extract the zero isosurface ( ), generate a triangular mesh model of the ore body surface.

[0335] Based on the hardware implementation of the above program modules, and in order to implement the method of the embodiments of this application, the embodiments of this application also provide an electronic device. Figure 7 The diagram shows only an exemplary structure of the electronic device, not the entire structure; implementation is possible as needed. Figure 7The diagram shows part or all of the structure. As shown in Figure 3, the electronic device 700 provided in this embodiment includes: at least one processor 701, a memory 702, a user interface 703, and at least one network interface 704. The various components in the electronic device 700 are coupled together via a bus system 705. It can be understood that the bus system 705 is used to implement communication between these components. In addition to a data bus, the bus system 705 also includes a power bus, a control bus, and a status signal bus. However, for clarity, all buses are labeled as bus system 705 in Figure 7.

[0336] The user interface 703 may include a monitor, keyboard, mouse, trackball, click wheel, buttons, touchpad, or touch screen.

[0337] The memory 702 in this embodiment is used to store various types of data to support the operation of the electronic device. Examples of such data include any computer program used to operate on the electronic device.

[0338] The 3D ore body modeling method based on a non-Euclidean distance field disclosed in this application can be applied to, or implemented by, a processor 701. The processor 701 may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the 3D ore body modeling method based on a non-Euclidean distance field can be completed by integrated logic circuits in the processor 701 or by instructions in software form. The processor 701 can be a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 701 can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software module can be located in a storage medium, which is located in memory 702. The processor 701 reads the information in memory 702 and, in conjunction with its hardware, completes the steps of the ore body three-dimensional modeling method based on non-Euclidean distance field of the electronic device provided in this application embodiment.

[0339] In an exemplary embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers (MCUs), microprocessors, or other electronic components to perform the aforementioned methods.

[0340] It is understood that memory 702 can be volatile memory or non-volatile memory, or both. Specifically, non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), ferromagnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc, or compact disc read-only memory (CD-ROM); magnetic surface memory can be disk storage, or volatile memory can be random access memory (RAM) used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Synchronous Static Random Access Memory (SSRAM), Dynamic Random Access Memory (DRAM), Synchronous Dynamic Random Access Memory (SDRAM), Double Data Rate Synchronous Dynamic Random Access Memory (DDRSDRAM), Enhanced Synchronous Dynamic Random Access Memory (ESDRAM), SyncLink Dynamic Random Access Memory (SLDRAM), and Direct Rambus Random Access Memory (DRRAM).The memories described in the embodiments of this application are intended to include, but are not limited to, these and any other suitable types of memories.

[0341] In an exemplary embodiment, this application also provides a computer storage medium, specifically a computer-readable storage medium storing a computer program thereon. This computer program can be executed by a processor to complete the steps of the method described in this application embodiment. The computer-readable storage medium can be a memory such as ROM, PROM, EPROM, EEPROM, Flash Memory, magnetic surface memory, optical disc, or CD-ROM.

[0342] It should be noted that terms such as "first" and "second" are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0343] Furthermore, the technical solutions described in the embodiments of this application can be arbitrarily combined without conflict. The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for three-dimensional modeling of ore bodies based on a non-Euclidean distance field, characterized in that, The method includes: Obtain the original ore body outline and the first voxel of the target ore body, wherein the first voxel is the original regular grid in the three-dimensional space of the target ore body; Using the first ore body contour line among the adjacent ore body contour lines of the original ore body contour line as the reference layer, the second ore body contour line adjacent to the first ore body contour line is subjected to affine normalization processing to generate a normalized ore body contour line. The affine normalization processing includes: orientation alignment processing based on rotation transformation of minimum bounding rectangle, centroid alignment processing based on translation transformation of centroid, and scale unification processing based on scaling transformation of area ratio. Based on the inter-layer voxel weighted affine transformation rule, the vertices of the first voxel located between the first ore body contour line and the second ore body contour line are transformed to construct the second voxel. The second voxel includes a planar mesh covering the first ore body contour line and the normalized ore body contour line. Constructing a conformal circular distance field for the layer containing the contour line in the second voxel; the construction of the conformal circular distance field for the layer containing the contour line in the second voxel includes: performing conformal topological disk mapping on the ore body contour line in the second voxel to generate the mapped boundary vertex coordinates, and fixing the mapped boundary vertices on the unit circumference based on the mesh boundary constraint conditions; performing global conformal transformation on the planar mesh of the layer containing the contour line based on the global conformal distortion optimization objective function that satisfies the Cauchy-Riemann conformal constraint to generate the optimized inner and outer vertex coordinates of the inner and outer mesh vertices of the second voxel in the unit disk parameter domain; generating a conformal transformation mesh based on the mapped boundary vertex coordinates and the optimized inner and outer vertex coordinates; calculating the Euclidean distance from each vertex in the conformal transformation mesh to the unit circumference based on the Euclidean distance calculation rules; and inversely mapping the Euclidean distance back to the original regular planar mesh to construct the conformal circular distance field for the layer containing the contour line in the second voxel. Determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel; the determination of the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel includes: obtaining the projection points of the second voxel vertices of the intermediate layer between adjacent contour lines in the second voxel, which are respectively vertically projected onto the intermediate layer projection points of the adjacent contour lines; the intermediate layer projection points include: the first intermediate layer projection point projected onto the first contour line in the adjacent contour lines and the second intermediate layer projection point projected onto the second contour line adjacent to the first contour line in the adjacent contour lines; based on the topological spatial relationship between the intermediate layer projection points and the contour line layer planar mesh and the conformal circular distance field value of the mesh cell of the contour line layer of the second voxel, solve for the conformal circular distance field value of the intermediate layer projection points; the topological spatial relationship includes: the first topological spatial relationship where the intermediate layer projection point falls on the mesh vertex, the second topological spatial relationship where the intermediate layer projection point falls on the mesh edge, and the third topological spatial relationship where the intermediate layer projection point falls inside the mesh cell; based on the conformal circular distance field weighted interpolation calculation rule and the conformal circular distance field value of the intermediate layer projection points, determine the distance field value corresponding to the intermediate layer between adjacent contour lines in the second voxel. The conformal circular distance field of the layer containing the second voxel contour and the conformal circular distance field of the middle layer of the second voxel are inversely mapped to each first voxel vertex in the first voxel to generate the original voxel distance field. The zero isosurface is extracted from the original voxel distance field based on the moving cube algorithm, and a triangular mesh model of the ore body surface of the target ore body is generated.

2. The method according to claim 1, characterized in that, The step of performing affine normalization on the outline of the second ore body adjacent to the outline of the first ore body to generate a normalized ore body outline includes: Based on the calculation rules for the area and centroid of the region enclosed by the outline of the first ore body, the outline centroid of the first ore body is determined. Based on the two-dimensional minimum bounding rectangle of the first ore body outline and the two-dimensional minimum bounding rectangle of the second ore body outline, the long side vector of the rectangle is determined. The long side vector of the rectangle is the strike vector, which includes the reference strike, the strike to be transformed, and the strike angle between the reference strike and the strike to be transformed. Based on the translation rule, the centroid of the second ore body outline is translated to the centroid of the first ore body outline for centroid alignment. The translation rule is as follows: ； in, Let be the coordinates of the k-th vertex of the translated outline of the second ore body. The coordinates of the kth vertex of the original second ore body outline are given. The coordinates of the centroid of the first ore body outline are: These are the original centroid coordinates of the second ore body outline; Based on a two-dimensional rotation transformation matrix and rotation rules, the outline of the second ore body after centroid alignment is rotated so that the direction of the second ore body outline is aligned with the direction of the first ore body outline; the two-dimensional rotation transformation matrix is ​​constructed based on the direction angle. The rotation rule is as follows: ； in, Let be the coordinates of the k-th vertex of the rotated outline of the second ore body. Let be the coordinates of the k-th vertex of the translated outline of the second ore body. Based on the angle of approach Constructed two-dimensional rotation matrix; Based on the scaling rules of the area scaling factor, the coordinates of the vertices of the outline of the second ore body after centroid alignment are scaled and transformed to perform scale unification processing and generate the normalized ore body outline. The scaling rule is as follows: ； in, These are the coordinates of the vertices of the normalized ore body outline. This is the area scaling factor. These are the coordinates of the vertices of the rotated second ore body outline. The coordinates of the centroid of the first ore body outline are given.

3. The method according to claim 2, characterized in that, The centroid calculation rules include horizontal centroid coordinate calculation rules and vertical centroid calculation rules. The step of determining the centroid of the first ore body outline based on the area enclosed by the first ore body outline and the centroid calculation rules includes: Based on the area of ​​the region enclosed by the first ore body outline and the calculation rules for the lateral centroid coordinates, the lateral coordinates of the centroid are determined. Based on the area of ​​the region enclosed by the first ore body outline and the calculation rules for the longitudinal centroid coordinates, the longitudinal coordinates of the centroid are determined. The outline centroid is generated based on the lateral coordinates of the centroid, the longitudinal coordinates of the centroid, and the height of the first ore body outline. The calculation rule for the horizontal centroid coordinates is as follows: ； in, Let be the lateral coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline; The rule for calculating the longitudinal centroid coordinates is as follows: ； in, Here is the longitudinal coordinate of the centroid of the first ore body's outline. Let n be the area enclosed by the outline of the first ore body, and n be the total number of vertices of the outline of the first ore body. , ) represents the coordinates of the i-th vertex of the first ore body outline. , (i) represents the coordinates of the (i+1)th vertex of the first ore body outline.

4. The method according to claim 1, characterized in that, The interlayer voxel weighted affine transformation rule is as follows: ； ； in, Let (i,j) be the coordinates of the vertex at index (i,j) in the k-th layer of the second voxel. The first weight value of the p-th layer of the baseline layer. For the affine transformation operator of the p-th layer of the baseline layer, For the affine transformation operator of the adjacent reference layer p+1, Let the coordinates be the vertex coordinates of the first voxel. This is the second weight value of the (p+1)th layer adjacent to the baseline layer. The height of the p-th layer of the reference layer. The height of the (p+1)th adjacent reference layer. Let k be the height of the intermediate layer.

5. The method according to claim 1, characterized in that, The Cauchy-Riemann conformal constraint is: ； in, For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk; The objective function for global conformal distortion optimization is: ； in, The total energy of conformal distortion of the global mesh; To traverse all quadrilateral cells of the original mesh; For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the lateral deformation gradient. For the original mesh The original two-dimensional coordinates of the vertex, The inner and outer mesh vertices of the second voxel are optimized within the parameter domain of the unit disk to determine their coordinates. For parameter domain coordinates The first-order partial derivative with respect to the original planar coordinates characterizes the longitudinal deformation gradient.

6. The method according to claim 1, characterized in that, The Euclidean distance calculation rule is as follows: ； in, Let be the Euclidean distance from each vertex in the conformal transformation mesh to the unit circle. The layer number where the outline is located. These are the row and column numbers of the grid, respectively. : The inside of the disc; :circumference; : The outside of the disk, The inner and outer mesh vertices of the second voxel are optimized for their inner and outer vertex coordinates within the parameter domain of the unit disk.

7. The method according to claim 1, characterized in that, The process of solving for the conformal circular distance field value of the intermediate layer projection point based on the topological spatial relationship between the intermediate layer projection point and the contour layer planar mesh, and the conformal circular distance field value of the mesh cell of the second voxel contour layer, includes: If the topological spatial relationship is the first topological relationship, then the conformal circular distance field value of the projection point is the conformal circular distance field value of the vertex of the quadrilateral mesh that coincides with the projection point of the intermediate layer. If the topological spatial relationship is the second topological relationship, then obtain the two vertices of the target mesh edge of the intermediate projection point, and solve for the conformal circular distance field value of the projection point based on the first field value calculation rule; the first field value calculation rule is: ； in, The conformal circularized distance field value for the projection points of the intermediate layer. The starting vertex from the intermediate layer projection point to the edge of the target mesh. , The terminating vertex from the intermediate layer projection point to the edge of the target mesh. distance, Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value; If the topological spatial relationship is a third topological relationship, then a bilinear interpolation rule is constructed based on the normalized local coordinates of the intermediate projection point; based on the bilinear interpolation rule, the conformal circular distance field value of the projection point is solved, and the bilinear interpolation rule includes: a horizontal linear interpolation rule and a vertical linear interpolation rule; The bilinear interpolation rule is as follows: ； The horizontal linear interpolation rule is as follows: ； The vertical linear interpolation rule is as follows: ； in, The conformal circularized distance field value for the projection points of the intermediate layer. Starting vertex The conformal circularized distance field value, To terminate the vertex The conformal circularized distance field value, (u,v) is the normalized local coordinate of the intermediate projection point. For horizontally normalized coordinates, The coordinates are normalized vertically.

8. The method according to claim 1, characterized in that, The conformal circularized distance field weighted interpolation calculation rule is as follows: ； in, The final conformal circularized distance field value for the intermediate layer k of the second voxel. Let be the vertical distance from the intermediate voxel point of intermediate layer k to the p-th layer; Let be the vertical distance from the voxel point of the intermediate layer k to the (p+1)th layer. The distance field value projected onto the p-th layer. This represents the distance field value projected onto the (p+1)th layer.

9. An electronic device, characterized in that, include: A processor and a memory for storing a computer program capable of running on the processor, wherein the processor, when running the computer program, performs the steps of the method as described in any one of claims 1 to 8.

10. A computer storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 8.

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