Triangulation network cutting method and application

Abstract

The invention discloses a triangulation network cutting method and application. The triangulation network cutting method comprises the steps that the mobile device collects image data of an actually-measured target, geometric data are formed through an algorithm, an automatically-generated original three-dimensional model is cut, accurate three-dimensional model basic data fitting the actual form of the actually-measured target are output, and the three-dimensional model is obtained. Comprising three aspects of conversion of an original three-dimensional model coordinate system, cutting and inverse conversion of the three-dimensional model coordinate system.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer industrial applications, and particularly relates to a triangular mesh cutting method and application. Background Art

[0002] Three-dimensional models are crucial for tasks such as digital twin systems, plant construction, and planning schemes, and there is an urgent need for a high-precision and high-quality three-dimensional data foundation. However, three-dimensional real-scene models automatically constructed using methods such as aerial photos and laser scanning point clouds still have many problems, such as uneven walls, missing corners, water holes, and floating ground features. To effectively solve the above problems, a software system for processing three-dimensional model data is developed, including model data import, display, merging, model data editing (model repair), local superposition and replacement of three-dimensional models, local monomerization of models, removal of suspended matter, local flattening of models, straightening of corner lines, repair and reconstruction of skeleton lines (triangular patches), texture editing and modification, etc. A method for automatically generating accurate three-dimensional models by developing geometric data from image data of mobile devices such as binocular cameras and mobile phones through algorithms is developed to provide an efficient and practical data acquisition and processing solution for the filling industry. Summary of the Invention

[0003] The present invention aims to overcome the deficiencies of the prior art and provides a triangular mesh cutting method and application.

[0004] To achieve the above objective, the technical solution provided by the present invention is as follows: The triangular mesh cutting method is to collect image data of the measured target by a mobile device, form geometric data through an algorithm, and cut the automatically generated original three-dimensional model to output accurate three-dimensional model basic data that fits the true form of the measured target, including three aspects: coordinate system conversion of the three-dimensional model, cutting, and inverse coordinate system conversion of the three-dimensional model: (1) Coordinate system conversion: Three-dimensional selection is achieved through a series of bottom points P and elevation values H of the original three-dimensional model, that is , and then the rotation matrix R is obtained by the angle between the normal vector of the bottom surface and the z-axis direction; the specific steps are as follows: Step a: Calculate the normal vector of the bottom surface: ; Among them, is the normal vector of the bottom surface; Step b: Calculate the rotation angle: ; Among them, is the unit vector in the z-axis direction, =(0, 0, 1), is and Included angle; Step c: Calculate the rotation axis: Through And Calculate the rotation axis : ; Step d: Calculate the rotation matrix R: Given that the rotation axis is the z-axis and the rotation angle is θ, the rotation matrix R can be obtained through the Rodrigues rotation formula: ; Step e: Coordinate transformation: Project the 3D model onto the bottom surface of the cube or polyhedron through the rotation matrix R: ; Wherein, Is the coordinate of the transformed 3D model, Is the original spatial coordinate of the 3D model, and R is the rotation matrix; (2) Cutting: Cut the upper bottom surface, lower bottom surface and side surface of the 3D model; (3) Inverse coordinate transformation of the 3D model to obtain the basic data of the precise 3D model: ; Wherein, Is the spatial coordinate of the original 3D model, Is the coordinate transformed during the cutting of the 3D model, Is the inverse matrix of the rotation matrix.

[0005] The above triangular mesh cutting method is a triangular mesh cutting method based on the digital twin system and can be applied in the digital twin system. It can be applied to the fine control of mine filling.

[0006] The following further describes the present invention: In the present invention, during the coordinate system transformation of the 3D cutting, the calculation of the rotation axis ω Is one of the core steps. Its purpose is to determine an axis such that the bottom surface normal vector V dface Can be aligned with the standard z-axis direction after rotating a certain angle θ around this axis. The following is the specific calculation formula and derivation process of the rotation axis ω : The rotation axis ω is a straight line in space such that after rotating around this axis, the original bottom surface normal vector V dface Coincides with the target direction Vz (i.e., the unit vector in the z-axis direction). According to three-dimensional geometry, the direction of the rotation axis is determined by the following cross product relationship and is perpendicular to the plane where V dface And Vz are located: ω ∝ V dface × Vz;

[0007] Step 1: Calculate The cross product of and Assumption: (Calculated from the three points on the bottom surface ); (Unit vector in the standard z-axis direction); The cross product formula is:

[0008] Step 2: Normalize the cross product result The rotation axis needs to be a unit vector, so the cross product result needs to be normalized: ; 3. Special cases and verification When is parallel to : If , then the cross product result is the zero vector, and no rotation is required at this time .

[0009] Geometric meaning verification: The rotation axis lies in the XOY plane ( component is 0), and is perpendicular to the projection of in the XOY plane, which conforms to geometric intuition.

[0010] 4. Summary of the complete formula The calculation formula for the rotation axis is: ; where: (Standard axis direction unit vector); Calculated from the three points on the bottom surface : .

[0011] The three-dimensional cutting described in the present invention refers to cutting the original triangular mesh in the form of a cube or polyhedron. Compared with the two-dimensional XOY plane cutting, the bottom surface of the three-dimensional cutting is not limited to the XOY plane and can be a plane in any direction, and it will be cut by the upper and lower bottom surfaces and multiple side surfaces. Since the bottom surface of the three-dimensional cutting is not limited to the XOY plane, directly cutting with multiple side lines of the bottom surface is relatively complex in the calculation process. Therefore, coordinate transformation is required before cutting. After the coordinate transformation, it is equivalent to the two-dimensional cutting of the XOY plane. After the cutting is completed, the coordinate inverse transformation can be performed again to return to the original coordinate system, and the three-dimensional cutting of the triangular mesh can be realized.

[0012] Three-dimensional cutting enables the refined control of the filling process through local model sectioning and dynamic simulation. The three-dimensional model of the goaf is cut by multiple planes to generate filling channel profiles at different depths. Combined with computational fluid dynamics (CFD) simulation, the flow path and accumulation pattern of the filling material in the complex goaf are simulated. By adjusting the cutting angle, the filling blind areas (such as the corner retention areas) are analyzed, and the positions of the grouting ports and the grouting pressure parameters are optimized to ensure the filling density. In the digital twin platform, the pressure and flow data of the filling pipe are collected in real time through sensors and mapped to the cut filling channel model to dynamically correct the simulation parameters, realizing a closed-loop of "monitoring - simulation - regulation" and improving the filling efficiency and safety.

[0013] The triangular mesh cutting method based on the digital twin system is a technical means that combines real-time data acquisition and high-precision modeling analysis. The digital twin system realizes the real-time monitoring and data acquisition of the real world by integrating physical models, sensor data, and simulation simulations; while triangular mesh cutting is a common method in the fields of geographic information systems, computer graphics, and modeling, which can divide the object surface or geographical space into many small triangular meshes to realize refined modeling and analysis.

[0014] The triangular mesh cutting method based on the digital twin system brings higher-precision and more real-time data processing and analysis capabilities to the fields of geographic information systems, modeling and simulation, resource management, etc., providing important technical support for the digitalization and intelligent application of the real world. By combining real-time data with high-precision modeling, it will bring more accurate and efficient solutions to various industries and promote digital transformation and intelligent development.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: It breaks through the limitations of traditional two-dimensional XOY plane cutting, allows the bottom surface to be any spatial plane, and performs three-dimensional cutting on the three-dimensional model through the upper and lower bottom surfaces and multiple side surfaces, expanding the flexibility and application scenarios of cutting.

[0016] By calculating the bottom surface normal vector, rotation angle, and rotation axis, and combining with the Rodrigues rotation formula to generate the rotation matrix (R), the original coordinate system is dynamically transformed to the target plane for cutting. Subsequently, it is restored to the original coordinate system through the inverse matrix (R -1 ), ensuring the geometric consistency of the model after cutting.

[0017] Normal vector calculation (determining the bottom surface direction through formula derivation); generating the rotation angle based on the angle between the normal vector and the Z-axis; calculating the rotation axis through cross product; applying the Rodrigues rotation formula to generate the rotation matrix to achieve efficient coordinate transformation. That is, the rotation matrix is generated and the algorithm is optimized.

[0018] Through experiments, it is verified that the cutting edge is strictly consistent with the range line, proving the accuracy and practicality of the triangular mesh cutting method described in the present invention in complex three-dimensional models, and solving the problem of easy error generation of traditional cutting methods on non-planar bottom surfaces.

[0019] Supports the cutting frameworks of cubes and arbitrary polyhedra, adapts to different geometric structures through a unified coordinate transformation method, and improves the generality and scalability of the algorithm. Description of the Drawings

[0020] Figure 1 : Experimental result diagram of Example 1; (A) Diagram: Shows the original three-dimensional model before cutting, composed of irregular triangular meshes (TIN), exposing the original state and defects of the model, providing a benchmark for cutting requirements; (B) Diagram: Effect after three-dimensional cutting, showing the refined structure after cutting, supporting volume analysis, defect repair, or digital twin integration. Detailed Implementation Manner

[0021] The described triangular mesh cutting method is to collect image data of the measured target by a mobile device, form geometric data through an algorithm, and cut the automatically generated original three-dimensional model, outputting accurate three-dimensional model basic data that fits the true shape of the measured target, including three aspects: coordinate transformation of the three-dimensional model, cutting, and inverse transformation of the three-dimensional model coordinate system: (1) Coordinate transformation: Three-dimensional selection is achieved through a series of bottom surface points of the original three-dimensional model P and elevation values H , that is , and then the rotation matrix R is obtained through the angle between the normal vector of the bottom surface and the z-axis direction; the specific steps are as follows: Step a: Calculate the bottom surface normal vector: ; Among them, is the normal vector of the bottom surface; Step b: Calculate the rotation angle: ; Among them, is the unit vector in the z-axis direction, = (0, 0, 1), is and the included angle of; Step c: Calculate the rotation axis: Through and calculate the rotation axis : ; Step d: Calculate the rotation matrix R: Given that the rotation axis is the z-axis and the rotation angle is θ, the rotation matrix R can be obtained through the Rodrigues rotation formula: ; Step e: Coordinate transformation: Project the 3D model onto the bottom surface of the cube or polyhedron through the rotation matrix R: ; Among them, is the coordinate of the transformed 3D model, is the original space coordinate of the 3D model, and R is the rotation matrix; (2) Cutting: Cut the upper bottom surface, lower bottom surface and side surface of the 3D model; (3) Inverse transformation of 3D model coordinates: After cutting the upper and lower bottom surfaces and side surfaces of the 3D model, at this time, the coordinate system of the 3D model coordinates is inconsistent with the coordinate system of the original scene, and an inverse transformation of the 3D model coordinates is required to obtain the accurate 3D model basic data: Among them, is the space coordinate of the original 3D model, is the coordinate transformed when cutting the 3D model, is the inverse matrix of the rotation matrix.

[0022] Triangulation cutting effect: Based on the above cutting algorithm, a cutting experiment is carried out on the 3D model, Figure 1For the experimental results, the original 3D model is composed of a dense irregular triangular mesh (TIN), and its surface presents natural terrain or complex geometric features (such as concave and convex walls, overhanging structures). The cutting plane penetrates the model along a custom direction (such as inclined or vertical), forming a clear cutting boundary where the triangular meshes are neatly aligned without serrations or breaks. The cut cross-section is marked with a highlighted color (such as blue), which forms a sharp contrast with the surface of the original model (gray), facilitating the observation of the internal structure. The triangular patches (triangular facets) at the cutting edge maintain continuity without mesh distortion or holes, verifying the topological stability of the algorithm. It can be seen from the figure that the cutting edge and the range line are consistent, indicating that the cutting algorithm has a good cutting effect in the 3D model.

Claims

1. A triangulated network cutting method, characterized in that: The triangulation cutting method is to collect image data of the measured target by a mobile device, form geometric data through an algorithm, cut the automatically generated original 3D model, and output accurate 3D model basic data that fits the real shape of the measured target, including three aspects: original 3D model coordinate system conversion, cutting and 3D model coordinate system inverse conversion: (1) Coordinate system conversion: 3D selection is a series of bottom points of the original 3D model. P and elevation values H realized, that is , and then obtain the rotation matrix R through the angle between the normal vector of the bottom surface and the z-axis direction; the specific steps are as follows: Step a: Calculate the bottom surface normal vector: ； in, is the normal vector of the bottom surface; Step b: Calculate the rotation angle: ； in, is the unit vector in the z-axis direction, =(0,0,1), for and The angle of Step c: Calculate the axis of rotation: pass and Calculate the rotation axis : ； Step d: Calculate the rotation matrix R: Given that the rotation axis is the z axis and the rotation angle is θ, the rotation matrix R can be obtained using the Rodriguez rotation formula: ； Step e: Coordinate transformation: Project the 3D model onto the bottom surface of a cube or polyhedron using the rotation matrix R: ； in, is the transformed three-dimensional model coordinate, is the original space coordinate of the three-dimensional model, and R is the rotation matrix; (2) Cutting: cutting the upper bottom surface, lower bottom surface and side surface of the 3D model; (3) Inverse transformation of 3D model coordinates to obtain accurate 3D model basic data: ； in, is the spatial coordinate of the original 3D model, is the coordinate converted when cutting the 3D model, is the inverse of the rotation matrix.

2. The triangulated network cutting method according to claim 1, characterized in that: The triangulated network cutting method is a triangulated network cutting method based on a digital twin system.

3. The triangulated network cutting method as described in claim 1 or 2 is applied in a digital twin system.

4. Application of the triangulated network cutting method as described in claim 1 or 2 in refined control of mine filling.

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