A three-dimensional aggregate modeling method and system based on association unit

Abstract

The present invention discloses a three-dimensional aggregate modeling method and system based on association units, which relates to the technical field of three-dimensional modeling, including: setting parameters such as model dimensions, aggregate shape and gradation; generating aggregate according to the gradation; generating a background grid, selecting some grid points as placement points, and performing cyclic random placement of aggregates according to the association units to complete modeling. The modeling method of the present invention is simple and efficient, can realize modeling with high aggregate content, and can be used for simulation calculation of three-dimensional soil-rock mixture and concrete aggregate.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional modeling, and more particularly to a three-dimensional aggregate modeling method and system based on association units. Background Art

[0002] Three-dimensional aggregate modeling is an important research direction in fields such as civil engineering and materials science. Aggregates are the main components of composite materials such as concrete, and their shape, size, distribution and other characteristics have a significant impact on the overall performance of composite materials. Traditional aggregate modeling methods often rely on manual operations or simple geometric shape generation, which are not only inefficient but also difficult to accurately simulate the complex distribution and morphology of real aggregates in composite materials.

[0003] With the continuous development of computer technology, three-dimensional aggregate modeling methods based on computer simulation have gradually become a development trend. However, existing three-dimensional aggregate modeling methods still face many challenges. For example, how to accurately simulate the gradation, content and distribution uniformity of aggregates while ensuring modeling efficiency; how to set parameters such as the inclination and aspect ratio of aggregates according to actual needs to better simulate the behavior of real aggregates in composite materials.

[0004] Therefore, in order to promote the development of three-dimensional aggregate modeling technology, how to improve the efficiency of three-dimensional aggregate modeling is a problem that technical personnel in this field need to solve urgently. Summary of the invention

[0005] In view of this, the present invention provides a three-dimensional aggregate modeling method and system based on association units.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A three-dimensional aggregate modeling method based on association units comprises the following steps:

[0008] Step 1: Establish a 3D particle model, set the model shape and size, aggregate content RP, aggregate gradation, and background grid layer number N mesh 、Number of associated unit layers n layer , aggregate inclination range θ, aggregate aspect ratio r LD , aggregate generation method and grid point utilization ρ GP ; Set the coordinate parameters of the model container;

[0009] Step 2: According to aggregate gradation and background grid layer number N mesh , generate the background grid and randomly select the grid points that can be placed;

[0010] Step 3, combine the unit information matrix and set the associated unit;

[0011] Step 4: According to the aggregate content RP and aggregate gradation, aggregate particles are generated step by step;

[0012] Step 5: According to the associated units, the aggregate particles are randomly placed in order from large to small to the available grid points until all aggregates are fully placed, and the modeling is completed.

[0013] Furthermore, in step 1, when setting the coordinate parameters of the model container, the container information of the model is set by importing the generated model: by importing the generated model in stl format, reading the three-dimensional model information stored in the file, and obtaining the volume V of the model through the Polyhedron_VAC function. all .

[0014] Furthermore, in step 2, the method for generating the background grid is:

[0015] Step 2.1: Set the background grid spacing according to the smallest aggregate particle size in the grading:

[0016] d grid =min(D i ) / N mesh

[0017] Among them, the particle size distribution is defined as sizeDistribution = [D 11 D 12 ;D 21 D 22 ;...;D n1 D n2 ], particle size D i2 >D i1 , i=1,2,...,n,N mesh is the number of background grid layers;

[0018] Step 2.2: According to the length of the three dimensions of the model and d grid Generate background grid points, number of grid points in the x direction Where round is the rounding function, X max , X min are the maximum and minimum values ​​of the model's x coordinates, respectively; similarly, the number of grid points Y in the y and z directions is obtained grid , Z grid ; Then use the ndgrid function to generate the number of background grid points generated by the grid point matrix: X grid ×Y grid ×Z grid ;

[0019] Step 2.3, set the background grid state nodeFlag, which is divided into three states:

[0020]

[0021] First, the background points on the boundary of the model area are set to a state where aggregate cannot be placed. The number of grid points on the specific boundary that are set to a state where aggregate cannot be placed is determined by N. mesh / 2 is rounded up to determine; secondly, after all the background grid points are randomly arranged, the ρGP part of all the background grid points is taken as the placement points according to the grid point utilization rate ρGP.

[0022] Furthermore, in step 3, the composition of the unit information matrix is ​​as follows:

[0023] Expand each grid point in order and convert the original X grid 1. grid Column, Z grid The matrix of rows is converted to X grid ×Y grid ×Z grid A matrix with 1 row and 1 column,

[0024]

[0025] Assemble each grid point coordinate and the other 7 associated node coordinates into a unit information matrix, Elements = [ID1 ID2 ID3 ID4 ID5 ID6 ID7 ID8], where ID1 is the set of each grid point's body coordinates, and ID2 is the set of each grid point's associated grid point 2 coordinates, and the same goes for the others.

[0026] Furthermore, in step 4, the step of generating aggregate particles step by step is:

[0027] Step 4.1, calculate the number of aggregate particles at each level:

[0028] First, calculate the equivalent average radius of aggregate for each gradation:

[0029]

[0030] Where a and b are the lower and upper limits of the particle size in each gradation, respectively, and the equivalent average volume is:

[0031]

[0032] Thus the amount of aggregate in each gradation can be estimated:

[0033]

[0034] Among them, the total volume of aggregate V Rock =V all ×RP,V all is the total volume of the model, RP is the aggregate content, and RP iis the content of aggregate in each level of mixing interval;

[0035] Step 4.2: Generate aggregates randomly in a loop until the grading requirements are met:

[0036] The equivalent radius of aggregate in this gradation range is generated by the rand function:

[0037] R Geg =rand(n i , 1)×(ba)+a

[0038] Then calculate the total volume of all aggregate particles in this gradation range:

[0039]

[0040] By comparing the total volume of randomly generated aggregates with the total volume of aggregates required in the grading interval, it is detected whether the generation of aggregates this time meets the requirements. The requirements in each grading interval vary according to the number of particle sizes. If the requirements are met, the loop is exited to generate the equivalent radius of aggregates in the next grading interval.

[0041] When the generated aggregate is within the allowable error range, the largest particle generated under the gradation interval will be selected and the error will be added to the particle, so as to achieve the accuracy of generating aggregate particles completely according to the preset gradation, and record the equivalent radius of each aggregate particle.

[0042] Furthermore, in step 4.2, the requirements for the generation of aggregate are:

[0043]

[0044] Among them, m i is a function of the number of particles in the gradation.

[0045] Furthermore, the random point generation convex hull method is used to randomly generate polyhedral aggregate particles:

[0046] A spherical coordinate system is established. A function is used to generate a random number of polyhedron vertices, and the number of vertices is controlled between 15 and 30. Then, the azimuth, elevation and radius are randomly generated, and the radius is controlled between 0.7 and 1.1. Then, the index and volume vol of the unit polyhedron are obtained through the convhull function. The unit polyhedron is scaled according to the preset volume of each aggregate. The scaling ratio is:

[0047]

[0048] After scaling, the spherical coordinates are converted to Cartesian coordinates to obtain the coordinates of each convex polyhedron.

[0049] Furthermore, in step 5, a circulation method is used to place the aggregate particles:

[0050] Step 5.1: Fine-tune the aggregate according to the preset aspect ratio and inclination:

[0051] Set the aspect ratio range to:

[0052] r LD =[aR1, aR2]

[0053] The aspect ratio of the i-th aggregate particle is a random number rR in the range i , elongated on the long axis and shortened in the direction of the minor axis This ensures that the volume remains unchanged;

[0054] The rotation of aggregate particles is achieved through the change of spherical coordinates, according to the set rotation axis direction and angle range θ = [I, α1, α2], where I is the rotation direction, that is, the rotation axis, set by the three-dimensional direction vector, α1, α2 are the upper and lower limits of the rotation angle respectively; the changes of azimuth and elevation angles △θ and Δρ in spherical coordinates are obtained by coordinate transformation, and then the new spherical coordinates are converted into Cartesian coordinates to obtain the coordinates of aggregate particles according to the preset inclination angle;

[0055] Step 5.2: Select aggregate and place it at random grid points:

[0056] If in the i-th grading interval [D i1 , D i2 ] contains j aggregate particles, then all grid points where particles can be placed are placed cyclically, and the coordinates of the selected aggregate particles are added to the grid point coordinates to obtain the global coordinates of the aggregate if it is translated to the grid point. For aggregate m, set ver m =[X m , Y m , Z m ], the number of vertices is n, then X m , Y m , Z m are the three-dimensional coordinates of n vertices; among all the coordinates, the maximum and minimum values ​​are taken to obtain the coordinate range of the aggregate particles, and the X coordinate range is The same goes for other coordinates;

[0057] Get the row number range of aggregate particles based on the grid size and aggregate vertex coordinate range:

[0058]

[0059] Among them, floor is the function of rounding down, ceil is the function of rounding up, and the column and row number ranges are the same, that is, col = [col min ,colmax ],lay=[lay min , lay max ];

[0060] When the number of associated unit layers n is set layer After that, the range becomes row=[row min -n layer , row max +n layer ], the same goes for other numbers;

[0061] Within this range, the function is used to screen whether each grid point in the range is located inside the aggregate. If the status of the internal grid points and the associated cell points of the aggregate are both in the placeable state, the aggregate is placed successfully, and the status of all vertices of the internal grid points and the grid where the aggregate vertices are located is set to the non-placeable state. If there is a non-placeable node state, the placement position is changed and re-screened. If the particles cannot be placed after cycling through all the placeable grid points, it is necessary to change the aggregate grading and the density of the background grid and re-model.

[0062] A three-dimensional aggregate modeling system based on association units, comprising:

[0063] Parameter setting module, used to establish a three-dimensional particle model, set the model shape and size, aggregate content RP, aggregate gradation, background grid layer number N mesh 、Number of associated unit layers n layer , aggregate inclination range θ, aggregate aspect ratio r LD , aggregate generation method and grid point utilization ρ GP ; Set the coordinate parameters of the model container;

[0064] The grid setting module is used to set the number of background grid layers N according to the aggregate gradation and background grid layer N. mesh , generate the background grid and randomly select the grid points that can be placed;

[0065] The associated unit setting module is used to combine the unit information matrix and set the associated unit;

[0066] Aggregate particle generation module, used to generate aggregate particles step by step according to aggregate content RP and aggregate gradation;

[0067] The particle placement module is used to randomly place aggregate particles from large to small according to the associated units to the available grid points until all aggregates are fully placed, that is, the modeling is completed.

[0068] It can be seen from the above technical solutions that the present invention provides a three-dimensional aggregate modeling method and system based on association units, which has the following beneficial effects compared with the prior art:

[0069] (1) The present invention greatly improves the efficiency of three-dimensional aggregate modeling by introducing the concept of association units and using the background grid point state parameter nodeFlag for overlap detection.

[0070] (2) The present invention can ensure the minimum gap between adjacent aggregates through the multi-layer association unit setting, thereby making the distribution of aggregates in the model more uniform.

[0071] (3) The present invention randomly selects some grid points as placeable grid points by setting the initial grid point state, and adopts the random placement method to improve the modeling efficiency, which can more effectively avoid the overlap and unreasonable distribution of aggregates, and help to improve the reliability and stability of the model.

[0072] (4) The present invention can set the aggregate content, aggregate grading, aggregate distribution uniformity, aggregate particle orientation and aspect ratio according to requirements. This customizability enables the model to more accurately simulate complex situations in the real world, thereby improving the practicality and accuracy of the model.

[0073] In summary, the modeling method of the present invention is simple and efficient, can realize modeling with high aggregate content, and is used for simulation calculation of three-dimensional soil-rock mixture and concrete aggregate. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0075] Figure 1 It is a schematic diagram of the steps of the modeling method of the present invention;

[0076] Figure 2 It is a schematic diagram of the unit information matrix;

[0077] Figure 3 It is the modeling effect diagram of the present invention. DETAILED DESCRIPTION

[0078] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0079] The embodiment of the present invention discloses a three-dimensional aggregate modeling method based on association units, see Figure 1 , including the following steps:

[0080] Step 1: Establish a 3D particle model, set the model shape and size, aggregate content RP, aggregate gradation, and background grid layer number N mesh 、Number of associated unit layers n layer , aggregate inclination range θ, aggregate aspect ratio r LD , aggregate generation method (random points generate convex hull) and grid point utilization ρ GP ; Set the coordinate parameters of the model container.

[0081] When setting the coordinate parameters of the model container, set the container information of the model by importing the generated model: import the generated model in stl format, read the three-dimensional model information stored in the file, and get the volume V of the model through the Polyhedron_VAC function all .

[0082] Step 2: According to aggregate gradation and background grid layer number N mesh , generate a background grid and randomly select available grid points.

[0083] Among them, the method of generating the background grid is:

[0084] Step 2.1: Set the background grid spacing according to the smallest aggregate particle size in the grading:

[0085] d grid =min(D i ) / N mesh

[0086] Among them, the particle size distribution is defined as sizeDistribution = [D 11 D 12 ;D 21 D 22 ;...;D n1 D n2 ], particle size D i2 >D i1 , i=1,2,...,n,N mesh The number of background grid layers is generally controlled at 5-10. The larger the value, the better the aggregate generation, but the lower the modeling efficiency;

[0087] Step 2.2: According to the length of the three dimensions of the model and d grid Generate background grid points, number of grid points in the x direction Where round is the rounding function, X max , X min are the maximum and minimum values ​​of the model's x coordinates, respectively; similarly, the number of grid points Y in the y and z directions is obtained grid, Z grid ; Then use the ndgrid function to generate the number of background grid points generated by the grid point matrix: X grid ×Y grid ×Z grid ;

[0088] Step 2.3, set the background grid state nodeFlag, which is divided into three states:

[0089]

[0090] First, the background points on the boundary of the model area are set to a state where aggregate cannot be placed. The number of grid points on the specific boundary that are set to a state where aggregate cannot be placed is determined by N. mesh / 2 is rounded up to determine; secondly, after all the background grid points are randomly arranged, according to the grid point utilization rate ρ GP Take ρ of all background grid points GP Since the number of 3D background grid points increases sharply compared to 2D, some grid points can be selected for placement, which can improve the efficiency of modeling.

[0091] The background grid is set mainly to improve modeling efficiency. First, all grid point states nodeFlag are set to 0. According to the above random selection method, some grid points are set as grid points where aggregate particles can be placed. At this time, the nodeFlag of these grid points is set to -1. In this way, when looping through all grid points, only grid points with a state of -1 need to be retrieved, which will greatly reduce the amount of computer calculations. If the state of all grid points in the center of the particle and the coverage of the particle are in a state of being placed (no grid point with a state of 1), the aggregate particle is placed successfully, and the state of all grid points within the range of the particle needs to be set to 1.

[0092] Step 3: Combine the unit information matrix and set the associated units, see Figure 2 .

[0093] Among them, the composition of the unit information matrix is ​​as follows:

[0094] Expand each grid point in order and convert the original X grid 1. grid Column, Z grid The matrix of rows is converted to X grid ×Y grid ×Z grid A matrix with 1 row and 1 column,

[0095]

[0096] Assemble each grid point coordinate and the other 7 associated node coordinates into a unit information matrix, Elements = [ID1 ID2 ID3 ID4 ID5 ID6 ID7 ID8], where ID1 is the set of each grid point's body coordinates, and ID2 is the set of each grid point's associated grid point 2 coordinates, and the same goes for the others.

[0097] Step 4: According to the aggregate content RP and aggregate gradation, aggregate particles are generated step by step:

[0098] Step 4.1. Calculate the number of aggregate particles at each level.

[0099] First, calculate the equivalent average radius of aggregate for each gradation:

[0100]

[0101] Where a and b are the lower and upper limits of the particle size in each gradation, respectively, and the equivalent average volume is:

[0102]

[0103] Thus the amount of aggregate in each gradation can be estimated:

[0104]

[0105] Among them, the total volume of aggregate V Rock =V all ×RP,V all is the total volume of the model, RP is the aggregate content, and RP i is the content of aggregate in each level of mixing interval;

[0106] Step 4.2: Generate aggregates randomly in a loop until the grading requirements are met.

[0107] The equivalent radius of aggregate in this gradation range is generated by the rand function:

[0108] R Geg =rand(n i , 1)×(ba)+a

[0109] Then calculate the total volume of all aggregate particles in this gradation range:

[0110]

[0111] By comparing the total volume of randomly generated aggregates with the total volume of aggregates required in the grading interval, it is detected whether the generation of aggregates this time meets the requirements. The requirements in each grading interval vary according to the number of particle sizes. If the requirements are met, the loop is exited to generate the equivalent radius of aggregates in the next grading interval.

[0112] The requirements for aggregate generation are:

[0113]

[0114] Among them, m i is a function of the number of particles in the gradation. The more particles there are, the larger this value is, which ensures that the volume of the part that exceeds or falls short of the requirement is reduced or increased accordingly to the allowable adjustment range according to the number of particles. When there are many particles, the corresponding error range should be smaller to facilitate the subsequent adjustment of the volume of the largest particle in the gradation.

[0115] When the generated aggregate is within the allowable error range, the largest particle generated under the gradation interval will be selected and the error will be added to the particle, so as to achieve the accuracy of generating aggregate particles completely according to the preset gradation, and record the equivalent radius of each aggregate particle.

[0116] In this embodiment, a random point convex hull generation method is used to randomly generate polyhedral aggregate particles, specifically:

[0117] A spherical coordinate system is established. A function is used to generate a random number of polyhedron vertices, and the number of vertices is controlled between 15 and 30. Then, the azimuth, elevation and radius are randomly generated, and the radius is controlled between 0.7 and 1.1. Then, the index and volume vol of the unit polyhedron are obtained through the convhull function. The unit polyhedron is scaled according to the preset volume of each aggregate. The scaling ratio is:

[0118]

[0119] After scaling, the spherical coordinates are converted to Cartesian coordinates to obtain the coordinates of each convex polyhedron.

[0120] Step 5: According to the associated units, the aggregate particles are randomly placed in order from large to small to the available grid points until all aggregates are fully placed, and the modeling is completed.

[0121] Aggregate particles are placed in a circular manner. The specific steps are as follows:

[0122] Step 5.1: Fine-tune the aggregate according to the preset aspect ratio and inclination.

[0123] Since the particles were generated on a unit sphere and then scaled according to the aggregate equivalent radius during the previous modeling, the aggregate particles can be scaled as spheres, and the aspect ratio range is set to:

[0124] r LD =[aR1, aR2]

[0125] The aspect ratio of the i-th aggregate particle is a random number rR in the range i , elongated on the long axis and shortened in the direction of the minor axis This ensures that the volume remains unchanged;

[0126] The rotation of aggregate particles is achieved through the change of spherical coordinates, according to the set rotation axis direction and angle range θ = [I, α1, α2], where I is the rotation direction, that is, the rotation axis, set by a three-dimensional direction vector, and α1 and α2 are the upper and lower limits of the rotation angle respectively; the changes in azimuth and elevation angles △θ and △ρ in spherical coordinates are obtained by coordinate transformation, and then the new spherical coordinates are converted into Cartesian coordinates to obtain the coordinates of the aggregate particles according to the preset inclination angle;

[0127] Step 5.2: Select aggregates and place them at random grid points.

[0128] If in the i-th grading interval [D i1 , D i2 ] contains j aggregate particles, then all grid points where particles can be placed are placed cyclically, and the coordinates of the selected aggregate particles are added to the grid point coordinates to obtain the global coordinates of the aggregate if it is translated to the grid point. For aggregate m, set ver m =[X m , Y m , Z m ], the number of vertices is n, then X m , Y m , Z m are the three-dimensional coordinates of n vertices; among all the coordinates, the maximum and minimum values ​​are taken to obtain the coordinate range of the aggregate particles, and the X coordinate range is The same goes for other coordinates;

[0129] Get the row number range of aggregate particles based on the grid size and aggregate vertex coordinate range:

[0130]

[0131] Among them, flo0r is the floor rounding function, ceil is the ceiling rounding function, and the column and row number ranges are similar, that is, col = [col min ,col max ],lay=[lay min , lay max ];

[0132] When the number of associated unit layers n is set layer After that, the range becomes row=[row min -n layer , row max +n layer ], the same goes for other numbers;

[0133] Within this range, the function is used to screen whether each grid point in the range is located inside the aggregate. If the status of the internal grid points and the associated cell points of the aggregate are both in the placeable state, the aggregate is placed successfully, and the status of all vertices of the internal grid points and the grid where the aggregate vertices are located is set to the non-placeable state. If there is a non-placeable node state, the placement position is changed and re-screened. If the particles cannot be placed after cycling through all the placeable grid points, it is necessary to change the aggregate grading and the density of the background grid and re-model.

[0134] After the modeling is completed, the model needs to be post-processed and visualized through software such as Paraview. Figure 3 .

[0135] Another embodiment of the present invention further discloses a three-dimensional aggregate modeling system based on an association unit, comprising:

[0136] Parameter setting module, used to establish a three-dimensional particle model, set the model shape and size, aggregate content RP, aggregate gradation, background grid layer number N mesh 、Number of associated unit layers n layer , aggregate inclination range θ, aggregate aspect ratio r LD , aggregate generation method and grid point utilization ρ GP ; Set the coordinate parameters of the model container;

[0137] The grid setting module is used to set the number of background grid layers N according to the aggregate gradation and background grid layer N. mesh , generate the background grid and randomly select the grid points that can be placed;

[0138] The associated unit setting module is used to combine the unit information matrix and set the associated unit;

[0139] Aggregate particle generation module, used to generate aggregate particles step by step according to aggregate content RP and aggregate gradation;

[0140] The particle placement module is used to randomly place aggregate particles from large to small according to the associated units to the available grid points until all aggregates are fully placed, that is, the modeling is completed.

[0141] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0142] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A three-dimensional aggregate modeling method based on association units, characterized in that: The following steps are involved: Step 1: Establish a 3D particle model, set the model shape and size, aggregate content RP, aggregate gradation, and background grid layers , number of associated unit layers Aggregate tendency range , Aggregate aspect ratio , aggregate generation method and grid point utilization ; Set the coordinate parameters of the model container; Step 2: According to aggregate grading and background grid layers , generate the background grid and randomly select the grid points that can be placed; Step 3, combine the unit information matrix and set the associated unit; Step 4: According to the aggregate content RP and aggregate gradation, aggregate particles are generated step by step; Step 5: According to the associated units, the aggregate particles are randomly placed in order from large to small to the available grid points until all the aggregates are fully placed, and the modeling is completed; In step 5, the aggregate particles are placed in a circular manner: Step 5.1: Fine-tune the aggregate according to the preset aspect ratio and inclination: Set the aspect ratio range to: r LD =[aR1, aR2], then the aspect ratio of the i-th aggregate particle is a random number within this range , elongated on the long axis , and shorten in the direction of the minor axis , thus ensuring that the volume remains unchanged; The rotation of aggregate particles is achieved by changing the spherical coordinates according to the set rotation axis direction and angle range. , where I is the rotation direction, i.e. the rotation axis, which is set by the three-dimensional direction vector, are the upper and lower limits of the rotation angle respectively; the changes in azimuth and elevation angles in spherical coordinates are obtained through coordinate transformation , and then transform the new spherical coordinates into Cartesian coordinates to obtain the coordinates of the aggregate particles according to the preset inclination angle; Step 5.2: Select aggregate and place it at random grid points: If in the i-th grading interval [D i1 , D i2 ] contains j aggregate particles, then all grid points where particles can be placed are placed cyclically, and the coordinates of the selected aggregate particles are added to the grid point coordinates to obtain the global coordinates of the aggregate if it is translated to the grid point. For aggregate m, set ver m =[X m , Y m , Z m ], the number of vertices is n, then are the three-dimensional coordinates of n vertices; among all the coordinates, the maximum and minimum values ​​are taken to obtain the coordinate range of the aggregate particles, and the X coordinate range is , the same goes for other coordinates; Get the row number range of aggregate particles based on the grid size and aggregate vertex coordinate range: Among them, floor is the floor rounding function, ceil is the ceiling rounding function, and the column and row number ranges are similar, that is, , ; When the number of associated unit layers is set After that, the range becomes , the same applies to other numbers; Within this range, the function is used to screen whether each grid point in the range is located inside the aggregate. If the status of the internal grid points and the associated cell points of the aggregate are both in the placeable state, the aggregate is placed successfully, and the status of all vertices of the internal grid points and the grid where the aggregate vertices are located is set to the non-placeable state. If there is a non-placeable node state, the placement position is changed and re-screened. If the particles cannot be placed after cycling through all the placeable grid points, it is necessary to change the aggregate grading and the density of the background grid and re-model.

2. A three-dimensional aggregate modeling method based on association units according to claim 1, characterized in that: In the step 1, when setting the coordinate parameters of the model container, the container information of the model is set by importing the generated model: by importing the generated model in stl format, reading the three-dimensional model information stored in the file, and The function gets the volume of the model .

3. A three-dimensional aggregate modeling method based on association units according to claim 1, characterized in that: In step 2, the method for generating the background grid is: Step 2.1: Set the background grid spacing according to the smallest aggregate particle size in the grading: The particle size distribution is defined as , particle size , is the number of background grid layers; Step 2.2: According to the length and Generate background grid points, number of grid points in the x direction , where round is the rounding function, are the maximum and minimum values ​​of the model's x-coordinate, respectively; similarly, the number of grid points in the y and z directions is obtained , ; Then use the ndgrid function to generate the number of background grid points generated by the grid point matrix: ; Step 2.3, set the background grid state nodeFlag, which is divided into three states: First, the background points on the model area boundary are set to a state where aggregate cannot be placed. The number of grid points on the specific boundary that are set to a state where aggregate cannot be placed is based on / 2 is rounded up to determine; secondly, all background grid points are randomly arranged according to the grid point utilization rate Take all background grid points Some of them can be used as drop points.

4. A three-dimensional aggregate modeling method based on association units according to claim 3, characterized in that: In step 3, the composition of the unit information matrix is ​​as follows: Expand each grid point in order, OK, List, The matrix of rows is converted to × × A matrix with 1 row and 1 column, Assemble each grid point coordinate and the other 7 associated node coordinates into a unit information matrix, , is the set of coordinates of each grid point, is the set of associated grid point 2 coordinates for each grid point, and the same goes for the others.

5. A three-dimensional aggregate modeling method based on association units according to claim 1, characterized in that: In step 4, the steps of gradually generating aggregate particles are: Step 4.1, calculate the number of aggregate particles at each level: First, calculate the equivalent average radius of aggregate for each gradation: Where a and b are the lower and upper limits of the particle size in each gradation, respectively, and the equivalent average volume is: Thus, the amount of aggregate in each gradation can be estimated: The total volume of aggregate = , is the total volume of the model, RP is the aggregate content, and RP i is the content of aggregate in each level of mixing interval; Step 4.2: Generate aggregates randomly in a loop until the grading requirements are met: The equivalent radius of aggregate in this gradation range is generated by the rand function: Then calculate the total volume of all aggregate particles in this gradation range: By comparing the total volume of randomly generated aggregates with the total volume of aggregates required in the grading interval, it is detected whether the generation of aggregates this time meets the requirements. The requirements in each grading interval vary according to the number of particle sizes. If the requirements are met, the loop is exited to generate the equivalent radius of aggregates in the next grading interval. When the generated aggregate is within the allowable error range, the largest particle generated under the gradation interval will be selected and the error will be added to the particle, so as to achieve the accuracy of generating aggregate particles completely according to the preset gradation, and record the equivalent radius of each aggregate particle. .

6. A three-dimensional aggregate modeling method based on association units according to claim 5, characterized in that: In step 4.2, the requirements for the generation of aggregates are: in, is a function of the number of particles in the gradation.

7. A three-dimensional aggregate modeling method based on association units according to claim 5, characterized in that: The random point generation convex hull method is used to randomly generate polyhedral aggregate particles: A spherical coordinate system is established. A function is used to generate a random number of polyhedron vertices, and the number of vertices is controlled between 15 and 30. Then, the azimuth, elevation and radius are randomly generated, and the radius is controlled between 0.7 and 1.

1. Then, the index and volume vol of the unit polyhedron are obtained through the convhull function, and the volume is scaled according to the preset volume of each aggregate. The scaling ratio is: After scaling, the spherical coordinates are converted to Cartesian coordinates to obtain the coordinates of each convex polyhedron.

8. A three-dimensional aggregate modeling system based on association units, characterized in that: include: Parameter setting module, used to establish a three-dimensional particle model, set the model shape and size, aggregate content RP, aggregate gradation, and background grid layer number , number of associated unit layers Aggregate tendency range , Aggregate aspect ratio , aggregate generation method and grid point utilization ; Set the coordinate parameters of the model container; The grid setting module is used to set the number of background grid layers according to the aggregate grading and background grid layers. , generate the background grid and randomly select the grid points that can be placed; The associated unit setting module is used to combine the unit information matrix and set the associated unit; Aggregate particle generation module, used to generate aggregate particles step by step according to aggregate content RP and aggregate gradation; The particle placement module is used to randomly place aggregate particles from large to small according to the associated units to the available grid points until all aggregates are fully placed, that is, the modeling is completed; In the particle delivery module, a cyclic method is used to deliver aggregate particles: Step 5.1: Fine-tune the aggregate according to the preset aspect ratio and inclination: Set the aspect ratio range to: r LD =[aR1, aR2], then the aspect ratio of the i-th aggregate particle is a random number within this range , elongated on the long axis , and shorten in the direction of the minor axis , thus ensuring that the volume remains unchanged; The rotation of aggregate particles is achieved through the change of spherical coordinates, according to the set rotation axis direction and angle range θ = [I, α1, α2], where I is the rotation direction, that is, the rotation axis, which is set by the three-dimensional direction vector. are the upper and lower limits of the rotation angle respectively; the changes in azimuth and elevation angles in spherical coordinates are obtained through coordinate transformation , and then transform the new spherical coordinates into Cartesian coordinates to obtain the coordinates of the aggregate particles according to the preset inclination angle; Step 5.2: Select aggregate and place it at random grid points: If in the i-th grading interval If there are j aggregate particles in the grid, all grid points where particles can be placed are placed cyclically, and the global coordinates of the aggregate if translated to the grid point are obtained by adding the coordinates of the selected aggregate particles to the grid point. For aggregate m, set ver m =[X m , Y m , Z m ], the number of vertices is n, then are the three-dimensional coordinates of n vertices; among all the coordinates, the maximum and minimum values ​​are taken to obtain the coordinate range of the aggregate particles, and the X coordinate range is , the same goes for other coordinates; Get the row number range of aggregate particles based on the grid size and aggregate vertex coordinate range: Among them, floor is the floor rounding function, ceil is the ceiling rounding function, and the column and row number ranges are similar, that is, , ; When the number of associated unit layers is set After that, the range becomes , the same applies to other numbers; Within this range, the function is used to screen whether each grid point in the range is located inside the aggregate. If the status of the internal grid points and the associated cell points of the aggregate are both in the placeable state, the aggregate is placed successfully, and the status of all vertices of the internal grid points and the grid where the aggregate vertices are located is set to the non-placeable state. If there is a non-placeable node state, the placement position is changed and re-screened. If the particles cannot be placed after cycling through all the placeable grid points, it is necessary to change the aggregate grading and the density of the background grid and re-model.

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