A method and system for forming an ellipsoidal particle packing

Abstract

The application discloses a method and system for forming an elliptical particle accumulation body, and applies to the fields of geotechnical engineering and material science technology, and comprises the following steps: defining a space boundary and a calculation rule; generating and placing bottom-layer elliptical particles in a left-to-right placement order: determining a circular arc segment in contact with a container boundary line, and determining the center of a first bottom-layer elliptical particle based on translation and offset calculation of a left boundary and a lower boundary; randomly generating a bottom-layer elliptical particle, forming an intrusion block with a previous elliptical particle, and performing placement judgment of the bottom-layer elliptical particle based on line segment information after offset of the lower boundary and the right boundary of the container; generating and placing upper-layer elliptical particles: randomly generating an upper-layer elliptical particle, traversing a current accumulation body surface elliptical particle set to form a corresponding intrusion block, and performing placement judgment of the upper-layer elliptical particle based on line segment information after offset of the left boundary, the right boundary and the upper boundary of the container. The application realizes generation of an elliptical particle accumulation body with high density and low porosity.

Description

A method and system for forming elliptical particle aggregates Technical Field

[0001] This invention relates to the fields of geotechnical engineering and materials science, and more specifically to a method and system for forming elliptical particle deposits. Background Technology

[0002] In the October 2021 issue of *Acta Geotechnica*, Volume 16, titled "Size distribution of freeparticles in soils: a geometric modelling approach," Bi et al. utilize a novel method to determine the free and skeletal particles of a specific soil gradation, generating a particle packing model based on the geometric compatibility of the particles. A closed rectangle is designated as the initial container to hold all the particles. During particle generation, the container... The upper connected region is the area where the next particle is generated, where the first particle is placed. Before each particle, by extracting the region The boundary is denoted as ,Will Move inward a distance Obtain the boundary , List all discontinuous points in ascending order of their y-coordinates. Then the first One particle was placed At [1], the radius is .area The newly added particle splits into two parts: the smaller part becomes the interparticle pore, and the larger part becomes a new region to accommodate the next particle. Then the cycle begins again, continuing until all particles have been generated.

[0003] In his paper "A packing generation scheme for the granular assemblies with planar elliptical particles" published in Volume 21 of the International Journal for Numerical and Analytical Methods in Geomechanics in 1997, Wang proposed that ellipses can be approximated by piecewise connected arcs. Elliptical particles are described by four connected arcs. For any ellipse translated from the origin and rotated relative to the horizontal axis, the coordinates of the endpoints and radius centers of each arc can be easily obtained by superimposing rigid body nodes, which simplifies the contact detection process.

[0004] In the paper "Establishment of a Two-Dimensional Microstructural Model and Numerical Simulation of Soil-Rock Mixtures" published in the August 2017 issue of *Rock and Soil Mechanics* (Vol. 38, No. 8), Chen Li et al. proposed an EAB block placement algorithm based on the Shi contact theory for the background mesh during the modeling stage. This new algorithm avoids repeated block placement and overlap determination, improving the efficiency of block placement modeling. Randomly generated convex polygons are used to represent the blocks in the soil-rock mixture. During the placement of these random convex polygons, the convex polygon to be placed must not overlap with the already placed convex polygons. To facilitate the determination of whether two convex polygons overlap and to determine the position of the convex polygon to be placed, the concept of an Entrance Block is introduced. The already placed convex polygon is defined as B, and the convex polygon to be placed is defined as A. Assuming... For any selected reference point on A, a series of calculations using the EAB algorithm in section 2.2.2 of the literature can yield the region represented by the intrusive block formed by the two: the convex polygon A is represented by a counterclockwise vertex sequence as follows: ,and and The same point. A convex polygon B can be represented by a counter-clockwise sequence of vertices as follows: ,and and The same point. The side vectors of convex polygon A. Then its interior normal vector is Similarly, if the side vectors of convex polygon B... Then its interior normal vector is When the boundary nodes of a polygon are arranged counterclockwise, the inner normal vectors all point inside the polygon. (1) Traverse all vertices of polygon A. (i = 0, 1, 2 … n-1), and the interior normal vectors of all edges of polygon B. (j=0,1,2 … k-1), if satisfying Then the edge It could be an edge that intrudes into block E(A,B), where Let be the coordinates of the starting point of the edge. Let be the coordinates of the endpoint of the edge. (2) Traverse all vertices of polygon B. (j=0,1,2 … k-1), and the interior normal vectors of all edges of polygon A. (i = 0, 1, 2 … n-1), if satisfying Then the edge It could be an edge that intrudes into block E(A,B), where Let be the coordinates of the starting point of the edge. Let be the coordinates of the endpoint of the edge. (3) Connect all possible edges obtained in the above two steps to obtain the intrusive block E(A,B). If point If a point is located outside the intrusive block region or on the boundary of the region, then convex polygon A and convex polygon B do not overlap. If it is located within the intrusive block region, then convex polygon A overlaps with convex polygon B.

[0005] A similar existing patent is: A method for generating two-dimensional soil-rock mixtures based on elliptical stacking and random fields (CN109241646B). This patent is based on the elliptical fast wavefront stacking algorithm developed by Liu Xinrong et al., which performs high-quality, low-porosity tangential stacking of the generated elliptical equivalent rocks.

[0006] For a long time, due to considerations of computational complexity, most studies have used circular (or spherical) particles to construct aggregates. While circular particles are very simple and efficient in contact detection and computation, their isotropic geometry cannot simulate the angularity and orientation of real particles, leading to significant differences between simulation results and actual conditions in terms of shear strength, etc. The main drawback of existing technologies stems from the complexity brought about by the transformation from circular to elliptical shapes:

[0007] Secondary drawback: It is difficult to generate high-density packings. Due to the complexity of contact determination and the large amount of computation, the generated packings in the simulation of particle settling often have excessively high porosity, which does not conform to the actual situation of densely packed materials.

[0008] The core drawback is the computationally complex contact determination process, leading to low generation efficiency. For circular particles, contact determination is relatively simple, requiring only the sum of the center distance and the radius. However, for elliptical particles, contact determination involves complex geometric calculations, such as finding the minimum distance between two ellipses or determining if overlapping regions exist. This complex calculation needs to be performed on all neighboring particles in each iteration, causing the computational cost to increase exponentially, becoming the main bottleneck in generating large-scale elliptical stacks.

[0009] Therefore, how to overcome the limitations of circular particle models and provide a method and system specifically for forming elliptical particle accumulations, so as to efficiently and accurately generate numerical models of elliptical particle accumulations that are closer to the real particle shapes of natural soil, gravel and other materials, and provide a more reliable model basis for fine numerical analysis in geotechnical engineering, materials science and other fields, is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] In view of this, the present invention provides a method and system for forming an elliptical particle stack.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] A method for forming an elliptical particle accumulation includes:

[0013] Step 1: Define the spatial boundary and calculation rules for the elliptical particle stacking; wherein, the elliptical particle is approximated by four connected circular arcs;

[0014] Step 2: Generate and place the bottom layer of elliptical particles in a left-to-right order:

[0015] Determine the arc segment that contacts the boundary line of the two-dimensional rectangular container, and determine the center of the first bottom elliptical particle based on the translation and offset calculations of the left and lower boundaries.

[0016] Randomly generate bottom elliptical particles, which form an intrusive block with the previous elliptical particle. Based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, determine the placement of the bottom elliptical particles.

[0017] Step 3: Generate and place the upper layer of elliptical particles:

[0018] Randomly generate upper-layer elliptical particles, traverse the current set of surface elliptical particles of the stack to form corresponding intrusive blocks, and make a judgment on the placement of upper-layer elliptical particles based on the line segment information of the left, right and upper boundaries of the two-dimensional rectangular container after offset.

[0019] Step 4: After the bottom layer of elliptical particles and the top layer of elliptical particles are stacked, output the final geometric parameters of all elliptical particles to obtain the numerical model of the elliptical particle stack. The final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse.

[0020] Optionally, in step 1, the spatial boundaries and calculation rules for the elliptical particle packing are defined, specifically as follows:

[0021] Define a two-dimensional rectangular container: set the length, width, and boundaries of the container, define each boundary of the container as a directed line segment, and specify the direction perpendicular to each directed line segment and pointing into the container as the positive normal direction;

[0022] Initialize key parameters: Set the initial delivery sequence number j=0 and the threshold for the number of failed delivery iterations;

[0023] Unified geometric rules: The positive direction of the arc is set to counterclockwise. The numbering of the arc segments of the ellipse and the arc segment intruding into the block is also set to counterclockwise. The unit vector from the center of the circle to the starting point of the arc is defined as the outward vector of the starting edge of the arc, the unit vector from the starting point of the arc to the center of the circle is defined as the inward vector of the starting edge of the arc, the unit vector from the center of the circle to the ending point of the arc is defined as the outward vector of the ending edge of the arc, and the unit vector from the ending point of the arc to the center of the circle is defined as the inward vector of the ending edge of the arc.

[0024] Optionally, in step 2, the arc segment that contacts the boundary line of the two-dimensional rectangular container is determined as follows:

[0025] Calculate the unit normal vector of the boundary line of a two-dimensional rectangular container;

[0026] The boundary unit normal vector is cross-producted with the inward vector of the starting edge of the k-th arc. When the cross-product result is negative, the boundary unit normal vector is then cross-producted with the inward vector of the terminal edge of the k-th arc. When the cross-product result is positive, the arc segment in contact with the boundary line is determined to be the k-th arc segment.

[0027] Optionally, in step 2, the center of the first bottom-layer elliptical particle is determined based on the translation and offset calculations of the left and lower boundaries, specifically as follows:

[0028] The boundary line is translated along the positive direction of the normal vector by a distance equal to the radius of the selected arc segment. The offset distance of the ellipse center is also taken into account. The final offset line segment endpoint coordinates are obtained by subtracting the coordinates of the selected arc segment center from the coordinates of the ellipse center.

[0029] Calculate the intersection point of the two line segments after offsetting the left and lower boundaries of the two-dimensional rectangular container, and use it as the center of the first elliptical particle.

[0030] Optionally, the formation process of the intrusive block is as follows:

[0031] The coordinates of the center of ellipse A are The coordinates of the centers of each arc segment of ellipse A are: , radius is (1≤k≤4); the center coordinates of ellipse B are The coordinates of the centers of each arc segment of ellipse B are: , radius is (1≤i≤4); The inward vectors of the initial side and the inward vectors of the terminal side of the k-th (1≤k≤4) arc segment of ellipse A are respectively and ;for When k=4, i.e., k+1=5, it represents the inward vector of the terminal side of the 4th arc of ellipse A, which is also the inward vector of the initial side of the 1st arc of ellipse A; the outward vectors of the initial side and the outward vector of the terminal side of the i-th (1≤i≤4) arc of ellipse B are respectively and ;for When i=4, that is, i+1=5, it represents the outward vector of the terminal side of the 4th arc of ellipse B, that is, the outward vector of the initial side of the 1st arc of ellipse B.

[0032] The process of forming an intrusive block is as follows:

[0033] For each arc of ellipse A, iterate through each arc of ellipse B and determine whether the two arcs can form an arc that intrudes into the block; for example, the k-th (1≤k≤4) arc of ellipse A and the i-th (1≤i≤4) arc of ellipse B.

[0034] calculate and The order of precedence :

[0035] (1) Time indicates First, then calculate and The order of precedence ;

[0036] Time indicates First, then it can be obtained. exist and In the middle, calculate again and The order of precedence ;

[0037] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0038] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0039] (2) Time indicates First, then calculate and The order of precedence ;

[0040] Time indicates First, then it can be obtained. exist and In the middle, calculate again of Order of precedence ;

[0041] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0042] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0043] (3) Time judgment and If the directions are the same or opposite, ( and (Same direction), then calculate of Order of precedence ;

[0044] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0045] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0046] Finally, all the information of the arc segments, including the center coordinates, radius, outward vector of the initial edge, and outward vector of the terminal edge, is stored, and the arc segments are connected in sequence to obtain the intrusive block E(A,B).

[0047] Optionally, in step 2, based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, the placement judgment of the bottom elliptical particles is performed, specifically as follows:

[0048] Traverse the arc segments of the intruding block, obtain the intersection points with the line segments after the lower boundary offset, and determine whether the intersection point is on the current arc segment to obtain the correct intersection point information; if there is one intersection point, store this intersection point; if there are two intersection points, store the intersection point with the larger x-coordinate of the two intersection points.

[0049] Determine if the x-coordinate of the intersection point is less than the x-coordinate of the line segment after the right boundary offset. If it is less, the intersection point is the center of the elliptical particle, and the deployment is successful. Store the ellipse information and number j=j+1. If it is greater, the deployment fails. Repeat the generation and deployment operation of the bottom elliptical particle until the number of deployment failures reaches the preset number of deployment failure iterations of the bottom elliptical particle. The deployment of the bottom elliptical particle is then completed.

[0050] Optionally, in step 3, the initial set of elliptical particles on the surface of the accumulation body is the set formed by numbering the elliptical particles at the bottom layer after the bottom layer elliptical particles have been generated.

[0051] Optionally, in step 3, the placement of upper-layer elliptical particles is determined based on the line segment information of the left, right, and upper boundaries of the two-dimensional rectangular container after offset. Specifically:

[0052] Based on the offset line segment information of the left and right boundaries of the two-dimensional rectangular container, the intrusion block is traversed to obtain the intersection points A and B with the largest ordinates, as well as the intrusion block numbers m and n where A and B are located.

[0053] Using intersection point A, the arc segment containing A in the intruding block m is divided into two arc segments according to the original order. and With arc segment Starting from the reference arc, a clockwise arc loop is formed: traverse the current set of elliptical particles on the surface of the accumulation body and find the intersection points of subsequent intruding blocks with the reference arc. When there is one intersection point with an intruding block, store this intersection point as the intersection point of the reference arc with that intruding block; when there are two intersection points with an intruding block, store the intersection point with the larger ordinate as the intersection point of the reference arc with that intruding block.

[0054] If the current reference arc has no intersection with any subsequent intruding blocks, the reference arc enters the next loop; if the total number of intersections between the current reference arc and all subsequent intruding blocks is not zero, the arc loop exits; when the total number of intersections is one, this intersection is used as the new intersection A, and the above arc segment division and reference arc loop operation are performed again; when the total number of intersections is greater than one, the intersections are sorted using a comparison function, and the intersection closest to intersection A is selected as the new intersection A, and the above arc segment division and reference arc loop operation are performed again; when intersection A and intersection B are located in the same intruding block, the intersection with the smallest ordinate value among all stored information of intersection A is output;

[0055] Determine if the intersection point with the smallest output ordinate value is less than the ordinate of the endpoint of the line segment offset from the upper boundary of the two-dimensional rectangular container. If it is less, this intersection point is taken as the center of the elliptical particle, the placement is successful, and the elliptical particles in the current set of elliptical particles on the surface of the stack are updated. If it is greater, the placement fails. Repeat the generation and placement operation of the upper elliptical particles until the number of placement failures reaches the preset number of placement failure iterations for the upper elliptical particles, and the placement of the upper elliptical particles is completed.

[0056] Optionally, based on the successfully deployed upper-layer elliptical particles, update the elliptical particles in the current set of elliptical particles on the surface of the accumulation body, specifically as follows:

[0057] For successfully deployed upper-layer elliptical particles, the number is j=j+1. If the center of the elliptical particle is determined by the line segment offset from the left boundary of the rectangular container and the intruding block of elliptical particle m, the new particle number j is inserted before elliptical particle m. If the center of the elliptical particle is determined by the line segment offset from the right boundary of the rectangular container and the intruding block of elliptical particle n, the new particle number j is inserted after elliptical particle n. If the center of the elliptical particle is determined by the intruding blocks of elliptical particle m and elliptical particle n, the new particle number j is inserted between these two particles. If there are other particle numbers between elliptical particle m and elliptical particle n, these other particle numbers should be deleted.

[0058] The present invention also provides a system for forming elliptical particle packs using a method for forming elliptical particle packs, comprising:

[0059] Spatial boundary and calculation rule definition module: used to define the spatial boundary and calculation rules of elliptical particle stacking; wherein, the elliptical particle is approximated by four connected circular arcs;

[0060] Bottom Elliptical Particle Generation and Placement Module: Used to generate and place bottom elliptical particles in a left-to-right placement order.

[0061] Determine the arc segment that contacts the boundary line of the two-dimensional rectangular container, and determine the center of the first bottom elliptical particle based on the translation and offset calculations of the left and lower boundaries.

[0062] Randomly generate bottom elliptical particles, which form an intrusive block with the previous elliptical particle. Based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, determine the placement of the bottom elliptical particles.

[0063] Upper Elliptical Particle Generation and Placement Module: Used to generate and place upper elliptical particles.

[0064] Randomly generate upper-layer elliptical particles, traverse the current set of surface elliptical particles of the stack to form corresponding intrusive blocks, and make a judgment on the placement of upper-layer elliptical particles based on the line segment information of the left, right and upper boundaries of the two-dimensional rectangular container after offset.

[0065] The numerical model output module for elliptical particle packing is used to output the final geometric parameters of all elliptical particles after the bottom and top layers of elliptical particles are packed, thus obtaining the numerical model of the elliptical particle packing. The final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse.

[0066] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for forming elliptical particle packs. This method is specifically designed for elliptical particles, and its core lies in the organic combination of determining the elliptical position using an intrusive block and optimizing the overall packing formation process. By adopting an elliptical position determination method based on the intrusive block, the computation time for each iteration is greatly reduced, making it possible to generate large-scale elliptical particle packs, significantly improving generation efficiency. Simultaneously, it effectively avoids particle overlap, resulting in a tightly packed state and successfully generating high-density, low-porosity elliptical particle packs, which better conforms to the actual material packing characteristics. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0068] Figure 1 is a schematic diagram of the method flow provided by the present invention.

[0069] Figure 2 is a schematic diagram of the container length, width, and boundary settings provided by the present invention.

[0070] Figure 3 is a schematic diagram of the center of the first bottom elliptical particle (number j=1) provided by the present invention.

[0071] Figure 4 is a schematic diagram of the successful deployment of the bottom elliptical particles provided by the present invention.

[0072] Figure 5 is a schematic diagram of the completion of the bottom elliptical particle placement provided by the present invention.

[0073] Figure 6 is a schematic diagram of the completion of the upper layer elliptical particle delivery provided by the present invention.

[0074] Figure 7 is a schematic diagram of the numerical model of the elliptical particle stack obtained after the final stacking is completed according to the present invention. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Example 1:

[0077] Embodiment 1 of the present invention discloses a method for forming an elliptical particle pack, as shown in Figure 1, comprising:

[0078] Step 1: Define the spatial boundary and calculation rules for the elliptical particle stack; wherein, the elliptical particle is approximated by four connected circular arcs.

[0079] The spatial boundaries and calculation rules for elliptical particle packing are defined as follows:

[0080] Define a two-dimensional rectangular container: set the length, width and boundaries of the container as shown in Figure 2, and define each boundary of the container as a directed line segment, and specify the direction perpendicular to each directed line segment and pointing into the container as the positive normal direction;

[0081] Initialize key parameters: Set the initial delivery sequence number j=0 and the threshold for the number of failed delivery iterations;

[0082] Unified geometric rules: The positive direction of the arc is set to counterclockwise. The numbering of the arc segments of the ellipse and the arc segment intruding into the block is also set to counterclockwise. The unit vector from the center of the circle to the starting point of the arc is defined as the outward vector of the starting edge of the arc, the unit vector from the starting point of the arc to the center of the circle is defined as the inward vector of the starting edge of the arc, the unit vector from the center of the circle to the ending point of the arc is defined as the outward vector of the ending edge of the arc, and the unit vector from the ending point of the arc to the center of the circle is defined as the inward vector of the ending edge of the arc.

[0083] Step 2: Generate and place the bottom layer elliptical particles in a left-to-right order, including the coordinates of the ellipse center and major and minor axes, the radius of the arc segment, the outward vector of the initial side and the outward vector of the terminal side, etc.

[0084] Determine the arc segment that contacts the boundary line of the two-dimensional rectangular container, and determine the center of the first bottom elliptical particle (number j=1) based on the translation and offset calculation of the left and lower boundaries, as shown in Figure 3.

[0085] Randomly generate bottom-level elliptical particles, which form an intrusive block with the previous elliptical particle. Based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, determine the placement of the bottom-level elliptical particles.

[0086] Determine the arc segment that contacts the boundary line of the two-dimensional rectangular container, specifically as follows:

[0087] Calculate the unit normal vector of the boundary line of a two-dimensional rectangular container;

[0088] The boundary unit normal vector is cross-producted with the inward vector of the starting edge of the k-th arc. When the cross-product result is negative, the boundary unit normal vector is then cross-producted with the inward vector of the terminal edge of the k-th arc. When the cross-product result is positive, the arc segment in contact with the boundary line is determined to be the k-th arc segment.

[0089] Based on the translation and offset calculations of the left and lower boundaries, the center of the first bottom-layer elliptical particle is determined, specifically as follows:

[0090] The boundary line is translated along the positive direction of the normal vector by a distance equal to the radius of the selected arc segment. The offset distance of the ellipse center is also taken into account. The final offset line segment endpoint coordinates are obtained by subtracting the coordinates of the selected arc segment center from the coordinates of the ellipse center.

[0091] Calculate the intersection point of the two line segments after offsetting the left and lower boundaries of the two-dimensional rectangular container, and use it as the center of the first elliptical particle.

[0092] The formation process of the intrusive mass is as follows:

[0093] The coordinates of the center of ellipse A are The coordinates of the centers of each arc segment of ellipse A are: , radius is (1≤k≤4); the center coordinates of ellipse B are The coordinates of the centers of each arc segment of ellipse B are: , radius is (1≤i≤4); The inward vectors of the initial side and the inward vectors of the terminal side of the k-th (1≤k≤4) arc segment of ellipse A are respectively and ;for When k=4, i.e., k+1=5, it represents the inward vector of the terminal side of the 4th arc of ellipse A, which is also the inward vector of the initial side of the 1st arc of ellipse A; the outward vectors of the initial side and the outward vector of the terminal side of the i-th (1≤i≤4) arc of ellipse B are respectively and ;for When i=4, i.e. i+1=5, it represents the outward vector of the terminal side of the 4th arc of ellipse B, which is the outward vector of the initial side of the 1st arc of ellipse B; (the outward vector of the terminal side of the current arc coincides with the outward vector of the initial side of the next arc).

[0094] The process of forming an intrusive block is as follows:

[0095] For each arc of ellipse A, iterate through each arc of ellipse B and determine whether the two arcs can form an arc that intrudes into the block; for example, the k-th (1≤k≤4) arc of ellipse A and the i-th (1≤i≤4) arc of ellipse B.

[0096] calculate and The order of precedence :

[0097] (1) Time indicates First, then calculate and The order of precedence ;

[0098] Time indicates First, then it can be obtained. exist and In the middle, calculate again and The order of precedence ;

[0099] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0100] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0101] (2) Time indicates First, then calculate and The order of precedence ;

[0102] Time indicates First, then it can be obtained. exist and In the middle, calculate again of Order of precedence ;

[0103] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0104] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0105] (3) Time judgment and If the directions are the same or opposite, ( and (Same direction), then calculate of Order of precedence ;

[0106] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0107] Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively , , radius is ;

[0108] Finally, all the information of the arc segments, including the center coordinates, radius, outward vector of the initial edge, and outward vector of the terminal edge, is stored, and the arc segments are connected in sequence to obtain the intrusive block E(A,B).

[0109] Based on the line segment information after offsetting the lower and right boundaries of the two-dimensional rectangular container, the deployment of the bottom-layer elliptical particles is determined, specifically as follows:

[0110] Traverse the arc segments of the intruding block, obtain the intersection points with the line segments after the lower boundary offset, and determine whether the intersection point is on the current arc segment to obtain the correct intersection point information; if there is one intersection point, store this intersection point; if there are two intersection points, store the intersection point with the larger x-coordinate of the two intersection points.

[0111] Determine if the x-coordinate of the intersection point is less than the x-coordinate of the line segment after the right boundary offset. If it is less, the intersection point is the center of the elliptical particle, and the deployment is successful, as shown in Figure 4. Store the ellipse information and number j=j+1. If it is greater, the deployment fails. Repeat the generation and deployment operation of the bottom elliptical particle until the number of deployment failures reaches the preset deployment failure iteration number of the bottom elliptical particle. The deployment of the bottom elliptical particle is completed, as shown in Figure 5.

[0112] Step 3: Generate and place the upper layer of elliptical particles:

[0113] Randomly generate upper-layer elliptical particles, traverse the current stack surface elliptical particle set j_list to form the corresponding intrusion block, and make the upper-layer elliptical particle placement judgment based on the line segment information of the left, right and upper boundaries of the two-dimensional rectangular container after offset.

[0114] The initial set of elliptical particles on the surface of the accumulation body is the set formed by numbering the elliptical particles at the bottom layer after the bottom layer elliptical particles have been generated.

[0115] The deployment of upper-layer elliptical particles is determined based on the line segment information of the left, right, and upper boundaries of the two-dimensional rectangular container after offset. Specifically:

[0116] Based on the offset line segment information of the left and right boundaries of the two-dimensional rectangular container, the intrusion block is traversed to obtain the intersection points A and B with the largest ordinates, as well as the intrusion block numbers m and n where A and B are located.

[0117] Using intersection point A, the arc segment containing A in the intruding block m is divided into two arc segments according to the original order. and With arc segment Starting from the reference arc, a clockwise arc loop is formed: traverse the current set of elliptical particles on the surface of the accumulation body and find the intersection points of subsequent intruding blocks with the reference arc. When there is one intersection point with an intruding block, store this intersection point as the intersection point of the reference arc with that intruding block; when there are two intersection points with an intruding block, store the intersection point with the larger ordinate as the intersection point of the reference arc with that intruding block.

[0118] If the current reference arc has no intersection with any subsequent intruding blocks, the reference arc enters the next loop; if the total number of intersections between the current reference arc and all subsequent intruding blocks is not zero, the arc loop exits; when the total number of intersections is one, this intersection is used as the new intersection A, and the above arc segment division and reference arc loop operation are performed again; when the total number of intersections is greater than one, the intersections are sorted using a comparison function, and the intersection closest to intersection A is selected as the new intersection A, and the above arc segment division and reference arc loop operation are performed again; when intersection A and intersection B are located in the same intruding block, the intersection with the smallest ordinate value among all stored information of intersection A is output;

[0119] Determine whether the intersection point with the smallest output ordinate value is less than the ordinate of the endpoint of the line segment after offset from the upper boundary of the two-dimensional rectangular container. If it is less, this intersection point is taken as the center of the elliptical particle, the placement is successful, and the elliptical particles in the current set of elliptical particles on the surface of the stack are updated; if it is greater, the placement fails. Repeat the generation and placement operation of the upper elliptical particles until the number of placement failures reaches the preset number of placement failure iterations for the upper elliptical particles, and the placement of the upper elliptical particles is completed, as shown in Figure 6.

[0120] Based on the successfully deployed upper-layer elliptical particles, update the elliptical particles in the current set of elliptical particles on the surface of the accumulation body, specifically as follows:

[0121] For successfully deployed upper-layer elliptical particles, the number is j=j+1. If the center of the elliptical particle is determined by the line segment offset from the left boundary of the rectangular container and the intruding block of elliptical particle m, the new particle number j is inserted before elliptical particle m. If the center of the elliptical particle is determined by the line segment offset from the right boundary of the rectangular container and the intruding block of elliptical particle n, the new particle number j is inserted after elliptical particle n. If the center of the elliptical particle is determined by the intruding blocks of elliptical particle m and elliptical particle n, the new particle number j is inserted between these two particles. If there are other particle numbers between elliptical particle m and elliptical particle n, these other particle numbers should be deleted.

[0122] Step 4: After the bottom layer of elliptical particles and the top layer of elliptical particles are stacked, as shown in Figure 7, output the final geometric parameters of all elliptical particles to obtain the numerical model of the elliptical particle stack. The final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse.

[0123] Example 2:

[0124] Embodiment 2 of the present invention discloses a system for forming elliptical particle packs using a method for forming elliptical particle packs, comprising:

[0125] Spatial boundary and calculation rule definition module: used to define the spatial boundary and calculation rules of elliptical particle stacking; wherein, the elliptical particle is approximated by four connected circular arcs.

[0126] Bottom Elliptical Particle Generation and Placement Module: Used to generate and place bottom elliptical particles in a left-to-right placement order.

[0127] Determine the arc segment that contacts the boundary line of the two-dimensional rectangular container, and determine the center of the first bottom elliptical particle based on the translation and offset calculations of the left and lower boundaries.

[0128] Randomly generate bottom-level elliptical particles, which form an intrusive block with the previous elliptical particle. Based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, determine the placement of the bottom-level elliptical particles.

[0129] Upper Elliptical Particle Generation and Placement Module: Used to generate and place upper elliptical particles.

[0130] Randomly generate upper-layer elliptical particles, traverse the current set of surface elliptical particles of the stack to form corresponding intrusive blocks, and determine the placement of upper-layer elliptical particles based on the line segment information of the left, right and upper boundaries of the two-dimensional rectangular container after offset.

[0131] The numerical model output module for elliptical particle packing is used to output the final geometric parameters of all elliptical particles after the bottom and top layers of elliptical particles are packed, thus obtaining the numerical model of the elliptical particle packing. The final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse.

[0132] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0133] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for forming an elliptical particle accumulation of soil and gravel, characterized in that, The process includes: Step 1: Defining the spatial boundaries and calculation rules for the elliptical particle accumulation used to generate soil and gravel; wherein the elliptical particle is approximated by four connected circular arcs; Step 2: Generating and placing the bottom layer of elliptical particles in a left-to-right placement order: Determining the circular arc segment in contact with the boundary line of the two-dimensional rectangular container, and determining the center of the first bottom layer elliptical particle based on the translation and offset calculations of the left and lower boundaries; Randomly generating bottom layer elliptical particles to form an intrusion block with the previous elliptical particle, and making a placement judgment based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container; Step 3: Generating and placing the upper layer of elliptical particles: Randomly generating upper layer elliptical particles, traversing the current set of surface elliptical particles of the accumulation body to form the corresponding intrusion block, and making a placement judgment based on the line segments after the offset of the left, right, and upper boundaries of the two-dimensional rectangular container. The information is used to determine the placement of the upper elliptical particles; Step 4: After the bottom elliptical particles and the upper elliptical particles are stacked, the final geometric parameters of all elliptical particles are output to obtain the numerical model of the elliptical particle accumulation body used to generate soil and gravel; wherein, the final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse; the placement of the upper elliptical particles is determined based on the line segment information after the offset of the left, right and upper boundaries of the two-dimensional rectangular container, specifically: the intrusion block is traversed based on the line segment information after the offset of the left and right boundaries of the two-dimensional rectangular container, respectively, to obtain the intersection points A and B with the largest ordinates and the intrusion block numbers m and n where A and B are located; using the intersection point A, the circular arc segment where A is located in the intrusion block m is divided into two circular arc segments according to the original order. and With arc segment Starting with the reference arc, a clockwise arc loop is executed: traversing the current set of elliptical particles on the surface of the accumulation body, the intersection points of subsequent intruding blocks with the reference arc are calculated. When there is one intersection point with an intruding block, this intersection point is stored as the intersection point of the reference arc and that intruding block; when there are two intersection points with an intruding block, the intersection point with the larger ordinate is stored as the intersection point of the reference arc and that intruding block; if the current reference arc has no intersection points with any subsequent intruding blocks, the reference arc enters the next loop; if the total number of intersection points between the current reference arc and all subsequent intruding blocks is not zero, the arc loop exits; when the total number of intersection points is one, this intersection point is used as the new intersection point A, and the above arc segment division and reference arc loop operation are executed again; when the total number of intersection points is greater than one, ... The intersection points are sorted using a comparison function. The intersection point closest to intersection point A is selected as the new intersection point A, and the above-mentioned arc segment division and reference arc loop operation are performed again. When intersection point A and intersection point B are located in the same intrusive block, the intersection point with the smallest ordinate value among all the stored information of intersection point A is output. It is determined whether the intersection point with the smallest ordinate value is less than the ordinate of the endpoint of the line segment after the offset of the upper boundary of the two-dimensional rectangular container. If it is less, this intersection point is used as the center of the elliptical particle, the deployment is successful, and the elliptical particles in the current stack surface elliptical particle set are updated. If it is greater, the deployment fails. The generation and deployment operation of the upper elliptical particles is repeated until the number of deployment failures reaches the preset deployment failure iteration number of the upper elliptical particles, and the deployment of the upper elliptical particles is completed.

2. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, In step 1, the spatial boundaries and calculation rules for the elliptical particle accumulation used to generate soil and gravel are defined, specifically as follows: Define a two-dimensional rectangular container: set the length, width, and boundaries of the container, and define each boundary of the container as a directed line segment, and specify the direction perpendicular to each directed line segment and pointing inwards from the container as the positive normal direction; Initialize key parameters: set the initial placement sequence number j=0, and the threshold for the number of iterations for placement failure; Unify geometric rules: set the positive direction of the arc to counterclockwise, and the numbering of the arc segments of the ellipse and the intruding block should be counterclockwise, and define the unit vector from the center of the circle to the starting point of the arc as the outward vector of the starting edge of the arc, the unit vector from the starting point of the arc to the center of the circle as the inward vector of the starting edge of the arc, the unit vector from the center of the circle to the ending point of the arc as the outward vector of the ending edge of the arc, and the unit vector from the ending point of the arc to the center of the circle as the inward vector of the ending edge of the arc.

3. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, In step 2, the arc segment that contacts the boundary line of the two-dimensional rectangular container is determined as follows: Calculate the unit normal vector of the boundary line of the two-dimensional rectangular container; perform a cross product between the boundary unit normal vector and the inward vector of the starting edge of the k-th arc segment. If the cross product result is negative, perform a cross product between the boundary unit normal vector and the inward vector of the terminal edge of the k-th arc segment. If the cross product result is positive, the arc segment that contacts the boundary line is determined to be the k-th arc segment.

4. The method for forming an elliptical particle accumulation of soil and gravel according to claim 3, characterized in that, In step 2, based on the translation and offset calculations of the left and lower boundaries, the center of the first bottom elliptical particle is determined. Specifically, the boundary line is translated along the positive direction of the normal vector by a distance equal to the radius of the selected arc segment. The offset distance of the ellipse center is also considered. By subtracting the coordinates of the center of the selected arc segment from the coordinates of the ellipse center, the coordinates of the endpoints of the line segments after the final offset are obtained. The intersection of the two line segments after the offset of the left and lower boundaries of the two-dimensional rectangular container is calculated and used as the center of the first elliptical particle.

5. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, The formation process of the intrusive block is as follows: the center coordinates of ellipse A are... The coordinates of the centers of each arc segment of ellipse A are: , radius is , 1≤k≤4; the center coordinates of ellipse B are The coordinates of the centers of each arc segment of ellipse B are: , radius is , 1≤i≤4; the inward vectors of the initial side and the inward vectors of the terminal side of the k-th arc of ellipse A are respectively and Wherein, the value of parameter k ranges from 1 to k to 4; for When k=4, i.e., k+1=5, it represents the inward vector of the terminal side of the 4th arc of ellipse A, which is also the inward vector of the initial side of the 1st arc of ellipse A; the outward vectors of the initial side and the terminal side of the i-th arc of ellipse B are respectively... and Wherein, the value of parameter i ranges from 1 to i ≤ 4; for When i=4, i.e., i+1=5, it represents the outward vector of the terminal side of the 4th arc of ellipse B, which is the outward vector of the initial side of the 1st arc of ellipse B. The process of forming the intruding block is as follows: For each arc of ellipse A, traverse each arc of ellipse B and determine whether the two arcs can form an arc that intrudes into the block; such as the kth arc of ellipse A and the ith arc of ellipse B; where the values ​​of parameters k and i are in the range of 1≤k≤4 and 1≤i≤4; Calculation and The order of precedence ：（1） Time indicates First, then calculate and The order of precedence ； Time indicates First, then it can be obtained. exist and In the middle, calculate again and The order of precedence ； Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is ； Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is ；（2） Time indicates First, then calculate and The order of precedence ； Time indicates First, then it can be obtained. exist and In the middle, calculate again of Order of precedence ； Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is ； Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is ；（3） Time judgment and If the directions are the same or opposite, of Order of precedence ;in, express and Same direction; Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is ； Time indicates Prior to this, the outward vectors of the initial and final sides of the formed intrusive block arc segment are respectively... and The x and y coordinates of the center of the circle are respectively 、 , radius is Finally, all the information of the arc segments obtained, including the center coordinates, radius, outward vector of the initial edge, and outward vector of the terminal edge, is stored, and the arc segments are connected in sequence to obtain the intrusive block E(A,B).

6. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, In step 2, based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container, the placement judgment of the bottom elliptical particles is made. Specifically, the arc segments of the intruding block are traversed to obtain the intersection points with the line segments after the offset of the lower boundary, and it is determined whether the intersection point is on the current arc segment to obtain the correct intersection point information; if there is an intersection point, the intersection point is stored. If there are two intersection points, store the intersection point with the larger x-coordinate. Determine if the x-coordinate of the obtained intersection point is less than the x-coordinate of the line segment after the right boundary offset. If it is less, this intersection point is the center of the elliptical particle, the deployment is successful, and the ellipse information and number j=j+1 are stored. If it is greater, the deployment fails. Repeat the generation and deployment operation of the bottom elliptical particle until the number of deployment failures reaches the preset deployment failure iteration number of the bottom elliptical particle, and the deployment of the bottom elliptical particle is completed.

7. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, In step 3, the initial set of elliptical particles on the surface of the accumulation body is the set formed by numbering the elliptical particles at the bottom layer after the bottom layer elliptical particles have been generated.

8. The method for forming an elliptical particle accumulation of soil and gravel according to claim 1, characterized in that, Based on the successfully deployed upper-layer elliptical particles, update the elliptical particles in the current set of surface elliptical particles in the stack. Specifically: for successfully deployed upper-layer elliptical particles, the number is j=j+1. If the center of the elliptical particle is determined by the line segment offset from the left boundary of the rectangular container and the intruding block of elliptical particle m, insert the new particle number j before elliptical particle m; if the center of the elliptical particle is determined by the line segment offset from the right boundary of the rectangular container and the intruding block of elliptical particle n, insert the new particle number j after elliptical particle n; if the center of the elliptical particle is determined by the intruding blocks of elliptical particle m and elliptical particle n, insert the new particle number j between these two particles. If there are other particle numbers between elliptical particle m and elliptical particle n, delete those other particle numbers.

9. A system for forming elliptical particle deposits of soil and gravel, utilizing the method for forming elliptical particle deposits of soil and gravel as described in any one of claims 1-8, characterized in that, include: The module defining spatial boundaries and calculation rules is used to define the spatial boundaries and calculation rules for generating elliptical particle stacks of soil and gravel; wherein the elliptical particles are approximated by four connected circular arcs; the module for generating and placing bottom-layer elliptical particles is used to generate and place bottom-layer elliptical particles in a left-to-right order: determining the circular arc segment in contact with the boundary line of the two-dimensional rectangular container, and determining the center of the first bottom-layer elliptical particle based on the translation and offset calculations of the left and lower boundaries; randomly generating bottom-layer elliptical particles to form an intrusive block with the previous elliptical particle, and making a placement judgment of the bottom-layer elliptical particles based on the line segment information after the offset of the lower and right boundaries of the two-dimensional rectangular container; the module for generating upper-layer elliptical particles... The generation and placement module is used to generate and place upper-layer elliptical particles: randomly generate upper-layer elliptical particles, traverse the current set of elliptical particles on the surface of the accumulation body to form corresponding intrusive blocks, and make placement judgments based on the line segment information of the left, right, and upper boundaries of the two-dimensional rectangular container after offset; the elliptical particle accumulation numerical model output module is used to output the final geometric parameters of all elliptical particles after the bottom layer elliptical particles and the upper layer elliptical particles have been accumulated, and obtain the elliptical particle accumulation numerical model used to generate soil and gravel; wherein, the final geometric parameters include: center coordinates, major and minor axes, and the outward vectors of the initial and final sides of the four circular arcs corresponding to the ellipse.

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