A three-dimensional aggregate modeling method based on surface subdivision and step-by-step reshaping

Abstract

The application discloses a three-dimensional aggregate modeling method based on surface subdivision and step-by-step reshaping, and belongs to the field of granular material modeling simulation, and specifically comprises the following steps: a basic convex aggregate is established in a unit cube by using a convex hull algorithm; new vertices are generated at the midpoints of each edge of each triangular facet of the aggregate, so that the aggregate surface is subdivided; principal component analysis is used to determine the aggregate particle size and establish a local coordinate system; a displacement coefficient of the aggregate vertex is determined, which is specifically composed of an upper limit value of the displacement coefficient, a vertex scope factor and a vertex displacement floating coefficient, and is used for respectively controlling the overall intensity of aggregate shape reshaping, the moving range of densely distributed vertices and the difference in the moving range of the vertices; the vertices are moved according to the displacement coefficient in the local coordinate system, so that the shape of the reshaped aggregate is parameterized; and through repeated execution of the above shape reshaping process based on surface subdivision, an aggregate model with increasing fidelity is obtained.

Description

Technical Field

[0001] This invention belongs to the field of particulate material simulation and relates to an aggregate modeling technology, specifically a three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping. Background Technology

[0002] Asphalt mixtures are particle-reinforced materials, typically composed of asphalt, coarse aggregate, fine aggregate, and mineral powder. The morphological characteristics of the aggregates significantly influence the interaction between the aggregates and asphalt. Exploring the mechanism by which aggregate shape characteristics affect the mechanical behavior of mixtures can promote our understanding of the complex behavior of mixture materials. Generally, aggregate shape can be fully characterized by three independent shape characteristics: morphology, angularity, and surface texture. Each shape characteristic has corresponding index parameters. For example, morphology can be evaluated by indices such as sphericity and flatness. Although obtaining aggregate shape parameters and mechanical property indices of mixtures through experimental methods and performing correlation analysis is a feasible research approach, the data collected is usually limited due to the long experimental cycle and high cost. In addition to experimental research methods, microstructure simulation technology based on random aggregates can achieve efficient modeling through computers and algorithms, and is therefore increasingly used to simulate the microstructure of asphalt mixtures containing coarse aggregates and asphalt mortar. In this method, the shape of the coarse aggregate is parameterized and controlled by the random aggregate method. Based on the established virtual asphalt mixture specimens, numerical methods can be used to simulate the mechanical behavior of asphalt mixtures. The realism and shape controllability of virtual aggregates are key to exploring the mechanism by which aggregate shape characteristics affect the mechanical behavior of mixtures.

[0003] In existing studies, two-dimensional aggregate models are commonly used to generate mesoscopic models of asphalt mixtures to improve simulation efficiency. However, two-dimensional aggregate models cannot fully reflect the complex interactions between aggregates and mortar in three-dimensional space. In existing three-dimensional asphalt mixture mesoscopic structures established based on random aggregate methods, the aggregates used are mostly simplified to spheres, ellipsoids, and convex bodies, thus failing to consider the shape characteristics of real aggregates, such as concave surfaces and textures, in the simulation of the mechanical behavior of asphalt mixtures. Currently, there are few reports on three-dimensional aggregate simulation techniques that can simultaneously consider the concave surface and texture characteristics of aggregates and effectively control shape parameters.

[0004] Therefore, there is an urgent need for a three-dimensional aggregate modeling method that can effectively generate and control concave surfaces and textures. Summary of the Invention

[0005] This invention proposes a 3D aggregate modeling method based on surface subdivision and progressive reshaping. The invention repeatedly applies a shape reshaping process based on surface subdivision to basic convex aggregates, generating concave surfaces and continuously refined textures, thereby improving the realism of the aggregate model.

[0006] The technical solution of the present invention:

[0007] A three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping includes the following steps:

[0008] Step 1. Generate basic convex aggregates within a unit cube. Specifically:

[0009] (1.1) Randomly generate a set of points with more than 4 points within the unit cube, and use the convex hull algorithm to generate the convex hull of these points. The convex hull is composed of triangular facets; use the convex hull as the basic convex aggregate.

[0010] (1.2) Using principal component analysis, determine the three principal directions of all vertices of the basic convex aggregate. Project all vertices onto these three principal directions and determine the length between the farthest projection points of these vertices on each principal direction. Sort the three lengths from largest to smallest, which are the longest, middle, and smallest dimensions of the aggregate, respectively, and represent them as L... l L m and L s Indicates; the medium-length dimension L m Define the aggregate size as the particle size; calculate the aggregate flatness (BPD) and sphericity (QD), BPD = L s / L m , Let the flatness tolerance value be RX. BPD The allowable value for sphericity is RX. QD If either the flatness or sphericity is less than the set allowable value, repeat steps (1.1) to (1.2) until the condition is met, that is, both the flatness and sphericity are greater than the set allowable value.

[0011] Step 2. Perform a surface subdivision-based shape reshaping process n times on the basic convex aggregate to obtain n aggregate models with increasing realism. Specifically:

[0012] (2.1) Generate new vertices and subdivide aggregate surfaces: Generate new vertices at the midpoint of each edge of each triangular facet that constitutes the aggregate, connect the new vertices in each triangular facet, divide each triangular facet into four smaller triangular facets, and subdivide the original triangular facets.

[0013] (2.2) Establish the local coordinate system of aggregate: Determine the centroid of aggregate as the origin O of the local coordinate system, use principal component analysis to determine the three principal directions of all vertices of aggregate, and use these three principal directions as the directions of the coordinate axes of the local coordinate system of aggregate.

[0014] (2.3) Determine the displacement coefficient F of the aggregate vertex: The displacement coefficient of the aggregate vertex is obtained by multiplying the upper limit value β of the displacement coefficient of the vertex, the scope factor ξ of the vertex, and the displacement floating coefficient fd of the vertex, that is, F=β×ξ×fd.

[0015] i. Determine the upper limit of the vertex shift coefficient β: The value of β is directly related to the number of times step (2.3) is executed. If it is the first time step (2.3) is executed, then β takes any value in [0,1]; in each subsequent execution of step (2.3), the value of β used is m times the value of β in the previous execution of step (2.3), where m < 1.

[0016] ii. Determine the scope factor ξ of the vertex: Define the scope of the vertex as the triangular facets connected to the vertex; calculate the average area a of the triangular facets contained in the scope of the vertex, calculate the average area a' of all triangular facets of the aggregate, and the scope factor ξ of the vertex = a / a'. If the calculated ξ > 1, then let ξ = 1.

[0017] iii. Determine the shift floating coefficient fd of the vertex, and choose any value within the range of greater than 0 and less than 1.

[0018] (2.4) Move the vertex according to the vertex displacement coefficient F: On the path directly connecting the vertex to the local coordinate system O, move the vertex in a direction closer to O. The distance moved is the vertex displacement coefficient F multiplied by the distance from the vertex to O.

[0019] (2.5) Store the coordinates of the vertices of all the triangular facets of the current aggregate, and you will get the geometric model of the aggregate after shape reshaping.

[0020] (2.6) Steps (2.1) to (2.5) are shape reshaping processes based on surface subdivision; for the latest obtained shape-reshaped aggregate model, repeat steps (2.1) to (2.5); by using the surface subdivision-based shape reshaping process n times, a total of n shape-reshaped aggregate models with increasing realism are obtained.

[0021] Step 3. Generate aggregate models with different levels of realism and specified particle size. For all aggregate models obtained after shape reshaping in Step 2, determine the aggregate particle size using the method in Step (1.2); for each aggregate model, move the aggregate vertex on the straight line established between the aggregate vertex and O, such that the distance between the aggregate vertex and O after the movement is divided by the distance between the aggregate vertex and O before the movement, which is equal to the ratio of the required aggregate particle size to the aggregate particle size before the vertex is moved, thereby obtaining aggregate models with different levels of realism and specified particle size.

[0022] This invention is highly effective and has the following advantages:

[0023] 1. Most current random aggregate modeling methods cannot effectively consider concave surfaces and textures. This invention can generate three-dimensional aggregate models with concave surfaces and textures.

[0024] 2. This invention enables parametric control of aggregate shape. In the surface subdivision-based shape reshaping process proposed in this invention, the value of the displacement coefficient directly determines the effect of aggregate shape change. The upper limit value β of the displacement coefficient determines the overall severity of aggregate shape reshaping, the domain factor ξ of the vertices is used to reduce the movement amplitude of densely distributed vertices, and the displacement floating coefficient fd controls the difference in vertex movement amplitude, making the aggregate shape reshaping random and thus making the model more realistic.

[0025] 3. By repeatedly executing the shape reshaping process based on surface subdivision, this invention can obtain aggregate models with gradually increasing realism, providing a variety of geometric detail levels for aggregates in the microstructure model of asphalt mixtures, so as to balance simulation realism and model complexity. Attached Figure Description

[0026] Figure 1 This is a flowchart of a three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping as described in this invention.

[0027] Figure 2 This is a schematic diagram of the basic convex aggregate obtained by the convex hull algorithm in an embodiment of the present invention.

[0028] Figure 3 This is a schematic diagram of the aggregate surface subdivision process in an embodiment of the present invention.

[0029] Figure 4 This is a schematic diagram of the local coordinate system determined by principal component analysis and the centroid of aggregate in an embodiment of the present invention.

[0030] Figure 5 This is a schematic diagram of the domain of the aggregate vertex in an embodiment of the present invention.

[0031] Figure 6 This is a schematic diagram of a basic convex aggregate and three aggregate models with increasing realism obtained through three surface subdivision-based shape reshaping processes in an embodiment of the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0033] This invention relates to a three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping. The entire process is shown in the attached figure. Figure 1 As shown, the specific steps include:

[0034] A three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping includes the following steps:

[0035] Step 1. Generate basic convex aggregates within a unit cube. Specifically:

[0036] (1.1) Randomly generate a set of points with more than 4 points within the unit cube, and use the convex hull algorithm to generate the convex hull of these points. The convex hull is composed of triangular facets; use the convex hull as the basic convex aggregate.

[0037] In this embodiment, 30 points are randomly generated within the unit cube space, and the convex hull algorithm is used to obtain the following... Figure 2 The basic convex aggregate shown consists of 19 points, with the remaining 11 points located within the convex hull.

[0038] (1.2) Using principal component analysis, determine the three principal directions of all vertices of the basic convex aggregate. Project all vertices onto these three principal directions and determine the length between the farthest projection points of these vertices on each principal direction. Sort the three lengths from largest to smallest, which are the longest, middle, and smallest dimensions of the aggregate, respectively, and represent them as L... l L m and L s Indicates; the medium-length dimension L m Define the aggregate size as the particle size; calculate the aggregate flatness (BPD) and sphericity (QD), BPD = L s / L m , Let the flatness tolerance value be RX. BPD The allowable value for sphericity is RX. QD If either the flatness or sphericity is less than the set allowable value, repeat steps (1.1) to (1.2) until the condition is met, that is, both the flatness and sphericity are greater than the set allowable value.

[0039] Based on experience in aggregate screening engineering, the medium-length dimension of the aggregate is used as the aggregate particle size. Furthermore, flat aggregates and aggregates with low sphericity are not suitable for practical engineering applications; therefore, this method considers allowable values ​​for flatness and sphericity to control the generation of the digital aggregate model. In the embodiment, RX is set... BPD and RX QD Both are 0.3. Figure 2 The L-shaped basic convex aggregate shown m =0.89088, that is, the particle size is 0.89088, L l =1.2981, L s =0.7272, BPD=0.8164, QD=0.7271. Among them, BPD and QD are both greater than the set tolerance values.

[0040] Step 2. Perform a surface subdivision-based shape reshaping process n times on the basic convex aggregate to obtain n aggregate models with increasing realism. Specifically:

[0041] (2.1) Generate new vertices and subdivide aggregate surfaces: Generate new vertices at the midpoint of each edge of each triangular facet that constitutes the aggregate, connect the new vertices in each triangular facet, divide each triangular facet into four smaller triangular facets, and subdivide the original triangular facets.

[0042] Figure 3 This is a schematic diagram of the aggregate surface subdivision process.

[0043] (2.2) Establish the local coordinate system of aggregate: Determine the centroid of aggregate as the origin O of the local coordinate system, use principal component analysis to determine the three principal directions of all vertices of aggregate, and use these three principal directions as the directions of the coordinate axes of the local coordinate system of aggregate.

[0044] Figure 4 This is a local coordinate system determined by principal component analysis and the aggregate centroid.

[0045] (2.3) Determine the displacement coefficient F of the aggregate vertex: The displacement coefficient of the aggregate vertex is obtained by multiplying the upper limit value β of the displacement coefficient of the vertex, the scope factor ξ of the vertex, and the displacement floating coefficient fd of the vertex, that is, F=β×ξ×fd.

[0046] i. Determine the upper limit of the vertex shift coefficient β: The value of β is directly related to the number of times step (2.3) is executed. If it is the first time step (2.3) is executed, then β takes any value in [0,1]; in each subsequent execution of step (2.3), the value of β used is m times the value of β in the previous execution of step (2.3), where m < 1.

[0047] In this embodiment, the initial value of β is 0.2, and m is 0.5. Therefore, the β used in the next iteration is always 0.5 times the β used in the previous iteration. The reason for using a continuously decreasing β value is that the aggregate surface is continuously subdivided. If the vertex movement amplitude does not decrease accordingly, there may be a situation where the vertex movement amplitude is larger than the size of the subdivided aggregate triangle, which would greatly reduce the realism of the aggregate model.

[0048] ii. Determine the scope factor ξ of the vertex: Define the scope of the vertex as the triangular facets connected to the vertex; calculate the average area a of the triangular facets contained in the scope of the vertex, calculate the average area a' of all triangular facets of the aggregate, and the scope factor ξ of the vertex = a / a'. If the calculated ξ > 1, then let ξ = 1.

[0049] Figure 5 This is a schematic diagram of the domain of aggregate vertices. Vertices with small domains mean that surrounding vertices are densely packed, and it is necessary to reduce the differences in the movement amplitude of these vertices to avoid frequent and drastic shape changes in local areas.

[0050] iii. Determine the shift floating coefficient fd of the vertex, and choose any value within the range of greater than 0 and less than 1.

[0051] (2.4) Move the vertex according to the vertex displacement coefficient F: On the path directly connecting the vertex to the local coordinate system O, move the vertex in a direction closer to O. The distance moved is the vertex displacement coefficient F multiplied by the distance from the vertex to O.

[0052] (2.5) Store the coordinates of the vertices of all the triangular facets of the current aggregate, and you will get the geometric model of the aggregate after shape reshaping.

[0053] (2.6) Steps (2.1) to (2.5) are shape reshaping processes based on surface subdivision; for the latest obtained shape-reshaped aggregate model, repeat steps (2.1) to (2.5); by using the surface subdivision-based shape reshaping process n times, a total of n shape-reshaped aggregate models with increasing realism are obtained.

[0054] Let n = 3, Figure 6 This diagram illustrates a basic convex aggregate and three aggregate models with increasing realism obtained after three rounds of shape reshaping based on surface subdivision. Due to the different vertex shift coefficients, the reshaped aggregate naturally forms a concave surface after vertex shifting. Through multiple rounds of surface subdivision and shape reshaping, the size of the smallest basic unit of aggregate geometry, the triangular facet, can be continuously reduced, refining the aggregate surface texture and gradually increasing the aggregate realism. Note that increasing the number of times the surface subdivision-based shape reshaping process is used results in an aggregate model with richer texture and more realistic shape, but the model complexity also increases accordingly. Users can set the number of times the surface subdivision-based shape reshaping process is used as needed.

[0055] Step 3. Generate aggregate models with different levels of realism and specified particle size. For all aggregate models obtained after shape reshaping in Step 2, determine the aggregate particle size using the method in Step (1.2); for each aggregate model, move the aggregate vertex on the straight line established between the aggregate vertex and O, such that the distance between the aggregate vertex and O after the movement is divided by the distance between the aggregate vertex and O before the movement, which is equal to the ratio of the required aggregate particle size to the aggregate particle size before the vertex is moved, thereby obtaining aggregate models with different levels of realism and specified particle size.

Claims

1. A three-dimensional aggregate modeling method based on surface subdivision and progressive reshaping, characterized in that, Includes the following steps: Step 1. Generate basic convex aggregate in a unit cube; Specifically: (1.1) Randomly generate a set of points with more than 4 points within the unit cube, and use the convex hull algorithm to generate the convex hull of these points. The convex hull is composed of triangular facets; use the convex hull as the basic convex aggregate. (1.2) Using principal component analysis, determine the three principal directions of all vertices of the basic convex aggregate. Project all vertices onto these three principal directions and determine the length between the farthest projection points of these vertices on each principal direction. Sort the three lengths from largest to smallest, which are the longest, middle, and smallest dimensions of the aggregate, respectively, and represent them as L. l L m and L s express; Medium length dimension L m Defined as the particle size of the aggregate; Calculate aggregate flatness (BPD) and sphericity (QD), BPD = L s / L m , Let the flatness tolerance value be RX. BPD The allowable value for sphericity is RX. QD If either the flatness or sphericity is less than the set allowable value, repeat steps (1.1) to (1.2) until the condition is met, that is, both the flatness and sphericity are greater than the set allowable value. Step 2. Perform a surface subdivision-based shape reshaping process n times on the basic convex aggregate to obtain n aggregate models with increasing realism; specifically: (2.1) Generate new vertices and subdivide aggregate surfaces: Generate new vertices at the midpoint of each edge of each triangular facet that constitutes the aggregate, connect the new vertices in each triangular facet, divide each triangular facet into four smaller triangular facets, and subdivide the original triangular facets. (2.2) Establish the local coordinate system of aggregate: Determine the centroid of aggregate as the origin O of the local coordinate system, use principal component analysis to determine the three principal directions of all vertices of aggregate, and use these three principal directions as the directions of the coordinate axes of the local coordinate system of aggregate. (2.3) Determine the displacement coefficient F of the aggregate vertex: The displacement coefficient of the aggregate vertex is obtained by multiplying the upper limit value β of the displacement coefficient of the vertex, the scope factor ξ of the vertex, and the displacement floating coefficient fd of the vertex, that is, F=β×ξ×fd; i. Determine the upper limit of the vertex shift coefficient β: The size of β is directly related to the number of times step (2.3) is executed; if it is the first time step (2.3) is executed, then β takes any value in [0,1]; the value of β used in each subsequent execution of step (2.3) is m times the value of β in the previous execution of step (2.3), where m<1; ii. Determine the scope factor ξ of the vertex: Define the scope of the vertex as the triangular facets connected to the vertex; calculate the average area a of the triangular facets contained in the scope of the vertex, calculate the average area a' of all triangular facets of the aggregate, the scope factor ξ of the vertex = a / a', if the calculated ξ>1, then let ξ=1; iii. Determine the shift floating coefficient fd of the vertex, and choose any value within the range of greater than 0 and less than 1; (2.4) Move the vertex according to the vertex displacement coefficient F: On the path directly connecting the vertex to the local coordinate system O, move the vertex in a direction closer to O. The distance moved is the vertex displacement coefficient F multiplied by the distance from the vertex to O. (2.5) Store the coordinates of the vertices corresponding to all the triangular facets of the current aggregate, and you will get the geometric model of the aggregate after shape reshaping; (2.6) Steps (2.1) to (2.5) are the shape reshaping process based on surface subdivision; For the newly obtained reshaped aggregate model, repeat steps (2.1) to (2.5); By employing a surface subdivision-based shape reshaping process n times, a total of n shape reshaping aggregate models with increasing realism are obtained. Step 3. Generate aggregate models with different levels of realism and specified particle size; for all aggregate models after shape reshaping obtained in Step 2, determine the aggregate particle size using the method in Step (1.2); For each aggregate model, the aggregate vertex is moved along the straight line established between the aggregate vertex and O, such that the distance between the aggregate vertex and O after the movement is divided by the distance between the aggregate vertex and O before the movement, which is equal to the ratio of the required aggregate particle size to the aggregate particle size before the vertex is moved. This results in aggregate models with different degrees of realism and the required particle size.

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