Controllable random porous structure modeling method based on fractal Brownian motion

Abstract

The invention provides a controllable random porous structure modeling method based on fractal Brownian motion, and the method comprises the steps: carrying out the grid division of a three-dimensional space, and obtaining a regular grid; based on the regular grid, low-frequency noise is generated through the Berlin noise; limiting the structural range of the regular grid through Simplex noise, and generating high-frequency noise; performing noise superposition on the low-frequency noise and the high-frequency noise to obtain fractal Brownian motion; determining a value of an implicit field through fractal Brownian motion; the contour surface of the implicit field is extracted through a Marking Cubes algorithm, and a complete grid is obtained; and carrying out visual display on the complete grid to obtain a modeling model. According to the method, an implicit field with statistical self-similarity and multi-scale characteristics is generated through multi-layer noise superposition, and the complexity of a natural porous structure is perfectly met. And high-flexibility pore control is realized through parameters such as frequency gain, amplitude attenuation and a threshold value, and the calculation efficiency is remarkably improved.

Description

Technical Field

[0001] The invention relates to the technical field of geometric modeling and computer graphics, and in particular to a controllable random porous structure modeling method based on fractal Brownian motion. Background Art

[0002] Existing porous structure modeling technologies mainly include methods based on regular geometry, random point distribution, and classical mathematical models, but all of them have significant limitations. The regular geometry method generates a single structural shape and lacks natural randomness; although the random point distribution method has a certain degree of randomness, it lacks the ability to express details and multi-scales; although classical mathematical models (such as TPMS) generate continuous and smooth structures, the pore distribution is too regular, making it difficult to truly simulate the complex morphology of bone tissue. In addition, these methods also have obvious deficiencies in parameter adjustment flexibility and high-resolution computational efficiency. Therefore, it is very necessary to design a controllable random porous structure modeling method based on fractal Brownian motion. Summary of the Invention

[0003] The purpose of the present invention is to provide a controllable random porous structure modeling method based on fractal Brownian motion. By superimposing multiple layers of noise, an implicit field with statistical self-similarity and multi-scale characteristics is generated, and pore control is achieved through various parameters to improve the computational efficiency and flexibility of pore control.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A controllable random porous structure modeling method based on fractal Brownian motion comprises the following steps:

[0006] Gridding the three-dimensional space to obtain a regular grid;

[0007] Generate low-frequency noise using Perlin noise based on a regular grid;

[0008] Simplex noise is used to limit the structural range of regular grids and generate high-frequency noise;

[0009] The low-frequency noise and high-frequency noise are superimposed to obtain fractal Brownian motion;

[0010] Determine the value of the implicit field through fractal Brownian motion;

[0011] The implicit field is extracted using the Marching Cubes algorithm to obtain a complete grid.

[0012] The complete mesh is visualized to obtain the modeling model.

[0013] Alternatively, the expression for Perlin noise is: Among them, w(i,j,k) is the interpolation weight function, g ijk is the random gradient vector of the regular grid nodes, <·,·> is the dot product operation, p is a point in the regular grid, and p ijk are the coordinates of the discrete grid nodes.

[0014] Alternatively, the expression for Simplex noise is: Among them, g i is the gradient vector of the structure vertex, p i are the coordinates of the simplex vertices, x is the input point, and n is the number of structure vertices.

[0015] Alternatively, the expression for fractal Brownian motion is: Among them, α i is the amplitude attenuation factor, β i is the frequency gain factor, and N is the number of superimposed layers.

[0016] Optionally, the value of the implicit field is determined by fractal Brownian motion, specifically: the fractal Brownian motion is used as the implicit field function, and the value of the implicit field is calculated by the implicit field function; the calculation formula of the implicit field value is: F(x,y,z)=FBM(x,y,z)-T; where FBM(x,y,z) is fractal Brownian motion and T is the isosurface threshold.

[0017] Optionally, the implicit field isosurface is extracted using the Marching Cubes algorithm to obtain a complete mesh, including:

[0018] Regularly divide the three-dimensional space to generate a cube grid;

[0019] Calculate the value of the implicit field at each cube vertex in the cube mesh;

[0020] Determine the topology of the isosurface based on the value of the implicit field and generate triangular fragments;

[0021] The triangle segments are stitched together to form a complete mesh.

[0022] Optionally, the value of the implicit field at each cube vertex in a cube mesh is calculated as:

[0023] Where gain represents the amplitude attenuation ratio of each layer of noise relative to the previous layer, lacunarity is a control parameter for the degree of void sparsity and the growth rate of the structural scale, scale is the initial frequency factor, T is the isosurface threshold, and N is the number of superimposed layers.

[0024] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the present invention provides a controllable random porous structure modeling method based on fractal Brownian motion, the method comprising: meshing the three-dimensional space to obtain a regular grid; based on the regular grid, generating low-frequency noise through Perlin noise; limiting the structural range of the regular grid through Simplex noise and generating high-frequency noise; superimposing the low-frequency noise and the high-frequency noise to obtain fractal Brownian motion; determining the value of the implicit field through fractal Brownian motion; extracting the isosurface of the implicit field through the Marching Cubes algorithm to obtain a complete grid; visualizing the complete grid to obtain a modeling model. This method generates an implicit field with statistical self-similarity and multi-scale characteristics by superimposing multiple layers of noise, which perfectly matches the complexity of natural porous structures. It also achieves highly flexible pore control through parameters such as frequency gain, amplitude attenuation and threshold, significantly improving computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0026] Figure 1 This is a flow chart of the random porous structure modeling method of the present invention;

[0027] Figure 2 Generate a flow chart for the complete grid of the present invention;

[0028] Figure 3 It is a three-dimensional schematic diagram of the modeling model of the present invention;

[0029] Figure 4 It is a side schematic diagram of the modeling model of the present invention. DETAILED DESCRIPTION

[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0031] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] like Figure 1As shown, the present invention provides a controllable random porous structure modeling method based on fractal Brownian motion, comprising the following steps:

[0033] Step 100: Meshing the three-dimensional space to obtain a regular grid;

[0034] Specifically, the spatial range of the three-dimensional space is (-L x ,L x )×(-L y ,L y )×(-L z ,L z ), where L is the boundary length of the spatial domain, which is used to define the size of the three-dimensional space and is not specifically limited in this embodiment.

[0035] Step 200: Generate low-frequency noise using Perlin noise based on a regular grid;

[0036] Specifically, Perlin noise generates random gradients on regular grid nodes and generates smooth noise values ​​through interpolation calculation. The expression of Perlin noise is:

[0037]

[0038] Among them, w(i,j,k) is the interpolation weight function, g ijk is the random gradient vector of the regular grid nodes, <·,·> is the dot product operation, p is a point in the regular grid, and p ijk are the coordinates of the discrete grid nodes.

[0039] It should be noted that the low-frequency noise generated by Perlin noise has good continuity and low-frequency characteristics, and can generate natural textures and forms.

[0040] Step 300: limiting the structural range of the regular grid by using Simplex noise and generating high-frequency noise;

[0041] Specifically, Simplex noise is calculated by replacing the cube grid with positive simplexes (such as triangles in two dimensions or tetrahedrons in three dimensions), which significantly reduces the computational complexity in high-dimensional space. The expression of Simplex noise is:

[0042]

[0043] Among them, g i is the gradient vector of the structure vertex, p i is the coordinate of the simplex vertex, x is the input point, n is the number of structure vertices, xp i is the offset between the input point and the current vertex, the dot product g i·(xp i ) is used to calculate the contribution of gradients and input points.

[0044] It should be noted that the calculation method of simplex noise in three-dimensional or higher-dimensional space is similar to that in two-dimensional space. The computational complexity can be reduced by simply using higher-dimensional simplexes.

[0045] Step 400: Superimposing low-frequency noise and high-frequency noise to obtain fractal Brownian motion;

[0046] Fractal Brownian motion is an extension of standard Brownian motion. It controls the geometric characteristics of motion by introducing the Hurst exponent into the standard Brownian motion, and generates a field with statistical self-similarity and multi-scale characteristics, making the motion trajectory of the geometric characteristics richer.

[0047] Furthermore, the expression of standard Brownian motion is: Where η(τ) is zero-mean Gaussian white noise, and B(t) is the random trajectory corresponding to time t. The definition of fractal Brownian motion is: Where H is the fractal dimension control factor, with a value of (0, 1). When H = 0.5, the motion trajectory is standard Brownian motion; when H > 0.5, the motion trajectory exhibits persistence (i.e., trend continuation); when H < 0.5, the motion trajectory exhibits anti-persistence (i.e., trend reversal).

[0048] Specifically, the expression of fractal Brownian motion in this embodiment is:

[0049]

[0050] Among them, α i is the amplitude attenuation factor, α i =gain i , which decreases with the power of gain as the number of layers i is used to control the intensity of the noise in each layer, β i is the frequency gain factor, β i =scale·lacunarity i , which increases with the number of layers i according to the power of lacunarity, is used to control the scale of each layer of noise. N is the number of superimposed layers, which is used to control the detail richness of the noise. Scale is the initial frequency factor.

[0051] It should be noted that Perlin noise is used to generate a smooth base texture at low dimensions, while Simplex noise is used at high dimensions to improve computational efficiency and ensure that the generated structure has more natural texture characteristics. By switching the dimensions of the two noise processing methods, the periodicity problem that may occur with a single noise is avoided. Furthermore, the noise superposition method discretizes the global integral properties of fractal Brownian motion in physics while preserving the statistical self-similarity and multi-scale properties.

[0052] Step 500: Determine the value of the implicit field through fractal Brownian motion;

[0053] Specifically, in three-dimensional space, fractal Brownian motion is used as an implicit field function to describe the properties of a point (such as a pore or solid), and the implicit field value is calculated by the implicit field function. The implicit field value is calculated as follows:

[0054] F(x,y,z)=FBM(x,y,z)-T;

[0055] Among them, FBM(x, y, z) is fractal Brownian motion, and T is the isosurface threshold, which is used to control the size and distribution density of pores.

[0056] Step 600: Extract the isosurface of the implicit field by the Marching Cubes algorithm to obtain a complete grid; the specific steps are as follows: Figure 2 As shown, including:

[0057] Step 601: Regularly divide the three-dimensional space to generate a cube grid;

[0058] Step 602: Calculate the implicit field value of each cube vertex in the cube mesh;

[0059] Specifically, the implicit field value of each cube vertex in the cube mesh is calculated as:

[0060]

[0061] Among them, gain represents the amplitude attenuation ratio of each layer of noise relative to the previous layer. The smaller its value, the weaker the impact of the noise in the subsequent layers. Lacunarity is an important parameter that controls the sparsity of voids and the growth rate of the structural scale in the fractal structure. It is used to control the growth rate of noise frequency with the number of layers. The larger its value, the richer the details of the model. The parameters scale and T can be used to achieve precise adjustment of global and local pore characteristics.

[0062] Step 603: Determine the topology of the isosurface according to the value of the implicit field and generate triangle segments;

[0063] Specifically, first read the scalar values ​​of the 8 vertices of the cube mesh respectively, convert the scalar values ​​above the isosurface threshold (0 in this embodiment) into Boolean values, and then re-encode them into an 8-bit binary number (ranging from 0 to 255). By searching the edgeTable table and the triTable table, the position and form of the intersection of the current cube mesh and the isosurface are determined, such as which edges are passed through and the combination of triangles. Then, the intersection coordinates of the edges passed through by the isosurface are calculated by linear interpolation. Finally, the intersection coordinates are connected into triangular faces according to the edge combination recorded in the triTable table, thereby obtaining triangle fragments.

[0064] More specifically, the linear interpolation method is expressed as:

[0065]

[0066] Among them, v1 and v2 are the edge endpoint coordinates, and f1 and f2 are the scalar values ​​of the corresponding edge endpoint coordinates.

[0067] Step 604: stitch the triangle segments together to obtain a complete mesh.

[0068] Specifically, all the triangle fragments of the cube are aggregated and the vertex indices are unified, and then spliced ​​into a continuous closed triangle mesh model, thereby forming the required porous structure surface (ie, a complete mesh).

[0069] Step 700: Visualize the complete grid to obtain a model.

[0070] like Figure 3 and Figure 4 As shown, this embodiment uses PyVista to visualize the generated complete mesh, and the exported model is a standard 3D file.

[0071] The beneficial effects of the present invention are as follows:

[0072] 1) By superimposing multiple layers of noise, the non-periodic distribution of pores is achieved while preserving the multi-scale characteristics, reflecting the different scale changes from coarse to fine in the model;

[0073] 2) Make the pore network of the model more natural and complex, which is more in line with the requirements of bone tissue engineering for pore structure complexity, controllability and diversity;

[0074] 3) By adjusting the frequency gain, amplitude attenuation factor, and threshold parameters in the fractal Brownian motion, greater flexibility and precise control are provided, enabling the pore size, distribution density, and connectivity of the porous structure to be finely tuned while also improving computational efficiency.

[0075] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0076] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A controllable random porous structure modeling method based on fractal Brownian motion, characterized in that: The steps include: Gridding the three-dimensional space to obtain a regular grid; Based on the regular grid, generating low-frequency noise by Perlin noise; Limiting the structural range of the regular grid by using Simplex noise and generating high-frequency noise; Superimposing the low-frequency noise and the high-frequency noise to obtain a fractal Brownian motion; determining a value of an implicit field through the fractal Brownian motion; Extracting the isosurface of the implicit field by the Marching Cubes algorithm to obtain a complete grid; The complete grid is visualized to obtain a modeling model.

2. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 1, characterized in that: The expression of the Perlin noise is: Among them, w(i,j,k) is the interpolation weight function, g ijk is the random gradient vector of the regular grid nodes, <·,·> is the dot product operation, p is a point in the regular grid, and p ijk are the coordinates of the discrete grid nodes.

3. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 1, characterized in that: The expression of the Simplex noise is: Among them, g i is the gradient vector of the structure vertex, p i are the coordinates of the simplex vertices, x is the input point, and n is the number of structure vertices.

4. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 1, characterized in that: The expression of the fractal Brownian motion is: Among them, α i is the amplitude attenuation factor, β i is the frequency gain factor, and N is the number of superimposed layers.

5. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 1, characterized in that: The value of the implicit field is determined by the fractal Brownian motion, specifically: the fractal Brownian motion is used as the implicit field function, and the value of the implicit field is calculated by the implicit field function; the calculation formula of the value of the implicit field is: F(x,y,z)=FBM(x,y,z)-T; wherein FBM(x,y,z) is the fractal Brownian motion, and T is the isosurface threshold.

6. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 1, characterized in that: The isosurface of the implicit field is extracted using the Marching Cubes algorithm to obtain a complete mesh, including: Regularly dividing the three-dimensional space to generate a cubic grid; Calculating a value of the implicit field at each cube vertex in the cube mesh; Determining the topological form of the isosurface according to the value of the implicit field and generating triangular segments; The triangle segments are spliced ​​together to obtain the complete mesh.

7. The controllable random porous structure modeling method based on fractal Brownian motion according to claim 6, characterized in that: The implicit field value of each cube vertex in the cube grid is calculated as: Where gain represents the amplitude attenuation ratio of each layer of noise relative to the previous layer, lacunarity is a control parameter for the degree of void sparsity and the growth rate of the structural scale, scale is the initial frequency factor, T is the isosurface threshold, and N is the number of superimposed layers.

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