Full-process system and method for random asteroid morphology modeling and output

Abstract

The present invention belongs to the technical field of asteroid modeling, and in particular, relates to a full-process system and method for random asteroid morphology modeling and output. The system includes a morphology modeling module and a model output module. The morphology modeling module is used to simulate a random asteroid matrix through a gridded random shape model, control the surface control points of the random asteroid matrix to offset relative to the surface, customize the number and size of different landforms generated, add craters, hills and stones in turn, and simulate irregular undulating landforms through noise functions to obtain a random asteroid model; the model output module is used to view the operation results and model files of each step of the morphology modeling module in a static and dynamic three-dimensional visualization manner, and is also used to print a random asteroid model through a 3D printing device. The present invention can quickly and accurately establish an asteroid morphology model, and output visualization effects and physical objects, thereby improving modeling efficiency and supporting scientific research needs and popular science education in related fields.

Description

Technical Field

[0001] The present invention belongs to the technical field of asteroid modeling, and in particular to a full-process system and method for random asteroid morphology modeling and output. Background Art

[0002] There are a huge number of asteroids in space. Among the asteroids discovered by humans so far, there are more than 30,000 near-Earth asteroids alone. Asteroids have different morphological features (three-dimensional shape + topography), and morphological modeling is an important part of human understanding, detection, research and defense against asteroids.

[0003] In terms of the implementation of asteroid morphology modeling, the current method mainly uses ground-based optical observation data and photometric laws to invert and generate asteroid convex models. However, the resolution and accuracy of modeling by this method are low, and it cannot reflect the actual topography of the asteroid surface. In addition, three-dimensional models can be reconstructed using images taken by probes flying over or around asteroids. However, only a very small number of asteroids, such as 24513Itokawa, 433Eros, and 101955Bennu, have been achieved. Limited by the cost of launch and exploration, only NASA's Lucy probe is expected to fly over and explore 11 asteroids in a single mission in the near future. In fact, most asteroid exploration missions are aimed at a specific asteroid to achieve flyby or flyby exploration.

[0004] In order to generate a large number of virtual asteroid models with high precision and low cost, support simulation verification of multiple technologies (such as disposal optimization simulation of planetary defense, verification of asteroid navigation and landing algorithms, simulation of asteroid terrain evolution, etc.), and meet the needs of asteroid exploration, research and defense, virtual asteroid models can be generated by random simulation methods. For example, using random shape models can generate irregular shapes, and using fractal technology can generate realistic terrain. The most widely used fractal technology is the fractional Brownian motion model, such as random midpoint displacement, fractional noise, Poisson fault, etc. Random midpoint displacement is suitable for simulating boulders, and Poisson faults and noise functions of different frequencies (such as "Perlin noise" and "simplex noise") can be superimposed to simulate various fractal terrains. With the continuous deepening of research, machine learning optimization algorithms have also begun to be used in random asteroid morphology modeling. For example, the AstroGen algorithm uses particle swarm optimization to achieve random asteroid parameter adaptation, optimizes implicit shape representation and noise-based surface terrain respectively, and generates a high-precision model. However, the algorithm spends several hours on machine learning and parameter optimization, which greatly reduces the modeling efficiency.

[0005] In summary, the current research on asteroid morphology modeling has the following problems: 1. The resolution of inversion modeling based on ground-based optical observation data is low; 2. The mission cycle based on flyby or rendezvous detection is long and the cost is high; 3. The current random simulation modeling algorithm is too complex, which greatly increases the difficulty of modeling and reduces the efficiency of modeling. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and propose a full-process system and method for random asteroid morphology modeling and output. A high-precision random asteroid model can be quickly generated, and visualization effects, model files and 3D prints can be output. The invention can support scientific research needs and popular science education in related fields.

[0007] In order to achieve the above-mentioned purpose, the present invention proposes a full-process system for random asteroid morphology modeling and output, including: a morphology modeling module and a model output module, wherein:

[0008] The morphology modeling module is used to simulate a random asteroid matrix through a gridded random shape model, control the surface control points of the random asteroid matrix to offset relative to the surface, customize the number and size of different landforms generated, add craters, hills and rocks in sequence, and simulate irregular undulating landforms through a noise function to obtain a random asteroid model;

[0009] The model output module is used to view the operation results and model files of each step of the morphology modeling module in a static and dynamic three-dimensional visualization manner, and is also used to print random asteroid models through a 3D printing device.

[0010] Preferably, the morphology modeling module includes generating a base unit; the processing of generating the base unit includes: generating a unit sphere of a uniform triangular grid, then randomizing it, adding large grid subdivisions, and thus generating a base of a random asteroid.

[0011] Preferably, the randomization comprises:

[0012] Assume the radius of the random asteroid matrix is θ, is the spherical coordinate parameter, r is the logarithmic radius Indirectly, s is expanded through spherical harmonics to satisfy the following formula:

[0013]

[0014]

[0015] β 2 =ln(σ 2 +1)

[0016] Where a is the average radius of the matrix; β is the standard deviation of the logarithmic radius; σ is the radius The normalized standard deviation of ; l and m are the order and series of spherical harmonics respectively; P lm (cosθ) is the Legendre expansion polynomial; a lm and b lm are spherical harmonic coefficients, and their distributions are independent zero-mean Gaussian random variables with variances of:

[0017]

[0018]

[0019] Among them, when m = 0, δ m0 =1, when m≠0, δ m0 =0;c l is represented by the spherical harmonic function order l and the related angle Γ(deg); i l is the modified Bessel function;

[0020] The three-dimensional shape of the random asteroid matrix is ​​determined based on l, σ and Γ.

[0021] Preferably, the large grid subdivision includes:

[0022] Find the minimum edge length l of the triangle mesh min ;

[0023] Traverse each set of surface control points, if the length of a side exceeds 2l min , then add a midpoint on the edge, update the vertex information, and repeat this step until each set of surface control points has been traversed.

[0024] Preferably, the topography modeling module includes a topography adding unit, and the topography adding unit includes:

[0025] The random asteroid matrix is ​​divided into eight hexagrams. For each hexagram, the following processing is performed on the requirements of the concave or convex topography of the feature landforms of this drama:

[0026] Add craters: Randomly select n grid points on the surface of a random asteroid as the crater center. For each crater, create a concave parabola and find the diameter of the i-th crater. For all grid points within the range, the depth of the crater bottom is The new coordinates of the grid points after the depression in the Cartesian coordinate system are obtained, and the "size-frequency" distribution law of the crater is simulated using the power law distribution;

[0027] Add hills: Randomly select n grid points on the surface of a random asteroid base as the hill centers. For each hill, create a convex parabola and find the diameter of the i-th hill. For all grid points within the range, let the height of the i-th hill be Get the new coordinates of the protruded grid points in the Cartesian coordinate system; use the power law distribution to simulate the "size-frequency" distribution law of the hills;

[0028] Adding stones: Randomly select n grid points on the surface of a random asteroid substrate as the center of the stone. For each stone, create a convex cuboid and find the side length of the i-th stone. For all grid points within the range, let the height of the i-th stone be Get the new coordinates of the protruded grid points in the Cartesian coordinate system; use the power law distribution to simulate the "size-frequency" distribution law of the stone;

[0029] Add Noise: Set the order, frequency and peak value of Perlin noise and add it to the surface of random asteroid substrate to simulate irregular undulating terrain.

[0030] Preferably, the model output module includes outputting a three-dimensional visualization image, a model file and a 3D printout of the random asteroid model.

[0031] On the other hand, the present invention proposes a full-process method for random asteroid morphology modeling and output, which is implemented according to the above system and includes:

[0032] The morphology modeling module simulates a random asteroid matrix through a gridded random shape model. By controlling the offset of the control points on the surface of the random asteroid matrix relative to the surface, the number and size of different landforms generated are customized, craters, hills and rocks are added in sequence, and the irregular undulating landforms are simulated through the noise function to obtain a random asteroid model.

[0033] The model output module uses static and dynamic three-dimensional visualization to provide the operation results of each step of the morphology modeling module, and outputs the random asteroid model to the 3D printing device for printing.

[0034] Compared with the prior art, the advantages of the present invention are:

[0035] The present invention includes the entire process of asteroid modeling and physical object processing. It can quickly and accurately establish an asteroid morphology model and output visualization effects and physical objects, thereby improving modeling efficiency and supporting scientific research needs and popular science education in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a uniform grid unit sphere;

[0037] Figure 2 is a gridded random shape model, where the standard deviations σ of Figure 2(a), Figure 2(b), and Figure 2(c) are 0.3, 0.3, and 0.5 respectively; the correlation angles Γ are 40 degrees, 50 degrees, and 50 degrees respectively;

[0038] Figure 3 It is the effect of adding craters;

[0039] Figure 4 It is the effect of adding hills;

[0040] Figure 5 It is the effect of adding stones;

[0041] Figure 6 It is composed of system modules;

[0042] Figure 7 It is a schematic diagram of the system software interface;

[0043] Figure 8 It is a stochastic modeling three-dimensional visualization effect;

[0044] Fig. 9 This is an example of the effect of 3D printing on asteroids. DETAILED DESCRIPTION

[0045] The present invention proposes a random modeling method based on a grid random shape model combined with a characteristic terrain and landform addition algorithm, and develops a full-process system for asteroid morphology modeling and output. The system can accurately and quickly generate asteroid models, visualize them, and output corresponding 3D printing models.

[0046] In the random modeling module: users can select one of the low, medium, and high density grid unit balls to generate random shapes as the random asteroid matrix, and add craters, hills, rocks and other characteristic landforms on it. In the model output module, the present invention supports output:

[0047] 1. Model building process and final "static + dynamic" 3D visualization effect;

[0048] 2. ".obj" files of models with different mesh densities;

[0049] 3. ".stl" file that can be received by 3D printing equipment;

[0050] 4. Random asteroid model 3D prints.

[0051] The experimental results show that the modeling time under the three grid densities is about 10s, 30s, and 300s respectively, which is much shorter than the several hours of modeling and optimization time required by traditional machine learning algorithms. Taking the asteroid model with an equivalent diameter of 5cm as an example, its 3D printing takes only 37min. In summary, the present invention includes the whole process of asteroid modeling and physical processing, which can quickly and accurately establish the asteroid morphology model, and output the visualization effect and physical object, which improves the modeling efficiency and supports the scientific research needs and popular science education in related fields.

[0052] This paper proposes a random modeling method based on a grid random shape model combined with a characteristic terrain and landform addition algorithm, and develops a full-process system for asteroid morphology modeling and output, which can quickly and accurately establish an asteroid morphology model and output visualization effects and physical objects. The specific technical solution is as follows:

[0053] 1. Introduction to system composition

[0054] The present invention consists of a morphology modeling module and a model output module. The morphology modeling module simulates the random asteroid matrix through a gridded random shape model, and then uses a characteristic terrain and landform addition algorithm to customize the number and size of different landforms generated, and sequentially adds craters, stones, and hills, and simulates irregular undulating landforms through a noise function, thereby simulating the morphological characteristics of random asteroids. The model output module uses a "static + dynamic" three-dimensional visualization method to view the operation results of each step of random modeling, and finally prints the random asteroid model through a 3D printing device to complete the full process of random asteroid morphology modeling and output.

[0055] 2. Random Shape Model

[0056] like Figure 1 The figure shows the unit sphere under the uniform grid. Assume that the radius of the random asteroid matrix is θ, is the spherical coordinate parameter, r is the logarithmic radius Indirectly, s is expanded through spherical harmonics to satisfy the following formula:

[0057]

[0058]

[0059] β 2 =ln(σ 2 +1) (3)

[0060] Where a is the average radius of the matrix; β is the standard deviation of the logarithmic radius; σ is the radius The normalized standard deviation of

[0061] l and m are the order and series of spherical harmonics respectively; Plm (cosθ) is the Legendre expansion polynomial; a lm and b lm are spherical harmonic coefficients, and their distributions are independent zero-mean Gaussian random variables with variances of:

[0062]

[0063]

[0064] Among them, when m = 0, δ m0 =1, when m≠0, δ m0 =0;c l It is represented by the spherical harmonic function order l and the related angle Γ(deg); i l is the modified Bessel function. The three-dimensional shape of the random asteroid matrix is ​​determined according to l, σ and Γ. The final generated grid random shape model effect is shown in Figure 2. Figure 2 (a), Figure 2 (b), Figure 2 (c) The average radius a = 70m, and the spherical harmonic function expansion order l = 10.

[0065] 3. Grid division method

[0066] During the meshing process, a unit sphere of a uniform triangular mesh is first generated, and then it is randomized according to equations (1) to (5) to generate the matrix of the random asteroid.

[0067] It should be noted that the uniform triangular mesh will lead to uneven mesh size during the randomization process, which is more obvious for slender asteroids. To correct this phenomenon, we added a large mesh subdivision process after randomization. This process finds the minimum side length l of the triangular mesh min , and then traverse each set of surface control points. If the length of an edge exceeds 2l min , then add a midpoint on the edge, and finally update the vertex information to reduce the impact of grid unevenness on the subsequent addition of feature landforms.

[0068] 4. Feature terrain and landform addition algorithm

[0069] Characteristic terrain features include craters, hills, rocks, and irregular undulating terrain simulated by Perlin noise. The core idea of ​​the algorithm is to select grid points on the surface of the random shape model and make them offset relative to the surface under geometric constraints to shape the characteristic effect.

[0070] (1) Add craters

[0071] Randomly select n grid points on the surface of a random asteroid as the center of the crater. For each crater, create a concave parabola and find the diameter of the i-th crater All grid points within the range. Assume that the depth of the crater bottom is The horizontal distance between the jth grid point in the i-th crater and the center of the crater is The new coordinates of the grid points after the depression in the Cartesian coordinate system are obtained, and the power law distribution is used to simulate the "size-frequency" distribution law of the crater. The random asteroid matrix is ​​divided into eight hexagrams relative to the mass center. Taking the first hexagram as an example, is the original coordinate of the jth grid point in the i-th crater, then the grid point coordinates after adding the crater are updated to:

[0072]

[0073]

[0074] Among them, for the second to eighth hexagrams, the symbol groups after the first term on the right side of the equal sign should be (+,-,-), (+,+,-), (-,+,-), (-,-,+), (+,-,+), (+,+,+), (-,+,+). For simplicity, a power law distribution function is used to create the "size-frequency" distribution of craters on random asteroids. Assume Distributed in range, then in the diameter interval The number of craters in the area is:

[0075]

[0076] Where k is the power law distribution constant; B is the power law distribution exponent, usually B = 3. The effect of adding craters is as follows Figure 3 A total of 200 craters were added, with a minimum diameter of 5m and a maximum diameter of 35m.

[0077] (2) Adding hills

[0078] Randomly select n grid points on the surface of a random asteroid substrate as the centers of the hills. For each hill, create a convex parabola and find the diameter of the i-th hill For all grid points within the range, let the hill height be The horizontal distance between the jth grid point on the surface of the i-th hill and the center of the hill is The new coordinates of the raised grid points in the Cartesian coordinate system are obtained, and the power law distribution is used to simulate the "size-frequency" distribution law of the hills. The random asteroid matrix is ​​divided into eight quadrants relative to the mass center. Taking the first quadrant as an example, is the original coordinate of the jth grid point on the surface of the i-th boulder; the coordinate of the grid point after adding the hill is updated to:

[0079]

[0080]

[0081] For the second to eighth hexagrams, the symbol groups after the first term on the right side of the equal sign should be (-,+,+), (-,-,+), (+,-,+), (+,+,-), (-,+,-), (-,-,-), (+,-,-). For simplicity, a power law distribution function is used to create the "size-frequency" distribution of hills on random asteroids. Assume Distributed in range, then in the diameter interval The number of craters in the area is:

[0082]

[0083] The effect of adding hills is as follows Figure 4 A total of 1000 hills were added, with a minimum diameter of 10m and a maximum diameter of 12m.

[0084] (3) Add stones

[0085] Randomly select n grid points on the surface of a random asteroid as the center of the stone. For each stone, create a raised cuboid to better show the sharp edges of the stone. Find the side length of the i-th stone All grid points within the range, assuming the stone height is The new coordinates of the raised grid points in the Cartesian coordinate system are obtained, and the power law distribution is used to simulate the "size-frequency" distribution law of the rocks. The random asteroid matrix is ​​divided into eight quadrants relative to the mass center. Taking the first quadrant as an example, is the original coordinate of the jth grid point on the surface of the i-th stone; the coordinate of the jth grid point on the surface of the i-th stone is updated to:

[0086]

[0087]

[0088] For the second to eighth hexagrams, the symbol groups after the first term on the right side of the equal sign should be (-,+,+), (-,-,+), (+,-,+), (+,+,-), (-,+,-), (-,-,-), (+,-,-). For simplicity, a power law distribution function is used to create the "size-frequency" distribution of rocks on random asteroids. Assume Distributed in range, then in the diameter interval The number of craters in the area is:

[0089]

[0090] The effect of adding stones is as follows Figure 5 A total of 2,000 stones were added, with the smallest side length being 2m and the largest side length being 3m.

[0091] (4) Adding noise

[0092] Perlin noise is often used to simulate terrain. It is based on random generation and uses easing curves for smooth interpolation to make the result more natural. However, a single Perlin noise can only simulate monotonous and repetitive terrain, so different Perlin noise combinations can be used to create complex terrain. Set the order, frequency, and peak value of Perlin noise and add it to the surface of a random asteroid matrix to simulate irregular undulating terrain. The basic principle of Perlin noise includes the following three steps:

[0093] 1) Initialize the gradient;

[0094] 2) Establish sampling space;

[0095] 3) Perform interpolation calculation based on the gradient and easing curve of the nearest reference point.

[0096] Perlin noise mainly includes three parameters: order N, frequency f and amplitude a. N represents the superposition of N Perlin noises, which controls the complexity of the landform; f controls the density of landform fluctuations; a controls the degree of landform fluctuations. f and a change with the superposition of noise. Here we use a simple change method, specifically:

[0097]

[0098] The mathematical expression of Perlin noise is as follows:

[0099]

[0100] Among them, p is the proportional coefficient of the amplitude on the continuous order, i represents the i-th superimposed noise function, and n i (x) is a function that generates random values, 2 i Used to control the scale. The process of adding noise is done simultaneously with the process of adding stones.

[0101] 5. Model output implementation

[0102] Random asteroid morphology modeling can output "static + dynamic" three-dimensional visualization effects, ".obj" files, ".stl" files, and 3D prints. The "static + dynamic" three-dimensional visualization effect can directly display the results of random shape generation and feature terrain addition, and can also display the ".obj" model saved by the user in the model library. In addition, the present invention provides a function of converting "obj" files to "stl" files to support 3D printing equipment to receive and print out random asteroid 3D models.

[0103] like Figure 7 The following is a schematic diagram of the system software interface; Figure 8 It is a stochastic modeling three-dimensional visualization effect; Fig. 9 This is an example of the effect of 3D printing on asteroids.

[0104] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0105] Example 1

[0106] Embodiment 1 of the present invention proposes a full-process system for random asteroid morphology modeling and output, which includes the following steps:

[0107] Step 1: Create the base

[0108] Select the matrix mesh density (low, medium, high), set the spherical harmonic expansion coefficient, standard deviation and correlation angle, and generate a random shape model. If the user is not satisfied with the result of the generated matrix, he can adjust the parameters and generate it again, otherwise go to the next step.

[0109] Step 2: Adding Feature Landforms

[0110] Users add craters, hills, and rocks in order, and repeated addition is not supported. When adding each landform, users set its distribution quantity, minimum size, and maximum size. The system defaults to a power-law distribution for the "quantity-size" distribution. In addition, the system automatically adds Perlin noise to simulate landform fluctuations.

[0111] Step 3: Output "static + dynamic" 3D visualization images

[0112] The modeling results of the user creating the base, adding craters, adding hills, and adding stones can be directly output as "static + dynamic" 3D visualization images, so as to intuitively grasp the modeling effect and parameter settings. The ".obj" file output in the fourth step can also be output as a "static + dynamic" 3D visualization image to view the historical modeling results.

[0113] Step 4: Output modeling file

[0114] After completing all modeling processes, if the user wants to save the current modeling results and perform subsequent operations, the model can be saved as an ".obj" file to the specified path. In this step, the user can also open the model library, view and manage all the model files saved in it, and select one of them to convert to a ".stl" file for the 3D printing device to receive.

[0115] Step 5: Output 3D printing solid model

[0116] Import the random asteroid model ".stl" file into the 3D printing device, set the printing parameters, generally control the model equivalent diameter to about 5cm, and perform 3D printing.

[0117] Example 2

[0118] Embodiment 2 of the present invention proposes a full-process method for random asteroid morphology modeling and output, based on the system implementation of embodiment 1, the method includes:

[0119] The morphology modeling module simulates a random asteroid matrix through a gridded random shape model. By controlling the offset of the control points on the surface of the random asteroid matrix relative to the surface, the number and size of different landforms generated are customized, craters, hills and rocks are added in sequence, and the irregular undulating landforms are simulated through the noise function to obtain a random asteroid model.

[0120] The model output module uses static and dynamic three-dimensional visualization to provide the operation results of each step of the morphology modeling module, and outputs the random asteroid model to the 3D printing device for printing.

[0121] Innovation

[0122] 1. A full-process method for random asteroid morphology modeling and output is proposed. The main steps of this method are: create a matrix - add characteristic landforms - output "static + dynamic" 3D visualization images - output modeling files - output 3D printed solid models. In particular, each step of random modeling supports "static + dynamic" 3D visualization, which allows users to evaluate the modeling effect after each step.

[0123] 2. An algorithm for adding characteristic landforms to asteroids is proposed. The algorithm controls the surface control points of the substrate to offset relative to the surface, thereby shaping characteristic landforms. Specifically, the random asteroid substrate is divided into eight hexagrams. For each hexagram, the offset form of the three position components in the Cartesian coordinate system is adjusted according to the requirements of the characteristic terrain "concave" or "convex". Finally, the substrate surface is further irregularized by adding noise.

[0124] 3. Achieved a balance between accuracy and speed in asteroid morphology modeling and output. In view of the problem that the current random asteroid modeling cannot achieve a balance between accuracy and speed, the present invention greatly shortens the modeling time while improving the modeling accuracy as much as possible. Modeling and visual output only take about 30 seconds, and 3D printing depends on the machine speed and model size.

[0125] In view of the defect that the current asteroid morphology modeling cannot take into account both accuracy and speed, the present invention proposes a random modeling method based on a gridded random shape model combined with a characteristic terrain and landform addition algorithm, and develops a full-process system for asteroid morphology modeling and output.

[0126] In the present invention: the user first selects one of the low, medium and high density grids to generate a random shape model as the random asteroid matrix, and the surface control points of the three density grids are approximately 3000, 7500 and 47000 respectively. Then, add craters, hills and stones on the random shape surface in customized quantity and size. Then export and save as the corresponding random asteroid low, medium and high density model ".obj" files, and the model sizes are approximately 1MB, 3MB and 6MB respectively. Finally, it is converted into a ".stl" file that can be received by a 3D printing device and the model is printed. The modeling time under the three grid densities is approximately 10s, 30s and 300s respectively. Under the premise of the default printing of the asteroid equivalent diameter of about 5cm, the printing time is within 1h.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A full-process system for random asteroid morphology modeling and output, characterized in that: include: Morphology modeling module and model output module, among which, The morphology modeling module is used to simulate a random asteroid matrix through a gridded random shape model, control the surface control points of the random asteroid matrix to offset relative to the surface, customize the number and size of different landforms generated, add craters, hills and rocks in sequence, and simulate irregular undulating landforms through a noise function to obtain a random asteroid model; The model output module is used to view the operation results and model files of each step of the morphology modeling module in a static and dynamic three-dimensional visualization manner, and is also used to print a random asteroid model through a 3D printing device; The morphology modeling module includes generating a base unit; the processing of generating the base unit includes: generating a unit sphere of a uniform triangular grid, then randomizing, adding large grid subdivisions, thereby generating a base of a random asteroid; The randomization includes: Assume the radius of the random asteroid matrix is θ, is the spherical coordinate parameter, r is the logarithmic radius Indirectly, s is expanded through spherical harmonics to satisfy the following formula: b 2 =ln(σ 2 +1) Where a is the average radius of the matrix; β is the standard deviation of the logarithmic radius; σ is the radius The normalized standard deviation of ; l and m are the order and series of spherical harmonics respectively; P lm (cosθ) is the Legendre expansion polynomial; a lm and b lm are spherical harmonic coefficients, and their distributions are independent zero-mean Gaussian random variables with variances of: Among them, when m = 0, δ m0 =1, when m≠0, δ m0 =0;c l is the spherical harmonic function order l and the related angle Γ, in degrees; i l is the modified Bessel function; The three-dimensional shape of the random asteroid matrix is ​​determined based on l, σ and Γ.

2. The full-process system for random asteroid morphology modeling and output according to claim 1, characterized in that: The large grid subdivision includes: Find the minimum edge length l of the triangle mesh min ; Traverse each set of surface control points, if the length of a side exceeds 2l min , then add a midpoint on the edge, update the vertex information, and repeat this step until each set of surface control points has been traversed.

3. The full-process system for random asteroid morphology modeling and output according to claim 1, characterized in that: The topography modeling module includes a topography adding unit, and the topography adding unit includes: The random asteroid matrix is ​​divided into eight hexagrams. For each hexagram, the following processing is performed on the requirements of the concave or convex topography of the feature landforms of this drama: Add craters: Randomly select n grid points on the surface of a random asteroid as the crater center. For each crater, create a concave parabola and find the diameter of the i-th crater. For all grid points within the range, the depth of the crater bottom is Get the new coordinates of the grid points after the depression in the Cartesian coordinate system, and use the power law distribution to simulate the "size-frequency" distribution law of the crater; Add hills: Randomly select n grid points on the surface of a random asteroid base as the hill centers. For each hill, create a convex parabola and find the diameter of the i-th hill. For all grid points within the range, let the height of the i-th hill be Get the new coordinates of the protruded grid points in the Cartesian coordinate system; use the power law distribution to simulate the "size-frequency" distribution law of the hills; Adding stones: Randomly select n grid points on the surface of a random asteroid substrate as the center of the stone. For each stone, create a convex cuboid and find the side length of the i-th stone. For all grid points within the range, let the height of the i-th stone be Get the new coordinates of the protruded grid points in the Cartesian coordinate system; use the power law distribution to simulate the "size-frequency" distribution law of the stones; Add Noise: Set the order, frequency and peak value of Perlin noise and add it to the surface of random asteroid substrate to simulate irregular undulating terrain.

4. The full-process system for random asteroid morphology modeling and output according to claim 1, characterized in that: The model output module includes outputting a three-dimensional visual image, a model file and a 3D printout of a random asteroid model.

5. A full-process method for random asteroid morphology modeling and output, implemented by the system according to any one of claims 1 to 4, characterized in that: The method comprises: The morphology modeling module simulates a random asteroid matrix through a gridded random shape model. By controlling the offset of the control points on the surface of the random asteroid matrix relative to the surface, the number and size of different landforms generated are customized, craters, hills and rocks are added in sequence, and the irregular undulating landforms are simulated through the noise function to obtain a random asteroid model. The model output module uses static and dynamic three-dimensional visualization to provide the operation results of each step of the morphology modeling module, and outputs the random asteroid model to the 3D printing device for printing.

Images