WO2023116456A1

WO2023116456A1 - Simulation method for shear fracture of deformable object and material simulation method

Info

Publication number: WO2023116456A1
Application number: PCT/CN2022/137665
Authority: WO
Inventors: 钱银玲; 廖祥云; 孙寅紫; 王琼; 王平安
Original assignee: 深圳先进技术研究院
Priority date: 2021-12-21
Filing date: 2022-12-08
Publication date: 2023-06-29
Also published as: CN114462265A

Abstract

The present invention relates to a simulation method for shear fracture of a deformable object, which facilitates medical applications such as virtual operation training and interactive operation planning. A composite finite element model is used to simulate the shape of a deformable object, and when and how to generate new cutting are determined on the basis of Griffith energy minimization, so as to realize interactive virtual cutting simulation. Furthermore, a material simulation method is designed to ensure that the indentation is consistent with a cutter blade and the indentation induces deformation visually, so that a large amount of calculation is avoided.

Description

A simulation method and material simulation method for shear fracture of deformable objects

technical field

The present disclosure relates to surgery simulation, in particular to a shear fracture simulation method and a material simulation method for a deformable object.

Background technique

As the core module of virtual surgery training system, deformable target cutting simulation has been an important research topic. Existing methods focus on solving the three major task simulations of virtual cutting, that is, the simulation of deformed bodies, the detection and processing of collisions, and the integration in the calculation model.

According to the underlying situation deformation model, cutting simulation and other methods can be divided into three categories: grid-based methods, mesh-free methods and adaptive/multi-resolution methods. Among them, grid-based methods can effectively reconstruct cutting elements, the most common one being the finite element method (FEM). In recent years, the application of the extended finite element method to the cutting simulation of the deformation model has been studied to ensure that the deformation behavior near the cut surface is physically correct; the meshless technology reduces the dependence on the simulation mesh. The model employed by the method is represented by a set of mobile nodes that interact according to elastic governing equations. Since the visual quality of simulated objects is closely related to the accuracy of geometric representation, the improvement of visual effect will be accompanied by the steady linear growth of simulation units; and the adaptive multi-resolution method, in which the composite finite element method (CFEM) combines high-resolution visual The mesh is embedded in a fine hexahedral mesh and enables branching analysis.

No matter what kind of shearing simulation method is used, most of the existing shearing simulation methods follow the "intersection is fracture" mode, that is, as long as the cutting edge intersects with the object, cutting fracture will occur, and real software generally has a certain degree of fracture resistance. Ability, when the tool is pressed on the soft tissue, indentation usually occurs first, and tissue fracture occurs when the pressing energy accumulates to a certain extent. Therefore, there is a big gap between the existing shearing simulation results and the real soft body shearing phenomenon.

Contents of the invention

In view of this, the main purpose of the present application is to provide a highly realistic virtual cutting fracture simulation method and/or device for simulating the high-realistic cutting phenomenon of the fracture resistance of deformed objects.

In one aspect, the present invention proposes a method for simulating shear fracture of a deformable object, said method comprising the following steps:

S100. Simulating the shape of the deformable object based on the composite finite element model to obtain a connected mesh, and embedding the original object surface on the connected mesh to obtain a visualized mesh of the deformable object;

The establishment method of the composite finite element model is as follows: first import the model of the deformable object into the world coordinate system, make its center of gravity coincide with the origin of the world coordinate system, and then normalize the model; then construct the axisymmetric cube of the model , according to the first grid resolution, divide a cube surrounding the deformable object into several first grids, and store the information of each first grid; then according to the second grid resolution, divide each first grid dividing into second grids according to the second grid resolution, storing the second grid information; connecting the center points of adjacent second grids to form a connected grid;

S200. If cutting occurs, update the stored information of the first mesh, the second mesh and the connected mesh, combine to generate a cut surface, and reconstruct the visualized mesh.

Preferably, in the method, the update includes the following steps:

S201. Acquire grid nodes of the simulated tool, and acquire grid nodes of the second grid;

S202. Use wide phase collision detection to determine whether the grid nodes of the simulated tool overlap with the grid nodes of the second grid, and if so, execute S203; otherwise, execute S204;

S203. Obtain each point on the connection that intersects with the simulated tool, and then obtain the sign field distance value of the point, and execute S204;

S204. Obtain each visualized grid node, use wide phase collision detection to determine the first grid penetrated by the simulated tool, and then determine the penetrated point on the second grid through narrow phase collision detection, and obtain the point The sign field distance value of , execute S205;

S205. Using the signed distance field value of the point to establish an energy function of the connection grid connection, and by making the energy function obtain a minimum value, determine the first grid, the second grid, and the connection on the connection grid that need to update the stored information, Thereby updating the stored information.

Preferably, in the method, the calculation process of the energy function is as follows:

In the formula: t ^* is a pseudo-parameter of time evolution;

is the signed distance field value of the intersection point at the current time, which is the point on the connection intersecting with the tool trajectory;

In the formula: x is any position in the region of the initial undeformed state; Q is the energy density function of the deformable object on the deformed region at time t;

In the formula: S is a symmetric tensor obtained by decomposing Q into poles; I is an identity matrix with the same size as S; μ and λ are coefficients for calculation, and the calculation formula is as follows:

In the formula: E is the Young's modulus set according to the material of the deformable object, and V is Poisson's ratio;

e _g = ∫ _ΩH Ψdx+∫ _ΩD kdx

In the formula: e _g is the energy function, ΩH represents the connection state between all the second grids, Ψ is the energy density of each connection; is an open connection, and k is the energy release rate at which the connection state between the second grids changes from connected to disconnected.

Preferably, in the method, the cut surface is determined by the following steps to determine the grid nodes whose displacement will be changed due to the cutting operation:

Find the point that needs to be projected through the intersection with the simulated tool;

Based on the visualized grid, the triangular grid of these points is obtained, and then the Jacobian matrix of these triangular grids is obtained;

Uniformly sample the simulated blade to obtain sampling points;

For each point to be projected, after calculating the displacement projected to the sampling point of the simulated blade, the sum of the algebraic quality measures of all triangular meshes containing the point to be projected is calculated through the Jacobian matrix;

The location of the point projected onto the simulated tool is determined by minimizing the sum of the algebraic quality measures.

Preferably, in the method, the cut curved surface realizes the generation of section indentation by using B-spline, including the following steps:

Based on control points (x ₀ , y ₀ ), (x ₁ , y ₁ ), (x ₂ , y ₂ ), (x ₃ , y ₃ ), (x ₄ , y ₄ ), (x ₅ , y ₅ ) The indentation adjustment function is constructed using B-splines, where:

x ₀ =0, y ₀ =-a _i ; x ₁ =0.2 cos θ _i , y ₁ =a _i (0.2 sin θ _i -1);

_y2 = γ;

y ₃ =0,

y ₄ =0;

x ₅ =1, y ₅ =0;

Among them: a _i is the displacement of grid node v _i after projection, i is the grid node serial number to be projected, i=1, 2, ..., N, N is the number of nodes to be projected, and the node to be projected is Nodes whose displacement changes due to cutting or pressing;

D is the maximum geodesic distance; γ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation;

Obtain nodes within the maximum geodesic range of grid node v _i , use them as potential adjustment nodes, and continue to obtain nodes within the maximum geodesic range of potential adjustment nodes until the acquired nodes reach the set number;

Substitute the abscissa of the nodes to be adjusted into the indentation adjustment function to obtain the ordinates of these nodes after the indentation is generated, combined with the displacement a _i of the projected point, the new position of the adjusted node can be obtained, update the node information of these grids, and obtain the indentation The generated visualization grid.

Preferably, in the method, the γ is calculated by the following formula:

In the formula: τ is a value set according to the material, and E is Young's modulus.

Preferably, in the method, the maximum geodesic distance is related to the material and is calculated by the following formula:

In the formula, V is Poisson's ratio and E is Young's modulus.

On the other hand, a material simulation method is used to ensure that the indentation is consistent with the tool blade, and the visually plausible indentation-induced deformation avoids extensive calculations. The method adopts B-spline to adjust the generation of indentation, comprising the following steps:

Visual grids of construction materials;

x ₀ =0, y ₀ =-a _i ; x ₁ =0.2 cos θ _i , y ₁ =a _i (0.2 sin θ _i -1);

_y2 = γ;

y ₃ =0,

y ₄ =0;

x ₅ =1, y ₅ =0;

Wherein: a _i is the displacement of the grid node v _i due to pressing, i is the serial number of the grid node, i=1, 2, ..., N, N is the number of nodes affected by pressing;

Preferably, in the material simulation method, the γ is calculated by the following formula:

Finally, the present invention also relates to a terminal device comprising a memory, a processor and a computer program stored in the memory and operable on the processor, characterized in that when the processor executes the computer program Implement the steps of any one of the methods described above.

Compared with the prior art, the present invention adopts a co-rotating linear finite element model to design a frame supporting large deformation of soft objects, and adopts a compound finite element method, which balances simulation accuracy and algorithm efficiency well; cooperates with Griffith The cutting-fracture evolution model of energy conducts interactive virtual cutting simulation, which can determine when and how new cuttings are generated; in particular, a material simulation method is proposed to ensure that the indentation is consistent with the tool blade, and the visually plausible indentation induces Warp to avoid heavy calculations. Therefore, the present invention is very suitable for medical applications such as virtual surgery training and interactive surgery planning.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings that need to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those skilled in the art, other drawings can also be obtained based on these drawings without any creative effort.

Figure 1 is a schematic diagram of the simulation before cutting;

Figure 2 is a schematic diagram of simulation after cutting;

Figure 3. Schematic diagram of the indentation adjustment node involved before cutting with a tool;

Figure 4. Schematic diagram of the change of the indentation adjustment node during the cutting process;

Figure 5. Schematic diagram of the change of the indentation adjustment node after the cutting occurs;

Figure 6 is a schematic diagram of cutting without indentation treatment;

Figure 7. Schematic diagram of the construction of the indentation adjustment area;

Fig. 8 is a schematic diagram of cutting after indentation treatment;

Fig. 9 is a schematic diagram of simulation of cutting changes when cutting using the method of the present invention and using the basic composite finite element model;

Fig. 10 is a schematic diagram of simulation comparison when cutting different materials;

Fig. 11 is a schematic diagram of the simulation of cutting an object from deformation to fracture using another shape tool;

Fig. 12 is a simulation schematic diagram of the cutting change process when the method of the present invention is used to cut the liver arbitrarily;

Fig. 13 is a simulation schematic diagram of the cutting change process when the horse is randomly cut by the method of the present invention;

Fig. 14 is a simulation schematic diagram of the cutting change process when the method of the present invention is used to cut armadillo arbitrarily;

Fig. 15 is a simulation schematic diagram of the cutting change process when the method of the present invention is used to cut rabbits randomly.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the application with reference to the drawings in the embodiments of the application. Apparently, the described embodiments are only some, not all, embodiments of the application. Based on the embodiments in this application, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the scope of protection of this application.

The terms "comprising" and "having" and any variations thereof in the description and claims of this application are intended to cover a non-exclusive inclusion. For example, a process, method, system, product, or device comprising a series of steps or devices is not necessarily limited to those steps or devices explicitly listed, but may include steps or devices not expressly listed or for those processes, methods, products, or Other steps or devices inherent to the device.

In the description of the present application, it should be noted that the terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features . Thus, a feature defined as "first" and "second" may explicitly or implicitly include one or more of these features.

In a liver cutting simulation example, the simulation cutting experiment is carried out by the following method. The cross-sectional views perpendicular to the incision direction are shown in Figure 1 and Figure 2, Figure 1 is a schematic diagram before cutting, and Figure 2 is a cross-section after cutting picture. In this embodiment, the simulation takes the following steps:

In the above steps, the establishment method of the composite finite element model is: first import the model of the deformable object into the world coordinate system, make its center of gravity coincide with the origin of the world coordinate system, and then normalize the model; then construct For the axisymmetric cube of the model, according to the first grid resolution, a cube surrounding the deformable object is divided into several first grids, and the information of each first grid is stored; then, according to the second grid resolution, each A first grid is divided into a second grid according to the second grid resolution, and information of the second grid is stored; center points of adjacent second grids are connected to form a connected grid. The stored mesh information includes node information, and the connection mesh needs to store the intersection points and normals that intersect with the surface of the original object.

The first grid is mainly used for deformation calculation, and the higher dispersion ensures the real-time performance of the method. The second grid is used to approximate the actual shape of the object, and can represent the connection of each part of the object. Using the intersection of the lines between the original object surface and the second mesh, the visualized mesh can be obtained, which can represent the object itself more finely. Thus, the first grid spatially contains the second grid, the visualization grid. Preferably, the first grid is a hexahedron, and the second grid is a hexahedron. The original object surface consists of a triangular mesh.

In the cutting simulation process of variable objects, it is first necessary to determine the time when the cutting occurs, and the visual grid is simulated to show that the cut is broken. In the process of notch breaking, there will be two kinds of collisions. One is a collision between a knife and a deformable object, and the other is a collision between broken tissues of a deformable object. Therefore, the present invention uses a hash table in the simulation, puts the object to be detected into the space hash table, and combines the wide phase detection method to judge whether they overlap in space, that is, the tool, the deformable object, and the deformable object itself , Whether the disconnected tissues of the deformable object overlap on the relevant nodes. If there is a collision between the cutter and the deformable object, the simulated incision is broken, or there is a collision between broken tissues, which first grids are simulated to penetrate, and the specific position of the penetration is determined. When the notch is disconnected, the notch simulation is performed by updating the deformed node information. So for the coincident point in the collision, it may be the point where the deformation occurs. Using the distance value of the sign field at this point, establish the energy function of the connection grid connection, by making the energy function obtain the minimum value, determine the first grid, the second grid and the connection on the connection grid that need to update the stored information, so that update storage information,

The present invention is as follows to the computing process of energy function:

In the formula: t ^* is a pseudo-parameter of time evolution;

e _g = ∫ _ΩH Ψdx+∫ _ΩD kdx

The above process is to find the point that will be deformed due to the cutting pressure, but the simulation of the cut also needs to know the cutting depth. In one embodiment, the simulation of the depth of cut is realized in the following manner, namely: through the intersection with the simulated tool, find the points that need to be projected; based on the visualized grid, obtain the triangular mesh of these points, and then obtain these The Jacobian matrix of the triangular grid; uniformly sample the simulated blade to obtain sampling points; for each point to be projected, after calculating the displacement of its projection to the sampled point of the simulated blade, calculate all the points containing the point to be projected through the Jacobian matrix The sum of the algebraic quality measures of the triangular mesh; by minimizing the sum of the algebraic quality measures, the location of the point projected onto the simulated tool is determined. The process of this embodiment is shown in Figure 3-5. In Figure 3-5, Blade curve is the tool sampling point, which is obtained by uniformly sampling the edge of the simulated tool. Contact region vertice is a point that may need to be projected through the intersection with the tool. For a triangular mesh containing these points, construct the Jacobian matrix. Further, for all points that may need to be projected, calculate the distance from the point to the sampling point of the blade, which is the projection. The sum of the algebraic quality measures of all triangular meshes containing the point to be projected is calculated through the Jacobian matrix, and the point where the sum of the algebraic quality measures has the minimum value is the final determined projection point. The Local coordinate system is a coordinate system established according to the projected position. Local mesh that may need to adjust is the need to adjust the position visualization grid shown in the figure. Approximate indentation curve is an approximate concave knife edge.

If the cutting edge is not processed, the above simulated cutting edge is shown in Figure 6. As long as the cutting blade intersects with the model, cutting fracture will occur, which is different from the actual cutting experience. With an elastic surface, there will be no edges and corners after cutting, and there will be no significant discontinuity from the uncut part to the edge of the cut, as shown in Figure 7. In order to more realistically simulate the cutting edge and improve the simulation efficiency, the present invention proposes a material simulation method. The method uses the maximum geodesic distance related to the material parameters to find the vertex that needs to be deformed near the indentation, and realizes the simulation of the deformation and/or cutting process of objects with different hardness through the deformation model related to the material parameters.

In this deformation model, firstly, the visualization mesh of the material is constructed, and the construction method preferably adopts the method based on the composite finite element model in the above-mentioned simulation method for shear fracture of deformable objects. Second, based on the control points (x ₀ , y ₀ ), (x ₁ , y ₁ ), (x ₂ , y ₂ ), (x ₃ , y ₃ ), (x ₄ , y ₄ ), (x ₅ , y ₅ ), using B-splines to construct the indentation adjustment function, where: x ₀ =0, y ₀ =-a _i ; x ₁ =0.2 cos θ _i , y ₁ =a _i (0.2 sin θ _i -1);

_y2 = γ;

y ₃ =0,

y ₄ =0; x ₅ =1, y ₅ =0. Among them: a _i is the displacement of the grid node v _i due to pressing, i is the serial number of the grid node, i=1, 2, ..., N, N is the number of nodes affected by pressing, that is, the number of nodes to be deformed ;

D is the maximum geodesic distance; γ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation; obtain the nodes within the maximum geodesic range of the grid node v _i , Use them as potential adjustment nodes, and continue to obtain nodes within the maximum geodesic range of potential adjustment nodes until the number of acquired nodes reaches the set number; substitute the abscissa of the nodes to be adjusted into the indentation adjustment function, and obtain the The ordinate, combined with the displacement a _i of the projection point, can obtain the new position of the adjustment node, update the node information of these grids, and obtain the visualized grid after the indentation is generated. The deformation caused by indentation is related to the material of the object. The softer the material, the more pronounced the deformation will be. Therefore, the indentation adjustment is used to simulate the deformation of the material after being stressed. In order to be closer to the nature of the material, the maximum geodesic distance D can be calculated by the following formula:

In the formula, V is Poisson's ratio and E is Young's modulus.

Similarly, in order to facilitate the setting of material parameter values, γ is calculated by the following formula:

In the formula: τ is a value set according to the material, and E is the Young's modulus of the material.

Through the application of the above deformation model, the smooth transition between the cut surface and the original object surface can be realized, so that the simulation cut looks more natural and realistic, and the above calculation process can avoid a large number of calculations.

9-15 are comparison diagrams of respective simulation effects of cutting by the present invention.

Fig. 9 is a schematic diagram of the comparison with the simulation results of the basic composite finite element cutting. The first behavior is the basic cutting effect of the compound finite element method, and the second behavior is the intermediate result of crack evolution and indentation generation. The third behavior is based on the compound finite element model, and the simulation effect after further indentation adjustment. Each row of images consists of a front view of the cut effect and a corresponding magnified view. It can be seen from the figure that the shearing simulation in the method of the present invention is more realistic and natural.

Fig. 10 is a schematic diagram of the cutting effect of different materials. This set of comparison graphs shows the simulation effect of three different materials. Every two rows with similar colors represent the simulation effect of a material. The bottom row of these two rows shows the corresponding enlarged view. It can be seen from the figure that the shear simulation in the present invention is applicable to the simulation of different materials and has strong practicability.

Fig. 11 is a set of simulation results of cutting an object from deformation to fracture using another shape tool. The first to third groups are deformation, and the last group is fracture. Each set of images shows a side view of the cutting effect, a corresponding top view, and a partially enlarged view to see the details. It can be seen from these four sets of comparison diagrams that the method of the present invention has no limitation on the shape of the tool, and the cutting effect is still highly realistic.

12-15 are schematic diagrams of cutting process changes when the method of the present invention is used to cut liver, horse, armadillo and rabbit randomly.

It can be seen that the method of the present invention has wide applicability and practicability, can carry out lifelike and natural simulation for objects of any material, any cutter and any shape, and can simulate the real cutting phenomenon of the fracture resistance of deformed objects, It is convenient for medical applications such as virtual surgery training and interactive surgery planning, and has high practical and promotional value.

The above methods can all be realized by a terminal device, the terminal social security includes a memory, a processor, and a computer program stored in the memory and operable on the processor, and the computer program is executed by the processor The program is to realize the steps of any one of the above methods.

Through the description of the above embodiments, those skilled in the art can clearly understand that the disclosed method can also be implemented by means of software plus necessary general-purpose hardware. Memory, special components, etc. to achieve. In general, all functions completed by computer programs can be easily realized by corresponding hardware, and the specific hardware structure used to realize the same function can also be varied, such as analog circuits, digital circuits or special-purpose circuit etc. However, for the purposes of the present disclosure, in most cases, a software program implementation is a preferred embodiment.

To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

A simulation method for shear fracture of a deformable object, characterized in that said method comprises the following steps:

S100. Simulating the shape of the deformable object based on the composite finite element model to obtain a connected mesh, and embedding the original object surface on the connected mesh to obtain a visualized mesh of the deformable object;

The establishment method of the composite finite element model is as follows: first import the model of the deformable object into the world coordinate system, make its center of gravity coincide with the origin of the world coordinate system, and then normalize the model; then construct the axisymmetric cube of the model , according to the first grid resolution, divide a cube surrounding the deformable object into several first grids, and store the information of each first grid; then according to the second grid resolution, divide each first grid dividing into second grids according to the second grid resolution, storing the second grid information; connecting the center points of adjacent second grids to form a connected grid;

S200. If cutting occurs, update the stored information of the first mesh, the second mesh and the connected mesh, combine to generate a cut surface, and reconstruct the visualized mesh.
The method according to claim 1, wherein said updating comprises the following steps:

S201. Acquire grid nodes of the simulated tool, and acquire grid nodes of the second grid;

S202. Use wide phase collision detection to determine whether the grid nodes of the simulated tool overlap with the grid nodes of the second grid, and if so, execute S203; otherwise, execute S204;

S203. Obtain each point on the connection that intersects with the simulated tool, and then obtain the sign field distance value of the point, and execute S204;

S204. Obtain each visualized grid node, use wide phase collision detection to determine the first grid penetrated by the simulated tool, and then determine the penetrated point on the second grid through narrow phase collision detection, and obtain the point The sign field distance value of , execute S205;

S205. Using the signed distance field value of the point to establish an energy function of the connection grid connection, and by making the energy function obtain a minimum value, determine the first grid, the second grid, and the connection on the connection grid that need to update the stored information, Thereby updating the stored information.
The method according to claim 2, wherein the calculation process of the energy function is as follows:

In the formula: t * is a pseudo-parameter of time evolution;
is the signed distance field value of the intersection point at the current time, which is the point on the connection intersecting with the tool trajectory;

In the formula: x is any position in the region of the initial undeformed state; Q is the energy density function of the deformable object on the deformed region at time t;

In the formula: S is a symmetric tensor obtained by decomposing Q into poles; I is an identity matrix with the same size as S; μ and λ are coefficients for calculation, and the calculation formula is as follows:

In the formula: E is the Young's modulus set according to the material of the deformable object, and V is Poisson's ratio;

In the formula: e g is the energy function, ΩH represents the connection state between all the second grids, Ψ is the energy density of each connection; is an open connection, and k is the energy release rate at which the connection state between the second grids changes from connected to disconnected.
The method according to claim 1, wherein the curved surface after the cutting is determined by the following steps to change the grid nodes due to the cutting operation:

Find the point that needs to be projected through the intersection with the simulated tool;

Based on the visualized grid, the triangular grid of these points is obtained, and then the Jacobian matrix of these triangular grids is obtained;

Uniformly sample the simulated blade to obtain sampling points;

For each point to be projected, after calculating the displacement projected to the sampling point of the simulated blade, the sum of the algebraic quality measures of all triangular meshes containing the point to be projected is calculated through the Jacobian matrix;

The location of the point projected onto the simulated tool is determined by minimizing the sum of the algebraic quality measures.
The method according to claim 1, wherein the curved surface after the cutting realizes the generation of section indentation by using B-splines, comprising the following steps:

Based on control points (x 0 , y 0 ), (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ), (x 4 , y 4 ), (x 5 , y 5 ), using B-splines to construct the indentation adjustment function, where:

x 0 =0, y 0 =-a i ; x 1 =0.2 cosθ i , y 1 =a i (0.2 sinθ i -1);

y2 = γ;
y 3 =0,
y 4 =0;

x 5 =1, y 5 =0;

Wherein: a i is the displacement of grid node v i after projection, i is the grid node sequence number to be projected, i=1, 2,..., N; N is the number of nodes to be projected;
D is the maximum geodesic distance; γ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation;

Obtain nodes within the maximum geodesic range of grid node v i , use them as potential adjustment nodes, and continue to obtain nodes within the maximum geodesic range of potential adjustment nodes until the acquired nodes reach the set number;

Substitute the abscissa of the nodes to be adjusted into the indentation adjustment function to obtain the ordinates of these nodes after the indentation is generated, combined with the displacement a i of the projected point, the new position of the adjusted node can be obtained, update the node information of these grids, and obtain the indentation The generated visualization grid.
The method according to claim 5, wherein said γ is calculated by the following formula:

In the formula: τ is a value set according to the material, and E is Young's modulus.
The method according to claim 5, wherein the maximum geodesic distance is related to the material and is calculated by the following formula:

In the formula, V is Poisson's ratio and E is Young's modulus.
A material simulation method, characterized in that, said method adjusts the generation of indentation by adopting B-splines, comprising the steps of:

Visual grids of construction materials;

Based on control points (x 0 , y 0 ), (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ), (x 4 , y 4 ), (x 5 , y 5 ) The indentation adjustment function is constructed using B-splines, where:

x 0 =0, y 0 =-a i ; x 1 =0.2 cosθ i , y 1 =a i (0.2 sinθ i -1);

y2 = γ;
y3 = 0;
y 4 =0;

x 5 =1, y 5 =0;

Wherein: a i is the displacement of the grid node v i due to pressing, i is the serial number of the grid node, i=1, 2, ..., N, N is the number of nodes affected by pressing;
D is the maximum geodesic distance; γ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation;

Obtain nodes within the maximum geodesic range of grid node v i , use them as potential adjustment nodes, and continue to obtain nodes within the maximum geodesic range of potential adjustment nodes until the acquired nodes reach the set number;

Substitute the abscissa of the nodes to be adjusted into the indentation adjustment function to obtain the ordinates of these nodes after the indentation is generated, combined with the displacement a i of the projected point, the new position of the adjusted node can be obtained, update the node information of these grids, and obtain the indentation The generated visualization grid.
The method according to claim 8, wherein said γ is calculated by the following formula:

In the formula: τ is a value set according to the material, and E is Young's modulus.
A terminal device, comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, characterized in that, when the processor executes the computer program, the computer program according to claims 1 to 1 is implemented. 9. The steps of any one of the methods.