WO2023116456A1 - 一种用于可变形物体剪切断裂的仿真方法及材料仿真方法 - Google Patents

一种用于可变形物体剪切断裂的仿真方法及材料仿真方法 Download PDF

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WO2023116456A1
WO2023116456A1 PCT/CN2022/137665 CN2022137665W WO2023116456A1 WO 2023116456 A1 WO2023116456 A1 WO 2023116456A1 CN 2022137665 W CN2022137665 W CN 2022137665W WO 2023116456 A1 WO2023116456 A1 WO 2023116456A1
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grid
nodes
indentation
point
node
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钱银玲
廖祥云
孙寅紫
王琼
王平安
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Shenzhen Institute of Advanced Technology of CAS
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations

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  • the present disclosure relates to surgery simulation, in particular to a shear fracture simulation method and a material simulation method for a deformable object.
  • 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.
  • cutting simulation and other methods can be divided into three categories: grid-based methods, mesh-free methods and adaptive/multi-resolution methods.
  • grid-based methods can effectively reconstruct cutting elements, the most common one being the finite element method (FEM).
  • FEM finite element method
  • 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.
  • 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
  • CFEM composite finite element method
  • 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.
  • the present invention proposes a method for simulating shear fracture of a deformable object, said method comprising the following steps:
  • 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;
  • the update includes the following steps:
  • the calculation process of the energy function is as follows:
  • 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;
  • 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
  • S is a symmetric tensor obtained by decomposing Q into poles
  • I is an identity matrix with the same size as S
  • ⁇ and ⁇ are coefficients for calculation, and the calculation formula is as follows:
  • E is the Young's modulus set according to the material of the deformable object, and V is Poisson's ratio;
  • e g is the energy function
  • ⁇ H represents the connection state between all the second grids
  • ⁇ is the energy density of each connection
  • k is the energy release rate at which the connection state between the second grids changes from connected to disconnected.
  • the cut surface is determined by the following steps to determine the grid nodes whose displacement will be changed due to the cutting operation:
  • the triangular grid of these points is obtained, and then the Jacobian matrix of these triangular grids is obtained;
  • the location of the point projected onto the simulated tool is determined by minimizing the sum of the algebraic quality measures.
  • the cut curved surface realizes the generation of section indentation by using B-spline, including the following steps:
  • the indentation adjustment function is constructed using B-splines, where:
  • a i is the displacement of grid node v i after projection
  • N is the number of nodes to be projected
  • the node to be projected is Nodes whose displacement changes due to cutting or pressing
  • D is the maximum geodesic distance
  • ⁇ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation
  • the ⁇ is calculated by the following formula:
  • ⁇ is a value set according to the material, and E is Young's modulus.
  • the maximum geodesic distance is related to the material and is calculated by the following formula:
  • V Poisson's ratio
  • E Young's modulus
  • 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:
  • the indentation adjustment function is constructed using B-splines, where:
  • a i is the displacement of the grid node v i due to pressing
  • D is the maximum geodesic distance
  • ⁇ is a material-related parameter, which can be adjusted to adjust the displacement change of the control node due to indentation
  • the ⁇ is calculated by the following formula:
  • ⁇ is a value set according to the material, and E is Young's modulus.
  • 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.
  • 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.
  • 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
  • FIG. 1 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.
  • 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 .
  • a feature defined as “first” and “second” may explicitly or implicitly include one or more of these features.
  • 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
  • Figure 2 is a cross-section after cutting picture.
  • the simulation takes the following 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.
  • the first grid spatially contains the second grid, the visualization grid.
  • the first grid is a hexahedron
  • the second grid is a hexahedron.
  • the original object surface consists of a triangular mesh.
  • 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.
  • 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.
  • 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:
  • 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;
  • 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
  • S is a symmetric tensor obtained by decomposing Q into poles
  • I is an identity matrix with the same size as S
  • ⁇ and ⁇ are coefficients for calculation, and the calculation formula is as follows:
  • E is the Young's modulus set according to the material of the deformable object, and V is Poisson's ratio;
  • e g is the energy function
  • ⁇ H represents the connection state between all the second grids
  • ⁇ is the energy density of each connection
  • k is the energy release rate at which the connection state between the second grids changes from connected to disconnected.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • a i is the displacement of the grid node v i due to pressing
  • N is the number of nodes affected by pressing, that is, the number of nodes to be deformed
  • D is the maximum geodesic distance
  • ⁇ 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 maximum geodesic distance D can be calculated by the following formula:
  • V Poisson's ratio
  • E Young's modulus
  • ⁇ is calculated by the following formula:
  • ⁇ is a value set according to the material
  • E is the Young's modulus of the material.
  • 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
  • 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.
  • 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 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.

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Abstract

本公开涉及一种用于可变形物体的剪切断裂的仿真方法，方便虚拟手术训练和交互式手术规划等医学应用。通过采用复合有限元模型实现对可变形物体的外形进行模拟，基于格里菲斯能量最小化来确定何时以及如何产生新的切割，以实现交互式虚拟切削模拟；进一步地，通过设计一种材料仿真的方法，来保证压痕与刀具刀片一致，以及视觉上似是而非的压痕诱导变形，以避免大量的计算。

Description

一种用于可变形物体剪切断裂的仿真方法及材料仿真方法 技术领域
本公开涉及手术仿真，具体涉及一种用于可变形物体剪切断裂仿真方法及材料仿真方法。
背景技术
作为虚拟外科训练系统的核心模块，可变形目标切割仿真一直是一项重要的研究课题。现有方法重点在于解决虚拟切削的三大任务模拟，即变形体的模拟，碰撞的检测和处理，以及合并在计算模型中。
根据根本情况变形模型、切割仿真等方法都可以分为三类:基于网格的方法，无网格方法和自适应/多分辨率方法。其中，基于网格的方法可以有效地对切割单元进行重构，最常见的比如有限元法(FEM)。近年来研究将扩展有限元法应用于变形模型的切削仿真确保切面附近的变形行为在物理上是正确的；无网格技术减少了对仿真网格的依赖。该方法采用的模型由一组移动节点表示，这些节点根据弹性控制方程相互作用。由于模拟物体的视觉质量与几何表示的精度密切相关，视觉效果的提高将伴随着仿真单元的稳定线性增长；而自适应多分辨率方法，其中复合有限元法(CFEM)将高分辨率的视觉网格嵌入到精细的六面体网格中并能进行分支分析。
无论采用何种剪切仿真方法，现有的剪切仿真方法大多数方法都遵循“相交即断裂”模式，即只要切削刃与物体相交就会发生切削断裂，而真实软体一般具有一定的抗断裂能力，当刀具按压到软组织上 之后，通常会先产生压痕，当按压能量积累到一定程度是，才会发生组织断裂。所以现有剪切仿真结果与真实软体剪切现象差距甚大。
发明内容
有鉴于此，本申请的主要目的在于提供一种高度逼真的虚拟切削断裂仿真方法和/装置，用于模拟变形物体抗断裂能力的高真实感切削现象。
一方面，本发明提出了一种用于可变形物体的剪切断裂的仿真方法，所述方法包括下述步骤：
S100、基于复合有限元模型对可变形物体的外形进行模拟，获得连接网格，在连接网格上嵌入原始物体曲面，得到可变形物体的可视化网格；
所述复合有限元模型的建立方法为：先将可变形物体的模型导入世界坐标系，使其重心与世界坐标系的原点重合后，对模型进行归一化处理；然后构建模型的轴对称立方体，按照第一网格分辨率，将包围可变形物体的一个立方体划分为若干第一网格，存储每个第一网格信息；再按照第二网格分辨率，将每个第一网格按照第二网格分辨率划分为第二网格，存储第二网格信息；将相邻第二网格的中心点连接起来，组成连接网格；
S200、若发生切削，更新第一网格、第二网格以及连接网格的存储信息，结合生成切削后的曲面，重构可视化网格。
优选地，在所述方法中，所述更新包括下属步骤：
S201、获取模拟刀具的网格节点，获取第二网格的网格节点；
S202、使用宽相位碰撞检测判断模拟刀具的网格节点和第二网格的网格节点是否发生重合，若有，执行S203；否则，执行S204；
S203、获取每个与模拟刀具相交的连接上的点，进而获取该点的符号场距离值，执行S204；
S204、获取每个可视化网格节点，使用宽相位碰撞检测确定模拟刀具穿透到的第一网格，进而通过窄相位碰撞检测确定穿透到的第二网格上的点，并获取该点的符号场距离值，执行S205；
S205、利用点的符号距离场值，建立连接网格连接的能量函数，通过使能量函数取得最小值，确定需要更新存储信息的第一网格、第二网格以及连接网格上的连接，从而更新存储信息。
优选地，在所述方法中，所述能量函数的计算过程如下：
Figure PCTCN2022137665-appb-000001
式中：t *是时间演化的伪参数；
Figure PCTCN2022137665-appb-000002
为当前时间交点的符号距离场值，所述交点为与刀具轨迹相交的连接上的点；
Figure PCTCN2022137665-appb-000003
式中：x为初始未变形状态的区域的任意位置；Q为时间t时刻可变形物体在变形区域上的能量密度函数；
Figure PCTCN2022137665-appb-000004
式中：S是将Q进行极分解后得到的对称张量；I和S大小一样的单位矩阵；μ和λ为计算的系数，计算式如下：
Figure PCTCN2022137665-appb-000005
式中：E为根据可变形物体的材质设定的杨氏模量，V是泊松比；
e g＝∫ ΩHΨdx+∫ ΩDkdx
式中：e g为能量函数，ΩH表示所有第二网格之间为连接状态的连接，Ψ为每个连接的能量密度；ΩD表示所有第二网格之间的连接状态由连接变为断开的连接，k为第二网格之间的连接状态由连接变为断开的能量释放速率。
优选地，在所述方法中，所述切削后的曲面通过下述步骤确定因切削操作要改变位移的网格节点：
通过与模拟刀具的相交情况，找到需要进行投影的点；
基于可视化网格，获取这些点的三角网格，进而得到这些三角网格的雅克比矩阵；
对模拟刀刃进行均匀采样获取采样点；
对于每个待投影的点，计算其投影到模拟刀刃采样点的位移后，通过雅克比矩阵计算所有包含该待投影点的三角网格的代数质量测度之和；
通过使代数质量测度之和最小，确定投影到模拟刀具上的点的位置。
优选地，在所述方法中，所述切削后的曲面通过采用B样条实现剖面压痕的生成，包括下述步骤：
基于控制点(x 0，y 0)，(x 1，y 1)，(x 2，y 2)，(x 3，y 3)，(x 4，y 4),(x 5，y 5)用B样条构造压痕调整函数，其中：
x 0＝0，y 0＝-a i；x 1＝0.2 cos θ i，y 1＝a i(0.2 sin θ i-1)；
Figure PCTCN2022137665-appb-000006
y 2＝γ；
Figure PCTCN2022137665-appb-000007
y 3＝0,
Figure PCTCN2022137665-appb-000008
y 4＝0；
x 5＝1,y 5＝0；
其中：a i是网格节点v i投影后的位移，i是要进行投影的网格节点序号，i＝1，2，…，N，N为要投影的节点个数，要投影的节点是因切削或按压产生位移变化的节点；
Figure PCTCN2022137665-appb-000009
D为最大测地距离；γ为一个与材料相关的参数，可以通过调节该参数，调整该控制节点因压痕带来的位移变化；
获取网格节点v i的最大测地范围内的节点，将它们作为潜在调整节点，继续获取潜在调整节点的最大测地范围内的节点，直至获取的节点达到设定数目；
将要调整节点的横坐标代入压痕调整函数，获得压痕产生后这些节点的纵坐标，结合投影点的位移a i，可以获得调整节点的新位置，更新这些网格的节点信息，获得压痕产生后的可视化网格。
优选地，在所述方法中，所述γ通过下式计算：
Figure PCTCN2022137665-appb-000010
式中：τ为根据材料设定的一个值，E为杨氏模量。
优选地，在所述方法中，所述最大测地距离与材料相关，通过下式计算：
Figure PCTCN2022137665-appb-000011
式中，V是泊松比，E为杨氏模量。
另一方面，一种材料仿真方法，来保证压痕与刀具刀片一致，以 及视觉上似是而非的压痕诱导变形，以避免大量的计算。所述方法通过采用B样条调整压痕的生成，包括下述步骤：
构造材料的可视化网格；
基于控制点(x 0，y 0)，(x 1，y 1)，(x 2，y 2)，(x 3，y 3)，(x 4，y 4),(x 5，y 5)用B样条构造压痕调整函数，其中：
x 0＝0，y 0＝-a i；x 1＝0.2 cos θ i，y 1＝a i(0.2 sin θ i-1)；
Figure PCTCN2022137665-appb-000012
y 2＝γ；
Figure PCTCN2022137665-appb-000013
y 3＝0,
Figure PCTCN2022137665-appb-000014
y 4＝0；
x 5＝1,y 5＝0；
其中：a i是网格节点v i因按压产生的位移，i是网格节点序号，i＝1，2，…，N，N为按压影响的节点个数；
Figure PCTCN2022137665-appb-000015
D为最大测地距离；γ为一个与材料相关的参数，可以通过调节该参数，调整该控制节点因压痕带来的位移变化；
获取网格节点v i的最大测地范围内的节点，将它们作为潜在调整节点，继续获取潜在调整节点的最大测地范围内的节点，直至获取的节点达到设定数目；
将要调整节点的横坐标代入压痕调整函数，获得压痕产生后这些节点的纵坐标，结合投影点的位移a i，可以获得调整节点的新位置，更新这些网格的节点信息，获得压痕产生后的可视化网格。
优选地，在所述材料仿真方法中，所述γ通过下式计算：
Figure PCTCN2022137665-appb-000016
式中：τ为根据材料设定的一个值，E为杨氏模量。
最后，本发明还涉及一种终端设备，包括存储器、处理器以及存 储在所述存储器中并可在所述处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时实现上述任一所述方法的步骤。
与现有技术相比，本发明采用基于共旋转线性有限元模型设计了支持软物体大变形的框架，并采用复合有限元方法，很好地平衡了模拟精度和算法效率；配合格里菲斯能量的切割断裂演化模型进行交互式虚拟切削模拟，能够确定何时以及如何产生新的切割；特别提出了一种材料仿真方法，来保证压痕与刀具刀片一致，以及视觉上似是而非的压痕诱导变形，以避免大量的计算。因此，本发明非常适用于虚拟手术训练和交互式手术规划等医学应用。
附图说明
为了更清楚地说明本申请实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1、为切割前仿真的示意图；
图2、为切割后仿真的示意图；
图3、用刀具切削前的涉及的压痕调整节点示意图；
图4、切削过程中压痕调整节点的变化示意图；
图5、切削发生后压痕调整节点的变化示意图；
图6、为不做压痕处理的切削示意图；
图7、为压痕调整区域构建示意图；
图8、为作完压痕处理后的切削示意图；
图9、为采用本发明方法与采用基本复合有限元模型进行切割时切割变化仿真示意图；
图10、为对不同材料进行切割时的仿真对比示意图；
图11、为使用另一形状工具切削物体从变形到断裂过程的仿真示意图；
图12、为采用本发明方法对肝脏进行任意切割时切削变化过程的仿真示意图；
图13、为采用本发明方法对马进行任意切割时切削变化过程的仿真示意图；
图14、为采用本发明方法对犰狳进行任意切割时切削变化过程的仿真示意图；
图15、为采用本发明方法对兔子进行任意切割时切削变化过程的仿真示意图。
具体实施方式
下面将结合本申请实施例中的附图，对本申请实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅是本申请一部分实施例，而不是全部的实施例。基于本申请中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本申请保护的范围。
本申请的说明书和权利要求书的术语“包括”和“具有”以及他们的任何变形，意图在于覆盖不排他的包含。例如，包含了一系列步骤或设备的过程、方法、系统、产品或设备不必限于清楚地列出的那些步骤或设备，而是可包括没有清楚地列出的或对于这些过程、方法、产品或设备固有的其他步骤或设备。
在本申请的描述中，需要说明的是，术语“第一”、“第二”、仅用于描述目的，而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此，限定有“第一”、“第二”的特征可以明示或者隐含地包括一个或者更多个该特征。
在一个肝脏切削仿真实施例中，采用下述方法进行仿真模拟切削实验，与切口方向相垂直的剖面图如图1和图2所示，图1为切削前示意图，图2为切削后的剖面图。在这个实施例中，仿真采用下述步骤：
S100、基于复合有限元模型对可变形物体的外形进行模拟，获得连接网格，在连接网格上嵌入原始物体曲面，得到可变形物体的可视化网格；
S200、若发生切削，更新第一网格、第二网格以及连接网格的存储信息，结合生成切削后的曲面，重构可视化网格。
在上述步骤中，所述复合有限元模型的建立方法为：先将可变形物体的模型导入世界坐标系，使其重心与世界坐标系的原点重合后，对模型进行归一化处理；然后构建模型的轴对称立方体，按照第一网格分辨率，将包围可变形物体的一个立方体划分为若干第一网格，存储每个第一网格信息；再按照第二网格分辨率，将每个第一网格按照第二网格分辨率划分为第二网格，存储第二网格信息；将相邻第二网格的中心点连接起来，组成连接网格。存储的网格信息包括节点信息，连接网格中需要存储与原始物体曲面相交的交点和法线。
第一网格主要用于变形计算，较高的离散度保证了方法的实时性。 第二网格用于逼近物体实际形状，可以表示物体各部分的连接情况。利用原始物体曲面与第二网格之间连线的相交情况，得到可视化网格，可以更精细的表示物体本身。因此，第一网格在空间上包含第二网格，可视化网格。优选地，第一网格为六面体，第二网格为六面体。原始物体曲面由三角网格组成。
在可变物体的切削仿真过程中，首先要确定切削发生的时间，将可视化网格仿真出切口断开。在切口断开这个过程中，会存在两种碰撞。一种是刀具与可变形物体的碰撞，另一种是可变形物体的断开组织之间的碰撞。因此，本发明在仿真时采用哈希表，将要检测的对象放入空间哈希表中，结合宽相位检测法，判断它们在空间上的是否重合，即刀具和可变形物体、可变形物体自身、可变形物体断开的组织之间是否在相关节点上重合。如果有刀具和可变形物体的碰撞，则仿真切口断开，或者有断开组织之间的碰撞，则仿真穿透到了哪些第一网格，确定穿透的具体位置。对于切口断开时，通过更新发生形变的节点信息，进行切口模拟。因此对于碰撞中的重合的点，可能是发生变形的点。利用该点的符号场距离值，建立连接网格连接的能量函数，通过使能量函数取得最小值，确定需要更新存储信息的第一网格、第二网格以及连接网格上的连接，从而更新存储信息，
本发明对能量函数的计算过程如下：
Figure PCTCN2022137665-appb-000017
式中：t *是时间演化的伪参数；
Figure PCTCN2022137665-appb-000018
为当前时间交点的符号距离场值，所述交点为与刀具轨迹相交的连接上的点；
Figure PCTCN2022137665-appb-000019
式中：x为初始未变形状态的区域的任意位置；Q为时间t时刻可变形物体在变形区域上的能量密度函数；
Figure PCTCN2022137665-appb-000020
式中：S是将Q进行极分解后得到的对称张量；I和S大小一样的单位矩阵；μ和λ为计算的系数，计算式如下：
Figure PCTCN2022137665-appb-000021
式中：E为根据可变形物体的材质设定的杨氏模量，V是泊松比；
e g＝∫ ΩHΨdx+∫ ΩDkdx
式中：e g为能量函数，ΩH表示所有第二网格之间为连接状态的连接，Ψ为每个连接的能量密度；ΩD表示所有第二网格之间的连接状态由连接变为断开的连接，k为第二网格之间的连接状态由连接变为断开的能量释放速率。
上述过程是找到因受到切削压力而要发生变形的点，但是切口的仿真，还需要知道切削的深度。在一个实施例中，采用下述方式实现对切削深度的仿真，即：通过与模拟刀具的相交情况，找到需要进行投影的点；基于可视化网格，获取这些点的三角网格，进而得到这些三角网格的雅克比矩阵；对模拟刀刃进行均匀采样获取采样点；对于每个待投影的点，计算其投影到模拟刀刃采样点的位移后，通过雅克比矩阵计算所有包含该待投影点的三角网格的代数质量测度之和；通过使代数质量测度之和最小，确定投影到模拟刀具上的点的位置。这 个实施例处理过程如图3-5所示。图3-5中，Blade curve是刀具采样点，通过对模拟刀具的刀刃进行均匀采样获得。Contact region vertice是通过与刀具的相交情况，找到的可能需要进行投影的点。对于包含这些点的三角网格，构造雅克比矩阵。进一步对所有可能需要投影的点，计算该点移动到刀刃采样点的距离，即为所述投影。通过雅克比矩阵计算所有包含该待投影点的三角网格的代数质量测度之和，使代数质量测度之和取得最小值的点，为最终确定的投影点。Local coordinate system是根据投影的位置建立的坐标系。Local mesh that may need to adjust是图中示意的需要调整位置可视化网格。Approximate indentation curve是近似凹陷的刀口。
如果不对刀口进行处理，上面仿真的刀口如图6所示，只要切割刀片与模型相交就会发生切割断裂，这与实际的切割经验不同。具有弹性的表面，切削后是不会出现棱角，从未切削部分到切口的边缘是不会出现显著不连续的，如图7所示。本发明为了更逼真的模拟切削口，提高模拟效率，提出了一种材料仿真方法。该方法利用与材料参数相关的最大测地距离来寻找压痕附近的需要产生形变的顶点，通过与材料参数相关的变形模型实现模拟不同硬度的物体形变和/或切割过程。
在这个变形模型中，首先构造材料的可视化网格，构造方法优选采用上述用于可变形物体的剪切断裂的仿真方法中，基于复合有限元模型的方法。其次，基于控制点(x 0，y 0)，(x 1，y 1)，(x 2，y 2)，(x 3，y 3)，(x 4，y 4),(x 5，y 5)，用B样条构造压痕调整函数，其中： x 0＝0，y 0＝-a i；x 1＝0.2 cos θ i，y 1＝a i(0.2 sin θ i-1)；
Figure PCTCN2022137665-appb-000022
y 2＝γ；
Figure PCTCN2022137665-appb-000023
y 3＝0,
Figure PCTCN2022137665-appb-000024
y 4＝0；x 5＝1,y 5＝0。其中：a i是网格节点v i因按压产生的位移，i是网格节点序号，i＝1，2，…，N，N为按压影响的节点个数，即要进行变形的节点个数；
Figure PCTCN2022137665-appb-000025
Figure PCTCN2022137665-appb-000026
D为最大测地距离；γ为一个与材料相关的参数，可以通过调节该参数，调整该控制节点因压痕带来的位移变化；获取网格节点v i的最大测地范围内的节点，将它们作为潜在调整节点，继续获取潜在调整节点的最大测地范围内的节点，直至获取的节点达到设定数目；将要调整节点的横坐标代入压痕调整函数，获得压痕产生后这些节点的纵坐标，结合投影点的位移a i，可以获得调整节点的新位置，更新这些网格的节点信息，获得压痕产生后的可视化网格。压痕引起的变形与物体的材质有关。材料越软，变形就会越明显。因此压痕调整就是用来模拟材料在受到压力后的变形情况。为了更贴近材料的性质，在计算时，最大测地距离D可通过下式计算：
Figure PCTCN2022137665-appb-000027
式中，V是泊松比，E为杨氏模量。
同样的，为了便于材料参数值的设定，γ通过下式计算：
Figure PCTCN2022137665-appb-000028
式中：τ为根据材料设定的一个值，E为材料的杨氏模量。
通过上面一个变形模型的应用，可以实现切面与原始物体曲面的平滑过渡，使仿真切口看起来更加自然逼真，而且上述计算过程可以避免大量计算。
图9-15是采用本发明进行切削的各自仿真效果对比图。
图9为与基本复合有限元切割仿真结果对比示意图。第一行为复合有限元方法基本切割效果，第二行为裂缝演化和压痕生成的中间结果。第三行为基于复合有限元模型，进一步进行压痕调整后的仿真效果。每一行的图像由切割效果的前视图和相应的放大视图组成。由图可以看出，本发明方法中的剪切仿真更加逼真自然。
图10为不同材料的切割效果示意图。这组对比图展示了三种不同材料的模拟效果。每两行颜色相近代表一种材料的模拟效果。这两行的底部一行显示了相应的放大视图。由图可以看出，本发明中的剪切仿真适用于不同材料的仿真，实用性强。
图11为一组使用另一形状工具切削物体从变形到断裂过程的仿真结果图。第一组到第三组为变形，最后一组为断裂开。每一组图都展示了切割效果的侧视图，对应的顶视图，以及局部放大视图，以便看清细节。通过这四组对比图可以看出，本发明方法能够对工具形状不具有限制性，剪切效果依然是高度逼真。
图12-15分别为采用本发明方法对肝脏、马、犰狳和兔子进行任意切削时切削过程变化示意图。
由此可见，本发明方法具有很广的适用性和实用性，对任意材质、任意刀具以及任意形状的物体，都能进行具有逼真自然的仿真，能够模拟变形物体抗断裂能力的真实切削现象，方便虚拟手术训练和交互式手术规划等医学应用，具有较高的实用和推广价值。
上述方法均可以通过一种终端设备来实现，所述终端社保包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计 算机程序，通过所述处理器执行所述计算机程序时实现上述任一方法的步骤。
通过以上的实施方式的描述，所属领域的技术人员可以清楚地了解到本公开方法还可借助软件加必需的通用硬件的方式来实现，当然也可以通过专用硬件包括专用集成电路、专用CPU、专用存储器、专用元器件等来实现。一般情况下，凡由计算机程序完成的功能都可以很容易地用相应的硬件来实现，而且，用来实现同一功能的具体硬件结构也可以是多种多样的，例如模拟电路、数字电路或专用电路等。但是，对本公开而言更多情况下，软件程序实现是更佳的实施方式。
综上所述，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种用于可变形物体的剪切断裂的仿真方法，其特征在于，所述方法包括下述步骤：
    S100、基于复合有限元模型对可变形物体的外形进行模拟，获得连接网格，在连接网格上嵌入原始物体曲面，得到可变形物体的可视化网格；
    所述复合有限元模型的建立方法为：先将可变形物体的模型导入世界坐标系，使其重心与世界坐标系的原点重合后，对模型进行归一化处理；然后构建模型的轴对称立方体，按照第一网格分辨率，将包围可变形物体的一个立方体划分为若干第一网格，存储每个第一网格信息；再按照第二网格分辨率，将每个第一网格按照第二网格分辨率划分为第二网格，存储第二网格信息；将相邻第二网格的中心点连接起来，组成连接网格；
    S200、若发生切削，更新第一网格、第二网格以及连接网格的存储信息，结合生成切削后的曲面，重构可视化网格。
  2. 根据权利要求1所述的方法，其特征在于，所述更新包括下属步骤：
    S201、获取模拟刀具的网格节点，获取第二网格的网格节点；
    S202、使用宽相位碰撞检测判断模拟刀具的网格节点和第二网格的网格节点是否发生重合，若有，执行S203；否则，执行S204；
    S203、获取每个与模拟刀具相交的连接上的点，进而获取该点的符号场距离值，执行S204；
    S204、获取每个可视化网格节点，使用宽相位碰撞检测确定模拟 刀具穿透到的第一网格，进而通过窄相位碰撞检测确定穿透到的第二网格上的点，并获取该点的符号场距离值，执行S205；
    S205、利用点的符号距离场值，建立连接网格连接的能量函数，通过使能量函数取得最小值，确定需要更新存储信息的第一网格、第二网格以及连接网格上的连接，从而更新存储信息。
  3. 根据权利要求2所述的方法，其特征在于，所述能量函数的计算过程如下：
    Figure PCTCN2022137665-appb-100001
    式中：t *是时间演化的伪参数；
    Figure PCTCN2022137665-appb-100002
    为当前时间交点的符号距离场值，所述交点为与刀具轨迹相交的连接上的点；
    Figure PCTCN2022137665-appb-100003
    式中：x为初始未变形状态的区域的任意位置；Q为时间t时刻可变形物体在变形区域上的能量密度函数；
    Figure PCTCN2022137665-appb-100004
    式中：S是将Q进行极分解后得到的对称张量；I和S大小一样的单位矩阵；μ和λ为计算的系数，计算式如下：
    Figure PCTCN2022137665-appb-100005
    式中：E为根据可变形物体的材质设定的杨氏模量，V是泊松比；
    Figure PCTCN2022137665-appb-100006
    式中：e g为能量函数，ΩH表示所有第二网格之间为连接状态的 连接，Ψ为每个连接的能量密度；ΩD表示所有第二网格之间的连接状态由连接变为断开的连接，k为第二网格之间的连接状态由连接变为断开的能量释放速率。
  4. 根据权利要求1所述的方法，其特征在于，所述切削后的曲面通过下述步骤确定因切削操作要改变位移的网格节点：
    通过与模拟刀具的相交情况，找到需要进行投影的点；
    基于可视化网格，获取这些点的三角网格，进而得到这些三角网格的雅克比矩阵；
    对模拟刀刃进行均匀采样获取采样点；
    对于每个待投影的点，计算其投影到模拟刀刃采样点的位移后，通过雅克比矩阵计算所有包含该待投影点的三角网格的代数质量测度之和；
    通过使代数质量测度之和最小，确定投影到模拟刀具上的点的位置。
  5. 根据权利要求1所述的方法，其特征在于，所述切削后的曲面通过采用B样条实现剖面压痕的生成，包括下述步骤：
    基于控制点(x 0，y 0)，(x 1，y 1)，(x 2，y 2)，(x 3，y 3)，(x 4，y 4),，(x 5，y 5)，用B样条构造压痕调整函数，其中：
    x 0＝0，y 0＝-a i；x 1＝0.2 cosθ i，y 1＝a i(0.2 sinθ i-1)；
    Figure PCTCN2022137665-appb-100007
    y 2＝γ；
    Figure PCTCN2022137665-appb-100008
    y 3＝0,
    Figure PCTCN2022137665-appb-100009
    y 4＝0；
    x 5＝1,y 5＝0；
    其中：a i是网格节点v i投影后的位移，i是要进行投影的网格节 点序号，i＝1，2，…，N；N为要投影的节点个数；
    Figure PCTCN2022137665-appb-100010
    D为最大测地距离；γ为一个与材料相关的参数，可以通过调节该参数，调整该控制节点因压痕带来的位移变化；
    获取网格节点v i的最大测地范围内的节点，将它们作为潜在调整节点，继续获取潜在调整节点的最大测地范围内的节点，直至获取的节点达到设定数目；
    将要调整节点的横坐标代入压痕调整函数，获得压痕产生后这些节点的纵坐标，结合投影点的位移a i，可以获得调整节点的新位置，更新这些网格的节点信息，获得压痕产生后的可视化网格。
  6. 根据权利要求5所述的方法，其特征在于，所述γ通过下式计算：
    Figure PCTCN2022137665-appb-100011
    式中：τ为根据材料设定的一个值，E为杨氏模量。
  7. 根据权利要求5所述的方法，其特征在于，所述最大测地距离与材料相关，通过下式计算：
    Figure PCTCN2022137665-appb-100012
    式中，V是泊松比，E为杨氏模量。
  8. 一种材料仿真方法，其特征在于，所述方法通过采用B样条调整压痕的生成，包括下述步骤：
    构造材料的可视化网格；
    基于控制点(x 0，y 0)，(x 1，y 1)，(x 2，y 2)，(x 3，y 3)，(x 4，y 4),(x 5，y 5)用B样条构造压痕调整函数，其中：
    x 0＝0，y 0＝-a i；x 1＝0.2 cosθ i，y 1＝a i(0.2 sinθ i-1)；
    Figure PCTCN2022137665-appb-100013
    y 2＝γ；
    Figure PCTCN2022137665-appb-100014
    y 3＝0；
    Figure PCTCN2022137665-appb-100015
    y 4＝0；
    x 5＝1,y 5＝0；
    其中：a i是网格节点v i因按压产生的位移，i是网格节点序号，i＝1，2，…，N，N为按压影响的节点个数；
    Figure PCTCN2022137665-appb-100016
    D为最大测地距离；γ为一个与材料相关的参数，可以通过调节该参数，调整该控制节点因压痕带来的位移变化；
    获取网格节点v i的最大测地范围内的节点，将它们作为潜在调整节点，继续获取潜在调整节点的最大测地范围内的节点，直至获取的节点达到设定数目；
    将要调整节点的横坐标代入压痕调整函数，获得压痕产生后这些节点的纵坐标，结合投影点的位移a i，可以获得调整节点的新位置，更新这些网格的节点信息，获得压痕产生后的可视化网格。
  9. 根据权利要求8所述的方法，其特征在于，所述γ通过下式计算：
    Figure PCTCN2022137665-appb-100017
    式中：τ为根据材料设定的一个值，E为杨氏模量。
  10. 一种终端设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时实现如权利要求1至9任一项所述方法的步骤。
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