Computer research and development of a new soft tissue cutting algorithm based on voxel splitting Xiong Yueshan Luo Jun Tan Wei Wang Yanqi Guo Guangyou School of Computer Science, National University of Defense Technology, Changsha 410073) 2 (Technical Education Center of General Hospital of Chinese People's Liberation Army, Beijing 100853) 14; Revised date: 200å“0å“08 Fund Project: National Natural Science Foundation of China (60171028, 60371036) The fidelity of the feedback results is an important part of the virtual surgical system. The cutting effect is very important for the virtual surgical system. Impact. Real-time and realism are two key factors in measuring the effectiveness of cutting. Bro-Nielsenl1P coffee et al. use the body removal method to realize the cutting operation. The basic idea of ​​this kind of algorithm is to remove the tetrahedral element that the tool collides from the model. The calculation of the removal voxel method is small and the real-time performance is good. The shortcoming is that the removal of the voxel method violates the law of conservation of mass, and the cutting boundary has a jagged shape, which affects the realistic effect of the cutting process. The voxel splitting method is another cutting method. The basic idea is to decompose the cut voxels (tetrahedrons, hexahedrons, etc.) into a plurality of small voxels. Bielser et al. The meta-decomposition into 17 small voxels to achieve the cutting process, however, this processing method will make the number of voxels in the model increase sharply, real-time processing difficulties Bielser and Gross improve the above cutting algorithm, the improved method will no longer Each of the cut tetrahedral elements is decomposed into fixed 17 small tetrahedral elements, which decompose the tetrahedral elements into different numbers of small tetrahedrons according to different cutting conditions, and the cutting algorithm of Mor et al. The voxel splitting algorithm for the minimum number of tetrahedral elements is proposed, which minimizes the increase in the number of voxels. In order to solve the inherent shortcomings of voxel splitting, Han" Wen Nienhuys et al. proposed a method that does not increase voxels. The number of cutting algorithms that simultaneously produce precise cuts, their cutting algorithm is completed in the following four steps: the surface of the surface cut in the grid is copied and cut on the cutting plane
In this paper, a new voxel-cutting algorithm is studied, which focuses on the shortcomings of the previous voxel-split algorithm, and focuses on solving the problem of a large burden on the system due to the increase in the number of voxels. Decomposed into two processes of degradation processing and primitive decomposition, making the processing of special boundary conditions simpler. 2 Degradation processing and primitive decomposition We assume that in a small time interval, the motion of the tool can be approximated as translation. Simulating the intersection of the cutting plane and the tetrahedral element with the current position of the tool and the direction of movement of the tool can be divided into the following four categories (as shown): vertex intersection. The intersection of the cutting plane and the tetrahedral element is the apex of the tetrahedral element, such as the intersection of the C points in the middle. The intersection of the cutting plane and the tetrahedron is on one side of the tetrahedral element, such as the Pi point.
Patch intersection. The intersection of the cutting plane and the tetrahedron is within a patch of the tetrahedral element, such as the P2 point in the middle.
The inside of the body unit, such as the P3 point.
Definition 1. The intersection with the cutting plane The tetrahedral element with only the vertex intersection and the intersection point is called the fully-cut tetrahedral definition. 2. The intersection with the cutting plane contains the tetrahedral element of the intersection of the patch or the intersection of the voxel. Cut tetrahedron.
The degradation process transforms an incompletely cut tetrahedron into multiple fully-cut tetrahedrons, that is, eliminates all patch intersections and voxel intersections. The brief algorithm description of the degradation process is given below. The input of the algorithm is the cut-out tetrahedral element array obtained by the collision detection process. Q1 is the voxel intersection queue, which stores the binary group <P, T>, P represents the position information of the voxel intersection, T is the tetrahedral unit q2 where the voxel intersection is located, and stores the binary group <P, F>, P represents the position information of the intersection of the patches, and F is the index of the patch where the intersection of the patches is located (the corresponding voxel information can be obtained from the patch index).
If any tetrahedral element is taken from the cut tetrahedral element array, the intersection of the tetrahedral element and the cut plane voxel and the patch intersection is obtained. If it is the voxel intersection, it is inserted into If the tail of q1 is the intersection of the patch, it is inserted into the tail of q2. Turn 1 to get point P1, and get its corresponding voxel T1. Decompose voxel T1 to get 4 small tetrahedral elements, delete voxel T1 from the cut tetrahedral element array, and put these 4 small 4 The face unit is added to the array. The T of all other T=T1 tuples in q1 are modified and updated to the minimum bounding tetrahedron where point P1 is located. The transfer process ends. Otherwise, the point P1 is obtained, and the patch F1 at which the point is located is obtained. The two tetrahedral units T1 and T2 corresponding to the patch are obtained from the patch F1 (if the patch is a surface patch, only one body* cut culvert Delete the two individual elements and add the newly generated tetrahedral elements to the array in the four-sided tetrahedral element array with the tetrahedrons. Each of the other squares in q2 is F=Fl The tuple of the tuple is modified and updated to the minimum enveloping patch where Pi is located. The tetrahedron detected by the 5 collision can be divided into two types: a fully-cut tetrahedron and an incompletely-cut tetrahedron. Bielsei et al. The cutting conditions are divided into five categories. If special boundary conditions are taken into account, there are no less than 30 types of cutting. This process is not only complicated, but also may miss the processing of partial cutting.
By analyzing the different cutting conditions, we found that after the process of decomposing the cutting process into two processes of degenerate processing and elemental decomposition, the cutting condition of the tetrahedral unit after degrading treatment is only 10 kinds even considering the special condition of the boundary, so that It greatly reduces the complexity of the algorithm and facilitates the implementation of the cutting process. The elements in the array of tetrahedral elements obtained after the degradation process are completely cut tetrahedral elements, and their intersection with the cutting plane contains only vertex intersections and edge intersections. Taking into account the special conditions of the boundary, all the cutting conditions can be divided into the following 10 categories, as shown: the cutting condition of the tetrahedral unit after degradation processing (a) 1 vertex intersection; (b) 2 vertex intersections; (c 3 top intersections; (d) 1 edge intersection; (e) 1 edge intersection and 1 vertex intersection; (f) 1 edge intersection and 2 vertex intersections; (g) 2 edge intersections; (h ) 2 intersections of intersections and 1 vertex; (i) 3 intersections; (j) 4 intersections are the same as the degradation process, and the decomposition process of the primitives may also produce irregular tetrahedral elements during the production process. And avoid creating some irregular tetrahedral elements. The method of primitive decomposition is given.
Elementary decomposition (a) elementary decomposition of 1 edge intersection; (b) elementary decomposition of 2 edge intersections; (c) elementary decomposition of 3 edge intersections; (d) elementary decomposition of 4 edge intersections 3 post-cutting processing Post-cutting processing consists of two parts: vertex copying and slit forming. Vertexes corresponding to vertex intersections and edge intersections that are not on the cutting boundary need to be copied. We add a BOOL type attribute IsNeedClone for each intersection point to identify Whether the point needs to be replicated and the notch formation is achieved by means of deformation calculation. Due to the addition of several new tetrahedral elements in the above process, the updated contents include: updating the overall stiffness matrix K, the overall mass matrix M, and the overall damping matrix C. Some internal parameters in the dynamic finite element model calculation are also To update at the same time.
Here we use the SOR iteration method to solve the linear equations corresponding to the finite element method. Therefore, it is not necessary to update the inverse matrix of the overall stiffness matrix in combination with the degradation and primitive decomposition process. The cutting algorithm based on the finite element model in the virtual surgery system can Proceed as follows: load the model and initialize the parameters for the finite element calculation.
The force size is used to judge whether the cutting condition is satisfied. If the deformation calculation is not satisfied, the processing ends; otherwise, all the voxel intersection points and the patch intersections in the cutting processing model are started, and the degenerate processing is performed to obtain all the cut voxels and the cutting plane. The vertice intersection and the edge intersection perform a primitive decomposition operation.
Duplicate all vertices that are not on the cutting boundary.
Update all the parameters related to the deformation calculation, apply the force according to the method of forming the incision, and complete the cutting 4 experimental results. We use the above cutting algorithm to simulate the cutting of the 3 individual element model. The software and hardware configuration of the experiment is as follows: PentiumW2.4GHz CPU, 12MB Memory, 64MB graphics card, PHANToM force feedback device, Windows2000 operating system (a) is the result of cutting a single tetrahedron; (b) is the result of cutting the relatively regular tetrahedral mesh; (c) is the right The result of the cutting process of the external model of the leg in the virtual surgical system is the result of the Chinese map Ad experiment ail. Four sides; his "regular tetrahedral mesh leg external model d.http:// experimental results show Applying the cutting algorithm proposed in this paper to the virtual knee arthroscopy system, the realism and real-time requirements of the virtual system are achieved.
Xiong Yueshan, born in 1963, received his Ph.D. in February 1993. He was a postdoctoral researcher at Zhejiang University from 1993 to 1994. He is a professor and doctoral supervisor. He has published more than 50 research papers, of which 7 have entered the SCI search. The main research directions are digital image processing, virtual reality, numerical calculation and parallel algorithm.
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