CN108537797A - The distortion of the mesh optimization method of deformable objects cutting simulation in a kind of virtual operation - Google Patents

Abstract

The present invention provides a mesh deformation optimization method for cutting simulation of deformable objects in virtual surgery, which adopts geometry optimization and topology optimization, and combines multi-threading method to process multiple tasks in parallel, so as to solve the ill-conditioned units that appear in the cutting simulation process question. The method includes four steps, first, search for the target unit, and search for the grid unit to be processed according to the grid quality; second, the grid optimization preprocessing; third, the grid topology optimization process; fourth, the grid geometry optimization process. Steps 2, 3, and 4 use multi-threaded parallel processing. The invention can reduce the grid quantity while improving the grid quality, and can effectively improve the efficiency and stability of grid model deformation calculation.

Description

A Mesh Deformation Optimization Method for Deformable Object Cutting Simulation in Virtual Surgery

technical field

The invention relates to a method in virtual surgery cutting simulation, in particular to a grid deformation optimization method for deformable object cutting simulation in virtual surgery.

Background technique

Virtual surgery provides doctors with a virtual surgical environment and an interactive operating platform, which can be used for surgical planning, surgical training, and surgical simulation teaching. Compared with traditional surgical training and surgical teaching, virtual surgery has low cost and can be repeated. With the continuous development of virtual reality technology and the continuous improvement of computer hardware performance, virtual surgery has been more and more widely studied. The cutting simulation of deformable objects is a basic and key technology in virtual surgery, and virtual surgery requires the cutting simulation of deformable objects to have high accuracy and real-time performance.

Most of the current cutting simulations of deformable objects are based on grids, and the cutting simulation method based on tetrahedral meshes is currently the most widely used method. Tetrahedral meshes can construct models of almost arbitrary shapes through mesh subdivision, but ill-conditioned elements will appear during mesh generation and mesh division, and ill-conditioned elements will greatly reduce the computational efficiency and stability of deformation simulation. Moreover, grid division will greatly increase the number of grids, resulting in excessive calculation burden and affecting the accuracy and real-time performance of simulation. Therefore, the processing of grids has always been a research hotspot in cutting simulation. How to effectively control the quantity and quality of grids is still a very challenging problem so far.

The invention proposes a grid deformation optimization method for cutting simulation of deformable objects in virtual surgery. Using geometry optimization and topology optimization, combined with multi-threading method to process multiple tasks in parallel, can solve the problem of ill-conditioned elements in the cutting simulation process while reducing the number of meshes, effectively improving the efficiency and stability of mesh model deformation calculation sex.

Contents of the invention

The purpose of the present invention is to solve the problem of ill-conditioned units in the cutting simulation of deformable objects in virtual surgery, improve the mesh quality of the model, and improve the efficiency and stability of cutting simulation, and propose a cutting simulation method of deformable objects in virtual surgery Mesh deformation optimization method.

The present invention provides a mesh deformation optimization method for cutting simulation of deformable objects in virtual surgery. The method includes four steps:

The first step is to search for the target unit, and search for the grid unit that needs to be processed according to the grid quality. Each target unit is handed over to a thread for subsequent processing, as follows:

(a) For the volume grid, according to the volume length ratio criterion of the volume grid quality, the target unit is searched locally for the cutting operation;

(b) For surface grids, the search target unit for the cutting operation is performed according to the area-to-length ratio criterion of the surface grid quality;

(c) If two or more target units are adjacent to each other, use the polygon or polyhedron formed by them as a new target unit;

(d) Store the searched target units into the target unit queue, and assign them to sub-threads to execute subsequent steps in turn.

The second step is grid optimization preprocessing, which processes the local target area according to the searched target unit, as follows:

(a) Determine the surrounding units, and use the advantages of the proximity search of the K-D tree data structure to search for surrounding units that are connected to the vertices of the target unit (surface grid or volume grid);

(b) delete the vertices of the target unit, and delete the connection relationship between each vertex and the surrounding units, so as to obtain the target area, which is a polygon (or polyhedron);

(c) Update the topology of the mesh model according to the connection relationship between vertices.

The third step is the grid topology optimization process. The grid model after the preprocessing step is re-divided and the topology structure is updated to improve the grid quality of the target unit. The details are as follows:

(a) Regrid the target area, and use the boundary and internal point sets of the target area to perform Delaunay segmentation;

(b) Judging whether the grid quality meets the requirements, if it meets the requirements, execute (d), otherwise execute (c), according to the quality standards (1) and (2) described in the first step to search for the target unit to determine the target area Whether the unit meets the requirements;

(c) Add a new vertex in the target area and determine the position of the vertex, and then perform (a), the position of the new vertex is the center of the circumscribed circle of the largest triangle or tetrahedron in the target area, and the largest triangle or tetrahedron is the circumscribed circle of the target area The element with the largest circle radius;

(d) Update the topological structure of the mesh model according to the connection relationship between the vertices. If no new nodes are added, the fourth step of surface Laplace smoothing is performed directly.

The fourth step, the mesh geometry optimization process, performs geometric optimization on the mesh that has been topology optimized, adjusts the vertex position, and further improves the mesh quality, as follows:

(a) Perform mesh relaxation on the volumetric mesh of the target region;

(b) Laplace smoothing is performed on the cut local surface mesh, moving each node of the local surface mesh to the average position of its neighbors.

Each target area involved in steps 2, 3, and 4 is delivered to the thread pool as a separate task for parallel processing.

Compared with the prior art, the present invention has the advantages of:

1. Treating each ill-conditioned unit separately and locally optimizing it separately can improve the grid quality without affecting other grids.

2. Using geometry optimization and topology optimization, combined with multi-threading method to process multiple tasks in parallel, can reduce the number of grids while solving the problem of ill-conditioned elements in the cutting simulation process, and effectively improve the efficiency of grid model deformation calculation and stability.

3. The K-D tree structure combined with multi-threading is used to accelerate the search process of peripheral units, which can effectively improve the search speed and meet the real-time requirements in virtual cutting.

Description of drawings

Figure 1: A flowchart of a mesh deformation optimization method for cutting simulation of deformable objects in virtual surgery;

Figure 2: 2D schematic diagram of the target cell and target area;

Detailed ways

FIG. 1 shows a flow chart of a mesh deformation optimization method for cutting simulation of deformable objects in virtual surgery. The present invention will be further described below in combination with specific embodiments.

The present invention provides a mesh deformation optimization method for cutting simulation of deformable objects in virtual surgery. The main steps are introduced as follows:

The first step is to search for the target unit, and search for the grid unit to be processed according to the grid quality, and each target unit is handed over to a thread for subsequent processing.

(a) Store the nodes of the grid model in a three-dimensional K-D tree, save the grid units (tetrahedron or triangular face) related to different nodes into a hash table and update it in real time;

(b) For the volume grid, according to the volume length ratio standard of the volume grid quality, the target unit is searched locally for the cutting operation

where e _j (j=1, 2, 3, 4, 5, 6) is the length of the six sides of the tetrahedral mesh, V is the volume of the tetrahedral mesh, Q _V ∈ (0, 1), Q _V of The closer the value is to 1, the higher the quality of the tetrahedral grid is. When Q _V = 1, the grid unit is a regular tetrahedron. The threshold is set to 0.3, and the tetrahedral unit whose Q _V value is less than 0.3 is searched;

(c) For surface mesh, according to the area-to-length ratio criterion of the surface mesh quality, the search target unit for the cutting operation is performed

Where e _j (j=1, 2, 3) is the length of the three sides of the triangular face, A is the area of the triangular face, Q _F ∈ (0, 1), the closer the value of Q _F is to 1, it shows that the triangular network The higher the quality of the grid, when Q _F =1, the grid unit is a regular triangle. As shown in Figure 2, taking the 2D case as an example, the triangle ABC in the figure is a target unit that is searched, and the threshold is set to 0.3, and the search Q Tetrahedral elements with _F value less than 0.3;

(d) If two or more target units are adjacent to each other, use the polygon or polyhedron formed by them as a new target unit;

(e) Store the searched target units into the target unit queue, and assign them to sub-threads to execute subsequent steps in turn.

The second step is grid optimization preprocessing, which processes the local target area according to the searched target unit,

(a) Determine the surrounding units, and use the advantages of the K-D tree data structure proximity search to search for surrounding units that are connected to the vertices of the target unit (surface grid or volume grid). As shown in Figure 2, ABC is the target unit, and the dotted line indicates connection to peripheral units;

(b) delete the vertex of the target unit, and delete the connection relationship between each vertex and the peripheral unit, thereby obtaining the target area, the target area is a polygon (or polyhedron), as shown in Figure 2, the solid line represents the target unit obtained;

(c) Update the topology of the mesh model according to the connection relationship between vertices. ;

The third step is the grid topology optimization process. The grid model after the preprocessing step is re-divided and the topology structure is updated to improve the grid quality of the target unit.

(a) Regrid the target area, and use the boundary and internal point sets of the target area to perform Delaunay segmentation;

(b) Judging whether the grid quality meets the requirements, if it meets the requirements, execute (d), otherwise execute (c), according to the quality standards (1) and (2) described in the first step to search for the target unit to determine the target area Whether the unit meets the requirements;

(c) Add a new vertex in the target area and determine the position of the vertex, and then perform (a), the position of the new vertex is the center of the circumscribed circle of the largest triangle or tetrahedron in the target area, and the largest triangle or tetrahedron is the circumscribed circle of the target area The element with the largest circle radius;

(d) Update the topological structure of the mesh model according to the connection relationship between vertices, if no new nodes are added, then directly perform the fourth step of surface smoothing.

The fourth step is the mesh geometry optimization process. Perform geometry optimization on the mesh that has been topology optimized, adjust the vertex position, and further improve the mesh quality.

(a) Perform mesh relaxation on the target area body mesh, and perform the following operations for each node in the target area,

Among them, (x _i , y _i , z _i ) are the coordinates of the target node, (x _p , y _p , z _p ) are the adjusted coordinates of the target node, and N is the total number of all nodes connected to the target node;

To judge the quality of the adjusted grid, the judgment criteria are as follows:

Where Q _R is the associated quality coefficient (0<Q _R ≤1), Q _Vi is the quality standard of the search target unit described in the first step, where Q _Vi is the quality coefficient of the tetrahedron containing the target node, The larger Q _R is, the higher the grid quality is;

If the adjusted target node is located in the target area and is larger than the _QR value of the target node before adjustment, then move the target node to the adjusted position, otherwise let

x _p ＝(x _p + _xi )/2, y _p ＝(y _p +y _i )/2, z _p ＝(z _p +z _i )/2 (5)

Then repeat the above operations until the grid quality meets the quality criterion or the number of cycles reaches the upper limit, and the upper limit of the cycle is set by the user;

(b) Laplace smoothing is performed on the cut local surface mesh, moving each node of the local surface mesh to the average position of its neighbors.

Each target area involved in steps 2, 3, and 4 is delivered to the thread pool as a separate task for parallel processing.

Claims (5)

1. a mesh deformation optimization method for deformable object cutting simulation in virtual surgery, characterized in that the realization steps are as follows: The first step is to search for the target unit, and search for the grid unit to be processed according to the grid quality, and each target unit is handed over to a thread for subsequent processing; The second step is grid optimization preprocessing, which processes the local target area according to the searched target unit; The third step is the grid topology optimization process, which re-grids the grid model after the preprocessing step and updates the topology structure to improve the grid quality of the target unit; The fourth step is the mesh geometry optimization process, which performs geometric optimization on the mesh after performing topology optimization, adjusts the vertex position, and further improves the mesh quality; Each target area involved in steps 2, 3, and 4 is delivered to the thread pool as a separate task for parallel processing. 2. The mesh deformation optimization method of deformable object cutting simulation in a kind of virtual surgery according to claim 1, characterized in that: the search target unit described in the first step, (a) Store the nodes of the grid model in a three-dimensional K-D tree, save the grid units (tetrahedron or triangular face) related to different nodes into a hash table and update it in real time; (b) For the volume grid, according to the volume length ratio standard of the volume grid quality, the target unit is searched locally for the cutting operation where e _j (j=1, 2, 3, 4, 5, 6) is the length of the six sides of the tetrahedral mesh, V is the volume of the tetrahedral mesh, Q _V ∈ (0, 1), Q _V of The closer the value is to 1, the higher the quality of the tetrahedral grid is. When Q _V = 1, the grid unit is a regular tetrahedron. The threshold is set to 0.3 to search for tetrahedral units with a Q _V value less than 0.3; (c) For surface mesh, according to the area-to-length ratio criterion of the surface mesh quality, the search target unit for the cutting operation is performed Where e _j (j=1, 2, 3) is the length of the three sides of the triangular surface, A is the area of the triangular surface, Q _F ∈ (0, 1), the closer the value of Q _F is to 1, it shows that the triangular network The higher the quality of the grid, when _QF = 1, the grid unit is a regular triangle, the threshold is set to 0.3, and the triangular unit whose _QF value is less than 0.3 is searched; (d) If two or more target units are adjacent to each other, use the polygon or polyhedron formed by them as a new target unit; (e) Store the searched target units into the target unit queue, and assign them to sub-threads to execute subsequent steps in sequence. 3. The mesh deformation optimization method for deformable object cutting simulation in a virtual surgery according to claim 1, characterized in that: the mesh optimization preprocessing described in the second step, (a) Determine the surrounding units, and use the advantages of the K-D tree proximity search to search for surrounding units that are connected to the vertices of the target unit (surface grid or volume grid); (b) delete the vertices of the target unit, and delete the connection relationship between each vertex and the surrounding units, so as to obtain the target area, which is a polygon (or polyhedron); (c) Update the topology of the mesh model according to the connection relationship between vertices. 4. The mesh deformation optimization method for deformable object cutting simulation in a virtual surgery according to claim 1, characterized in that: the mesh topology optimization process described in the third step, (a) Regrid the target area, and use the boundary and internal point sets of the target area to perform Delaunay segmentation; (b) Judging whether the grid quality meets the requirements, if it meets the requirements, execute (d) directly, otherwise execute (c), and judge the target area according to the quality standards (1) and (2) described in the first step of searching for the target unit Whether the units within meet the requirements; (c) Add a new vertex in the target area and determine the position of the vertex, and then execute (a), the position of the new vertex is the center of the circumscribed circle of the largest triangle or tetrahedron in the target area, and the largest triangle or tetrahedron is the target area The element with the largest inscribed circle radius; (d) Update the topological structure of the mesh model according to the connection relationship between vertices. If no new nodes are added, then directly perform the Laplace smoothing in the fourth step of mesh geometry optimization. 5. The mesh deformation optimization method for deformable object cutting simulation in a virtual surgery according to claim 1, characterized in that: the mesh geometry optimization process described in the fourth step, (a) Perform mesh relaxation on the target area body mesh, and perform the following operations for each node in the target area, Among them, (x _i , y _i , z _i ) are the coordinates of the target node, (x _p , y _p , z _p ) are the adjusted coordinates of the target node, and N is the total number of all nodes connected to the target node; To judge the quality of the adjusted grid, the judgment criteria are as follows: Where Q _R is the associated quality coefficient (0<Q _R ≤1), Q _Vi is the quality standard of the search target unit described in the first step, where Q _Vi is the quality coefficient of the tetrahedron containing the target node, The larger Q _R is, the higher the grid quality is; If the adjusted target node is located in the target area and is larger than the _QR value of the target node before adjustment, then move the target node to the adjusted position, otherwise let x _p ＝(x _p + _xi )/2, y _p ＝(y _p +y _i )/2, z _p ＝(z _p +z _i )/2 (5) Afterwards, the above operations are repeated until the quality standard is met or the upper limit of the cycle is reached; (b) Laplace smoothing is performed on the cut local surface mesh, moving each node of the local surface mesh to the average position of its neighbors.