Implicit porous structure modeling method based on Voronoi subdivision

Abstract

The invention provides an implicit porous structure modeling method based on Voronoi subdivision, and relates to the technical field of implicit modeling. The method comprises the following steps: firstly, carrying out Voronoi space subdivision on a point set to generate a three-dimensional cell structure; constructing an internally tangent implicit field based on the surface normal and vertex coordinates; constructing a surface-level connected implicit field according to a surface-adjacency relationship, and further fusing to generate a unit-level implicit field; fusing all the unit fields to obtain a global implicit field, and extracting a contour surface to generate a porous structure. By adjusting control parameters, high-precision controllable modeling of the pore structure is achieved, and the method is suitable for bone trabecula structure matching.

Description

Technical Field

[0001] The present invention relates to the technical field of implicit modeling, and in particular to an implicit porous structure modeling method based on Voronoi subdivision. Background Art

[0002] Nature is rich in complex topologies, including porous structures. Representing the geometric structures represented by such complex topologies is extremely challenging. However, porous structures in the real world are often non-periodic, which often exhibit superior geometric and physical properties. Modeling controllable non-periodic porous structures is extremely challenging.

[0003] Implicit functions can express rich geometries, but implicit modeling can be imprecise when expressing complex microstructures. This is especially true when modeling porous structures with complex topologies. Existing modeling methods based on Voronoi space subdivision cannot independently express the structural characteristics of each pore, and provide insufficient control over pore size and pore diameter. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide an implicit porous structure modeling method based on Voronoi subdivision, which makes up for the lack of control strength of porous structures at the microscale. The porous structure generated by this method has a larger surface area ratio and more accurately matches the trabecular structure.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] An implicit porous structure modeling method based on Voronoi subdivision, comprising:

[0007] In the bounded open set, a point set for controlling pore distribution is obtained, and Voronoi space subdivision is performed on the point set to obtain a three-dimensional topological structure including a plurality of Voronoi cells;

[0008] For each Voronoi cell, a set of distances from point x to each face is calculated based on the normal vectors of all faces of the cell and the coordinates of any vertex on the face, and the distance sets are fused using a smooth fusion function to obtain an inscribed implicit field that maintains the continuity of the set smoothing order;

[0009] For each face of the Voronoi cell, a set of polygonal edges coplanar with the face is obtained based on the face-adjacency relationship, the distance from point x to the plane where each coplanar edge is located and to the plane where the face itself is located is calculated, and the face-level connected implicit field is obtained by fusing them through the smooth fusion function;

[0010] The inscribed implicit field and the surface-level connected implicit field are subjected to secondary fusion using the smooth fusion function to obtain the unit-level implicit field corresponding to the Voronoi cell;

[0011] Perform a combined operation on the search cell-level implicit fields of all Voronoi cells to generate a global implicit field that describes the complete aperiodic porous structure;

[0012] Perform isosurface extraction on the global implicit field to obtain the target porous geometric surface;

[0013] By adjusting at least one of the bounded open set, the point set, the smoothing order, the fusion range and the isosurface threshold, controllable modeling of pore size, shape, connectivity and overall porosity is achieved.

[0014] Preferably, the expression of the Voronoi cell is:

[0015] V i ={x∈Ω|||xp i ||≤||xp j ||,i≠j}

[0016] Where x represents a point in m-dimensional space, Ω represents a bounded open set, and p i and p j represents two points in the point set consisting of n points, ||xp n || represents point x and point p n The Euclidean distance between i Represents each of the Voronoi cells in m dimensions.

[0017] Preferably, the distance in the distance set is expressed as:

[0018]

[0019] Among them, d i (x) represents the distance from point x to the i-th face of the current cell, f i is the i-th face of the current Voronoi cell, is the unit normal vector of the ith face, is any vertex on the i-th face, and x represents a point in m-dimensional space.

[0020] Preferably, the expression of the inscribed implicit field is:

[0021] D c (x) = B u (D cs (x),n,δ)

[0022] Among them, Bu (·) represents the fusion operation, D cs (x) is the set of distances from point x in a single Voronoi cell to each surface k is the number of faces of the Voronoi cell, n is the smoothing order, and δ represents the range of fusion.

[0023] Preferably, the expression of the smooth fusion function is:

[0024]

[0025] in, is the implicit field scalar value obtained after fusion in step 1, is the signed distance from point x to the first face of the current Voronoi cell, max n,δ (·) is a smooth maximum operation with parameters.

[0026] Preferably, during the secondary fusion process, all surface-level connected implicit fields are processed in sequence using a linear iteration method to reduce the risk of global field degradation.

[0027] Preferably, the isosurface threshold σ is in the range of 0≤σ≤1, and the closer σ is to 0, the larger the pore size is, and the closer σ is to 1, the smaller the pore size is.

[0028] Preferably, the local continuity of the porous structure and the diameter of the connecting neck can be independently regulated by adjusting the smoothing order n and the range of fusion.

[0029] Preferably, the global implicit field is directly exported as a geometric file in a format recognizable by additive manufacturing after triangulation, so as to be used for the printing production of bone tissue engineering scaffolds or functional gradient materials.

[0030] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0031] The present invention provides an implicit porous structure modeling method based on Voronoi subdivision, comprising: obtaining a point set for controlling pore distribution within a bounded open set, and performing Voronoi space subdivision on the point set to obtain a three-dimensional topological structure containing a plurality of Voronoi cells; for each of the Voronoi cells, calculating a set of distances from a point x to each face based on the normal vectors of all faces of the cell and the coordinates of any vertex on the face, and performing a union operation and fusion on the distance sets using a smooth fusion function to obtain an inscribed implicit field that maintains the continuity of a set smoothing order; for each face of the Voronoi cell, obtaining a set of polygonal edges coplanar with it based on a face-adjacency relationship, and calculating the distances from point x to each coplanar face. The distance from the plane where the edge is located and to the plane where the face itself is located is obtained by fusing the surface-level connected implicit field through the smooth fusion function; the inscribed implicit field and the surface-level connected implicit field are secondary fused with the smooth fusion function to obtain the unit-level implicit field of the corresponding Voronoi cell; the search unit-level implicit field of all Voronoi cells is performed and fused to generate a global implicit field describing the complete non-periodic porous structure; the global implicit field is extracted from the isosurface to obtain the target porous geometric surface; by adjusting at least one of the bounded open set, the point set, the smoothing order, the fusion range and the isosurface threshold, the pore size, shape, connectivity and overall porosity are controlled and modeled. The method of generating porous structures of the present invention makes up for the lack of control strength of porous structures at the microscale. The porous structure generated by this method has a larger surface area ratio and more accurately matches the trabecular structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0033] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0034] Figure 2 A visualization diagram of the topological structure of the overall Voronoi cell subdivision provided by an embodiment of the present invention;

[0035] Figure 3 A visualization diagram of the topological structure of a single Voronoi cell provided in an embodiment of the present invention;

[0036] Figure 4 Result diagrams under different parameters provided by the embodiment of the present invention;

[0037] Figure 5 A schematic diagram of a global Voronoi subdivision provided in an embodiment of the present invention;

[0038] Figure 6 A schematic diagram of the connectivity of the inscribed implicit field provided by an embodiment of the present invention;

[0039] Figure 7 Schematic diagram of the geometric morphology of the Voronoi porous structure generated under different parameter combinations provided in an embodiment of the present invention;

[0040] Figure 8 A schematic diagram of a porous structure obtained under specific parameters provided in an embodiment of the present invention;

[0041] Figure 9 This is a schematic diagram of the first complex porous structure provided by an embodiment of the present invention;

[0042] Figure 10 A second schematic diagram of a complex porous structure provided by an embodiment of the present invention;

[0043] Figure 11 This is a third schematic diagram of a complex porous structure provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] The purpose of the present invention is to provide an implicit porous structure modeling method based on Voronoi subdivision, which makes up for the lack of control over porous structures at the microscale. The porous structure generated by this method has a larger surface area ratio and more accurately matches the trabecular structure.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 A flow chart of the method provided in the embodiment of the present invention is shown in FIG. Figure 1 As shown, the present invention provides an implicit porous structure modeling method based on Voronoi subdivision, comprising:

[0048] Step 100: obtaining a point set for controlling pore distribution within the bounded open set, and performing Voronoi space subdivision on the point set to obtain a three-dimensional topological structure containing a plurality of Voronoi cells;

[0049] Step 200: For each Voronoi cell, calculate the distance set from point x to each face based on the normal vectors of all faces of the cell and the coordinates of any vertex on the face, and use the smooth fusion function to perform a union operation on the distance set to obtain an inscribed implicit field that maintains the continuity of the set smoothing order;

[0050] Step 300: For each face of the Voronoi cell, obtain the set of polygonal edges coplanar with it based on the face-adjacency relationship, calculate the distance from point x to the plane where each coplanar edge is located and to the plane where the face itself is located, and fuse them through a smooth fusion function to obtain the face-level connected implicit field;

[0051] Step 400: The inscribed implicit field and the surface-level connected implicit field are secondary fused using a smooth fusion function to obtain the cell-level implicit field corresponding to the Voronoi cell;

[0052] Step 500: performing a combined operation on the search unit-level implicit fields of all Voronoi cells to generate a global implicit field describing the complete aperiodic porous structure;

[0053] Step 600: performing isosurface extraction on the global implicit field to obtain the target porous geometric surface;

[0054] Step 700: Achieve controllable modeling of pore size, shape, connectivity and overall porosity by adjusting at least one of the bounded open set, point set, smoothing order, fusion range and isosurface threshold.

[0055] Specifically, the specific steps of this embodiment are:

[0056] Based on computational geometry algorithms, the topological structure of the Vornoi space subdivision is obtained, which serves as the geometric property support of the porous structure.

[0057] The inscribed implicit field D of each Voronoi cell is defined by the distance function c (x).

[0058] The same method is used to define the connected implicit field D between adjacent Voronoi cells. t (x), using implicit mixing technology to mix the Vornoi cell implicit field and the connected implicit field, and the inscribed implicit field D c (x) and the connected implicit field D t (x) Mix to get the implicit field D of each independent Voronoi v (x). We can further obtain the overall implicit field F(x)

[0059] Take the implicit field F(x) = 0, and through the designed parameter R i and R jThe porous structure is designed and controlled to generate a non-periodic porous structure that meets the pore characteristics.

[0060] Furthermore, the present invention uses implicit functions and computational geometry as mathematical foundations, obtains a three-dimensional Voronoi diagram topology structure by subdividing the Voronoi space, and then uses implicit modeling technology and implicit hybrid technology to model the non-periodic porous structure. The specific process is as follows:

[0061] 1. Voronoi space subdivision

[0062] Given a bounded open set and a point set Then the Voronoi space subdivision can be defined as:

[0063] V i ={x∈Ω|||xp i ||≤||xp j ||,i≠j}

[0064] Among them, x represents a point in m-dimensional space, Ω represents a set, and p i and p j Represents two points in the set P of n points, ||xp n || represents point x and point p n The Euclidean distance between them is , and all x in the following formulas represent a point in m-dimensional space (m = 3 in this solution). Bold characters represent vectors, and plain characters represent scalars, the same below).

[0065] Among them, V i Represents each Voronoi cell in m dimension, the set is the Voronoi diagram of m-dimensional Ω, such as Figure 2 shown.

[0066] 2. Voronoi inscribed implicit field

[0067] Define the implicit distance field of the Voronoi cells as Figure 3 As shown, the distance from a point x in a Voronoi cell to each face can be expressed as:

[0068]

[0069] Among them, · is the vector dot product, f i is the i-th face of the current Voronoi cell, is the unit normal vector of the ith face, is any vertex on the i-th face. The implicit field of the Voronoi cell is defined as:

[0070] Dc (x) = B u (D cs (x),n,δ)

[0071] Among them, B is the designator of Blending, which means fusion operation, and u means Union. cs (x) is the set of distances from point x in a single Voronoi cell to each surface k is the number of faces in the Voronoi cell, n is the smoothing order, and δ represents the range of fusion. R i It is to facilitate the extraction of different isosurfaces of the implicit field of Voronoi cells, satisfying R i ≠R i-1 , k is the number of faces of Voronoi cells. B u It is the fusion operation function (smooth absolute function), which can achieve smooth mixing of implicit fields. n represents C n Continuity, δ, is used to control the range in which mixing occurs. It is defined as follows:

[0072]

[0073] max(·) represents the union operation of the fusion operation, x and y are two scalar values, n is the smoothing order, and δ represents the range of fusion.

[0074] in:

[0075]

[0076] In the above formula, x is the scalar value, which is the result of xy in the previous formula, n is the smoothing order, and δ represents the range of fusion.

[0077] Set D cs The elements of (x) are mixed in sequence to obtain the smoothness C n The Voronoi cell geometry is calculated as follows:

[0078]

[0079] The above formula is the iterative formula of linear fusion, which uses max() to merge and operate, and i is also the number of faces of the current cell. is the distance from point x to the i-th surface, n is the smoothing order, and δ represents the range of fusion.

[0080] Pick The isosurface of different parameters is shown in the figure below. Figure 4 As shown, d i (x) represents the distance from point x to the i-th face of the current cell, R i Is a scalar value.

[0081] 3. Global Voronoi subdivision:

[0082] Connectivity of the Inscribed Implicit Field

[0083] like Figure 5 As shown, each individual Voronoi cell is relatively closed. In order to form a connected component porous structure, adjacent Voronoi cells need to be connected. The method used is to use the coplanar information to construct a new connected implicit field. The idea is similar to the above definition of the field of Voronoi cells. Due to the duality of Voronoi, we only need to calculate the distance from point x to Figure 6 (b) The distances to the planes on which the sides of the coplanar polygons lie and to Figure 6 The distance from the plane of edge v2v3 in (a). Defined as follows:

[0084]

[0085] Among them, B u It is also a fusion operation and operation, d j (x) represents the distance to the surface where the edge of the current polygon is located and is orthogonal to the surface where the polygon is located, d i (x) represents the distance from point x to the face where the current coplanar polygon is located, m is the number of edges of the current coplanar polygon, n is the smoothing order, and δ represents the range of fusion. is any point on the jth side of the coplanar polygon, is the normal vector of the edge, satisfying m is the number of sides of the polygon that are coplanar. i ≠R i-1 ≠R j ≠R j-1 .

[0086] The connectivity of each face of each Voronoi cell together constitutes the total implicit field D of the current Voronoi cell and its neighboring cells. t (x):

[0087]

[0088] Among them, B u It is also a fusion operation and operation. is the connected implicit field of the i-th face of the current cell, k is the number of faces of the current cell, n is the smoothing order, and δ represents the range of fusion.

[0089] like Figure 7 As shown, the field of the Voronoi cell is mixed with the total field of the adjacent connected cells to obtain D(x):

[0090] D v (x) = -B u ({D t (x),-D c (x)},n,δ)

[0091] Among them, B u It is also a fusion operation and operation, D t (x) is the total connected implicit field of all faces of the current cell, D c (x) is the internal implicit field of the current cell, n is the smoothing order, and δ represents the range of fusion.

[0092] The implicit field F(x) of the entire Voronoi tessellation can be defined as:

[0093]

[0094] Where v is the vth cell in the global Voronoi subdivision, ∪ is the union operator, and N is the total number of cells. Here N is the number of Voronoi cells obtained by the global Voronoi subdivision. Figure 8 For F(x) = 0, the parameter R i =0.2, R j =0.6 to obtain a porous structure.

[0095] Figures 9 to 11 Several complex porous structures generated using the present invention are presented.

[0096] The focus of the present invention is to use the Voronoi topology to implicitly generate non-periodic and C n Continuous porous structures can be customized using the parameter R for each pore within the porous structure, achieving a high degree of freedom in porous structure modeling and enhancing control over porous structure generation. Compared to similar methods, the method for generating porous structures in this paper overcomes the lack of control over porous structures at the microscale. The porous structures generated by this method have a larger surface area ratio and more accurately match the trabecular bone structure.

[0097] The present invention can implicitly generate C n The continuous and highly liberalized porous structure, with a high degree of customization of the pore state, can be widely used in additive manufacturing and modeling of complex topological structures in bone tissue engineering.

[0098] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0099] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. An implicit porous structure modeling method based on Voronoi subdivision, characterized in that: include: In the bounded open set, a point set for controlling pore distribution is obtained, and Voronoi space subdivision is performed on the point set to obtain a three-dimensional topological structure including a plurality of Voronoi cells; For each Voronoi cell, a set of distances from point x to each face is calculated based on the normal vectors of all faces of the cell and the coordinates of any vertex on the face, and the distance sets are fused using a smooth fusion function to obtain an inscribed implicit field that maintains the continuity of the set smoothing order; For each face of the Voronoi cell, a set of polygonal edges coplanar with the face is obtained based on the face-adjacency relationship, the distance from point x to the plane where each coplanar edge is located and to the plane where the face itself is located is calculated, and the face-level connected implicit field is obtained by fusing them through the smooth fusion function; The inscribed implicit field and the surface-level connected implicit field are subjected to secondary fusion using the smooth fusion function to obtain the unit-level implicit field corresponding to the Voronoi cell; Perform a combined operation on the search cell-level implicit fields of all Voronoi cells to generate a global implicit field that describes the complete aperiodic porous structure; Perform isosurface extraction on the global implicit field to obtain the target porous geometric surface; By adjusting at least one of the bounded open set, the point set, the smoothing order, the fusion range and the isosurface threshold, controllable modeling of pore size, shape, connectivity and overall porosity is achieved.

2. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The expression of the Voronoi cell is: V i ={x∈Ω|||x-p i ||≤||x-p j ||,i≠j} Where x represents a point in m-dimensional space, Ω represents a bounded open set, and p i and p j represents two points in the point set consisting of n points, ||xp n || represents point x and point p n The Euclidean distance between i Represents each of the Voronoi cells in m dimensions.

3. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The distance expression in the distance set is: Among them, d i (x) represents the distance from point x to the i-th face of the current cell, f i is the i-th face of the current Voronoi cell, is the unit normal vector of the ith face, is any vertex on the i-th face, and x represents a point in m-dimensional space.

4. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The expression of the inscribed implicit field is: D c (x)=B u (D cs (x),n,δ) Among them, B u (·) represents the fusion operation, D cs (x) is the set of distances from point x in a single Voronoi cell to each surface k is the number of faces of the Voronoi cell, n is the smoothing order, and δ represents the range of fusion.

5. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The expression of the smooth fusion function is: in, is the implicit field scalar value obtained after fusion in step 1, is the signed distance from point x to the first face of the current Voronoi cell, max n,δ (·) is a smooth maximum operation with parameters.

6. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: During the secondary fusion process, all surface-level connected implicit fields are processed in sequence using a linear iteration method to reduce the risk of global field degradation.

7. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The isosurface threshold σ has a value range of 0≤σ≤1, and the closer σ is to 0, the larger the pore size is, and the closer σ is to 1, the smaller the pore size is.

8. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: By adjusting the smoothing order n and the fusion range, the local continuity of the porous structure and the connection neck diameter can be independently controlled.

9. The implicit porous structure modeling method based on Voronoi subdivision according to claim 1, characterized in that: The global implicit field is directly exported as a geometric file in a format recognizable by additive manufacturing after triangulation, so as to be used for the printing production of bone tissue engineering scaffolds or functional gradient materials.

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