Molecular grid model smoothing method and device
The three-dimensional grid model of the molecular surface is pretreated and smoothed by the Vino centroid mosaic method and the Catmull-Clark and Loop algorithms, which solves the problem of low quality of the molecular surface grid and achieves effective smoothing and quality improvement of the grid.
Patent Information
- Application Number
- CN202311654126.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-05
- Publication Date
- 2025-06-06
AI Technical Summary
The prior art is difficult to effectively smooth the three-dimensional grid model of molecular surfaces, resulting in low grid quality and cannot be directly used in downstream applications, affecting performance.
The Vino centroid mosaic method is used for pre-processing, unconventional vertices are removed, grid smoothing is performed through the Catmull-Clark algorithm and the Loop algorithm, and error control and reverse conversion are performed to obtain a smoothed three-dimensional grid model.
The quality of the molecular surface grid is improved, the problems of self-crossing, redundant elements, holes and isolated vertices are solved, and the grid is effectively smoothed, suitable for various downstream applications.
Smart Images
Figure CN120107092A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of computational geometry technology, and in particular to a molecular grid model smoothing method and device. Background Art
[0002] The three-dimensional mesh model of the surface of biological molecules is an important information in molecular science. It can provide different types of information to end users and researchers in different fields such as computer graphics, mathematics, molecular biology, biophysics, chemistry, etc. The molecular surface mesh model helps to obtain various molecular functional information, including structure prediction, docking and implicit solvent modeling, protein folding, molecular interaction, and calculation of its area and volume. Unfortunately, the mesh quality of the original mesh model generated from the molecular data cannot meet the requirements. There are common problems such as self-intersection, poor triangular mesh quality, irregularity, and roughness. It cannot be directly used for various downstream applications, which will cause the failure of downstream applications (such as molecular surface re-meshing or surface potential calculation) or affect its performance. Therefore, it is necessary to first refine and smooth the molecular mesh to improve the molecular surface mesh quality and make it suitable for various downstream applications.
[0003] Mesh smoothing by subdivision is a standard method, and there are some general smoothing algorithms for three-dimensional models. For example, the Catmull-Clark algorithm is very successful in smoothing B-spline surfaces. However, it generates quadrilateral meshes instead of typical triangular meshes, so it cannot be directly applied to molecular surface meshes; the Loop algorithm is an alternative to Catmull-Clark, which subdivides a triangle into four triangles and calculates new vertex positions to achieve a smoother surface. Similarly, the least squares surface smoothing method, the butterfly smoothing method, and the midpoint algorithm are also used for smoothing. However, most of these methods are effective for surface meshes with continuous curvature. Molecular surfaces have unique curvature changes, with sudden changes from concave to convex or from convex to concave, which is a challenge for mesh smoothing. At present, there is a lack of effective smoothing methods for molecular surface meshes, and there is no comparative experimental study on the smoothing effect of existing mesh smoothing methods on molecular surface meshes. Summary of the invention
[0004] In view of this, the present invention provides a molecular mesh model smoothing method and device to solve the above problems.
[0005] The first aspect of the present invention provides a molecular mesh model smoothing method, comprising: obtaining a three-dimensional mesh model of a molecular surface; preprocessing the triangular mesh in the three-dimensional mesh model by a Voronoi centroid tessellation method; removing irregular vertices in the preprocessed triangular mesh based on valence optimization and local re-meshing operators to obtain a standard triangular mesh; calculating and processing the standard triangular mesh by a Catmull-Clark algorithm to obtain positions of new vertices; connecting the new vertices based on a Loop algorithm to obtain a new triangular mesh; and performing error control and inverse conversion processing on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model.
[0006] In another implementation of the present invention, the molecular mesh model smoothing method further includes: eliminating major defects in the three-dimensional mesh model, wherein the major defects include self-intersections, redundant elements, holes, and isolated vertices.
[0007] In another implementation of the present invention, error control and reverse conversion processing are performed on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model, including: calculating the original three-dimensional mesh model M i And the smoothed 3D mesh model M f Hausdorff distance; for each vertex v i ∈M i , find its nearest vertex v f ∈M f , v i Marked as v f The original position of each vertex v f ∈M f Both return to their original position v i ∈M i Performs a reverse transformation, where each vertex is translated along its normal toward its original position.
[0008] In another implementation of the present invention, the Hausdorff distance is calculated as follows:
[0009] d H =max{d H (M i ,M f ),d H (M f ,M i )}
[0010] d H (M i ,M f )=max v i ∈M i {d(v i ,M i )}
[0011] d H (M f ,M i )=maxv f ∈M f {d(v f ,M i )}
[0012] Among them, M i is the original 3D mesh model, M f is the smoothed 3D mesh model, vertex v i ∈M i , v i The nearest vertex v f ∈M f .
[0013] In another implementation of the present invention, the molecular mesh model smoothing method further includes:
[0014] Calculate each vertex v f ∈M f The exact conversion amplitude dt vf :
[0015] dt vf =min[d H (v i , v f ),1 2{Mean(dt),d H (v i , v f )}]
[0016] Among them, d H (v i , v f ) is v f and v i The Hausdorff distance between , Mean(dt) is the local mean of the transformation.
[0017] The second aspect of the present invention provides a molecular mesh model smoothing device, including a model acquisition module for acquiring a three-dimensional mesh model of a molecular surface; a preprocessing module for preprocessing the triangular mesh in the three-dimensional mesh model by a Voronoi centroid tessellation method; a smoothing processing module for removing irregular vertices in the preprocessed triangular mesh based on valence optimization and local re-meshing operators to obtain a standard triangular mesh; calculating and processing the standard triangular mesh by a Catmull-Clark algorithm to obtain positions of new vertices; connecting new vertices based on a Loop algorithm to obtain a new triangular mesh; and performing error control and reverse conversion processing on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model.
[0018] The molecular mesh model smoothing method of the present invention is a mesh smoothing method specifically for molecular surface three-dimensional mesh models. Compared with the Catmull-Clarck method, the Catmull-Clarck method is used for quadrilateral meshes, while the method of the present invention stores these vertices and connects them into triangular meshes instead of quadrilateral meshes; retains the positions of original vertices (original mesh and newly created vertices) for reverse conversion; takes the Voronoi centroid tessellation method as the starting point and the three-dimensional smoothing algorithm as the end point, and controls the geometric loss (i.e. deformation) that may occur during the smoothing process through angle subdivision and error minimization error-driven smoothing method. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art description. By reading the detailed description of the following implementation, the advantages and benefits of the solutions become clear to those skilled in the art. The drawings are only used to illustrate the preferred implementation and are not considered to be limitations of the present invention. In the drawings:
[0020] Figure 1 The present invention is a flowchart of a molecular mesh model smoothing method and device according to an embodiment of the present invention.
[0021] Figure 2 The figure is a schematic diagram of a mesh smoothing process based on mesh subdivision according to an embodiment of the present invention.
[0022] Figure 3 This is a schematic diagram of the results of CVT processing and direct smoothing using Loop and our method according to one embodiment of the present invention.
[0023] Figure 4 Schematic diagram of concave and convex surfaces during the smoothing process of one embodiment of the present invention.
[0024] Figure 5 Schematic diagram of smoothing results of ADP (top) and 1WO0 (middle and bottom) according to an embodiment of the present invention.
[0025] Figure 6 Schematic diagram of smoothing results on AChE (upper) and 6BST (lower) according to an embodiment of the present invention.
[0026] Figure 7 Schematic diagram of smoothed results of CONNEXIN (upper two rows) and nAChR (lower two rows) according to an embodiment of the present invention. DETAILED DESCRIPTION
[0027] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be described clearly and in detail below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in the field based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.
[0028] Figure 1 A flow chart of the steps of a molecular mesh model smoothing method provided by an embodiment of the present invention, such as Figure 1 As shown, this embodiment mainly includes the following steps:
[0029] S101. Obtain a three-dimensional mesh model of the molecular surface.
[0030] S102, preprocessing the triangular mesh in the three-dimensional mesh model by using the Voronoi centroid tessellation method.
[0031] For example, since the input molecular surface meshes have many defects, in the preprocessing, all meshes are cleaned and their main defects, including self-intersections, redundant elements, holes and isolated vertices, are eliminated. Figure 3 As shown in the figure, from left to right, the pictures are: input mesh, mesh processed by CVT method, mesh processed by Loop method, mesh processed by Loop method based on CVT, mesh processed by Catmull-Clarck method, and the results after 1, 2, and 3 iterations respectively. It can be seen that the Voronoi centroid mosaic method (CVT) has a significant effect on smoothing, and the Voronoi centroid mosaic method (CVT) is used as a necessary initialization step for the smoothing algorithm.
[0032] S103, based on the valence optimization and local re-meshing operators, remove the irregular vertices in the pre-processed triangular mesh to obtain a standard triangular mesh.
[0033] Exemplarily, splitting is skipped in special vertices (i.e., vertices with valence ≥ 7). The regularity of vertices is improved by applying valence optimization and local remeshing operators (including edge splitting and collapse), and edge splitting is applied on all edges without considering any special vertex.
[0034] S104, calculating and processing the standard triangle mesh by using the Catmull-Clark algorithm to obtain the positions of new vertices.
[0035] S105. Connect the new vertices based on the Loop algorithm to obtain a new triangle mesh.
[0036] For example, Figure 2As shown, from left to right: the first picture is the input mesh (CVT initialization); the second picture inserts a new point, i.e., the green point, at the midpoint of the edge, and the position of the new point is calculated according to the Catmull-Clark method; the third picture establishes connections between the inserted new points to make it a triangular mesh similar to the Loop method; the fourth picture subdivides the triangular mesh based on the Catmull-Clarck method, and each input triangle is divided into three quadrilaterals.
[0037] It should be understood that, compared to the Catmull-Clarck method, which is used for quadrilateral meshes, the method of the present invention stores these vertices and connects them into triangular meshes, processing triangular meshes instead of quadrilateral meshes. The positions of the original vertices (the original three-dimensional mesh and the newly created vertices) are retained for reverse conversion.
[0038] S106: Perform error control and reverse conversion processing on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model.
[0039] For example, mesh smoothing algorithms often have a common limitation, namely deformation. During the smoothing process, concave surfaces move inwards, e.g. Figure 4 As shown, in the left image, the back side is the original surface, while the blue line is the smoothed surface, the molecular surface has a surprising pattern on the surface, changing from concave to convex and vice versa. So, in some parts of the surface, the mesh deforms inwards according to the concave-convexity of the part, and in other parts it deforms outwards.
[0040] It should be understood that in order to control this deviation, the Hausdorff distance d is used. H , and the geometric error is calculated for each vertex. Inspired by error-driven remeshing, this method prevents remeshing operators from producing geometric errors larger than a given threshold. Smoothing is first applied, but later each vertex is moved toward the average d of the original mesh. H To do this, the original mesh coordinates are stored beforehand, including the new (created by subdivision) and old vertices.
[0041] Specifically, the original 3D mesh model M i (Input surface mesh) and smoothed 3D mesh model M f The Hausdorff distance d between (output surface mesh) H The calculation of is as follows:
[0042] d H =max{d H (M i ,M f ),dH (M f ,M i )}
[0043] d H (M i ,M f )=maxv i ∈M i {d(v i ,M i )}
[0044] d H (M f ,M i )=maxv f ∈M f {d(v f ,M i )}
[0045] The Hausdorff distance is asymmetric, i.e., the second and third formulas do not necessarily produce the same value. However, in this invention, we only calculate d in one direction. H For each vertex v i M i , find its nearest vertex v f ∈M f , and v i Marked as v f The original position of each vertex v f ∈M f Both return to their original position v i ∈M i Perform the reverse transformation, transforming with the calculated Hausdorff distance. Since the direction of vertex transformation changes from concave to convex and vice versa, each vertex is transformed along its normal to the original position, and the magnitude of the transformation is calculated as the average of the calculated distances of the local vertices, that is, the original vertex v i In v f In other words, the transformation directions of the concave and convex regions are opposite.
[0046] The molecular mesh model smoothing method of the present invention is a mesh smoothing method specifically for molecular surface three-dimensional mesh models. Compared with the Catmull-Clarck method, the Catmull-Clarck method is used for quadrilateral meshes, while the method of the present invention stores these vertices and connects them into triangular meshes instead of quadrilateral meshes; retains the positions of original vertices (original mesh and newly created vertices) for reverse conversion; takes the Voronoi centroid tessellation method as the starting point and the three-dimensional smoothing algorithm as the end point, and controls the geometric loss (i.e. deformation) that may occur during the smoothing process through angle subdivision and error minimization error-driven smoothing method.
[0047] In another implementation of the present invention, the molecular mesh model smoothing method further includes: eliminating major defects in the three-dimensional mesh model, wherein the major defects include self-intersections, redundant elements, holes, and isolated vertices.
[0048] In another implementation of the present invention, error control and reverse conversion processing are performed on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model, including: calculating the original three-dimensional mesh model M i And the smoothed 3D mesh model M f Hausdorff distance; for each vertex v i ∈M i , find its nearest vertex v f ∈M f , v i Marked as v f The original position of each vertex v f ∈M f Both return to their original position v i ∈M i Performs a reverse transformation, where each vertex is translated along its normal toward its original position.
[0049] In another implementation of the present invention, the Hausdorff distance is calculated as follows:
[0050] d H =max{d H (M i ,M f ),d H (M f ,M i )}
[0051] d H (M i ,M f )=max v i ∈M i {d(v i ,M i )}
[0052] d H (M f ,M i )=maxv f ∈M f {d(v f ,M i )}
[0053] Among them, M i is the original 3D mesh model, M f is the smoothed 3D mesh model, vertex vi ∈M i , v i The nearest vertex v f ∈M f .
[0054] In another implementation of the present invention, the molecular mesh model smoothing method further includes:
[0055] Calculate each vertex v f ∈M f The exact conversion amplitude dt vf :
[0056] dt vf =min[d H (v i , v f ),1 2{Mean(dt),d H (v i , v f )}]
[0057] Among them, d H (v i , v f ) is v f and v i The Hausdorff distance between , Mean(dt) is the local mean of the transformation.
[0058] The method of the present invention has been proven to be feasible through experiments, simulations and use, and the results are good. Figure 5 , Figure 6 , Figure 7 As shown. Figure 5 In the figure, the smoothing methods used from left to right are: CVT, Butterfly, Midpoint, Loop, LS3, the method of the present invention (without CVT processing) and the method of the present invention (with CVT processing); Figure 6 In the figure, the smoothing methods used from left to right are: unprocessed input grid, Butterfly, Midpoint, Loop, LS3, the method of the present invention (without CVT processing) and the method of the present invention (with CVT processing); Figure 7 In the figure, all methods use CVT as the input grid, and the smoothing methods used in the picture from left to right are: CVT, Butterfly, Midpoint, Loop, LS3 and the method of the present invention.
[0059] A second aspect of the present invention provides a molecular mesh model smoothing device, comprising:
[0060] Model acquisition module: used to obtain the three-dimensional mesh model of the molecular surface.
[0061] Preprocessing module: used to preprocess the triangular mesh in the three-dimensional mesh model by Voronoi centroid tessellation method.
[0062] Smoothing processing module: It is used to remove irregular vertices in the preprocessed triangular mesh based on the valence optimization and local re-meshing operators to obtain a standard triangular mesh; the standard triangular mesh is calculated and processed by the Catmull-Clark algorithm to obtain the position of the new vertices; the new vertices are connected based on the Loop algorithm to obtain a new triangular mesh; the new triangular mesh is error controlled and reversely transformed to obtain the smooth result of the three-dimensional mesh model.
[0063] Thus far, specific embodiments of the present invention have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired results. Additionally, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing may be advantageous.
[0064] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.
[0065] In the description of the present invention, the terms "first" and "second" are only used to facilitate the description of different components or names, and cannot be understood as indicating or implying a sequential relationship, relative importance, or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features.
[0066] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.
[0067] It should be noted that although the specific embodiments of the present invention are described in detail in conjunction with the accompanying drawings, it should not be understood as limiting the scope of protection of the present invention. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still belong to the scope of protection of the present invention.
[0068] The examples of the embodiments of the present invention are intended to concisely illustrate the technical features of the embodiments of the present invention so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to be improper limitations of the embodiments of the present invention.
[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A molecular mesh model smoothing method, It is characterized in that include: Obtain a three-dimensional mesh model of the molecular surface; Preprocessing the triangular meshes in the three-dimensional mesh model by using the Voronoi centroid tessellation method; Based on the valence optimization and local re-meshing operators, the irregular vertices in the pre-processed triangle mesh are removed to obtain a standard triangle mesh; The standard triangle mesh is calculated and processed by using the Catmull-Clark algorithm to obtain the position of the new vertex; Connect the new vertices based on the Loop algorithm to obtain a new triangle mesh; The new triangular mesh is subjected to error control and inverse conversion processing to obtain a smooth result of the three-dimensional mesh model.
2. The method according to claim 1, It is characterized in that Also includes: Major defects in the three-dimensional mesh model are eliminated, including self-intersections, redundant elements, holes and isolated vertices.
3. The method according to claim 1, It is characterized in that The performing error control and reverse conversion processing on the new triangular mesh to obtain a smooth result of the three-dimensional mesh model includes: Calculate the original 3D mesh model M i And the smoothed 3D mesh model M f The Hausdorff distance; For each vertex v i ∈M i , find its nearest vertex v f ∈M f , v i Marked as v f The original location of Based on the Hausdorff distance, each vertex v f ∈M f Both return to their original position v i ∈M i Performs a reverse transformation, where each vertex is translated along its normal toward its original position.
4. The method according to claim 3, It is characterized in that The Hausdorff distance is calculated as follows: d H =max{d H (M i ,M f ),d H (M f ,M i )} d H (M i ,M f )=max v i ∈M i {d(v i ,M i )} d H (M f ,M i )=maxv f ∈M f {d(v f ,M i )} Among them, M i is the original 3D mesh model, M f is the smoothed 3D mesh model, vertex v i ∈M i , v i The nearest vertex v f ∈M f .
5. The method according to claim 4, It is characterized in that Also includes: Calculate each vertex v f ∈M f The exact conversion amplitude dt vf : dt vf =min[d H (v i ,v f ),1 2{Mean(dt),d H (v i ,v f )}] Among them, d H (v i , v f ) is v f and v i The Hausdorff distance between , Mean(dt) is the local mean of the transformation.
6. A molecular mesh model smoothing device, It is characterized in that include: Model acquisition module: obtain the three-dimensional mesh model of the molecular surface; Preprocessing module: preprocessing the triangular mesh in the three-dimensional mesh model by Voronoi centroid tessellation method; Smoothing processing module: Based on the valence optimization and local re-meshing operators, the irregular vertices in the pre-processed triangular mesh are removed to obtain a standard triangular mesh; the standard triangular mesh is calculated and processed by the Catmull-Clark algorithm to obtain the positions of new vertices; the new vertices are connected based on the Loop algorithm to obtain a new triangular mesh; the new triangular mesh is error controlled and reversely transformed to obtain the smooth result of the three-dimensional mesh model.