CN115935447B

CN115935447B - Mixed modeling method based on discrete Morse theory feature recognition

Info

Publication number: CN115935447B
Application number: CN202211402756.XA
Authority: CN
Inventors: 洪子橙; 钟芳宠; 吴海涛
Original assignee: Shanghai Platform For Smart Manufacturing Co Ltd
Current assignee: Shanghai Platform For Smart Manufacturing Co Ltd
Priority date: 2022-11-09
Filing date: 2022-11-09
Publication date: 2024-07-05
Anticipated expiration: 2042-11-09
Also published as: CN115935447A

Abstract

The invention discloses a mixed modeling method based on discrete Morse theory feature recognition, which comprises the following steps: acquiring a grid curved surface of an object to be measured, and calculating the geometric quantity of the grid curved surface; based on the geometric quantity, carrying out region segmentation on the grid curved surface to obtain a segmentation result; and carrying out local feature recognition on the segmented grid curved surface based on the segmentation result, and carrying out hybrid modeling based on the result of the local feature recognition. The method can keep the precision of the grid curved surface model and can carry out model modification more accurately and flexibly; the hybrid model can be characterized and rendered based on the mesh curved surface model, and can directly perform stretching and deformation operations by keeping parameter characteristics. Meanwhile, accurate positioning information can be provided for another grid model when the operation processes such as Boolean operation and the like are performed, and a more flexible modeling method is provided for a user.

Description

Mixed modeling method based on discrete Morse theory feature recognition

Technical Field

The invention relates to the field of three-dimensional prototype redesign and additive manufacturing, in particular to a hybrid modeling method based on discrete Morse theory feature recognition.

Background

The computer aided design and manufacturing technology has wide application in aerospace neighborhood, automobile manufacture, mold processing, rehabilitation aided manufacture and other neighborhood. Currently, in the product prototype modeling process, the main way is feature-based parametric modeling. In the modeling process, the focus of a user is not the geometric shape of the model, but an intelligent arrangement scheme of object characteristics and dimensions, so that when the model is atypical, the modeling is difficult and the efficiency is low. As the manufacturing industry changes to automation and intelligence, parametric models are difficult to accommodate with increasing demands for rapid CAD designs due to their low flexibility.

The triangular mesh model is a flexible and light model, adopts a triangular patch structure to describe the topological relation among data points, and has the advantages of high geometric accuracy, good integrity, strong topological consistency and the like. Along with the improvement of the three-dimensional vision measurement precision and efficiency, the capability of rapidly acquiring the triangular mesh model with fine geometric details is also enhanced. However, the increasing data volume is only expected to increase the operation speed of the computer, and the increasing storage space cannot meet the actual demands. The selection of a proper data representation mode, and the concise and effective description of the data representation mode on the premise of maximally storing information are one of the problems to be solved in the prior art.

Grid-parametric hybrid models describe objects using different model types, atypical shapes describe objects using grid curves, and typical shapes describe objects using parametric models. The grid-parameter mixed model can be utilized to realize flexible modification of the model, and the mixed model can absorb the advantages of the grid curved surface and the parameter curved surface, and is more accurate and higher in efficiency compared with the traditional modeling mode.

The existing grid-parameter mixed modeling technology is realized by performing Boolean operation on a grid curved surface and a parameter curved surface. The technology can add custom parameter features to the featureless discrete grid surface. However, since each element in the mesh surface is equivalent, there is no difficulty in accurately locating the feature. Therefore, the modeling mode can be only performed through manual interaction or spatial position assignment and the like, and the modeling efficiency and accuracy are greatly reduced. In a complex grid model, a plurality of typical curved surfaces, such as a cylinder, a plane, a sphere and the like, are often existed, partial characteristics of an input grid model are identified through a characteristic identification method, and a grid-parameter mixed model can be obtained. The designer can directly modify the parametric features of the hybrid model or use it for localization.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a hybrid modeling method based on discrete Morse theory feature recognition, wherein in the process of redesigning a three-dimensional model, a grid curved surface of an object is identified by a feature recognition mode to identify typical shape feature parameters in the grid curved surface model, and a non-feature grid model is changed into a grid-parameter hybrid model with feature constraint. The precision of the grid curved surface model can be maintained, and the model modification can be performed more accurately and flexibly; the hybrid model can be characterized and rendered based on the mesh curved surface model, and can directly perform stretching and deformation operations by keeping parameter characteristics. Meanwhile, accurate positioning information can be provided for another grid model when the operation processes such as Boolean operation and the like are performed, and a more flexible modeling method is provided for a user.

In order to achieve the technical purpose, the invention provides a hybrid modeling method based on discrete Morse theory feature recognition, which comprises the following steps:

s1, acquiring a grid curved surface of an object to be detected, and calculating the geometric quantity of the grid curved surface;

s2, based on the geometric quantity, carrying out region segmentation on the grid curved surface to obtain a segmentation result;

and S3, carrying out local feature recognition on the segmented grid curved surface based on the segmentation result, and carrying out mixed modeling based on the result of the local feature recognition.

Optionally, the geometric quantities include vertex normal vectors, vertex normal curvatures, vertex principal curvatures, and vertex curvature gradients.

Optionally, the calculation formula of the vertex normal vector is:

In the method, in the process of the invention, Vertex normal vector, which is vertex v _i; n is the number of vertexes; j is the j-th triangular patch; f _j is a triangular patch connected to vertex v _i; is the vertex angle of triangle f _j at vertex v _i; is the shape factor of the dough sheet; Is the outer normal of the triangular patch f _j; is the Euclidean distance from centroid to vertex v _i.

Optionally, the calculation formula of the vertex curvature gradient is:

wherein k ₁、k₂ represents principal curvatures corresponding to the two principal directions, respectively; { e ₁,e₂ } represents the principal direction gradient.

Optionally, generating a Morse unit by using a watershed algorithm, and performing region segmentation through the Morse unit.

Optionally, the watershed algorithm includes:

randomly selecting an initial triangle patch and carrying out greedy tracking to minimize the Morse function value of the adjacent triangle patches;

Continuously searching the initial triangular surface patches until a local minimum value is obtained;

The initial triangle patches are marked as local minimum triangles, and the mesh surface is divided into a plurality of Morse units by processing all triangle patches in the mesh surface.

Optionally, the Morse function is:

In the method, in the process of the invention, AndIs a mode of curvature gradient.

Optionally, the local feature identifying includes:

giving a curvature value range of the grid curved surface to represent a plane based on the segmentation result;

And calculating the average curvature and the positive and negative of the Gaussian curvature of each segmented grid curved surface based on the curvature value range.

The invention has the following technical effects:

The method can keep the precision of the grid curved surface model and can carry out model modification more accurately and flexibly; the hybrid model can be characterized and rendered based on the mesh curved surface model, and can directly perform stretching and deformation operations by keeping parameter characteristics. Meanwhile, accurate positioning information can be provided for another grid model when the operation processes such as Boolean operation and the like are performed, and a more flexible modeling method is provided for a user.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of a hybrid modeling method based on discrete Morse theory feature recognition according to an embodiment of the invention;

FIG. 2 is a schematic diagram of a ring neighborhood of vertices of a triangular mesh model in accordance with an embodiment of the present invention;

FIG. 3 is a schematic view of triangles with the same area, angle, centroid distance but different shapes according to the embodiment of the present invention;

FIG. 4 is a schematic diagram of a Morse unit and a watershed algorithm according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of Morse unit merging based on watershed algorithm according to an embodiment of the present invention;

FIG. 6 is a schematic view of five exemplary curved surfaces and their curvatures according to an embodiment of the present invention;

FIG. 7 is a diagram of an example of a hybrid modeling application of an embodiment of the present invention to an automotive sheet metal part tooling grid model.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

As shown in fig. 1, the invention discloses a hybrid modeling method based on discrete Morse theory feature recognition, which comprises the following steps:

In the traditional differential geometry, the implicit curved surface or the parameter curved surface has complete definition and calculation formula, so that geometric quantities such as normal vector, curvature and the like of the curved surface can be accurately calculated. The discrete triangular mesh curved surface is defined by the topological relation between the discrete point cloud and the nodes, and a differential formula in the traditional differential geometry cannot be applied to the discrete triangular mesh, so various geometric quantity estimation methods are generated.

Triangle mesh vertex method vector estimation is the basis for subsequent calculation of other geometric quantities. The triangular mesh model may be expressed as a linear table of vertices and triangular patches: m= { V, F }, wherein V= { V _i |1.ltoreq.i.ltoreq.n } is the set of all vertices in the triangular mesh model, and F= { F _j |1.ltoreq.j.ltoreq.m } is the set of all patches in the triangular mesh model.

Figure 2 is a schematic view of a ring neighborhood surface patch of a vertex v _i of a triangular mesh model,As the normal vector of vertex v _i, f _j represents a triangular patch that meets vertex v _i,Is the centroid of triangle f _j, G _j is the euclidean distance of the centroid to vertex v _i, a _j is the vertex angle of triangle f _j at vertex v _i,Is the outer normal of the triangular patch f _j.

The calculation formula of (2) is as follows:

In the method, in the process of the invention, The normal occupied weight provided for the dough piece f _j is calculated in the mode shown as the formula (4);

The calculation formula of (2) is as follows:

each triangular patch normal vector can be accurately determined by equation (2), and obviously, the weight selection in equation (1) determines the vertex normal vector estimation accuracy.

The geometry of triangles is many, such as area, centroid-to-vertex distance, vertex angle, etc. In general, the larger the area of the triangle, the angle of the vertex, the closer the shape is to a regular triangle, and the greater will be its contribution to the vertex normal; the further the centroid-to-vertex distance of the triangle, the greater the side length of the triangle, the less will the contribution to the vertex normal. Based on these characteristics, a certain geometric feature may be selected as the weight, or a combination of these features may be used to form a combination weight factor. However, for the weight factor of a single feature, there is a problem that triangle geometry is easily changed greatly but the same weight is expressed. As shown in fig. 3, two pairs of triangles have the same area, vertex angle and centroid distance, but have larger shape differences, and under the measurement of a single weight, the two pairs of triangles will express equal weights. Therefore, the measurement of the single weight is difficult to accurately reflect the real contribution of the patch to the vertex normal.

To improve the accuracy of the weight factor in describing the various geometric characteristics of a triangle, a shape factor μ is introduced that can express the shape of the triangle, defined as twice the ratio of triangle circumscribed circle radius to inscribed circle radius. The shape factor μ is:

Wherein a, b and c are three side lengths of triangle respectively, and different weights are given to triangular patches with different shapes by combining the shape quality center distance method of the shape factors.

In order to improve the estimation accuracy of the vertex normal vector in the characteristic areas with large curvature change, sharp edges and the like, the method is improved on the basis of the shape centroid weight, comprehensively considers the influence of the shape, the centroid distance and the angle of the vertex angle of the triangle on the vertex normal vector, and provides a new weight factor, wherein the new weight factor expression is as shown in the formula (4):

Wherein alpha is the angle of the vertex angle of the triangle, Is the distance from the vertex to the centroid, S represents the triangle area. For any triangular shape factor, mu, it is easy to prove that if and only if a=b=c,When μ takes the maximum value of 1. Furthermore, it is evident that μ tends to 0 if and only if a+b-c tends to 0. I.e. the three sides of the triangle tend to overlap, μ tends to be 0.

The weight factor is changed as follows:

Case 1：c→2a

in this embodiment, it is apparent that the apex angle α tends to pi. The weighting factor λ can be written as follows:

where k is a constant coefficient. It is apparent that in the present embodiment, 2a-c tends to be 0, and hence λ also tends to be 0, i.e., when the triangle tends to be straight, the weight factor tends to be 0.

Case 2: s0, G0 and m are constants.

In this embodiment, the weight factor λ can be written as follows:

Where k is a constant coefficient. It is apparent that in the present embodiment, c tends to be 0, and thus λ tends to be 0, that is, when the triangular patch is extremely small, the weight factor thereof also tends to be 0.

In summary, the weight factor proposed by the present invention can still maintain a limited value in the extreme case that three sides of a triangle and the smallest triangle are infinitely closely overlapped. Avoiding an abnormal increase of the weight factor when the parameters are very small.

Substituting the proposed new weight factors into normal vector estimation calculation to obtain:

After the normal vector of each node of the nodes in the grid curved surface is obtained, the normal vector is applied to perform normal curvature calculation along the direction of each side.

The normal curvature of curve (C) on parameter curved surface S is that r=r (S)The tangential plane is pi. The tangent vector of a point on the curved surface is perpendicular to the normal vector, i.e. there isTo two sides deriveThe condition of the combination curve on the curved surface is easily known:

Thus, in the triangular mesh model, the normal curvature along the direction of the mesh lines PP _i within the first-order neighborhood of the mesh node P, i.e., the edge curvature, can be expressed as:

{ r ₁,r₂ } is a set of orthogonal bases on the local tangential plane, and θ ₀ represents the angle between it and the principal direction { e ₁,e₂ }. From the Euler equation, in the { r ₁,r₂ } coordinate system, the normal curvature in the θ direction can be expressed as:

k_n(T_θ)＝acos²θ+bsinθ·cosθ+csin²θ (8)

Wherein the method comprises the steps of ,a＝k₁cos²θ₀+k₂sin²θ₀,b＝2(k₂-k₁)cosθ₀·sinθ₀,c＝k₁sin²θ₀+k₂cos²θ₀.

In the first-order neighborhood of the mesh node P, m normal curvatures can be obtained by the above equation (8). The maximum value of the normal curvature is set asA special coordinate system is established on the tangential plane where point P lies, such that e' ₁＝t_id,e₂＝e₁ n/||e₁n||,θ₀ represents the angle between its principal directions e ₁,e₂. The values of a, b, c in the above equation can be obtained by the least square method.

Let a=k _n(T_id from equation (8), the normal curvature along the θ _i direction is:

k_n(T_i)＝acos²θ_i+bcosθ_i·sinθ_i+csin²θ_i (9)

Where i=1, …, m. And (3) making:

K_i＝k_n(T_i)-acos²(θ_i)＝bcosθ_i·sinθ_i+csin²θ_i (10)

using a least squares method to minimize the sum of squares of the above equations, the solution is:

wherein:

Substituting the obtained a, b, c into formula (8) has:

the gaussian curvature, average curvature, principal curvature of the mesh nodes are:

s2, based on geometric quantity, carrying out region segmentation on the grid curved surface to obtain a segmentation result;

The mesh curvature gradients are calculated, the curvature gradient of each node is represented using a linear combination of principal direction gradients:

Since the two principal directions are mutually orthogonal, the modulus of curvature gradient can be expressed by:

Will be As a Morse function.

And generating Morse units by applying a watershed algorithm, and dividing the grid curved surface by the Morse units so as to minimize the f value in each unit. As shown in fig. 4, first, an initial triangle patch is randomly selected and greedy tracked, minimizing the Morse function value of the neighboring triangle patches. Then, the initial triangle patch is continuously searched until a local minimum is obtained. The initial triangle patch is then marked as a local minimum triangle and the mesh surface is divided into a plurality of Morse cells by processing all triangle patches within the mesh surface.

After all Morse units in the grid are calculated, a multi-stage Morse composite unit is generated based on watershed continuity combination, wherein the continuity is defined as the difference between the saddle point of the watershed and the local minimum point, and the difference refers to the topological 'stability' of combining adjacent Morse units, and the combined calculation formula is as follows:

f_persistence＝f_saddle-f_localmin (15)

Merging starts with the Morse cell with the smallest f _persistence until all cells are merged into one region. In this process, a binary tree is generated. In a binary tree, each Morse element has a "merge order" and "merge to" attribute, and each region is merged or split by changing the level of detail (LOD). FIG. 5 shows a multi-stage Morse composite unit generation process based on watershed algorithm.

And S3, carrying out local feature recognition on the segmented grid curved surface based on the segmentation result, and carrying out hybrid modeling based on the result of the local feature recognition.

After the feature segmentation result of S2, the next step is to perform recognition of local features. In S2, the mesh surface is divided into blocks by Morse unit, but the characteristic represented by each block is not yet identified. The shape of the segmented block can be rapidly identified by researching the positive and negative of the average curvature and the Gaussian curvature of each segmented block. However, since mesh models often have noise or surface undulations, in order to determine the mean curvature after weighted averaging and the positive and negative of gaussian curvature in each region, a curvature range of a given triangular mesh surface is required to represent a plane.

The average curvature of each vertex is Laplacian smoothed with the Gaussian curvature, and a histogram of both curvatures is constructed, which is effective in removing noise. If a plane is present in the model, a "valley" representing the plane is extracted from the histogram adjacent to the "peak" of the histogram. If no plane is present in the model, the width between the two closed "peaks" is used. The segmented feature blocks are divided into planar features, cylindrical features and spherical features. Since the cone and ring cannot be separated directly from the cylinder and sphere, respectively, the characteristics of the cylinder and sphere are listed using standard mean and gaussian curvature notation. It is necessary to distinguish between cones and rings by the principal curvature of the nodes. The maximum and minimum curvature histograms are reconstructed for the cylinder and sphere features, the effective zero point for each principal curvature is again determined, and the principal curvature distribution of each feature block, each vertex is utilized to distinguish between cones and cylinders, rings and spheres using the curvature rules in fig. 6.

Once the feature type is identified, specific parameters of the feature can be determined. The characteristic parameters are directly calculated by using discrete differential geometry. The parameters of each feature are determined using the following method.

(1) Plane:

Center point:

axial direction:

(2) Column:

radius:

Center point:

O_c(i)＝P(i)-n(i)*R_cly (21)

axial direction:

A_c(i)＝Norm(n(i)×(P(i)-O_cyl)×n(i)) (23)

(3) And (3) a circular ring:

Smaller radius:

Larger radius:

The outer ring is convex:

The outer ring is concave:

axial direction:

O_minor(i)＝P(i)-n(i)*R_{torus_minor} (28)

origin point:

n_p(i)＝Norm(n(i)-(n(i)*A_torus)*A_torus) (30)

(4) Sphere:

radius:

Center point:

(5) Conical:

radius (max):

axial direction:

Conical height:

H_cone＝h₁+h₂ (35)

taper angle:

Center point:

O_cone＝O_cone-A_cone*h₁,R_cone[h₁]>R_cone[h₂] (39)

O_cone＝O_cone-A_cone*h₂,R_cone[h₁]≤R_cone[h₂] (40)

Where P represents the vertex coordinates, m represents the number of vertices in the segment, k _m represents the average curvature of the vertices, k ₁ represents the larger value of the principal curvature, and k ₂ represents the smaller value of the principal curvature.

Fitting all the curved surface blocks conforming to the typical characteristics in the step 5 and extracting parameters in the grid model, and leaving the rest of the blocks to be not processed. Since its local features have been identified, the features can be used in CAD software, and feature-based modeling (stretching, deforming, rotating) can be performed based on the features. Meanwhile, positioning information and the like can also be provided for operations such as Boolean operation and the like.

Further, in the present embodiment, fig. 7 is a diagram showing an example of application of the present embodiment to hybrid modeling of a mesh model of an automotive sheet metal part, and illustrates a process of generating a hybrid model of the mesh model of the automotive sheet metal part. The tool digital-analog is obtained through a visual scanning device, and normal vectors, normal curvatures, main curvatures and curvature gradients of all nodes of the model are obtained through geometric quantity calculation of the grid model. And taking a mode of curvature gradient in the main curvature direction as a Morse function in a subsequent Morse theory, and further dividing the grid curved surface based on a watershed algorithm. Planar features (light gray planes) in the model are identified with cylindrical features (black curved surfaces) to form a grid-parameter hybrid model.

The hybrid model of the automobile sheet metal part tooling grid model is used for three-dimensional model redesign, and a foundation is provided for positioning of a quick-screwing screw (an object in a circle in fig. 7) based on parameter information provided by the characteristics of a cylinder and a plane. In the whole process, good topological characteristics and accuracy of the grid model are guaranteed. And the mixed model is more convenient and accurate than the grid model when being used in the subsequent redesign process. The model can be used for subsequent analysis and to guide processing.

The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims

1. The mixed modeling method based on discrete Morse theory feature recognition is characterized by comprising the following steps of:

S3, carrying out local feature recognition on the segmented grid curved surface based on the segmentation result, and carrying out mixed modeling based on the result of the local feature recognition;

the geometric quantity comprises a vertex normal vector, a vertex normal curvature, a vertex principal curvature and a vertex curvature gradient;

the calculation formula of the vertex curvature gradient is as follows:

Wherein k ₁、k₂ represents principal curvatures corresponding to the two principal directions, respectively; { e ₁,e₂ } represents the principal direction gradient;

the local feature identification includes:

calculating the average curvature and the positive and negative of Gaussian curvature of each segmented grid curved surface based on the curvature value range;

the method comprises the steps of identifying the shapes of segmented blocks by researching the positive and negative of the average curvature and the Gaussian curvature of each segmented block;

carrying out Laplacian smoothing on the average curvature and the Gaussian curvature of each vertex, and constructing histograms of the two curvatures; when a plane exists in the model, extracting from the histogram a "valley" representing the plane adjacent to the "peak" of the histogram; extracting the width between two closed "peaks" when no plane exists in the model; the segmented feature blocks are divided into plane features, cylindrical features and sphere features; constructing maximum and minimum curvature histograms for the cylindrical features and the spherical features again, determining the effective zero point of each principal curvature again, and distinguishing the cone and the cylinder, and the circular ring and the spherical surface by utilizing the principal curvature distribution of each feature block and each vertex and utilizing the curvature rule;

after the characteristic types are identified as planes, cylinders, circular rings, spheres and cones, calculating characteristic parameters by using discrete differential geometry;

After the local feature identification is completed, the local feature is applied to CAD software, and feature-based modeling, stretching, deformation and rotation are performed based on the local feature.

2. The hybrid modeling method based on discrete Morse theory feature recognition according to claim 1, wherein the calculation formula of the vertex vector is:

3. The hybrid modeling method based on discrete Morse theory feature recognition according to claim 1, wherein,

And generating a Morse unit by adopting a watershed algorithm, and dividing the region by the Morse unit.

4. A hybrid modeling method based on discrete Morse theory feature recognition as defined in claim 3, wherein the watershed algorithm comprises:

5. The hybrid modeling method based on discrete Morse theory feature recognition of claim 4, wherein the Morse function is: