Watertight method for trimmed surface boundary, and device

Abstract

The present application provides a watertight method for a trimmed surface boundary. The method comprises: on the basis of corresponding points of intersections of curved surfaces in parameter domains thereof, generating parameter domain boundary curves by means of interpolation; dividing parameter domains into a plurality of sub-regions, so that the parameter domain boundary curves are single-valued functions in the sub-regions thereof; on the basis of the corresponding points on the parameter domain boundary curves, using isoparametric lines to divide each sub-region where the parameter domain boundary curves are located into a plurality of rectangular regions, so that each parameter domain boundary curve has only one point passing through the vertex of the corresponding rectangular region, and mapping into a standard parameter domain a curved edge trapezoid defined by the parameter domain boundary curve and three edges of the rectangular region; respectively performing normative representation of the curved surfaces on the basis of the updated standard parameter domains, and respectively acquiring the degrees and control points of curved surface boundary curves at the intersection of the curved surfaces; and on the basis of the intersections, generating an intersection curve expression by means of interpolation, increasing the degrees of the intersecting curves to the degrees of the curved surface boundary curves, and replacing the control points of the curved surface boundary curves with the control points of the intersecting curves.

Description

Watertightening method and device for trimming surface boundaries Technical Field

[0001] The invention belongs to the field of computer-aided design and relates to a data processing method for a product geometric model. Background Art

[0002] The statements in this section are merely intended to provide background information related to the technical solution of the present application to aid understanding, and they do not necessarily constitute prior art with respect to the technical solution of the present application.

[0003] Geometric models are widely used in fields such as computer graphics, computer-aided design, computer-aided manufacturing, and computer-aided engineering to represent the shapes of products or objects. These geometric models accurately describe three-dimensional geometric shapes in a way that computers can understand. Most geometric models are designed using parametric surfaces and stored in specific data structures, significantly improving the efficiency of product model design, generation, simulation, modification, and optimization. Currently, the majority of mainstream geometric models use spline surface models, representing the three-dimensional geometry of products or objects as a series of regular and / or irregular surfaces. The tensor product form of non-uniform rational B-splines (NURBS) is the mainstream surface representation technology in computer-aided design (CAD) and computer-aided geometric design (CAGD). It has become a universal ISO international standard and plays an important and indispensable role in the design, analysis, and manufacturing of industrial products. Bezier surfaces (also known as Bézier surfaces) are a special form of NURBS. All NURBS surfaces can be represented as block-based Bezier patches. Bezier patches are defined in the standard parameter domain [0,1]×[0,1], making them easy to compute, store, and transform. The de Casteljau algorithm provides a tool for extracting partial surface patches from rectangular subregions bounded by arbitrary isoparametric lines. These subregions can be transformed back into standard parameter intervals through linear parametric transformations. For ease of explanation, the following examples assume that all spline surfaces and spline curves are converted to Bezier form.

[0004] Practical product design often involves complex curved surfaces. These shapes cannot generally be directly represented using a single spline surface. Instead, they are created by intersecting surfaces through operations, followed by trimming and combining to create a trimmed surface. The handling of surface intersections can impact the quality and precision of product design. If these intersections are not handled properly, gaps or overlaps can form at the product's surface boundaries, resulting in incomplete geometric entity definitions and hindering subsequent engineering analysis and manufacturing. Therefore, handling surface intersections remains a core issue in CAD.

[0005] According to algebraic theory, the algebraic degree of a Bezier surface with m×n parameters is 2mn. For a 3×3 degree surface commonly used in practical applications, its algebraic degree is 18. When two such surfaces intersect, the algebraic degree of the intersection line is as high as 324, which has no analytical solution in algebra and cannot be accurately represented. Therefore, the intersection line between two tensor product parameter surfaces can generally only be approximated by a low-order spline curve within a certain accuracy range. The error caused by the low-order spline curve approximation causes the intersection line between the two intersecting surfaces to generally not strictly fit on any of the two intersecting surfaces except for the intersection point. In other words, there is a gap between the low-order approximation intersection line and the two intersecting surfaces, so the definition of the product geometric model is incomplete and not closed, resulting in the product design not being closed at the intersection of the surfaces. This problem is called the "watertight problem".

[0006] Currently, a common approach to addressing watertightness in computer-aided design (CAD) is to mesh the boundaries and manually stitch the mesh together to achieve watertightness. However, there's no uniform standard for manually stitching gaps, and the results vary widely from person to person, often being approximate. Furthermore, for high-precision product designs, premature meshing can introduce unnecessary errors in subsequent simulation analysis. Furthermore, manually stitching meshes at the boundaries places an additional burden on design engineers, requiring significant time and effort, and impacting product design efficiency.

[0007] Summary of the Invention

[0008] Therefore, in order to solve the above-mentioned defects of the prior art, the present application provides a new watertight method for trimming surface boundaries to improve the accuracy of product geometric models.

[0009] According to a first aspect of an embodiment of the present application, a method for watertightening a trimmed surface boundary is provided, comprising the following steps:

[0010] S1: For any two intersecting surfaces in the product geometric model to be processed, find the corresponding points of the intersection of the two intersecting surfaces in their respective parameter domains, and generate parameter domain boundary curves based on the interpolation of the corresponding points in their respective parameter domains;

[0011] S2: partitioning the parameter domains of the two intersecting surfaces so that the parameter domain boundary curves in each sub-region after the division are all single-valued functions;

[0012] S3: For each sub-region containing a parameter domain boundary curve: divide the sub-region into a number of rectangular regions using isoparametric lines based on the intersection points on the parameter domain boundary curve, so that within the divided rectangular regions, the parameter domain boundary curve passes through a vertex of the rectangular region at one and only one point, and map the irregular parameter domain of a curved trapezoid formed by the parameter domain boundary curve and the three sides of the rectangular region into a standard parameter domain;

[0013] S4: based on the updated standard parameter domains of the two surfaces, the surfaces are respectively represented in a standardized manner, and the degrees and control points of the surface boundary curves at the intersection of the surfaces are respectively obtained;

[0014] S5: Generate an intersection curve expression based on the interpolation of the intersection points of the two intersecting surfaces, raise the degree of the intersection curve to the degree of the surface boundary curve, and replace the control points of the surface boundary curve with the control points of the intersection curve.

[0015] In some embodiments, there are eight types of irregular parameter domains of the curved trapezoid described in step S3, and any one type of irregular parameter domain can be equivalent to the irregular parameter domain of the optional one type after the rotational symmetry transformation of the remaining seven types.

[0016] In some embodiments, the method for mapping the irregular parameter domain to the standard parameter domain in step S3 is:

[0017] S3-1: Select any one type of irregular parameter domain, and perform rotational symmetry transformation on the remaining seven types of irregular parameter domains so that they are all equivalent to the selected one type of irregular parameter domain;

[0018] S3-2: Mapping the optional type of irregular parameter domain to a standard parameter domain.

[0019] In some embodiments, the method of mapping the irregular parameter domain to the standard parameter domain in step S3 is: mapping eight types of irregular parameter domains to standard parameter domains respectively.

[0020] In some embodiments, one of the eight types of irregular parameter domains is a curved-edge trapezoidal region described by the following condition in the parameter domain (u, v):

[0021] The method of mapping it to the standard parameter domain in the parameter domain (s, t) is:

[0022] Where α∈(0,1), the symbol f(·) represents the parameter domain boundary curve polynomial generated by interpolation, and the standard parameter domain in the parameter domain (s, t) is a rectangular region described by the following conditions:

[0023] In some embodiments, the method of expressing the surface specification based on the updated standard parameter domain in step S4 includes:

[0024] S4-1: Expand the surface expression into a polynomial with respect to s and t on the updated standard parameter domain s×t∈[0,1]×[0,1];

[0025] S4-2: Let the element A of the mapping matrix A ij The value of s in the polynomial i t j The coefficient of the term;

[0026] S4-3: Calculate the control point matrix after mapping The surface is canonically represented on the updated standard parameter domain.

[0027] In some embodiments, the mapped control point matrix The calculation method is:

[0028] in, is the m-th basis function coefficient matrix B m The inverse matrix of is the m×p+n basis function coefficient matrix B m×p+n The transposed matrix of the inverse matrix of .

[0029] According to a second aspect of an embodiment of the present application, a method for processing product geometric model data is further provided, comprising:

[0030] receiving data related to the product geometric model, wherein the product geometric model is a surface model;

[0031] The received data is watertightened using the method according to the first aspect of the embodiment of the present application.

[0032] According to a third aspect of an embodiment of the present application, a computer-readable medium is further provided, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the method described in the first aspect or the second aspect of the embodiment of the present application is implemented.

[0033] According to the fourth aspect of the embodiments of the present application, an electronic device is also provided, including: a processor and a memory, wherein the memory is used to store executable instructions; the processor is configured to implement the method described in the first aspect or the second aspect of the embodiments of the present application by executing the executable instructions.

[0034] Compared with the prior art, the solution of the present application, based on the standardized representation of the trimmed surface, modifies the control points of the surface boundary curve of the trimmed surface at the intersection into the control points of the intersection curve generated by interpolation of the surface intersection points. This makes the product geometric model not only unified in data structure and easy to define and maintain, but also geometrically continuous at the intersection of the surfaces, with complete and closed boundaries. The solution of the present application can, on the one hand, reduce the error of the surface boundary of the geometric model and improve the accuracy of the surface boundary. On the other hand, it can speed up the generation of product geometric models, product manufacturing, etc. It is especially convenient for the subsequent processing of large-scale product designs.

[0035] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are incorporated into and constitute a part of the specification, illustrating embodiments consistent with the present application and, together with the specification, serving to explain the principles of the present application. It is obvious that the drawings described below are merely some embodiments of the present application, and a person of ordinary skill in the art can derive other drawings based on these drawings without inventive effort. In the drawings:

[0037] FIG1 is a schematic flow chart of a method for water-tightening a trimmed surface boundary according to one embodiment of the present application;

[0038] FIG2 is a schematic diagram of segmenting a sub-region including a boundary curve in a parameter domain of a trimmed surface according to an embodiment of the present application;

[0039] 3(a)-3(h) are schematic diagrams of eight types of curved-edge trapezoids having only one curved boundary according to one embodiment of the present application;

[0040] 4(a)-4(b) are schematic diagrams of mapping an irregular parameter domain into a standard parameter domain according to one embodiment of the present application;

[0041] FIG5 is a schematic diagram of a standardized cropped surface generated according to an embodiment of the present application;

[0042] FIG6 is a schematic diagram of a watertight trimmed surface generated according to an embodiment of the present application. DETAILED DESCRIPTION

[0043] To make the purpose, technical solutions, and advantages of this application more clearly understood, the present application is further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the embodiments described are part of the embodiments of this application, rather than all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0044] In addition, described feature, structure or characteristic can be combined in one or more embodiments in any suitable manner.In the following description, many specific details are provided so as to provide a full explanation of the embodiments of the present application. However, it will be appreciated by those skilled in the art that the technical scheme of the present application can be put into practice without one or more of the specific details, or other methods, components, devices, steps etc. can be adopted. In other cases, known methods, devices, implementations or operations are not shown or described in detail to avoid blurring the various aspects of the application.

[0045] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically separate entities. That is, these functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0046] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, while others may be combined or partially combined. Therefore, the actual execution order may vary depending on the actual situation.

[0047] As mentioned above, complex surface shapes are often involved in product design, which requires mutual operations between surfaces to determine the intersection line, and then to be defined through cutting and combination. In other words, it is necessary to deal with the problem of cutting surfaces, and dealing with cutting surfaces inevitably involves boundary watertightening to ensure the complete closure of the product geometric model. In the prior art, the intersection line between two tensor product parameter surfaces is usually approximated by a low-order spline curve within a certain accuracy range. As a result, the intersection line between the two intersecting surfaces is generally not strictly fitted on any of the two intersecting surfaces except for the intersection point, which results in gaps or overlaps in the product at the intersection of the surfaces.

[0048] This application proposes a method for representing the data structure of surface intersections in a standardized form, and realizing watertightness of cut surfaces based on the data structure of standardized surface intersections. The data structure of standardized surface intersections refers to mapping the irregular parameter domain of the surface intersections into a standard parameter domain, and representing the original surface with the mapped standard parameters on the remapped standard parameter domain. According to the watertightness method of cut surfaces of this application, geometric product design is performed without manually stitching the gaps at the intersections of the surfaces. It is only necessary to set the required precision parameters to automatically complete the processing of the surface intersections, so that the two intersecting surfaces fit tightly without gaps, the geometric design is complete, and the precision is high. The surface of the product defined in this way is closed and naturally continuous.

[0049] For ease of description, the surfaces mentioned below are all Bezier surfaces. A trimmed surface consists of the retained portions of two intersecting Bezier surfaces. When this application involves processing the boundary between two intersecting surfaces, they can be split along the boundary to form a set of small surface patches. Therefore, in the following text, "surface" may refer to the original intersecting surfaces or these small surface patches. The distinction is not difficult to make in the context.

[0050] FIG1 shows a flow chart of a method for watertightening the boundary of a trimmed surface according to an embodiment of the present application. The method mainly includes the following steps: S1: for any two intersecting surfaces in the geometric model of the product to be processed, find the corresponding points of the intersection of the two intersecting surfaces in their respective parameter domains, and generate parameter domain boundary curves by interpolation in their respective parameter domains based on the corresponding points; S2: divide the parameter domains of the two intersecting surfaces into regions, so that in each sub-region containing the parameter domain boundary curve after the division, the parameter domain boundary curve is a single-valued function; S3: for each sub-region containing the parameter domain boundary curve, divide the sub-region into several rectangular regions based on the corresponding points of the intersection on the parameter domain boundary curve using isoparametric lines, so that in the division In the rectangular area after the update, the parameter domain boundary curve has only one point passing through a vertex of the rectangular area, and the irregular parameter domain of the curved trapezoid formed by the parameter domain boundary curve and the three sides of the rectangular area is mapped to a standard parameter domain; S4: based on the standard parameter domain updated by each of the two surfaces, the surfaces are respectively represented in a standardized manner, and the degrees and control points of the surface boundary curves at the intersection of the surfaces are respectively obtained; S5: an intersection curve expression is generated according to the interpolation of the intersection points of the two intersecting surfaces, the degree of the intersection curve is raised to the degree of the surface boundary curve, and the control points of the surface boundary curve are replaced by the control points of the intersection curve.

[0051] More specifically, in step S1, for any two intersecting surfaces in the product geometric model to be processed, the corresponding points of the intersection of the two intersecting surfaces in their respective parameter domains are obtained, and the parameter domain boundary curves are generated by interpolation in their respective parameter domains based on the corresponding points. The parameter domain boundary curves are spline curves. The two intersecting surfaces are respectively denoted as surfaces S 1 and surface S 2 , each surface can be represented by the following expression of m×n degree Bezier surface:

[0052] Among them, u×v∈[0,1]×[0,1]; the shape is like B k,l The symbol of (x) is the kth l-th Bernstein basis function of variable x, and its specific expression is in is the combination coefficient; The control points of the surface S(u,v) are contained in the convex hull of its control points. The grid of the control points of the surface S(u,v) is composed of a set of grid points at the boundary, which are the control points of the boundary curve at that location. For example, the vertex group (R 0,0 ... R i,0 ... R m,0 ), (R 0,0 ... R 0,j ... R 0,n ), (R 0,n ... R i,n ... R m,n ) and (R m,0 ... R m,j ... R m,n ) are the control points of the four boundary curves of the surface S(u,v).

[0053] A surface defined on the standard parameter domain [0,1]×[0,1] and having the form shown in formula (1) is a canonical Bezier surface. In this application, after the irregular parameter domain is mapped to the standard parameter domain, the original surface is represented by the mapped parameters on the remapped standard parameter domain, which is called the canonical representation of the surface.

[0054] As mentioned above, when two surfaces S 1 and S 2 When the intersection curve is not represented by an accurate analytical function, we can only obtain a series of intersection coordinates in three-dimensional space, which is set as P i (x i ,y i ,z i),i=1,2,...Q. The expression of the Bezier surface in formula (1) is generally understood as a three-dimensional vector form, implicitly containing the three components x, y, and z representing the points on the surface, that is, S(u,v)=(x(u,v),y(u,v),z(u,v)). Let

[0055] We can find out the intersection points on the surface S 1 (x 1 (u 1 ,v 1 ),y 1 (u 1 ,v 1 ),z 1 (u 1 ,v 1 ))'s parameter domain (u 1 ,v 1 ) in the corresponding point (Since the intersection point is on the surface S 2 Parameter domain (u 2 ,v 2 ) of the corresponding point The solution method is the same as , so it will not be repeated here. )

[0056] Find the intersection point on the surface S 1 and S 2 After the values ​​of the corresponding points in their respective parameter domains are interpolated in the parameter spaces of the two surfaces, spline curves on the two-dimensional parameter space are generated. These two spline curves are surface S 1 and S 2 For example, the two parameter domain boundary curves can be expressed as follows: 1 (β 1 )=[u 1 (β 1 ),v 1 (β 1 )] and C 2 (β 2 )=[u 2 (β 2 ),v 2 (β 2 )]. The above formula is a spline curve representation known in the art and will not be described in detail here.

[0057] If the parameter domain boundary curve C 1 (β 1 ) and C 2 (β 2 ) are respectively brought into the surface S 1 (u 1 ,v 1 ) and S2 (u 2 ,v 2 ) equation, we can get the curve SC on the two surfaces in three-dimensional space. 1 and SC 2 , they fit perfectly on their respective surfaces.

[0058] In step S2, the parameter domains of the two intersecting surfaces are divided into regions, so that in each sub-region containing the parameter domain boundary curve after the division, the parameter domain boundary curve is a single-valued function.

[0059] In the sub-regions obtained by dividing the parameter domains of the two intersecting surfaces, except for some sub-regions containing the parameter domain boundary curves, the remaining sub-regions are rectangular regions bounded by isoparametric lines. They can be transformed into standard parameter domains by linear transformation, which will not be described in detail below. However, these sub-regions containing the parameter domain boundary curves are irregular parameter domains because they are located at the intersection of the two surfaces. To facilitate subsequent processing, when dividing the parameter domain, it is necessary to make the parameter domain boundary curves in each sub-region containing the parameter domain boundary curves all single-valued functions. The purpose of this is to take into account the parameter domain boundary curve C 1 (β 1 ) and C 2 (β 2 ) in their respective parameter domains for the parameter (u 1 ,v 1 ) and (u 2 ,v 2 ) may be a multi-valued function, which will make subsequent normalization processing impossible. Therefore, the parameter domain must be divided to ensure that the parameter domain boundary curve is a single-valued function within the sub-region containing the parameter domain boundary curve. It should be noted that if the parameter domain boundary curve is a single-valued function in the parameter domain, then it is equivalent to dividing a sub-region.

[0060] In step S3, for each sub-region containing the parameter domain boundary curve, the sub-region is divided into several rectangular regions using isoparametric lines based on the corresponding points of the intersection points on the parameter domain boundary curve, so that within the divided rectangular region, the parameter domain boundary curve has one and only one point passing through a vertex of the rectangular region, and the irregular parameter domain of the curved trapezoid formed by the parameter domain boundary curve and the three sides of the rectangular region is mapped to a standard parameter domain.

[0061] The following describes step S3 in detail. 1 and S 2 Therefore, the following description will no longer use superscripts to distinguish different surfaces and their parameter domains.

[0062] In one embodiment, in a given parameter domain u×v∈[0,1]×[0,1], isoparametric lines u=u can be used based on the intersection points on the parameter domain boundary curve. i ∈[0,1],v=v i ∈[0,1] (i=1,2,...) Each subregion containing the parameter domain boundary curve is divided into several rectangular regions, ensuring that the parameter domain boundary curve has one and only one point passing through a vertex of the rectangular region in which it is located. The rectangular region can be normalized to the [0,1]×[0,1] parameter domain. For convenience, the following description uses a square region as an example.

[0063] As shown in FIG2 , the parameter domain boundary curve (line BDG) passes through two square areas and only passes through one vertex D of each square area, and forms a curved trapezoid ABCD and a curved trapezoid DEFG with its three sides each containing only one curve boundary.

[0064] There are eight types of curved-edge trapezoids generated using the segmentation method described above, each containing only a single curved boundary. These are shown in Figures 3(a) through 3(h). The curved-edge trapezoids ABCD and DEFG shown in Figure 2 correspond to the curved-edge trapezoids in Figures 3(a) and 3(c), respectively. Figures 3(a) through 3(h) show that these eight types of curved-edge trapezoids are equivalent after rotational symmetry transformation. Selecting any one of these irregular parameter domains yields the remaining seven types of irregular parameter domains equivalent to any of these types after rotational symmetry transformation. Therefore, any one of these types can be selected for discussion.

[0065] In one embodiment, the eight types of irregular parameter domains shown in FIG. 3( a ) to FIG. 3( h ) may be mapped to standard parameter domains respectively.

[0066] In yet another embodiment, FIG. 3( b ) to FIG. 3( h ) may be transformed into FIG. 3( a ), and then the irregular parameter domain shown in FIG. 3( a ) may be mapped into a standard parameter domain.

[0067] The specific mapping method is described below based on FIG3( a ).

[0068] In this embodiment, the method for normalizing the irregular parameter domain shown in Figure 3(a) to a standard parameter domain is to establish a parameter mapping model, specifically as shown in Figures 4(a) and 4(b). Assume that the general form of the parametric equation for the curved edge curve in Figure 4(a) is f(x). After the irregular parameter domain shown in Figure 4(a) is mapped to the standard parameter domain shown in Figure 4(b), the surface on it can be normalized to have a standard Bezier surface form, thus having a unified data structure.

[0069] The model in the parameter domain before mapping (as shown in Figure 4(a)) assumes the following conditions:

[0070] Where α∈(0,1). After mapping, the model in the parameter domain (as shown in Figure 4(b)) assumes the following conditions:

[0071] Among them, the new parameters s×t∈[0,1]×[0,1]. The conditions for realizing the mapping Γ are:

[0072] The model expression for realizing the mapping Γ is:

[0073] Among them, the symbol of the form f(x) is the parameter domain boundary curve generated by interpolation, which is a p-degree polynomial about x, f(x) = a p x p +a p-1 x p-1 +...+a0,p∈N, a p ≠ 0. Depending on the accuracy requirements of different applications, f(x) can be designed as a first-order, second-order, third-order or higher-order mapping.

[0074] In step S4, based on the surface S 1 and S 2 The updated standard parameter domain of each surface S 1 and S 2 Respectively standardize and obtain the surface S 1 and S 2 The degrees and control points of the surface boundary curves at the intersection are described in detail below.

[0075] When the irregular parameter domain is mapped to the standard parameter domain according to the above rules, the clipping surface built on it can be correspondingly standardized into the standard Bezier surface form, as described in detail below.

[0076] Substituting formula (6) corresponding to the mapping Γ into S(u,v) in formula (1), we can obtain the surface expression on the standard parameter domain. It should be noted that the degree of the Bernstein basis function on the renormalized standard parameter domain has changed from the original (u,v) times m and n times to (s,t) times m and m×p+n times respectively:

[0077] in, are the control points after mapping.

[0078] Let B q is the coefficient matrix of the q-order Bernstein basis function, which is a (q+1)×(q+1) square matrix, then: [B 0,q B1,q ... B q,q ]=[1 ww 2 ... w q ]B q ;Remember the control point matrix R=(R ij )(m+1)×(n+1), then the general expression of the matrix form of the Bezier surface is:

[0079] Among them, the superscript " T ” represents the transpose of a matrix.

[0080] Also note the control point matrix after mapping The matrix expression of the mapped Bezier surface is:

[0081] Let the mapping matrix is the matrix B q The inverse matrix of , the solution formula of the mapped control points is: Therefore, after the mapping matrix A is obtained, the mapped control point matrix can be obtained, that is, the clipping surface expression on the canonical parameter domain is obtained.

[0082] The solution process of the mapping matrix A is as follows: expand formula (9) into a polynomial about s and t, and determine the value of the element in the matrix A according to the coefficient of the polynomial, that is, the element A ij The value of the polynomial s i t j The coefficient of the term.

[0083] The following example illustrates the process of solving the matrix A.

[0084] Remember the matrix

[0085] If in the uOv parameter domain, l4:u=f(v),v∈[0,1] is one-time about v, that is, p=1,f(v)=a1v+a0,a1≠0. When m=n=3, A=(A i,j ) 4×7 , B3, They are:

[0086] Substituting the above known parameters into formula (9) and expanding it, we can obtain the surface expression represented by the parameters s and t, as shown below:

[0087] According to which i t j The coefficients of the terms are obtained, and the expressions of the elements in the matrix A are:

[0088] Further, in,

[0089] Figure 5 is a schematic diagram of a clipping surface generated according to an embodiment of the present application. In Figure 5, surface sf1 is the clipping surface to be retained, and surface sf2 is the surface to be clipped. Curve cu1 is the clipping boundary, and the asterisk points are the regenerated control points. Before the data at the intersection of the surfaces is standardized, due to the randomness of the intersection of the surfaces, the intersection lines on the two surfaces (the clipping boundaries of the two intersecting surfaces) do not represent the control points at which they are generated, that is, the surfaces are irregular at the intersection; after the standardization, the clipping boundaries of the two intersecting surfaces at the intersection are regular, that is, the clipping boundary curve has control points representing its generation, which lays the foundation for subsequent watertightness processing. At the same time, in the existing computer-aided design field, when faced with problems such as generating surface sf1 in the system, or processing the geometric product represented by surface sf1, it is necessary to store and represent the information of the clipping boundary curve cu1 to assist in determining whether the clipping boundary has been reached. In practical applications, a trimmed surface is often composed of hundreds or even thousands of intersecting surfaces. Using existing methods, the amount of boundary information that needs to be stored and represented is enormous, and the process of determining whether a boundary has been reached is also complex. However, according to the method described above, the trimmed surface to be retained is represented in a standard form such as Equation (1). This eliminates the need to store additional data or represent boundary information, omitting the boundary determination process and improving the efficiency of subsequent processing.

[0090] In the original surface S 1 and S 2 After remapping to the standard parameter domain, the surface S 1 and S 2 The shapes at the boundaries remain unchanged, so the degrees and control points of their respective surface boundary curves at the intersection can be obtained according to the standard expression.

[0091] In step S5, according to the surface S 1 and S 2 The intersection point interpolation generates the intersection curve expression, the degree of the intersection curve is raised to the degree of the surface boundary curve, and the control points of the surface boundary curve are replaced by the control points of the intersection curve. 1 and S 2 The intersection of the two points can be interpolated to generate a spline curve C representing the intersection line and converted into Bezier form. The intersection curve C is different from the original surface S obtained in step S4. 1 and S 2 The surface boundary curves at the intersection are canonically represented on the remapped standard parameter domain.

[0092] The intersecting curve C generated by interpolation is not completely on the surface S 1 and S 2 On, therefore, the intersection curve C and the renormalized surface S 1 and S 2 The three spatial curves of the surface boundary curves at the intersection do not completely overlap, that is, there are still gaps or overlaps between the two re-standardized intersecting surfaces, and the problem of incomplete and non-closed geometric model of the product has not been solved.

[0093] In one embodiment of the present application, the re-normalized surface S is modified 1 and S 2 The control points of the surface boundary curves at the intersection are replaced by the control points of the intersection curve C. In this way, the two re-normalized intersecting surfaces S 1 and S 2 The intersection curve C is used as the common boundary, and there are no gaps or overlaps, achieving a watertight representation of the boundaries of the intersecting surfaces, thereby ensuring that the product's geometric model is complete and closed.

[0094] It should be noted that the degree of the renormalized surface will increase if the original surface S 1 The degree of (u,v) is m×n, and the transformation polynomial used in the direction of parameter u (that is, the parameter domain boundary curve generated by interpolation) is p, then the degree of the transformed surface is m×(n×p+n). For example, for a common 3×3 degree surface, a 1st degree polynomial is used for transformation, and the degree of the normalized surface is 3×6. Therefore, the degree of the surface boundary curve on the intersecting surface may be higher than the degree of the intersection curve C. Before modifying the control points of the surface boundary curve, the degree of the intersection curve C should be raised to the same degree as the re-normalized surface S. 1 and S 2 The degree of the surface boundary curves at the intersection is the same. For Bezier curves or surfaces, raising the degree from a low degree to a high degree is a conventional technical means in this field and does not change the shape of the curve or surface.

[0095] In practical applications, in order to improve the efficiency of design and calculation, within the allowable range of error and accuracy, the surface S can be 1 and S 2 Appropriately reduce the number of times in the re-standardized standard parameter domain. The specific reduction depends on the application requirements.

[0096] Figure 6 shows a clipping surface generated according to an embodiment of the present application. As can be seen from Figure 6, the two intersecting surfaces of the product geometric model shown in the figure achieve seamless connection, solving the watertightness problem, and thus making the product design represented by the watertight geometric model closed and complete.

[0097] As mentioned above, in the current field of computer-aided design, when processing the boundaries of cut surfaces, discrete meshes or manual stitching methods are used to eliminate gaps or holes between intersecting surfaces. The problem with manual stitching is that the stitching results vary from person to person, resulting in large approximation errors. The geometric models generated by manually stitching boundaries have large errors and low precision. Products designed based on such geometric models have rough surfaces at the intersections, and the transitions between adjacent surfaces are unnatural. Furthermore, manual stitching is time-consuming, labor-intensive, and inefficient. Unlike commonly used methods for addressing "watertightness," the watertightening method used in this application treats irregular surfaces. This avoids the manual stitching gaps that can lead to different stitching results between people, reduces design errors, and improves design accuracy, resulting in closed intersections and natural transitions between adjacent surfaces. Furthermore, based on specified precision parameters, the system can automatically generate seamless cut surfaces, eliminating the need for additional manual stitching. This not only saves design engineers time and effort, allowing them to more easily create complex models, but also accelerates product development and improves manufacturing efficiency.

[0098] In another embodiment of the present application, a method for processing product geometric model data is also provided. The method mainly includes obtaining data related to the product geometric model, and using the watertightening method of clipping surface boundaries introduced above to watertighten the acquired geometric model data. The product geometric model data can be obtained through a communication connection such as a wired network or a wireless network, or can be obtained from a database or a computer-readable storage medium. The product geometric model data specification processed by the method of this embodiment removes the gaps in the model boundary and ensures the integrity and closure of the model. It not only reduces the error at the junction of the model surfaces and improves the accuracy of the junction of the model surfaces, which is beneficial to subsequent analysis and processing and manufacturing processes, but also reduces the uncertainty and errors in the data sharing process between different customers or systems.

[0099] The method of this embodiment is applicable to the definition, representation and application of geometric models in the fields of computer graphics, computer-aided design, computer-aided manufacturing, computer-aided engineering, etc. Since each facet of the boundary of the geometric model of a product or object is standardized, such a geometric model has a unified data structure, which is convenient for parallel processing and rapid generation of the geometric model of the product or object. Moreover, the surface of the geometric model of the product or object is composed of standardized facets, which can be more easily converted and interpreted in different systems, facilitate data sharing between suppliers, customers or collaborative partners, and reduce the risk of misunderstanding and error. Furthermore, the method automatically processes the boundaries of intersecting surfaces to generate a seamless, complete and closed model, reduce the error at the model surface boundaries, improve the accuracy at the model surface boundaries, make the product design generated according to the model more refined, and speed up the progress of the design engineer in completing the task, not only facilitate subsequent analysis and processing and manufacturing processes, reduce the risk in the product development process, but also shorten the development cycle and improve productivity.

[0100] Therefore, the above-mentioned solution of the present application can improve the quality and reliability of the product geometric model, which is conducive to the smooth progress and efficient output of the product design, analysis and manufacturing processes, and has broad application prospects in computer-aided design.

[0101] In one embodiment of the present application, a computer program product is further provided, which includes program codes. When the program codes are run on any computing device or data processing equipment, the steps of the method described in the above embodiments are executed.

[0102] In another embodiment of the present application, a computer-readable storage medium is provided, on which a computer program or executable instructions are stored. When the computer program or executable instructions are executed by a processor or other computing unit, the technical solution described in the above embodiment is implemented. The implementation principle is similar and will not be repeated here. In an embodiment of the present invention, a computer-readable storage medium can be any tangible medium that can store data and can be read by a computing device. Examples of computer-readable storage media include hard disk drives, network attached storage (NAS), read-only memory, random access memory, CD-ROM, CD-R, CD-RW, magnetic tape, and other optical or non-optical data storage devices. The computer-readable storage medium may also include computer-readable media distributed on a network-coupled computer system so that computer programs or instructions can be stored and executed in a distributed manner.

[0103] In another embodiment of the present application, an electronic device is provided, including a processor and a memory, wherein the memory is used to store executable instructions that can be executed by the processor, and the processor is configured to execute the executable instructions stored on the memory. When the executable instructions are executed, the technical solution introduced in any of the aforementioned embodiments is implemented. The implementation principle is similar and will not be repeated here.

[0104] References in this specification to "various embodiments," "some embodiments," "one embodiment," or "an embodiment" mean that a particular feature, structure, or property described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases "in various embodiments," "in some embodiments," "in one embodiment," or "in an embodiment" in various places throughout this specification do not necessarily refer to the same embodiment. Furthermore, particular features, structures, or properties may be combined in any suitable manner in one or more embodiments. Thus, particular features, structures, or properties shown or described in connection with one embodiment may be combined, in whole or in part, with features, structures, or properties of one or more other embodiments without restriction, as long as the combination is not illogical or inoperable.

[0105] In this specification, the terms "including," "having," and similar expressions are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. "A" or "an" does not exclude a plurality of cases. In addition, the elements in the drawings of this application are for illustrative purposes only and are not drawn to scale.

[0106] Although the present invention has been described through preferred embodiments, the present invention is not limited to the embodiments described herein but includes various changes and modifications that may be made without departing from the scope of the present invention.

Claims

1. A method for waterproofing the boundary of a trimmed surface, comprising: S1: For any two intersecting surfaces in the product geometric model to be processed, find the corresponding points of the intersection points of the two intersecting surfaces in their respective parameter domains, and interpolate the parameter domain boundary curves according to the corresponding points in their respective parameter domains; S2: Divide the parameter domains of the two intersecting surfaces so that within each sub-region containing the parameter domain boundary curve after division, the parameter domain boundary curve is a single-valued function; S3: For each sub-region containing the parameter domain boundary curve: divide the sub-region into several rectangular regions by isoparametric lines based on the corresponding points of the intersection points on the parameter domain boundary curve, so that within the divided rectangular regions, the parameter domain boundary curve passes through exactly one vertex of the rectangular region, and map the irregular parameter domain of the curvilinear trapezoid formed by the parameter domain boundary curve and three sides of the rectangular region to a standard parameter domain; S4: Canonically represent the surfaces based on the updated standard parameter domains of the two surfaces respectively, and obtain the degree and control points of the surface boundary curves at the intersection of the surfaces respectively; S5: Interpolate to generate an intersection curve expression according to the intersection points of the two intersecting surfaces, raise the degree of the intersection curve to the degree of the surface boundary curve, and replace the control points of the surface boundary curve with the control points of the intersection curve.

2. The method for waterproofing the boundary of a trimmed surface according to claim 1, wherein, the irregular parameter domains of the curvilinear trapezoids described in step S3 have eight types, and for any one type of irregular parameter domain, the remaining seven types of irregular parameter domains can be respectively equivalent to the selected one type of irregular parameter domain after rotational symmetry transformation.

3. The method for waterproofing the boundary of a trimmed surface according to claim 2, and the method for mapping the irregular parameter domain to a standard parameter domain described in step S3 is: S3-1: Select any one type of irregular parameter domain, and perform rotational symmetry transformation on the remaining seven types of irregular parameter domains respectively to make them all equivalent to the selected one type of irregular parameter domain; S3-2: Map the selected one type of irregular parameter domain to a standard parameter domain.

4. The method for waterproofing the boundary of a trimmed surface according to claim 2, and the method for mapping the irregular parameter domain to a standard parameter domain described in step S3 is: Map the eight types of irregular parameter domains to standard parameter domains respectively.

5. The watertight method for trimming the surface boundary according to claim 3 or 4, wherein one of the eight types of irregular parameter domains is a curvilinear trapezoidal region described by the following conditions in the parameter domain (u, v): The method of mapping it to the standard parameter domain in the parameter domain (s, t) is as follows: wherein, For α ∈ (0, 1), the symbol f(·) represents the polynomial of the boundary curve of the parameter domain generated by interpolation. The standard parameter domain in the parameter domain (s, t) is a rectangular region described by the following conditions:

6. The method for waterproofing the boundary of a trimmed surface according to claim 5, and the method for canonically representing the surface based on the updated standard parameter domain described in step S4 comprising: S4-1: Expand the expression of the surface into a polynomial about s and t on the updated standard parameter domain s×t∈[0,1]×[0,1]; S4-2: Let the element A of the mapping matrix A ij take the value of the coefficient of the s i t j term in the said polynomial; S4-3: Obtain the mapped control point matrix and canonically represent the surface on the updated standard parameter domain.

7. The watertight method for trimming the surface boundary according to claim 6, the mapped control point matrix is calculated as follows: wherein, is the inverse matrix of the m-th order basis function coefficient matrix B m , It is the transposed matrix of the inverse matrix of the basis function coefficient matrix B of order m×p + n m×p+n .

8. A method for processing product geometric model data, comprising: receiving data related to the product geometric model, where the product geometric model is a surface model; performing waterproofing processing on the received data by the method described in any one of claims 1-7.

9. A computer-readable medium having stored thereon a computer program, which when executed by a processor implements the method according to any one of claims 1 to 8.

10. An electronic device, comprising: a processor and a memory, wherein the memory is for storing executable instructions; the processor is configured to implement the method according to any one of claims 1 to 8 by executing the executable instructions.

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