Combined path swept surface construction method based on isoparametric line extraction

Abstract

The invention discloses a combined path swept surface construction method based on isoparametric line extraction. The method comprises the following steps: a geometric model comprises n swept contours and n swept paths; the scanning contours are in one-to-one correspondence with the scanning paths; initializing a path index k representing a sweeping path sequence number; s2, acquiring a sweeping path according to the path index k, and acquiring and updating a sweeping contour according to the sweeping path; obtaining a corresponding single-section scanning curved surface according to the scanning contour; s3, intercepting an isoparametric line of which the parameter value is 1 in the scanning contour direction of the single-section scanning curved surface; the isoparametric line represents the geometric contour of the tail end of the single-section swept curved surface and has the same geometric continuity and space continuation with the swept contour; the isoparametric line is used as a scanning contour corresponding to the scanning path under the next path index k; updating the path index k; backtracking to the step S2 until the path index k is equal to n; and S4, sewing all the generated single-section scanning curved surfaces by adopting a Brep structure, and constructing and outputting an overall three-dimensional scanning model.

Description

Technical Field

[0001] The present invention belongs to the field of geometric modeling and simulation, and relates to a method for constructing a swept surface in a combined path sweep, and specifically to a method for obtaining swept geometry in a Brep boundary representation method for geometric modeling and a method for splicing adjacent swept surfaces. Background Art

[0002] Geometric modeling and simulation technology is one of the core foundations of fields such as CAD / CAE. Across industries such as aerospace, automotive, architecture, healthcare, and industrial design, geometric modeling technology is widely used in 3D solid modeling, component design, structural analysis, and motion simulation.

[0003] The sweep method is a classic and widely used modeling technique in the field of geometric modeling. This method quickly constructs complex two-dimensional or three-dimensional geometric bodies with continuity requirements by translating, rotating or deforming one or more input two-dimensional contours (cross sections) along a predefined path. It is suitable for solid or surface modeling tasks with certain regularity or trajectory constraints. In actual engineering, sweep modeling is widely used in many fields such as mechanical parts design (such as pipelines, shafts, blades, etc.), building structure modeling (such as bridges, tunnels), product appearance design, three-dimensional animation modeling, and medical image reconstruction. Its modeling process can not only efficiently express the design intent, but also facilitate subsequent parametric modification and simulation processing such as finite element analysis (FEA) and computational fluid dynamics (CFD). Therefore, it is one of the core modeling methods in modern CAD / CAE systems.

[0004] In geometric modeling, geometric information can be expressed through line models, surface models, or solid models. Among them, the first two have simple expression forms and the presented entity information is incomplete, while the solid model can unambiguously represent the three-dimensional shape. Boundary representation, also known as Brep representation, is the most mature and unambiguous representation in geometric modeling. Brep does not directly describe the volume content of an object, but "wraps" the object through its surface constituent elements to achieve a complete expression of its geometry and topology. The present invention uses Brep representation to perform topological construction on the swept surface.

[0005] Most traditional sweeping methods generate swept surfaces based on a single path curve. There are few research methods for combined path sweeping (i.e., the sweeping path is composed of multiple non-G1 continuous curves), and the continuity of the swept surface in multiple segments cannot be guaranteed, thus failing to meet the requirements of geometric modeling. Summary of the Invention

[0006] The purpose of the present invention is to achieve that in combined path sweep modeling, the swept surface generated under each path segment can not only reasonably reflect the geometric characteristics of the selected contour curve and the current path curve, but also ensure the continuity with the adjacent surfaces. The swept surface constructed by this method can avoid common problems at the joints, such as hollowing, geometric distortion, and interlaced interference between surfaces, thereby significantly improving the geometric continuity and overall smoothness of the modeling results. In addition, the swept surface constructed by this method can be naturally spliced, avoiding the surface extension and intersection operations used for splicing in the existing methods, which is more intuitive and efficient. The isoparametric lines of the front sweep surface are reasonably used to establish the sweep profile of the back path, so that adjacent swept surfaces can be completely stitched together to ensure the continuity of the overall swept surface.

[0007] A single-segment swept surface is constructed based on the translation method. By performing a controlled translation or transformation of a given contour curve along a path, a three-dimensional surface with well-defined parametric properties is generated. To ensure good interoperability between surfaces, isoparametric lines on the surface are systematically selected and processed as the contour curves at the starting point of the next path segment, thus forming a recursive transfer mechanism for contours. These isoparametric lines not only inherit the geometric information of the previous surface end but also provide a reasonable starting contour for the next surface segment.

[0008] In existing methods, parametric line strategies are used to determine the final splicing curve. Furthermore, the splicing of adjacent swept surfaces requires a series of time-consuming or complex operations, such as extension and intersection, based on the u direction (along the sweep profile). The isoparametric line strategy of the present invention uses the v direction (along the sweep path) of the previous swept surface to obtain the starting profile of the next swept segment. This allows adjacent swept surfaces to be spliced ​​naturally, eliminating the need for complex post-processing operations such as extension and intersection.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is:

[0010] The combined path swept surface construction method based on isoparametric line extraction includes the following steps:

[0011] Step S1: Describing a geometric model using a Brep structure; the geometric model includes n sweep profiles and n sweep paths; the sweep paths are sequentially connected end to end and adjacent sweep paths are G0 continuous; the sweep profiles correspond to the sweep paths one by one; initializing a path index k representing the sequence number of the sweep path;

[0012] Step S2: acquiring the sweep path according to the path index k, and acquiring and updating the sweep profile according to the sweep path;

[0013] Obtaining a corresponding single-segment swept surface according to the swept profile;

[0014] Step S3, intercepting an isoparametric line of the single-segment swept surface with a parameter value of 1 along the direction of the swept profile; the isoparametric line represents the geometric profile of the end of the single-segment swept surface and has the same geometric continuity and spatial continuity as the swept profile; the isoparametric line serves as the swept profile corresponding to the next swept path under the path index k;

[0015] Update the path index k; return to step S2 until the path index k is equal to n;

[0016] Step S4: using the Brep structure to stitch all the generated single-segment swept surfaces, construct and output an overall three-dimensional swept model.

[0017] Preferably, the step S2 includes using NURBS to represent the sweep profile and the sweep path;

[0018] The sweep path curve is expressed as:

[0019]

[0020] Where m is the upper limit of the control point index of the sweep path, and the total number of control points is m+1; j is the variable of the control point index of the sweep profile; N j,q (v) represents the j-th B-spline basis function of the sweep path, with order q; represents the spatial position of the j-th control point; express The corresponding control point weight; V is the node vector of the sweep path, and the node vector is a set of non-decreasing parameter values ​​used to define the segmentation of the NURBS curve and the parameter range of each segment of the curve.

[0021] Preferably, the sweep profile curve is expressed as:

[0022]

[0023] Where n is the upper limit of the control point index of the sweep profile, and the total number of control points is n+1; i is the variable of the control point index of the sweep profile; N i,p (u) represents the i-th B-spline basis function of the swept profile, with order p; represents the spatial position of the i-th control point; express The corresponding control point weight; U is the node vector of the swept contour.

[0024] Preferably, in step S2, the corresponding single-segment swept surface is obtained using a translation method according to the swept profile.

[0025] Preferably, the translation method formula is as follows:

[0026] S k (u,v)=T k (v)+C k (v)

[0027] Among them, T k (v) represents the sweep path curve; C k (u) represents the swept profile curve.

[0028] As an example, in step S3, the single-segment swept surface S is intercepted. k The isoparametric line with a parameter value of 1 in the direction of the sweep profile of (u, v) is set to 1. The required isoparametric curve is the sweep profile of the next section of the sweep path. The formula is as follows:

[0029]

[0030] Among them, S k (1,v) represents an isoparametric curve; is the control point of the single-segment swept surface, is the weight corresponding to the control point.

[0031] The present invention has the following characteristics and beneficial effects:

[0032] 1. Unlike existing isoparametric line methods that use step-by-step bisection and other methods to extract isoparametric lines multiple times in the u direction for subsequent splicing, the present invention only needs to extract isoparametric lines once in the v direction as the subsequent sweep profile. Under the guidance of each path curve, the corresponding local swept surface is constructed respectively. Through the isoparametric line transfer and continuous section update mechanism, good geometric continuity is achieved between adjacent swept surfaces.

[0033] 2. Different from the current method that performs post-processing such as extending and splicing adjacent swept surfaces, the swept surfaces constructed by the present invention can be naturally spliced. Generally, the complex post-processing operations of the former are not required, which makes it more operable.

[0034] 3. The existing methods will affect the geometric characteristics of the corresponding swept path curve reflected by a single-segment swept surface to varying degrees after extension or trimming, while the present invention can accurately reflect the geometric characteristics of the selected contour section and the current path curve in each segment of the swept surface.

[0035] In summary, this method effectively solves the problems of geometric discontinuity, cross-sectional mismatch, and abrupt transitions caused by non-G1 path continuity in traditional multi-segment sweeping processes. The resulting overall swept model maintains good geometric continuity (G0-G1) and smoothness between segments, significantly improving the structural quality and visual consistency of the modeling results, providing a stable and reliable geometric foundation for subsequent simulation analysis, optimized design, and engineering manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the method of Example 1 of the present invention;

[0037] Figure 2 Schematic diagram of simulated sweeping according to embodiment 1 of the present invention;

[0038] Figure 3 Schematic diagram of the sweep profile of Example 1 of the present invention;

[0039] Figure 4 Schematic diagram of the sweep of an open curve along multiple straight paths according to Example 1 of the present invention;

[0040] Figure 5 Schematic diagram of sweeping an open curve along multiple spline curves according to Example 1 of the present invention;

[0041] Figure 6 Schematic diagram of the sweeping of a closed curve along multiple straight line paths according to Example 1 of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be further described below with reference to the accompanying drawings.

[0043] like Figure 1 The method for constructing a combined path swept surface based on isoparametric line extraction includes the following steps:

[0044] like Figure 2 As shown, step S1, using the Brep structure to describe the geometric model; the geometric model includes a sweep profile and a sweep path; there are n sweep paths and they are connected in sequence from beginning to end, each sweep path is a space curve, and adjacent sweep paths are G0 continuous; the path index k representing the sweep path sequence number is initialized to 0; the details are as follows:

[0045] First, the processing program inputs the geometry model to be processed. The geometry model consists of two main components: 1) the sweep profile C: the 2D cross-sectional profile used to sweep the surface, which can be a closed or open curve segment; 2) the sweep path T: used to guide the spatial transformation of the sweep profile C. Adjacent sweep paths do not satisfy G1 continuity (i.e., tangential discontinuity), so the sweep path T is not a smooth connection. After the input is completed, the path index k is initialized to 0.

[0046] Step S2: Obtain the sweep path according to the path index k, and then update the sweep profile according to the sweep path; and obtain the corresponding single-segment swept surface using the translation method according to the sweep profile; the details are as follows:

[0047] Get the NURBS representation of the swept profile and path (non-uniform rational B-splines, which can be used to represent analytical curves and free-form curves). Use NURBS curves T(v) and C(u) to represent the swept path and swept profile respectively, and use NURBS surface S(u,v) to represent the corresponding single-segment swept surface. Get the swept path T according to the path index k k (v) and update the sweep profile to C k (u), use the translation method to obtain the current swept surface S k (u,v).

[0048] Step S2.1: Use NURBS to represent the sweep profile and sweep path.

[0049] The swept path curve is expressed as:

[0050]

[0051] Where m is the upper limit of the control point index of the sweep path, and the total number of control points is m+1; j is the variable of the control point index of the sweep profile; N j,q (v) represents the j-th B-spline basis function of the sweep path, with order q; represents the spatial position of the j-th control point; express The corresponding control point weight; V is the node vector of the sweep path, and the node vector is a set of non-decreasing parameter values ​​used to define the segmentation of the NURBS curve and the parameter range of each segment of the curve.

[0052] The swept profile curve is represented as:

[0053]

[0054] Where n is the upper limit of the control point index of the sweep profile, and the total number of control points is n+1; i is the variable of the control point index of the sweep profile; N i,p (u) represents the i-th B-spline basis function of the swept profile, with order p; represents the spatial position of the i-th control point; express The corresponding control point weight; U is the node vector of the swept contour.

[0055] Step S2.2: Based on the NURBS representation of the sweep profile and the sweep path, the corresponding single-segment swept surface is obtained using the translation method, i.e., the current swept surface.

[0056] The translation method formula is as follows:

[0057] S k (u,v)=T k (v)+C k (u)

[0058] The current swept surface is defined on the node vectors U and V. According to the translation method, the current swept surface has the following control points:

[0059] P i,j =T j +Q i ,i=0,1,···,n; j=0,1,···,m

[0060] Among them, T j , Q i are the control vertices of the sweep path and sweep profile, and n and m are the corresponding control point indices (the same below).

[0061] The current swept mask has the following weights:

[0062]

[0063] in, The control point weights for the sweep profile and the current sweep. Control points are points in space that determine the overall shape of the curve; each control point can have a weight, which is a real value assigned to each control point that controls the influence of that point on the curve shape.

[0064] According to the translation method formula, the NURBS expression of the current swept surface is obtained as follows:

[0065]

[0066] In this embodiment, a sweep profile represented by a NURBS curve is input; a sweep path composed of three NURBS curves is input, and the continuity of adjacent curves is G0 continuity, so the parameter n is 3, the initial value of k is 0, and the maximum value is 2.

[0067] Get the current sweep path curve T according to the path index k k (v) and update the sweep profile to C k (u), use the translation method to obtain the current swept surface S k (u, v). When k is 0, the current sweep profile is the input profile of step S1, and the sweep path is:

[0068]

[0069] Therefore, according to the translation sweep formula, the NURBS representation of the first segment of the swept surface can be obtained as:

[0070]

[0071] Control vertices for the surface, The corresponding weight is determined by the common control vertices and weights of the outline and path:

[0072]

[0073] The surface generated by the translation method does not rotate or deform the cross-sectional profile during the translation process, and the generated surface generally has good G1 continuity. Through the translation method, this embodiment obtains a complete expression of the first swept surface and proceeds to step S3.

[0074] Step S3, intercepting an isoparametric line with a parameter value of 1 along the sweep profile direction of the current swept surface; updating the path index k; and repeating step S2 until the path index k is equal to n;

[0075] Step S3.1, intercept the current swept surface S k The isoparametric line with a parameter value of 1 in the u direction of (u, v). In step S2, the NURBS expression of the current swept surface has been obtained. The value of parameter u is set to 1 and substituted into the expression to obtain the required isoparametric curve, that is, the swept profile of the next segment:

[0076]

[0077] Among them, S k (1,v) represents an isoparametric curve; is the single-ended surface control point, is the weight corresponding to the control point.

[0078] Step S3.2: Return to step S2.1 and update the translation formula to:

[0079] S k+1 (u,v)=T k+1 (u,v)+S k (1,v)

[0080] When the value of k reaches n, proceed to step S4.

[0081] In this embodiment, based on the swept surface obtained in step S2, the next swept profile curve is obtained by intercepting its isoparametric line along the sweep profile direction (u direction). Through this strategy, the updated swept profile can well reflect the geometric characteristics of the input profile and fully reflect the sweep trend of the previous path. The next swept surface obtained can be perfectly connected with the previous swept surface. The parameter line is obtained as follows:

[0082]

[0083] After completing the update of the next sweep profile, jump to step S2 to obtain the next sweep surface:

[0084] S k+1 (u,v)=T k+1 (v)+C k+1 (n) = T k+1 (v)+S k (0,v)

[0085] In step S4, all generated single-segment swept surfaces are unified and stitched together using the Brep structure to construct the final integrated 3D swept model. Since the geometric continuity and topological consistency between adjacent swept surfaces have been ensured through isoparametric line transfer in steps S2 and S3, the adjacent swept surfaces share boundary contours during the stitching process, creating natural seams. Each segment of the surface also meets at least G0 continuity.

[0086] First, the single-segment swept surface set {S k},k=0,1···n-1.

[0087] Based on the Brep structure to stitch adjacent surfaces, for surface S k With S k+1 , their isoparametric lines S k (1,v) and S k+1 (0, v) is the same curve, so the two swept surfaces share the same edge in the Brep representation, and the surfaces can be completely stitched.

[0088] According to the isoparametric line extraction strategy of the present invention, adjacent swept surfaces are continuous, and the last isoparametric line of the previous swept surface and the first isoparametric line of the next swept surface are the same curve:

[0089] S k (1,v)=S k+1 (0,v)

[0090] This ensures continuity between adjacent swept surfaces. In the Brep representation, only one edge is needed to represent the topological information of the curve. Each swept surface is represented using a face topology, and each boundary curve of each face is defined by a topological edge. Adjacent face topologies share a single edge topology. Since the Brep representation and its topological construction are not the focus of this invention, they will not be explained in detail here.

[0091] Based on the above steps, the present invention obtains all the swept surfaces, continuously splices adjacent surfaces, constructs them topologically based on Brep representation, and outputs the final swept surface. Figure 2 Simulates the generation process of each swept surface, Figure 3 The sweep profile and path corresponding to each swept surface in a specific case are shown, and the isoparametric lines serving as the sweep profile are clearly shown. Figure 4 、 Figure 5 、 Figure 6 Different types of sweep profiles and paths are selected as inputs, all of which are sweep results under the present invention.

[0092] The sweeping results fully demonstrate the rationality of the combined path swept surface construction method based on isoparametric line extraction, and the final swept surface can achieve good continuity on the whole.

[0093] The above description is a further detailed description of the present invention in conjunction with specific / preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. Those skilled in the art of the present invention may make various substitutions or modifications to the described embodiments without departing from the scope of the present invention, and such substitutions or modifications should be considered to fall within the scope of protection of the present invention.

[0094] Parts of the present invention that are not described in detail belong to the common knowledge of those skilled in the art.

Claims

1. A combined path swept surface construction method based on isoparametric line extraction, characterized in that: The following steps are involved: Step S1: Describing a geometric model using a Brep structure; the geometric model includes n sweep profiles and n sweep paths; the sweep paths are sequentially connected end to end and adjacent sweep paths are G0 continuous; the sweep profiles correspond to the sweep paths one by one; initializing a path index k representing the sequence number of the sweep path; Step S2: acquiring the sweep path according to the path index k, and acquiring and updating the sweep profile according to the sweep path; Obtaining a corresponding single-segment swept surface according to the swept profile; Step S3, intercepting an isoparametric line having a parameter value of 1 along the sweep profile direction of the single-segment swept surface; The isoparametric line represents the geometric profile of the end of the single-segment swept surface and has the same geometric continuity and spatial continuity as the swept profile; The isoparametric line serves as the sweep profile corresponding to the sweep path under the next path index k; Update the path index k; return to step S2 until the path index k is equal to n; Step S4: using the Brep structure to stitch all the generated single-segment swept surfaces, construct and output an overall three-dimensional swept model.

2. The combined path swept surface construction method based on isoparametric line extraction according to claim 1, characterized in that: The step S2 includes using NURBS to represent the sweep profile and the sweep path; The sweep path curve is expressed as: Where m is the upper limit of the control point index of the sweep path, and the total number of control points is m+1; j is the variable of the control point index of the sweep profile; N j,q (v) represents the j-th B-spline basis function of the sweep path, with order q; represents the spatial position of the j-th control point; express The corresponding control point weight; V is the node vector of the sweep path, and the node vector is a set of non-decreasing parameter values ​​used to define the segmentation of the NURBS curve and the parameter range of each segment of the curve.

3. The combined path swept surface construction method based on isoparametric line extraction according to claim 2, characterized in that: The sweep profile curve is expressed as: Where n is the upper limit of the control point index of the sweep profile, and the total number of control points is n+1; i is the variable of the control point index of the sweep profile; N i,p (u) represents the i-th B-spline basis function of the swept profile, with order p; represents the spatial position of the i-th control point; express The corresponding control point weight; U is the node vector of the swept contour.

4. The method for constructing a combined path swept surface based on isoparametric line extraction according to claim 3, characterized in that: In step S2, the corresponding single-segment swept surface is obtained using a translation method according to the swept profile.

5. The method for constructing a combined path swept surface based on isoparametric line extraction according to claim 4, characterized in that: The translation method formula is as follows: S k (u,v)=T k (v)+C k (u) Among them, T k (v) represents the sweep path curve; C k (u) represents the swept profile curve.

6. The method for constructing a combined path swept surface based on isoparametric line extraction according to claim 5, characterized in that: In step S3, the single-segment swept surface S is intercepted. k The isoparametric line with a parameter value of 1 in the direction of the sweep profile of (u, v) is set to 1. The required isoparametric curve is the sweep profile of the next section of the sweep path. The formula is as follows: Among them, S k (1,v) represents an isoparametric curve; is the control point of the single-segment swept surface, is the weight corresponding to the control point.

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