A method for repairing surface defects for complex surface offset

Abstract

The present invention provides a method for repairing surface defects for complex surface offset, and the steps are as follows: input a composite surface model, and discretize the composite surface into single surface models; detect single defective surfaces and classify the defects: degenerate surfaces and surfaces with non-uniform control point heights; for degenerate surfaces, adopt a repair method of surface reconstruction by trimming the surface with a quadrilateral domain; for surfaces with non-uniform control point heights, adopt a repair method of optimizing the number and distance distribution of control points; aggregate all single surfaces into a composite surface; perform a surface offset operation on the composite surface to obtain an offset composite surface; according to the vehicle body modeling standard and expert knowledge, perform quality inspection and repair on the offset composite surface; output the repaired offset composite surface. The surface defect repair solution proposed by the present invention can identify two types of surface defects existing in a complex surface model, and specifically give an integrated solution from identification to repair, improving the success rate of surface offset.

Description

Technical Field

[0001] The present invention belongs to the field of computer-aided design and manufacturing, and discloses a method for repairing surface defects for complex surface offsetting. Background Art

[0002] In the process of body design and modeling, complex surface offsetting is a key and challenging operation. An automotive body is composed of a large number of complex free-form surfaces, and there are complex topological and geometric continuity problems between surfaces, and high requirements are imposed on the quality of surface modeling. Due to the differences in modeling methods and levels of different engineers, different types of single surface defects occur in the process of body surface modeling. These defective surfaces cause frequent failures in surface offsetting operations, seriously affecting the efficiency of body design, and there is an urgent need for more effective solutions.

[0003] Through retrieval and analysis of existing literature, complex surface offsetting and surface repair methods mainly include the following situations:

[0004] In the process of generating offset surfaces, Meng et al. proposed a superlinear convergence algorithm to distribute a set of movable points as evenly as possible, while keeping these points at a specified distance from the base surface throughout the optimization process. (Wenlong Meng, et al. Efficiently computing feature-aligned and high-quality polygonal offset surfaces. Computers & Graphics. 2018, 70: 62-70.). Shen et al. proposed a level set-based surface equidistant method, which regards the surface offsetting problem as a problem of generating a new interface from a dynamic initial surface with a constant normal velocity. (Hongyao Shen, et al. Generation of offset surface for tool path in NC machining. Int J Adv Manuf Technol. 2010, 46: 1043-1047.).

[0005] In terms of degenerate surface repair, Shi et al. proposed a method for interpolating quadrilateral regions with incompatible boundaries, which utilizes the property of multi-valued normal vectors at degenerate points to achieve continuity with the boundaries. (Kan-Le Shi, et al. Polynomial spline interpolation of incompatible boundary conditions with a single degenerate surface. Computer-Aided Design. 2014, 53: 28-35.). Chi Baotao et al. proposed a fully automatic geometric topology repair method based on T-Spline to achieve automatic recognition of degenerate surfaces, surface detection, and fully automatic geometric topology repair of T-Spline surface reconstruction in complex CAD geometric models. (Chi Baotao, et al. A fully automatic geometric topology repair method based on T-Spline. Acta Automatica Sinica. 2019, 45(08): 1511-1526.).

[0006] In terms of removing self-intersections of offset surfaces, Q Youn Hong et al. proposed a method for trimming offset surfaces by calculating on the original input surface (and its derivatives) and constructing intersecting osculating tori to replace an offset surface by offsetting the osculating tori of the given input regular surface. (Q Youn Hong, et al. Trimming offset surface self-intersections around near-singular regions. Computers & Graphics. 2019, 82: 84-94.). Xu et al. proposed a method for identifying and removing self-intersecting loops by mapping the offset path to a predefined plane, which is obtained by flattening the mesh surface using mesh mapping techniques. (Jinting Xu, et al. A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining. Computer-Aided Design. 2015, 62: 131-142.).

[0007] In summary, the related research has solved the problems of generating offset surfaces, identifying and repairing defects in surface models to a certain extent. However, there is little research on the influence of the quality of offset surfaces on subsequent operations and the geometric characteristics of surfaces in relevant modeling standards.

[0008] Surface offset refers to the offset surface S'(u,v) corresponding to the given parametric surface S(u,v), and the offset surface has the following representation:

[0009] S′(u,v)=S(u,v)+d(u,v)·n(u,v)(1)

[0010] where d(u,v) represents the offset distance and d(u,v)>0, and n(u,v) is the unit normal vector of the surface S(u,v). The normal vector N(u,v) of the surface S(u,v) is given by N(u,v)=S u ×S v where S u and S v are the partial derivatives in the u and v directions respectively. The maximum and minimum principal curvatures of the surface S(u,v) are к max and к min .(Nicholas M.P.,&Takashi M.(2005).ShapeInterrogation for Computer Aided Design and Manufacturing.)

[0011] The composite surface CS is defined as a topological structure in which several surfaces {S i}(i = 0,1,2,…,n) are connected to each other and conform to the manifold rule. Given the corresponding offset composite surface CS' of the composite surface CS, it has the following representation:

[0012] CS′=CS+d(u,v)·n(2)

[0013] where n is the unit normal vector of the composite surface CS, and d(u,v) is the offset distance and d(u,v)>0.

[0014] When the offset distance is a constant, that is, d(u,v) = d, when the surface offset distance is greater than the curvature radius of the surface, that is, d>1 / κ max or d>1 / κ min , irregular points and self - intersections will occur on the offset surface. When the offset distance is a variable, that is, d(u,v)≠d, and the offset distance of a point p on the surface is greater than the curvature radius of that point on the surface, that is, d(p)>1 / κ p-max or d(p)>1 / κ p-min , self - intersections will occur on the offset surface. (Wallner J,et al,Self-intersections ofoffset curves and surfaces.International Journal of Shape Modeling,2001,7(1):1-21.)

[0015] NURBS surface, also known as non-uniform rational B-spline surface, the rational fraction representation of a NURBS surface of degree p×q in the u and v directions is as follows:

[0016]

[0017] In the formula, {P i,j} is the control mesh composed of (m + 1)×(n + 1) control points in the u and v directions, i = 0, 1, …, m; j = 0, 1, …, n; w i,j is the control weight factor, i = 0, 1, …, m; j = 0, 1, …, n; N i,p (u), N j,q (v) are non-rational B-spline basis functions defined on the knot vectors U and V respectively. U and V are the knot vectors in the u direction and v direction respectively:

[0018]

[0019] where r = n + p + 1, s = m + q + 1. (Les A. Piegl, et al(1996). The NURBS Book.).

[0020] Due to the wide representation range and various good properties of NURBS surfaces, they have become the mainstream geometric representation method in CAD and CAM, and have been integrated into international standards such as IGES and STEP, and are widely used in the design and modeling of complex body surfaces. Therefore, in this invention, the representation form of NURBS surfaces is mainly considered for the offset of complex surfaces and the repair of defective surfaces. Summary of the Invention

[0021] The present invention provides a method for repairing surface defects for complex surface offset. This method mainly aims at the situation where the offset operation of the composite surface fails, and repairs the surface defects for the composite surface containing degenerate surfaces and surfaces with highly non-uniform control points respectively. At the same time, according to industry standards and expert knowledge, quality inspection and defect repair are carried out on the offset composite surface to ensure that the output surface model meets the engineering design requirements to a certain extent. It includes the following steps (as Figure 1 shown):

[0022] Step 1, input the composite surface model, and discretize the composite surface into a single surface model;

[0023] Step 2, detect the single defective surface and classify the defective surfaces: degenerate surfaces and surfaces with highly non-uniform control points;

[0024] Step 3, for degenerate surfaces, adopt the repair method of surface reconstruction by trimming the surface with a quadrilateral domain;

[0025] Step 4: For the non-uniform surface of control point heights, adopt a repair method that optimizes the number and distance distribution of surface control points.

[0026] Step 5: Aggregate all single surfaces into a combined surface.

[0027] Step 6: Perform a surface offset operation on the combined surface to obtain an offset combined surface.

[0028] Step 7: According to industry standards and expert knowledge, perform quality inspection and repair on the offset combined surface.

[0029] Step 8: Output the repaired offset combined surface.

[0030] Advantages of the present invention: (1) The surface defect repair solution proposed by the present invention can identify two types of surface defects existing in a complex surface model and specifically provide an integrated solution from identification to repair, improving the success rate of surface offset. (2) By performing quality inspection and repair on the offset combined surface, to a certain extent, it ensures that the finally output combined surface meets the requirements of body design engineering, having practical engineering significance. Description of the Drawings

[0031] Figure 1 is a schematic flow chart of a surface defect repair method for complex surface offset provided by the present invention;

[0032] Figure 2 is a schematic diagram of a surface defect repair method for complex surface offset involving discretization of a complex surface model;

[0033] Figure 3 is a schematic diagram of a surface defect repair method for complex surface offset involving detecting a degenerate surface using the minimum enclosing sphere method;

[0034] Figure 4 is a schematic diagram of a surface defect repair method for complex surface offset involving detecting a degenerate surface by calculating the angles of surface corner points;

[0035] Figure 5 is a schematic diagram of a surface defect repair method for complex surface offset involving calculating the Hausdorff distance between two adjacent columns of control point sets in the u direction;

[0036] Figure 6 (a) is a schematic diagram of a surface defect repair method for complex surface offset involving a degenerate surface;

[0037] Figure 6 (b) is a schematic diagram of a surface defect repair method for complex surface offset involving repairing a degenerate surface by trimming a surface with a quadrilateral domain;

[0038] Figure 7 (a) is a schematic diagram of a surface defect repair method for complex surface offset, involving uneven height distribution of control points on the surface;

[0039] Figure 7 (b) is a schematic diagram of a surface defect repair method for complex surface offset, involving the schematic diagram of optimizing the number and distance distribution of control points;

[0040] Figure 8 It is a schematic diagram of a surface defect repair method for complex surface offset, involving the combined surface offset operation. Specific implementation manner

[0041] In order to make the purpose and specific steps of the present invention clearer, the following further details the present invention in conjunction with the accompanying drawings and implementation cases. The specific implementation cases described here are only used to explain the present invention and are not used to limit the present invention.

[0042] Please refer to Figure 1 , a surface defect repair method for complex surface offset provided by the present invention can specifically solve two types of defective surfaces existing in the complex surface model, effectively improve the success rate of surface offset, and at the same time perform quality inspection and repair on the offset combined surface to ensure the quality of the output offset surface.

[0043] The described surface defect repair method for complex surface offset mainly includes the following steps:

[0044] In step 1, it specifically includes the following steps:

[0045] (1.1) Input the complex surface model CS0;

[0046] (1.2) Please refer to Figure 2 shown, define the single surface set SS, discretize the combined surface CS0 into single surfaces, encode and store all single surfaces as S i (i = 0, 1, 2,..., n);

[0047] In step 2, it specifically includes the following steps:

[0048] (2.1) Define the degenerate surface set DS and the non-uniform surface set NS of control point heights;

[0049] (2.2) Traverse all single surfaces S in the single surface set SS i , detect degenerate surfaces: use the minimum enclosing sphere method to calculate the farthest distance between all control points in the boundary region of the control point grid, please refer to Figure 3 , obtain the surface control point set {P i,j}, the control point sets of the $i$-th column in the $u$ direction $i = \{0, 1, \ldots, n\}$ and the $m$-th row in the $v$ direction are $\{P$ i,m}, where The minimum enclosing sphere is the smallest sphere that encloses all $\{P$ i,m}, and the minimum enclosing sphere MBS characterized by its center $c$ and radius $R$ is found by solving a constrained quadratic optimization problem Define $D = 2R$ as the degeneration distance coefficient of the degenerate surface. Set $\delta$ as the threshold for measuring the control point distribution in the measurement boundary or corner region. If $D \lt \delta$, the surface is determined to be a degenerate surface and stored in the degenerate surface set $DS$. Otherwise, go to step (2.3);

[0050] (2.3) Detect the degenerate surface: Calculate the corner angles of the quadrilateral domain surface by calculating the included angles of the vectors formed by the corners and their adjacent control points. Refer to Figure 4 , obtain the control point set $\{P$ i,j} of the surface. $P$ is a corner point of the surface, and its control point is $P$ 0,0 , and its adjacent non - coincident control point $P$ in the $u$ direction 1，0 , denoted as $P_1$, and the adjacent non - coincident control point in the $v$ direction is $P$ 0，1 , denoted as $P_2$. Define the angle of the surface corner point as $\theta$, and calculate the angle at point $P$ Similarly, calculate the angles of the remaining corner points. Set $\gamma$ as the angle threshold for measuring the corner point $P$. If $\theta \lt \gamma$ or $(180^{\circ}-\theta) \lt \gamma$, the surface is determined to be a degenerate surface and stored in the degenerate surface set $DS$. Otherwise, go to step (2.4);

[0051] (2.4) Detect the non - uniformity of the surface control points: Refer to Figure 5 , let the control point set of the $i$-th column in the $u$ direction be $\{P$ i,j}\ and the control point set of the $(i + 1)$-th column $\{P$ i+1,j \} ($i = 0, 1, 2, \ldots, n$). Calculate the Hausdorff distance $H$ between the control point sets of two adjacent columns in the $u$ direction in turn k+1 , $k = 0, 1, \ldots, n - 1$; Calculate the average distance between adjacent control points in the $u$ direction as The reasonable distance given by the user between two adjacent columns of control points in the $u$ direction is is the reasonable distance, and the default value is 0; Define the control point distribution coefficient of the surface in the $u$ direction Set $\alpha$ as the lower limit of the control point distribution coefficient. If $\eta \lt \alpha$, the surface is determined to be a highly non - uniform surface in the $u$ direction; Similarly, calculate the Hausdorff distance $H$ between the control point sets of two adjacent rows in the $v$ direction in turn l+1 ($l = 0, 1, \ldots, m - 1$); Calculate the average distance between adjacent control points in the $v$ direction as The reasonable distance given by the user between adjacent control points in the $v$ direction τ is a reasonable distance, with a default value of 0, defining the distribution coefficient of control points in the v direction of the surface Set β as the lower limit of the control point distribution coefficient. If Γ < β, the surface is determined to be a surface with non-uniform control point heights in the v direction and is stored in the set NS of surfaces with non-uniform control point heights. Otherwise, return to step (2.2) to detect the next single surface S i+1 .

[0052] In step 3, it specifically includes the following steps

[0053] (3.1) Traverse the set DS of degenerate surfaces detected in steps (2.2) and (2.3). Please refer to Figure 6 (a). For the degenerate surface S0, extract the boundary curve family {C0(t)} of the degenerate surface S0, where t1 ≤ t ≤ t2

[0054] (3.2) Please refer to Figure 6 (b). Construct a quadrilateral domain trimming surface with the boundary curve family {C0(t)} of the degenerate surface

[0055] (3.3) Remove the degenerate surface S0 and replace the degenerate surface S0 with the quadrilateral domain trimming surface ;

[0056] (3.4) For the quadrilateral domain trimming surface obtained in step (3.2) Use the method in step (2.4) to determine whether it is a surface with non-uniform control point heights. If so, store it in the set NS of surfaces with non-uniform control point heights. If not, return to step (3.1) to repair the next degenerate surface

[0057] In step 4, it specifically includes the following steps

[0058] (4.1) Traverse the set NS of surfaces with non-uniform control point heights obtained in (2.4). Please refer to Figure 7 (a). For the surface S1 with non-uniform control point heights, according to the vehicle body modeling standard and expert knowledge, set the upper limit of the number of control points to A × B, such as taking 20 × 20, set the lower limits of the distribution coefficients of control points in the u and v directions, and set the surface precision error threshold ζ. Please refer to Figure 7 (b). Optimize the number and distance distribution of control points in the u and v directions of the surface S1 with non-uniform control point heights so that its precision error from the original surface S1 meets the set surface precision error threshold ζ, that is Obtain the optimized surface

[0059] (4.3) Remove the surface with non-uniform control point heights obtained in step (2.4) and replace the surface with non-uniform control point distribution heights with the optimized surface obtained in step (4.1)

[0060] In step 5, the following steps are specifically included:

[0061] (5.1) Re - aggregate all single surfaces into a composite surface CS1;

[0062] In step 6, the following steps are specifically included:

[0063] (6.1) Select the composite surface CS1 to be surface - offset;

[0064] (6.2) Refer to Figure 8 , given an offset distance d and a normal n, perform a surface - offset operation to obtain an offset composite surface CS'1;

[0065] In step 7, the following steps are specifically included:

[0066] (7.1) For the offset composite surface CS'1, define a set of single surfaces SS', discretize the composite surface CS'1 into single surfaces, encode and store all single surfaces as S' i (i = 0, 1, 2, …, n);

[0067] (7.2) Define a set of non - uniformly offset surfaces of control points NS';

[0068] (7.3) For the single surfaces in the set SS', perform a non - uniformity detection of control points using the detection criteria given in step (2.4), and store the non - uniformly offset surfaces of control points obtained from the detection into the set NS';

[0069] (7.4) For the non - uniformly offset surface of control points S'1 in the set NS', perform surface optimization using the method of optimizing the number and distance distribution of surface control points in step (4.1);

[0070] (7.5) Remove the non - uniformly offset surfaces of control points obtained in step (7.3), and replace the non - uniformly distributed surfaces of control points with the repaired surfaces obtained in step (7.4);

[0071] (7.6) Re - aggregate all single surfaces into an offset composite surface CS'2.

[0072] In step 8, the following steps are specifically included:

[0073] (8.1) Output the repaired offset composite surface CS'2.

Claims

1. A method for repairing defects of an automobile body surface for offset of complex surfaces, characterized in that, The following steps are included: Step 1: Input the composite surface model, discretize the composite surface model into multiple single surface models, and encode each discretized single surface. Step 2: Detect the single surface model and classify the defective surfaces. The defective surfaces are divided into degenerate surfaces and surfaces with non-uniform control point heights. (2.1) Detect degenerate surfaces: For the boundary region of the control point grid of a given NURBS surface, use the minimum enclosing sphere method to calculate the maximum distance between all control points in this region, and then define the degenerate distance coefficient. Set the threshold for the control point distribution in the boundary region or corner region. If the degenerate distance coefficient is less than the given threshold, determine that this surface is a degenerate surface. For the corner region of the control point grid of a given NURBS surface, calculate the angles of the corner points of the quadrilateral surface by calculating the included angles of the vectors formed by the corner points and their adjacent control points. Set the angle threshold for the corner points. If the angle of the corner point is less than the given threshold, determine that this surface is also a degenerate surface. (2.2) Detect the non-uniformity of the surface control points: For the u and v direction control point grids of a given NURBS surface, the user gives the reasonable distances between adjacent two columns and rows of control points in the u and v directions of the surface, calculate the distribution coefficients of the control points in the u and v directions of the surface, and set the lower limits of the distribution coefficients in the u and v directions. If the distribution coefficients obtained according to the reasonable distances given by the user do not meet the set lower limits of the distribution coefficients, determine that this surface is a surface with non-uniform control point heights. Step 3: For degenerate surfaces, use the method of reconstructing the surface by trimming the surface with a quadrilateral domain. (3.1) For the degenerate surface obtained in step (2.1), extract the boundary curves of the degenerate surface to form a boundary curve family. (3.2) Construct a quadrilateral domain trimmed surface according to the generated boundary curve family of the degenerate surface. (3.3) Remove the degenerate surface obtained in step (2.1), and replace the degenerate surface with the quadrilateral domain trimmed surface generated in step (3.2). (3.4) For the quadrilateral domain trimmed surface obtained in step (3.3), use the method in step (2.2) to determine whether it is a surface with non-uniform control point heights. If so, use the method in step 4 for repair. If not, return to step (3.1) to repair the next degenerate surface. Step 4: For surfaces with non-uniform control point heights, use the method of optimizing the number and distance distribution of surface control points for repair. (4.1) For the surface with non-uniform control point heights obtained in step (2.2), according to the vehicle body modeling standard and expert knowledge, set the upper limit of the number of control points as A×B, set the lower limits of the distribution coefficients of the control points in the u and v directions of the surface, and set the surface accuracy error threshold. Optimize the number and distance distribution of the control points in the u and v directions of the surface with non-uniform control point heights, so that the accuracy error between the optimized surface and the surface with non-uniform control point heights obtained in step (2.2) meets the set surface accuracy error threshold, and obtain the optimized surface. (4.2) Remove the surface with non-uniform control point heights obtained in step (2.2), and replace the surface with non-uniform control point distribution heights with the optimized surface obtained in step (4.1). Step 5: Aggregate all single surfaces into a composite surface; Step 6: Perform a surface offset operation on the composite surface to obtain an offset composite surface; (6.1) Select the composite surface to be offset; (6.2) Specify the offset distance and normal direction, and perform a surface offset operation to obtain an offset composite surface; Step 7: According to industry standards and expert knowledge, perform quality inspection and repair on the offset composite surface; (7.1) Discretize the offset composite surface into multiple single surfaces, and encode each discretized single surface; (7.2) For the single surfaces obtained in step (7.1), use the inspection criteria given in step (2.2) to inspect the control point height non-uniform offset surface; (7.3) For the control point height non-uniform offset surface detected in step (7.2), use the method of optimizing the number and distance distribution of surface control points in step (4.1) to optimize the surface; (7.4) Remove the control point height non-uniform surface obtained in step (7.2), and replace the control point distribution height non-uniform surface with the optimized surface obtained in step (7.3); (7.5) Re-aggregate all single surfaces into an offset composite surface; Step 8: Output the repaired offset composite surface.

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