Error-controllable chip mounting method and device for CAD (Computer Aided Design) model

Abstract

The embodiment of the invention discloses an error-controllable chip mounting method and device for a CAD model, and relates to the technical field of computer graphics digital geometry processing. By analyzing the first basic form matrix of the curved surface, the measurement structure of the original curved surface is kept unchanged, then equidistant mapping with the plane is realized through re-parameterization, and the process of establishing equidistant mapping between the complex curved surface and the plane is successfully realized. In this way, a more accurate mapping relation is established between the plane material and the curved surface, and deformation and errors in the mapping process can be controlled while geometric features of the curved surface are reserved. Therefore, the problems of insufficient mapping precision, large deformation and errors and the like in an existing CAD model curved surface patch technology are solved, a more accurate mapping relation between a plane material and a CAD model complex curved surface is achieved, meanwhile, curved surface geometric features are reserved, mapping errors are minimized, and the quality and stealth performance of aircraft curved surface patch are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of digital geometry processing of computer graphics, and in particular to an error-controllable patching method and device for a CAD model. Background Art

[0002] In modern aviation, an aircraft's stealth performance is crucial for improving its battlefield survivability and combat effectiveness. Stealth technology is primarily achieved through radar invisibility, with core mechanisms including the application of radar-absorbing materials (RAM), geometric stealth, and metamaterials. However, current stealth technology faces numerous challenges in practical application, particularly in adapting to complex curved surfaces. For example, wings, as critical aircraft components, have complex curved shapes, and traditional stealth material patching methods have significant limitations when applied to these curved surfaces.

[0003] Traditional methods of coating absorbing materials make it difficult to ensure uniform coating thickness on curved wing surfaces. Due to the stretching and compression effects of the wing's curvature, the performance of the coating material is easily degraded, making it unable to effectively convert electromagnetic waves into heat energy, thus affecting the stealth effect. For metamaterials, the adaptability of their unit structure to the wing's curvature is even worse. The performance of metamaterials depends on their precise periodic structure and the regulation of electromagnetic parameters. When applied to the curved surface of a wing, the metamaterial unit structure is easily stretched or compressed due to the deformation of the curved surface, resulting in misaligned unit spacing and uncontrollable shifts in the resonant frequency, seriously affecting the realization of the stealth bandwidth design goal.

[0004] In terms of aircraft surface patching technology, a discrete differential geometry isometric mapping algorithm is used to discretize the surface into a series of points and edges. By processing these discrete elements, isometric mapping of the surface is achieved. Its advantages lie in its ability to process discrete data well and its high adaptability to discrete point cloud data obtained in actual engineering projects. It can be calculated directly on a discrete grid, avoiding errors that may occur during the discretization of continuous functions. It also has certain advantages when processing surfaces with complex topological structures, such as those with holes and boundaries. However, this algorithm also has limitations. Based on discrete data calculations, local roughness may occur when processing smooth surfaces, resulting in inaccurate mapping results. The discretization process may also lose surface detail information, affecting the final patching effect.

[0005] Therefore, how to further improve the method of aircraft surface patches, thereby improving the quality and stealth performance of aircraft surface patches, has become a topic that needs to be studied. Summary of the Invention

[0006] Embodiments of the present invention provide an error-controllable patching method and device for CAD models, which can solve the problems of insufficient mapping accuracy, large deformation and error in existing CAD model surface patching technology, and achieve a more accurate mapping relationship between planar materials and complex surfaces of CAD models, while retaining the surface geometric features and minimizing mapping errors, thereby improving the quality and stealth performance of aircraft surface patches.

[0007] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0008] In a first aspect, an embodiment of the present invention provides a method comprising:

[0009] S1. After establishing a CAD model of an aircraft surface, obtaining a first basic form matrix of the CAD model and performing decomposition;

[0010] S2. Reparameterize the aircraft surface using the decomposition results;

[0011] S3, performing polar coordinate conversion on the re-parameterized first basic form matrix, and establishing an error model between the first basic form matrix and the unit matrix;

[0012] S4. Obtaining a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range;

[0013] S5. Using the neighborhood range calculated in S4, an adaptive point scattering strategy is used to obtain an equidistant mapping relationship between the entire aircraft surface and the plane, and the mapping relationship is sent to the terminal device on the production side.

[0014] In a second aspect, an embodiment of the present invention provides a device comprising:

[0015] A data acquisition module, configured to obtain and decompose a first basic form matrix of a CAD model of an aircraft surface;

[0016] A pre-processing module is used to re-parameterize the aircraft surface using the decomposition results;

[0017] an error processing module, configured to convert the re-parameterized first basic form matrix into polar coordinates and establish an error model between the first basic form matrix and the unit matrix;

[0018] An analysis module is used to obtain a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range;

[0019] The result output module is used to use the calculated neighborhood range and a scattering strategy to obtain the isometric mapping relationship between the entire aircraft surface and the plane, and send the mapping relationship to the terminal device on the production side.

[0020] The error-controllable patching method and device for CAD models provided in an embodiment of the present invention analyzes the first basic form matrix of the surface, maintains the metric structure of the original surface unchanged, and then achieves isometric mapping between the surface and the plane through re-parameterization, successfully realizing the process of establishing isometric mapping between the complex surface and the plane. This enables a more accurate mapping relationship to be established between the planar material and the surface, and can control the deformation and error in the mapping process while retaining the geometric features of the surface. This solves the problems of insufficient mapping accuracy, large deformation and error in the existing CAD model surface patching technology, realizes a more accurate mapping relationship between the planar material and the complex surface of the CAD model, while retaining the geometric features of the surface and minimizing the mapping error, thereby improving the quality and stealth performance of the aircraft surface patch. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 A flow chart of an error-controllable patch method for CAD models provided by an embodiment of the present invention;

[0023] Figure 2 A flowchart of iterative solution for equidistant mapping areas under controllable errors provided by an embodiment of the present invention.

[0024] Figure 3 This is an example diagram of a wing surface patch in the aircraft calculation example provided by an embodiment of the present invention.

[0025] Figure 4 This diagram shows the calculation results for the UV parameter domain and the equidistant mapping area on a surface patch in an aircraft calculation example provided by an embodiment of the present invention. In the UV parameter domain, an adaptive point scattering strategy and algorithm are used to calculate the equidistant mapping area that covers the entire surface, as shown in the figure, and the corresponding equidistant mapping relationship. The corresponding area representation is further displayed on the surface patch.

[0026] Figure 5 This diagram illustrates the intersection of the UV parameter domain and the equidistant mapping region for any point on a surface patch, as used in an aircraft calculation example provided by an embodiment of the present invention. In the UV parameter domain, the algorithm calculates the equidistant mapping regions for adjacent points and the corresponding equidistant mapping equations. If the equidistant mapping regions of two points intersect, the corresponding region representation is further displayed on the surface patch.

[0027] Figure 6This diagram illustrates the checkerboard effect of the intersection of the UV parameter domain and the equally mapped region of any point on a surface patch in an aircraft calculation example provided by an embodiment of the present invention. In the UV parameter domain, the equally mapped region of adjacent points is first tessellated, and the intersecting tessellation is then homogenized, resulting in a clearer mapping transformation at the interface. The corresponding representation on the surface patch is further illustrated.

[0028] Figure 7 This is a pattern diagram on a plane domain in the aircraft calculation example provided by an embodiment of the present invention.

[0029] Figure 8 This is a mapping effect diagram of some equidistantly mappable areas in the aircraft calculation example provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0030] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention will be described in detail below, with examples of the embodiments illustrated in the accompanying drawings. Throughout, identical or similar reference numerals represent identical or similar elements or elements having identical or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and intended only to explain the present invention and are not to be construed as limiting the present invention. Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a," "an," "said," and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" as used in the description of the present invention refers to the presence of the stated features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when an element is referred to as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or intervening elements may be present. Furthermore, "connected" or "coupled" as used herein may include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and will not be interpreted in an idealized or overly formal sense unless defined as such herein.

[0031] This embodiment focuses on the application scenario of aerospace surface patching materials, involving the field of digital geometry processing technology in computer graphics. In order to solve the problems of insufficient mapping accuracy, large deformation and error in the existing CAD model surface patching technology, an isometric mapping method with controllable construction error for the continuous representation of the CAD model surface is adopted. This method is based on a continuous mathematical model. By analyzing the first basic form matrix of the surface, a more accurate mapping relationship between aerospace plane materials and complex surfaces of CAD models is achieved, the geometric features of the surface are retained and the mapping error is controlled. Taking the aircraft surface as an example, the complex surface can be unfolded into a plane domain, solving the limitations of the traditional stealth material patching method, such as poor adaptability of the metamaterial unit structure and easy resonant frequency offset, thereby improving the quality of aircraft surface patching and stealth performance. The specific implementation steps cover analyzing the first basic form, reparameterization, error control, determining the neighborhood range, establishing an isometric mapping relationship and processing the intersection.

[0032] The general concept of this embodiment includes the following: First, a CAD model surface is generated and a first fundamental form analysis of the surface is performed. The first fundamental form matrix is ​​calculated by inputting aircraft surface parameters. Then, using the positive definite symmetric matrix decomposition theorem and the necessary and sufficient condition theorem for establishing isometric mappings between surfaces, the first fundamental form matrix of the surface is decomposed into a diagonal matrix. The surface is then reparameterized to establish an isometric mapping with the plane. Next, within the premise of controllable error, the range of the surface within which an isometric mapping can be established with the plane based on the previously established mapping relationship is calculated. Specifically, the mapping error is controlled by controlling the error between the reparameterized first fundamental form matrix and the unit matrix. Finally, within the controllable error range, the isometric mapping relationship between the entire surface patch and the plane is derived, and the intersection of the isometric mapping region is processed to achieve a clearer mapping effect.

[0033] The embodiment of the present invention provides a patch method for a CAD model with controllable error, such as Figure 1 、 2 Shown, including:

[0034] S1. After establishing the CAD model of the aircraft surface, obtain the first basic form matrix of the CAD model and decompose it; wherein, relevant parameters need to be input into the CAD, for example: in the actual engineering of aircraft surface patch design, it is first necessary to input the various parameter structures of the aircraft surface S. The surface S here represents a specific surface part of the aircraft, such as the surfaces of the wings, fuselage, etc. At the same time, a fixed point P must be determined. The fixed point can be a representative position on the surface S, such as the center point of the surface or a key connection point. In addition, the allowable error range T must be clearly defined. This error range is determined based on the design requirements of the aircraft and the actual application scenarios, and it directly affects the patch fitting accuracy. Finally, the initial length ρ of the iteration calculation of the equidistant mapping area is input, which is the starting value for subsequent iterative calculations.

[0035] S2. Reparameterize the aircraft surface using the decomposition results;

[0036] S3, performing polar coordinate conversion on the re-parameterized first basic form matrix, and establishing an error model between the first basic form matrix and the unit matrix;

[0037] S4. Obtaining a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range;

[0038] S5. Using the neighborhood range calculated in S4, a customized point scattering strategy is used to obtain an equidistant mapping relationship between the entire aircraft surface and the plane, and the mapping relationship is sent to the terminal device on the production side.

[0039] Optionally, before sending the mapping relationship to the terminal device on the production side, the method further includes: processing the intersection of the equidistant mapping ranges of adjacent points to obtain a clearer mapping transformation. The method for processing the intersection includes: dividing the equidistant mapping range of adjacent points into a grid; and uniformizing the grid of the intersection to obtain a clearer mapping transformation at the intersection.

[0040] Among them, the terminal equipment on the production side, such as large-scale 3D printing equipment, intelligent patch manufacturing plants and other places that can produce and manufacture aircraft surface patches, can be regarded as the so-called production side. The terminal equipment on the production side can be understood as the control terminal used to control the aircraft surface patch manufacturing and processing equipment, such as the employee computer of the workshop technician. Through the point scattering strategy, the equidistant mapping relationship established on the entire aircraft surface patch and the plane is obtained, so that the area corresponding to these points that can be mapped with a preserved length can cover the entire surface patch. In aircraft engineering, the adaptive point scattering strategy can ensure that the patch can fully cover the surface. By processing the boundary part of the equidistant mapping area of ​​adjacent points, it can ensure that the patch can fully cover the surface and ensure the splicing accuracy between patches.

[0041] In this embodiment, S1 includes generating a first basic form matrix of the aircraft surface S at a fixed point P on the aircraft surface S. The first basic form matrix of the surface S is calculated at the fixed point P on the aircraft surface S. This matrix describes the local geometric properties of the surface near that point and is crucial for subsequent isometric mapping calculations. In aircraft engineering, it reflects the curvature and shape characteristics of the surface and serves as fundamental data for patch design.

[0042] Matrix decomposition involves decomposing the first fundamental form matrix of a surface into a diagonal matrix using the theorem of positive symmetric matrix decomposition and the theorem of necessary and sufficient conditions for establishing isometric mappings between surfaces. In aircraft surface patch design, this decomposition can simplify complex surface geometry, facilitating subsequent parameterization and isometric mapping calculations. Specifically, the first fundamental form matrix is ​​decomposed to obtain a diagonal matrix as follows:

[0043]

[0044] Among them, the orthogonal matrix P can be taken as:

[0045]

[0046] Wherein, E, F, and G represent the first basic form coefficients of the surface S, and λ1 and λ2 represent the eigenvalues ​​of the first basic form matrix respectively.

[0047] In S2 of this embodiment, the aircraft surface is reparameterized using the obtained diagonal matrix. Surface reparameterization refers to reparameterizing the aircraft surface using the obtained diagonal matrix to obtain transformation coefficients. In aircraft engineering, reparameterization can transform the coordinate system of the surface to make it more suitable for isometric mapping calculations. Specifically, the transformation equation is:

[0048]

[0049] Among them, u and v represent the first and second original parameters of the surface, w and r represent the two parameters after the surface is reparameterized, u0 and v0 represent the two original coordinate parameters corresponding to the point P on the surface, and w0 and r0 represent the corresponding coordinate parameters of the point P on the surface after reparameterization.

[0050] Polarization and Error Calculation: Polarization is performed on the reparameterized first fundamental form matrix of the aircraft surface to control the error between the first fundamental form matrix and the unit matrix. The error calculation uses the Frobenius norm. In aircraft surface patch design, controlling this error can evaluate and control the accuracy of the isometric mapping between the aircraft surface and the plane, ensuring that the patch can accurately fit the surface. The error is defined as follows:

[0051]

[0052] Taylor expansion can be performed on each error to analyze the following:

[0053]

[0054] Where I represents the identity matrix, ξ and η represent the reparameterized coordinate parameters, Respectively represent the values ​​of the first basic form matrix coefficients E, F, G of the surface at point P (w0, r0), E w , F w , G w Represents the first-order derivative of the first basic form matrix coefficients E, F, G of the surface with respect to the parameter w, E r , F r , G r Represents the first-order derivative of the matrix coefficients E, F, G of the first basic form of the surface with respect to the parameter r, E w | (ξ，η) ,F w | (ξ，η) ,G w | (ξ，η) , is the parameter representation of the first derivative of the first basic form matrix coefficients E, F, G of the surface obtained for the parameter w at the point (ξ, η), E r | (ξ，η) ,F r | (ξ，η) ,G r | (ξ，η) , is the parametric representation of the first derivative of the first basic form matrix coefficients E, F, G of the surface with respect to the parameter r at the point (ξ, η).

[0055] In this embodiment, S4 includes:

[0056] S41. Obtain the first-order and second-order derivative structures of the aircraft surface S, as well as the coefficients of the reparameterized mapping change. Specifically, based on the given aircraft surface S and sampling points P, calculate the first-order and second-order derivative structures of surface S, and further calculate the coefficients of the reparameterized mapping change. This derivative information reflects the local rate of change of the surface and is crucial for determining the range of isometric mapping.

[0057] S42, after polar coordinate conversion, the scattered points p on the parameter domain (ρ, θ) are i Mapped to the parameter domain (u, v). According to the error model, the maximum range of the allowable error ρ is obtained t_range =T / max(M i ), where the fixed point P is in the direction of the fixed angle θ and the scattered points p are uniformly taken in the range [0,ρ]. i , ρ represents the distance to the fixed point P, i is a positive integer and i=1,…,m, m represents the number of points, ρ t_range The corresponding length is ρ tmax In the research, development, and manufacturing of aircraft, this step can determine the maximum range in which a curved surface can be equidistantly mapped to a flat surface at a specific angle.

[0058] S43, perform iterative update, where the iteration end condition is ρ range <ρ max If the iteration end condition is not met, ρ0=ρ max , ρ0 represents the range of scatter points to be updated, ρ max represents the updated ρ after the last iteration tmax value, the maximum range of error allowed after the first iteration ρ range =ρ t_range ,ρ range The corresponding length is Through iterative updates, a more accurate range of equidistant mapping can be gradually approached. Repeating step S42 ultimately yields a neighborhood range on the aircraft surface where equidistant mapping can be established with the plane near the sampled point. In aircraft surface patch design, this neighborhood range determines the patch placement range and accuracy.

[0059] The specific formula is as follows. For polar coordinates of (w, r), for a fixed θ∈[0,2π) we have:

[0060] ξ∈(w0,w),η∈(r0,r)→ζ∈(0,ρ)

[0061] E-1=E ρ | ζ ·ρ=(E w | ζ ·cosθ+E r | ζ ·sinθ)·ρ

[0062] F=F ρ | ζ ·ρ=(F w | ζ ·cosθ+F r | ζ ·sinθ)·ρ

[0063] G-1=G ρ | ζ ·ρ=(G w | ζ ·cosθ+G r | ζ ·sinθ)·ρ

[0064] Among them, ζ and η represent the coordinates of the two coordinate axes of polar coordinates, E ρ | ζ , F ρ | ζ , G ρ | ζ , which represents the first basic form matrix coefficients E, F, G of the surface for the first derivative value of parameter ρ at a fixed angle θ direction with a length of ζ from point P after polar coordinate conversion, E w | ζ , F w | ζ , G w | ζ , E r | ζ , F r | ζ , G r | ζ The first basic form matrix coefficients E, F, and G representing the surface are converted to polar coordinates and are the first-order derivative values ​​of the parameters w and r at a distance ζ from point P in the direction of a fixed angle θ.

[0065] The error value is calculated using the Frobenius norm, and the error value is within the given error range ε, that is,

[0066]

[0067] get:

[0068]

[0069] Among them, ε represents the given error range and M represents the optimization parameter.

[0070] M=MAX{(E w | ζ ·cosθ+E r | ζ ·sinθ) 2 ·ρ 2 +(F w | ζ ·cosθ+F r | ζ ·sinθ) 2 ·ρ 2 +(Gw | ζ ·cosθ+G r | ζ ·sinθ) 2}

[0071] Furthermore, the method further includes processing the intersections of the equally mapped ranges of adjacent points to obtain a clearer mapping transformation. In this embodiment, processing the intersections includes processing the intersections of the equally mapped ranges of adjacent points to obtain a clearer mapping transformation. In aircraft surface patch design, processing the intersections can avoid overlaps or gaps between patches, improving patch fit quality and overall aircraft performance.

[0072] This embodiment further provides a patch device with controllable error for a CAD model, comprising:

[0073] A data acquisition module, configured to obtain and decompose a first basic form matrix of a CAD model of an aircraft surface;

[0074] A pre-processing module is used to re-parameterize the aircraft surface using the decomposition results;

[0075] an error processing module, configured to convert the re-parameterized first basic form matrix into polar coordinates and establish an error model between the first basic form matrix and the unit matrix;

[0076] An analysis module is used to obtain a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range;

[0077] The result output module is used to use the calculated neighborhood range and an adaptive point scattering strategy to obtain the isometric mapping relationship between the entire aircraft surface and the plane, and send the mapping relationship to the terminal device on the production side.

[0078] In this embodiment, a continuous function mapping is used to achieve isometric mapping between general CAD model surfaces and planes, while also addressing overlapping areas. By maintaining the surface's first fundamental form, this method achieves isometric mapping between complex surfaces and planes, thereby establishing a more accurate mapping relationship between planar materials and surfaces. This method preserves the surface's geometric features while minimizing deformation and errors during the mapping process. This improves the quality and performance of CAD model surface patches, providing more effective technical support for engineering applications such as aircraft stealth material patches.

[0079] Specifically, by analyzing the first fundamental form matrix of the surface, the metric structure of the original surface is kept unchanged, and then the isometric mapping between the complex surface and the plane is achieved by re-parameterization, successfully realizing the process of establishing isometric mapping between the complex surface and the plane. This enables a more accurate mapping relationship to be established between the planar material and the surface, and can control the deformation and error in the mapping process while retaining the geometric characteristics of the surface. The continuous function differential geometry algorithm used is based on a continuous mathematical model and realizes the isometric mapping of the surface by solving partial differential equations and other methods. It can provide an accurate mathematical description, has a good effect on smooth surfaces, can ensure the smoothness and continuity of the mapping results, avoids the local non-smoothness problem of discrete algorithms, has high theoretical accuracy, and can better approximate the real isometric mapping. The present invention is precisely intended to propose a material surface patching method based on isometric mapping with controllable errors to overcome the shortcomings of the existing technology and improve the quality and stealth performance of aircraft surface patches.

[0080] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited to this. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for patching a CAD model with controllable error, characterized in that: include: S1. After establishing a CAD model of an aircraft surface, obtaining a first basic form matrix of the CAD model and performing decomposition; S2. Reparameterize the aircraft surface using the decomposition results; S3, performing polar coordinate conversion on the re-parameterized first basic form matrix, and establishing an error model between the first basic form matrix and the unit matrix; S4. Obtaining a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range; S5. Using the neighborhood range calculated in S4, obtain an isometric mapping relationship between the entire aircraft curved surface and the flat surface, and send the mapping relationship to the terminal device on the production side.

2. The method according to claim 1, characterized in that S1 includes: At a fixed point P on the aircraft surface S, a first basic form matrix of S is generated; The method of decomposing the first basic form matrix and obtaining a diagonal matrix is: Among them, E, F, and G are all coefficients of the first basic form of the surface, and λ1 and λ2 represent the two eigenvalues ​​of the first basic form matrix.

3. The method according to claim 1 or 2, characterized in that In S2, the aircraft surface is reparameterized by the obtained diagonal matrix to obtain the transformation relationship: Among them, u and v represent the first and second original parameters of the surface, w and r represent the two parameters after the surface is reparameterized, u0 and v0 represent the two original coordinate parameters corresponding to the point P on the surface, and w0 and r0 represent the corresponding coordinate parameters of the point P on the surface after reparameterization.

4. The method according to claim 3, characterized in that In S3, the error model includes: Where I represents the identity matrix, ξ and η represent the reparameterized coordinate parameters, Respectively represent the values ​​of the first basic form matrix coefficients E, F, G of the surface at point P (w0, r0), E w , E w , G w Represents the first-order derivative of the first basic form matrix coefficients E, F, G of the surface with respect to the parameter w, E r , F r , G r Represents the first-order derivative of the matrix coefficients E, F, G of the first basic form of the surface with respect to the parameter r, E w | (ξ，η) ,F w | (ξ，η) ,G w | (ξ，η) , is the parameter representation of the first derivative of the first basic form matrix coefficients E, F, G of the surface obtained for the parameter w at the point (ξ, η), E r | (ξ，η) ,F r | (ξ，η) ,G r | (ξ，η) , is the parametric representation of the first derivative of the first basic form matrix coefficients E, F, G of the surface with respect to the parameter r at the point (ξ, η).

5. The method according to claim 1, characterized in that S4 include: Obtain the first-order derivative and second-order derivative structures of the aircraft surface S, as well as the coefficients of the mapping changes after reparameterization; After polar coordinate conversion, the maximum range of allowable error ρ is obtained according to the error model. t_range =T / max(M i ), where the fixed point P is in the direction of the fixed angle θ and the scattered points p are uniformly taken in the range [0,ρ]. i , ρ represents the distance to the fixed point P, i is a positive integer and i=1,…,m, m represents the number of points, ρ t_range The corresponding length is ρ tmax ; Perform iterative update, where the iteration end condition is ρ range <ρ max If the iteration end condition is not met, ρ0=ρ max , ρ0 represents the range of scatter points to be updated, ρ max Represents ρ after the last iteration tmax The updated value of the maximum range of error allowed after the first iteration is ρ range =ρ t_range ,ρ range The corresponding length is 6. The method according to claim 5, characterized in that The polar coordinate conversion includes: ξ∈(w0,w),η∈(r0,r)→ζ∈(0,ρ) E-1=E ρ | ζ ·ρ=(E w | ζ ·cosθ+E r | ζ ·sinθ)·ρ F=F ρ | ζ ·ρ=(F w | ζ ·cosθ+F r | ζ ·sinθ)·ρ G-1=G ρ | ζ ·ρ=(G w | ζ ·cosθ+G r | ζ ·sinθ)·ρ Among them, ζ and η represent the coordinates of the two coordinate axes of polar coordinates, E ρ | ζ , F ρ | ζ , G ρ | ζ , which represents the first basic form matrix coefficients E, F, G of the surface for the first derivative value of parameter ρ at a fixed angle θ direction with a length of ζ from point P after polar coordinate conversion, E w | ζ , F w | ζ , G w | ζ , E r | ζ , F r | ζ , G r | ζ The first basic form matrix coefficients E, F, and G representing the surface are converted to polar coordinates and are the first-order derivative values ​​of the parameters w and r at a distance ζ from point P in the direction of a fixed angle θ.

7. The method according to claim 1, characterized in that Also includes: The intersection of the equally mapped ranges of adjacent points is processed to obtain a clearer mapping transformation.

8. The method according to claim 7, characterized in that The methods for handling intersections include: Divide the range of adjacent points that can be mapped equidistantly into a grid; The intersecting parts of the chessboard are homogenized.

9. A patch device with controllable error for CAD models, characterized in that: include: A data acquisition module, configured to obtain and decompose a first basic form matrix of a CAD model of an aircraft surface; A pre-processing module is used to re-parameterize the aircraft surface using the decomposition results; an error processing module, configured to convert the re-parameterized first basic form matrix into polar coordinates and establish an error model between the first basic form matrix and the unit matrix; An analysis module is used to obtain a neighborhood range of isometric mapping between the aircraft surface and the plane within a preset error range; The result output module is used to use the calculated neighborhood range and a scattering strategy to obtain the isometric mapping relationship between the entire aircraft surface and the plane, and send the mapping relationship to the terminal device on the production side.

Images