Bidirectional interpolation curved surface optimization method with guide line and related system

Abstract

The invention discloses a bidirectional interpolation curved surface optimization method with a guide line and a related system, and the method comprises the steps: constructing an original bidirectional interpolation curved surface based on a bidirectional curve grid, and giving a to-be-approached guide line; sampling is carried out on the guide curve, sampling points are projected to the original bidirectional interpolation curved surface, the original bidirectional interpolation curved surface is corrected based on the sampling points and projection coordinates of the sampling points on the original bidirectional interpolation curved surface to obtain a corrected curved surface, and the corrected curved surface and the original bidirectional interpolation curved surface are subjected to compatibility processing; therefore, optimization of the original bidirectional interpolation curved surface can be completed, the problem which cannot be solved by a traditional curved surface fitting algorithm is solved, and accurate fitting of a multidirectional curve network can be realized. Moreover, in a multidirectional curve network fitting situation, the algorithm can ensure accurate interpolation of curves as many as possible, and maximize the number of interpolated curves.

Description

Technical Field

[0001] The invention belongs to the technical field of curved surface construction, and in particular relates to a bidirectional interpolation curved surface optimization method with guide lines and a related system, which are suitable for generating curved surfaces of ships. Background Art

[0002] There are two types of surface generation techniques: interpolation methods and approximation methods. Ship surfaces are generally generated using interpolation methods. Depending on the interpolation method, the construction techniques also have different names, such as sweeping, rotation, and lofting. Ship models generally contain at least three types of parallel curve sets (waterline, transverse section line, and longitudinal section line). When the generated surface needs to pass through three types of curves at the same time, the surface construction method needs to be specially designed. Among the traditional interpolation methods, the method closest to this situation was proposed by Gordon. The generated surface is a surface interpolated on a bidirectional curve grid (hereinafter referred to as Gordon surface). However, the surface interpolated on a bidirectional curve grid has the disadvantages of being difficult to control in quality, balancing the approximation accuracy and calculation time, and being difficult to handle complex surfaces. Summary of the invention

[0003] The purpose of the present invention is to provide a bidirectional interpolation surface optimization method with guide lines and a related system to overcome the problems of difficult control of the quality of the constructed surface and low approximation accuracy in the prior art.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A bidirectional interpolation surface optimization method with guide lines comprises the following steps:

[0006] S1, construct the original bidirectional interpolation surface based on the bidirectional curve grid, and give the guide line to be approximated;

[0007] S2, sampling on the guide curve and projecting the sampling points onto the original bidirectional interpolation surface;

[0008] S3, based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface, the original bidirectional interpolation surface is corrected to obtain a corrected surface;

[0009] S4, compatibility processing is performed on the modified surface and the original bidirectional interpolation surface, thereby completing the optimization of the original bidirectional interpolation surface.

[0010] Preferably, a U-direction lofted surface is constructed based on the U-direction section line, a V-direction lofted surface is constructed based on the V-direction section line, and a tensor product surface interpolated on the intersection grid is constructed using the V-direction mixed basis function of the U-direction lofted surface and the U-direction mixed basis function of the V-direction lofted surface;

[0011] The original bidirectional interpolation surface is constructed based on the U-direction lofted surface, the V-direction lofted surface and the tensor product surface.

[0012] Preferably, the displacement Q from each sampling point to the corresponding projection point and the parameter coordinates of the projection point on the original bidirectional interpolation surface are recorded.

[0013] Preferably, the basis function of the modified surface is determined based on the number of isoparametric constraints; the fixed boundary control points are set to 0, and the isoparametric constraints of the internal control points are set to form a constraint equation; then the value (point) of the original bidirectional interpolation surface at the projection coordinate of the sampling point is made equal to the displacement corresponding to the sampling point to form an unconstrained equation; the Lagrange multiplier method is used to solve a set of control points that satisfy the constraint equation and minimize the error of the unconstrained equation, and the original bidirectional interpolation surface is corrected based on the control points to obtain a modified surface.

[0014] Preferably, a node insertion or thinning algorithm is used to make the modified surface and the original bidirectional interpolation surface compatible, and their control points are added to obtain a modified surface.

[0015] Preferably, if the accuracy of the corrected surface approximating the guide line does not meet the requirement, the corrected surface and the original bidirectional interpolation surface are further corrected until the accuracy of the corrected surface approximating the guide line meets the set requirement.

[0016] In a second aspect, a bidirectional interpolation surface optimization system with guide lines includes a surface construction module, a sampling module, a correction module and an optimization module;

[0017] The surface construction module constructs the original bidirectional interpolation surface based on the bidirectional curve grid and gives the guide line to be approximated;

[0018] The sampling module samples the guide curve and projects the sampling points onto the original bidirectional interpolation surface;

[0019] A correction module corrects the original bidirectional interpolation surface based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a corrected surface;

[0020] The optimization module can optimize the original bidirectional interpolation surface by making the modified surface and the original bidirectional interpolation surface compatible.

[0021] Preferably, a U-direction lofted surface is constructed based on the U-direction section line, a V-direction lofted surface is constructed based on the V-direction section line, and a tensor product surface interpolated on the intersection grid is constructed using the V-direction mixed basis function of the U-direction lofted surface and the U-direction mixed basis function of the V-direction lofted surface;

[0022] The original bidirectional interpolation surface is constructed based on the U-direction lofted surface, the V-direction lofted surface and the tensor product surface.

[0023] In a third aspect, a computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for optimizing a bidirectional interpolation surface with guide lines when executing the computer program.

[0024] In a fourth aspect, a computer-readable storage medium stores a computer program, wherein the computer program, when executed by a processor, implements the steps of the above-mentioned bidirectional interpolation surface optimization method with guide lines.

[0025] Compared with the prior art, the present invention has the following beneficial technical effects:

[0026] The present invention provides a method for optimizing a bidirectional interpolation surface with a guide line. The original bidirectional interpolation surface is constructed based on a bidirectional curve grid, and a guide line to be approximated is given; sampling is performed on the guide curve, and the sampling points are projected onto the original bidirectional interpolation surface. The original bidirectional interpolation surface is corrected based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a corrected surface. The corrected surface and the original bidirectional interpolation surface are compatible, and the optimization of the original bidirectional interpolation surface can be completed, which solves the problem that the traditional surface fitting algorithm cannot solve, and can achieve accurate fitting of a multidirectional curve network. Moreover, in the multidirectional curve network fitting scenario, the algorithm can ensure accurate interpolation of as many curves as possible and maximize the number of interpolation curves. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 In the figure a, there are multiple U-direction cross-sectional line diagrams. Figure 1 b in the figure is a diagram of multiple V-section lines. Figure 1 In the figure, c is a graph of multiple arbitrary guide lines. Figure 1 d in the middle is a schematic diagram for setting multiple U-direction section lines, multiple V-direction section lines and multiple arbitrary guide lines.

[0028] Figure 2 The figure is a schematic diagram of constructing the original bidirectional interpolation surface in an embodiment of the present invention.

[0029] Figure 3 a in the figure is a schematic diagram of projecting the sampling points onto the original bidirectional interpolation surface structure in an embodiment of the present invention. Figure 3 b in Figure 3 Schematic diagram of the locally enlarged structure on a.

[0030] Figure 4 Schematic diagram of the process of the bidirectional interpolation surface optimization method with guide lines in an embodiment of the present invention.

[0031] Figure 5 a in the figure is a schematic diagram of the modified curved surface structure in an embodiment of the present invention, Figure 5 b in Figure 5 Schematic diagram of the locally enlarged structure on a. DETAILED DESCRIPTION

[0032] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0033] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0034] The present invention provides a bidirectional interpolation surface optimization method with a guide line, which specifically comprises the following steps:

[0035] S1, construct the original bidirectional interpolation surface based on the bidirectional curve grid, and give the guide line to be approximated;

[0036] S2, sampling on the guide curve and projecting the sampling points onto the original bidirectional interpolation surface;

[0037] S3, based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface, the original bidirectional interpolation surface is corrected to obtain a corrected surface;

[0038] S4, compatibility processing is performed on the modified surface and the original bidirectional interpolation surface, thereby completing the optimization of the original bidirectional interpolation surface.

[0039] In the specific implementation of the present application, a U-direction lofted surface S is constructed based on the U-direction section line. u-loft (u,v), construct a V-direction lofted surface S based on the V-direction section line v-loft (u,v), using U-direction lofting surface S u-loft V-direction mixed basis function and V-direction lofted surface S of (u,v) v-loftThe U-direction mixed basis function of (u,v) constructs a tensor product surface S interpolated on the intersection grid tp (u,v);

[0040] Based on U-direction lofting surface S u-lof (u,v), V-direction lofted surface S v-loft (u,v) and the tensor product surface S tp (u,v) constructs the original bidirectional interpolation surface, and the result is as follows Figure 2 As shown, its expression is:

[0041] S Gordon (u,v)=S u-loft (u,v)+S v-loft (u,v)-S tp (u,v)

[0042] Specifically, in the embodiments of the present application, Figure 1 As shown in a, there are multiple U-direction section lines like Figure 1 As shown in b, there are multiple V-shaped cross-section lines like Figure 1 As shown in c, multiple arbitrary guide lines like Figure 1 As shown in d, a schematic diagram of setting multiple U-direction section lines, multiple V-direction section lines and multiple arbitrary guide lines. The present invention strictly passes through a given bidirectional curve by generating a curved surface and approximates the specified guide line.

[0043] Sampling on the guide line and projecting the sampling points onto the original bidirectional interpolation surface, the result is as follows Figure 3 As shown in a in ; record the displacement Q of each sampling point to the corresponding projection point and the parameter coordinates (u, v) of the projection point on the original bidirectional interpolation surface, and construct the local structure diagram of the surface as shown in Figure 3 As shown in b.

[0044] The basis function of the modified surface is determined based on the number of isoparametric constraints; the fixed boundary control points are set to 0, and the isoparametric constraints of the internal control points are set to form a constraint equation; then the value (point) of the original bidirectional interpolation surface at the projection coordinate of the sampling point is made equal to the corresponding displacement at the sampling point to form an unconstrained equation; the Lagrange multiplier method is used to solve a set of control points that satisfy the constraint equation and minimize the error of the unconstrained equation, and the original bidirectional interpolation surface is corrected based on the control points to obtain the modified surface.

[0045] Specifically, let {Q i}, i = 0, ..., r is the data point to be fitted, and the data point to be fitted is the displacement from the sampling point of the guide line to its projection point. is the v value at the internal U-direction isoparm, is the u value at the internal V-direction isoparm.

[0046] For each unconstrained data item Q i Specify weights, w0,…,w r > 0. These weights exert an additional influence on the compactness of the approximation for each unconstrained data item; the weights specified here are unrelated to the weights in the NURBS sense.

[0047] The unconstrained data items are approximated in the least squares sense, and the constrained data items are interpolated using a (p,q)-order non-rational surface S(u,v) with (n′+1)×(m′+1) control points.

[0048] n′ is the number of rows of control points, m′ is the number of columns of control points, p is the degree in the u direction, and q is the degree in the v direction.

[0049] Assume the following vectors and matrices:

[0050] The vector of r+1 points to be fitted:

[0051]

[0052] The vector of (n′+1)(m′+1) control points:

[0053]

[0054] A diagonal matrix of (r+1)×(r+1) scalars:

[0055]

[0056] (r+1)×(n′+1)(m′+1) scalar matrix:

[0057]

[0058] in is a parameter coordinate corresponding to an unconstrained data item yes

[0059] A scalar:

[0060]

[0061] 2(m′+n′)×(n′+1)(m′+1) scalar matrix;

[0062]

[0063] (n0-1)(n′-1)×(n′+1)(m′+1)U-direction isoparametric constraint coefficient matrix:

[0064]

[0065] (n1-1)(m′-1)×(n′+1)(m′+1)V-direction isoparametric constraint coefficient matrix:

[0066]

[0067] Determining the target surface is a constrained minimization problem, and Lagrange multipliers are used to solve it. Introduce the Lagrange multiplier vector to obtain a block equation system. From this system, first obtain the solution of the Lagrange multiplier, and then obtain the solution of the control point;

[0068] make

[0069]

[0070] is the Lagrange multiplier vector, where each λ k All are one with Q k Quantities of the same dimension;

[0071]

[0072] is the coefficient matrix of the constraint equation. Then the unconstrained equation is:

[0073] NP=Q

[0074] The constraint equation is:

[0075] MP=0

[0076] The error of the unconstrained equation is Q-NP, and the weighted sum of squares of these error terms needs to be minimized and MP=0.

[0077] Construct the Lagrangian function about A and vector P:

[0078]

[0079] Setting its gradient to 0 gives:

[0080] -2(Q T WN-P T N T WN)+A T M=0

[0081] MP=0

[0082] Transposing A and extracting the factor 2 from A yields:

[0083] N T WNP+M T A=N T WQ

[0084] MP=0

[0085] Or, in block matrix form:

[0086]

[0087] Solve this equation to obtain A and the vector P. If N T WN and M(N T WN) -1 M T are all reversible, then this equation has a unique solution.

[0088] Write the expression for the vector P:

[0089] P=(N T WN) -1 N T WQ-(N T WN) -1 M T A

[0090] Multiplying by M on the left, we get:

[0091] MP=M(N T WN) -1 N T WQ-M(N T WN) -1 M T A

[0092] Therefore:

[0093] M(N T WN) -1 M T A=M(N T WN) -1 N T WQ

[0094] So the expression of A is:

[0095] A=(M(N T WN) -1 M T ) -1 M(N T WN) -1 N T WQ

[0096] Substitute A into the expression for vector P and solve for vector P.

[0097] Now, the corrected surface can be constructed using the vector P and the precomputed node vectors:

[0098]

[0099] The modified surface O(u,v) and the original bidirectional interpolation surface S are transformed by using node insertion or thinning algorithm. Gordon (u,v) are made compatible, and their control points are added to obtain the corrected surface S Guided (u,v).

[0100] S Guided (u,v)=O(u,v)+S Gordon (u,v)

[0101] If the accuracy of the corrected surface approaching the guide line does not meet the requirements, the corrected surface and the original bidirectional interpolation surface are further corrected to achieve an effect that is closer to the guide line.

[0102] In the specific implementation mode of the present application, the result is as follows Figure 5 In a and b, the distance between the corrected surface and the guide line is significantly reduced, and the surface is approached to the guide line within the specified error range (0.1, ignoring the distance unit).

[0103] The present invention modifies the surface to make it close to the guide line when the Gordon surface interpolates two groups of curves. In order to make the surface close to the guide line, the method uses the Lagrange multiplier method to construct a modified surface, and then superimposes it on the original surface. Since the Gordon surface regards the bidirectional curve grid as isoparametric lines, the same isoparametric line constraints can be added during the construction of the modified surface, so that the modified surface still strictly passes through the initial two types of curves.

[0104] In yet another embodiment of the present invention, a bidirectional interpolation surface optimization system with guide lines is provided, comprising a surface construction module, a sampling module, a correction module and an optimization module;

[0105] The surface construction module constructs the original bidirectional interpolation surface based on the bidirectional curve grid and gives the guide line to be approximated;

[0106] The sampling module samples the guide curve and projects the sampling points onto the original bidirectional interpolation surface;

[0107] A correction module corrects the original bidirectional interpolation surface based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a corrected surface;

[0108] The optimization module can optimize the original bidirectional interpolation surface by making the modified surface and the original bidirectional interpolation surface compatible.

[0109] A U-direction lofted surface is constructed based on the U-direction section line, a V-direction lofted surface is constructed based on the V-direction section line, and a tensor product surface interpolated on the intersection grid is constructed using the V-direction mixed basis function of the U-direction lofted surface and the U-direction mixed basis function of the V-direction lofted surface;

[0110] The original bidirectional interpolation surface is constructed based on the U-direction lofted surface, the V-direction lofted surface and the tensor product surface.

[0111] In yet another embodiment of the present invention, a terminal device is provided. The terminal device includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions; the processor described in the embodiment of the present invention can perform the operation of the bidirectional interpolation surface optimization method with a guide line, including the following steps: constructing an original bidirectional interpolation surface based on a bidirectional curve grid, and giving a guide line to be approximated; sampling on the guide curve, and projecting the sampling points onto the original bidirectional interpolation surface; modifying the original bidirectional interpolation surface based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a modified surface; and compatibility processing is performed on the modified surface and the original bidirectional interpolation surface to complete the optimization of the original bidirectional interpolation surface.

[0112] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory, or a non-volatile memory (non-volatile memory), such as at least one disk storage.

[0113] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the method for optimizing a bidirectional interpolation surface with a guide line in the above-mentioned embodiment; one or more instructions in the computer-readable storage medium are loaded by the processor and the following steps are executed: constructing an original bidirectional interpolation surface based on a bidirectional curve grid, and giving a guide line to be approximated; sampling on the guide curve, and projecting the sampling points onto the original bidirectional interpolation surface; modifying the original bidirectional interpolation surface based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a modified surface; and compatibility processing is performed on the modified surface and the original bidirectional interpolation surface to complete the optimization of the original bidirectional interpolation surface.

[0114] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0115] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0116] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A bidirectional interpolation surface optimization method with guide lines, characterized in that: The following steps are involved: S1, construct the original bidirectional interpolation surface based on the bidirectional curve grid, and give the guide line to be approximated; S2, sampling on the guide curve and projecting the sampling points onto the original bidirectional interpolation surface; S3, based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface, the original bidirectional interpolation surface is corrected to obtain a corrected surface; S4, compatibility processing is performed on the modified surface and the original bidirectional interpolation surface, thereby completing the optimization of the original bidirectional interpolation surface.

2. The method for optimizing a bidirectional interpolation surface with guide lines according to claim 1, characterized in that: A U-direction lofted surface is constructed based on the U-direction section line, a V-direction lofted surface is constructed based on the V-direction section line, and a tensor product surface interpolated on the intersection grid is constructed using the V-direction mixed basis function of the U-direction lofted surface and the U-direction mixed basis function of the V-direction lofted surface; The original bidirectional interpolation surface is constructed based on the U-direction lofted surface, the V-direction lofted surface and the tensor product surface.

3. The method for optimizing a bidirectional interpolation surface with guide lines according to claim 1, characterized in that: Record the displacement Q from each sampling point to the corresponding projection point and the parameter coordinates of the projection point on the original bidirectional interpolation surface.

4. The method for optimizing a bidirectional interpolation surface with guide lines according to claim 3, characterized in that: Determine the basis function of the modified surface based on the number of isoparametric constraints; set the fixed boundary control points to 0, set the isoparametric constraints of the internal control points, and form a constraint equation; then let the value (point) of the original bidirectional interpolation surface at the projection coordinate of the sampling point be equal to the corresponding displacement at the sampling point to form a non-constrained equation; The Lagrange multiplier method is used to solve a set of control points that satisfy the constraint equations and minimize the errors of the unconstrained equations. The original bidirectional interpolation surface is corrected based on the control points to obtain the corrected surface.

5. The method for optimizing a bidirectional interpolation surface with guide lines according to claim 4, characterized in that: The modified surface and the original bidirectional interpolation surface are made compatible by using a node insertion or thinning algorithm, and their control points are added to obtain the modified surface.

6. The method for optimizing a bidirectional interpolation surface with guide lines according to claim 1, characterized in that: If the accuracy of the corrected surface approaching the guide line does not meet the requirement, the corrected surface and the original bidirectional interpolation surface are further corrected until the accuracy of the corrected surface approaching the guide line meets the set requirement.

7. A bidirectional interpolation surface optimization system with guide lines, characterized in that: It includes surface construction module, sampling module, correction module and optimization module; The surface construction module constructs the original bidirectional interpolation surface based on the bidirectional curve grid and gives the guide line to be approximated; The sampling module samples the guide curve and projects the sampling points onto the original bidirectional interpolation surface; A correction module corrects the original bidirectional interpolation surface based on the sampling points and the projection coordinates of the sampling points on the original bidirectional interpolation surface to obtain a corrected surface; The optimization module can optimize the original bidirectional interpolation surface by making the modified surface and the original bidirectional interpolation surface compatible.

8. The bidirectional interpolation surface optimization system with guide lines according to claim 7, characterized in that: A U-direction lofted surface is constructed based on the U-direction section line, a V-direction lofted surface is constructed based on the V-direction section line, and a tensor product surface interpolated on the intersection grid is constructed using the V-direction mixed basis function of the U-direction lofted surface and the U-direction mixed basis function of the V-direction lofted surface; The original bidirectional interpolation surface is constructed based on the U-direction lofted surface, the V-direction lofted surface and the tensor product surface.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for optimizing a bidirectional interpolation surface with guide lines as claimed in any one of claims 1 to 6 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for optimizing a bidirectional interpolation surface with guide lines as claimed in any one of claims 1 to 6 are implemented.

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