A globally consistent geometry design method for blade-like surfaces based on PHT splines

Abstract

The present invention relates to a globally consistent geometric design method for blade-like surfaces based on PHT splines, which uses Polynomial Splines over Hierarchical T-meshes (PHT-splines) surfaces to fit complex blade-like surfaces and their geometric features with high precision. The main technical solution includes: through a boundary-consistent reparameterization process, the splicing and cutting parameter domain is a globally consistent complete single parameter domain, which serves as the definition domain of the PHT spline; comprehensively considering the geometric features and boundary information, rationally sampling to obtain the set of data points to be fitted and calculating the corresponding high-order geometric information; by controlling the hierarchical subdivision of the grid, blade-like surfaces represented by PHT splines are obtained with high precision fitting. The present invention solves the discontinuity problem caused by cutting and splicing in traditional design methods, ensures the global consistency of the overall design, and improves the design accuracy and efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical design, and in particular relates to a globally consistent geometric design method for blade-like surfaces based on PHT splines. Background Art

[0002] Geometric modeling began to rise with the rapid development of computer-aided technology. Geometric modeling primarily encompasses surface modeling and solid modeling, with surface modeling being a key area of ​​research in computer-aided geometric design. Non-Uniform Rational B-Splines (NURBS), defined on tensor product meshes, have been widely used to represent various geometric objects, driving the rapid development of modern geometric modeling research. NURBS, with its efficient evaluation algorithms and intuitive control grids that allow designers to edit and modify surfaces, has become the standard geometric representation for industrial models. With the rapid development of modern industry, model topology and geometric details have become increasingly complex, posing challenges for traditional NURBS representations. This is primarily due to the fact that NURBS is defined on a regular tensor product mesh, making it infeasible for local refinement and inconvenient for multi-piece splicing. Locally refined splines were developed in this context. By introducing T-points or a hierarchical structure, NURBS enables local refinement and facilitates the splicing of multiple pieces of arbitrary topology. Essentially, these approaches consider splines on T-meshes.

[0003] Blade surfaces exhibit complex geometric features such as bends, sweeps, and twists. Traditional design methods typically rely on local approximations and piecewise design, stitching together multiple cropped NURBS surface patches. While this approach can meet design requirements, due to geometric topology limitations, Boolean operations such as cropping and splicing introduce discontinuities, making it difficult to ensure consistent overall surface design. This increases complexity and uncertainty in the design process, while also compromising machining accuracy and efficiency. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a globally consistent geometric design method for blade-like surfaces based on PHT splines. Through global reparameterization that satisfies boundary consistency, a global correspondence between the target geometry and a single complete parameter domain is established. This enables high-precision fitting of complex surface geometric features using a single PHT spline (Polynomial Splines over Hierarchical T-meshes, PHT-splines) surface, and obtains a surface expression oriented towards engineering indicators, which is conducive to the integrated design, manufacturing and CNC machining of blade-like surfaces.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A globally consistent geometric design method for blade-like surfaces based on PHT splines includes the following steps:

[0007] Step 1: Input the blade surface model stored in STEP format ,in, Represents a blade surface model Middle A blade-like surface patch based on clipped NURBS representation The parameter variables, Represents a blade surface model Leaf-like surface patches based on clipped NURBS representation the number of

[0008] Step 2: From the blade surface model Get and record each blade-like surface patch based on the clipped NURBS representation The boundary curve And the corresponding clipping parameter domain The parametric boundary curve , among which blade-like surface patches is the curved quadrilateral obtained by clipping, that is ;

[0009] Step 3: Blade-like surface patch Corresponding clipping parameter domain Implementing boundary-consistent reparameterization to meet engineering metrics constraints , get the corresponding rule parameter domain , and ensure different blade surface pieces Corresponding rule parameter domain Continuity of parameter distribution at the splice, where Respectively represent the definitions in the rule parameter domain Parameter variables on ;

[0010] Step 4: Stitching by boundary consistent reparameterization All rule parameter fields obtained , and implement a globally consistent reparameterization , to obtain a complete single parameter domain , as the domain of the PHT spline surface, where Respectively, they are defined in a complete single parameter domain Parameter variables on ;

[0011] Step 5: Blade-like surface patch obtained based on reparameterization , comprehensively considering the fitting target and accuracy, reasonably sampling to obtain the set of data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The set of data points to be fitted by the boundary and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the reparameterized inverse process on the blade surface patch The parameter coordinates on Represents the geometric coordinates of the sampling point, and the superscript -1 represents the inverse operation of the function;

[0012] Step 6: Set the data points to be fitted Parameterized to a complete single parameter domain The corresponding relationship is formed , and use high-order geometric information to interpolate the data point set to be fitted Obtain PHT spline surface based on uniform subdivision grid ;in, Represents the composite operation of functions, ;

[0013] Step 7: Based on the design standards of blade-like surfaces and the engineering indicators that meet boundary consistency, the segmentation and sampling features are comprehensively considered, and the approximation error constraint is introduced to obtain the approximation error of the PHT spline surface. The local subdivision is implemented in the uniform subdivision control grid to generate a hierarchical control grid, and a high-precision approximate blade surface model is obtained based on the hierarchical subdivision control grid. PHT spline surface .

[0014] Furthermore, in step 2, the blade-like surface expressed based on NURBS is composed of multiple clipped NURBS surface patches, and the corresponding parameter domain is a clipped curved-edge quadrilateral. The specific analysis method is as follows:

[0015] Step 2-1: Record each blade surface The boundary curve ;

[0016] Step 2-2: On each boundary curve Corresponding clipping parameter domain In the document, the parameter boundary curve based on NURBS is recorded And the corresponding parameter value range ;

[0017] Step 2-3: Follow the blade surface Adjacency relationship in Euclidean space, adjust boundary curve and parametric boundary curves The parameter direction makes the target complete single parameter domain The parameters of and , the corresponding parameter value range .

[0018] Furthermore, in step 3, for each cropped surface piece , it is necessary to ensure that the geometric boundaries before and after reparameterization are consistent, the isoparameters are approximately evenly distributed, and the regular parameter domain corresponding to all clipped surface patches is guaranteed The parameter distribution continuity at the splicing point is implemented as follows:

[0019] Step 3-1: Blade-like surface patch Corresponding clipping parameter domain For a curved quadrilateral, record two sets of opposite sides separately and ,in, The parameter boundary curve obtained by reordering and adjusting the parameter directions in steps 2-3;

[0020] Step 3-2: Record the cropping parameter fields separately The four corner points of:

[0021] ,

[0022] ,

[0023] ,

[0024] ,

[0025] in, is the boundary parameter curve The parameter value range of

[0026] Step 3-3: Use bilinear interpolation to interpolate each leaf surface patch Corresponding clipping parameter domain Implementing boundary-consistent reparameterization is the corresponding rule parameter domain :

[0027] .

[0028] Furthermore, in step 4, the method for performing global consistent reparameterization to obtain a complete single parameter domain is as follows:

[0029] Step 4-1: Follow the blade-like surface patch Initial implementation of globally consistent reparameterization of adjacency relations in Euclidean space ,according to OK Arrange columns and concatenate all rule parameter fields , get the intermediate parameter domain ,in, Respectively represent the definitions in the intermediate parameter domain Parameter variables on ;

[0030] Step 4-2: Implement global consistent reparameterization again ,Right now , to obtain a complete single parameter domain is the domain of the PHT spline surface, ,in, Respectively, they are defined in a complete single parameter domain The parameter variables on the blade surface are recorded as and .

[0031] Furthermore, in step 5, the method of sampling the set of data points to be fitted at the geometric features and calculating the corresponding high-order geometric information is as follows:

[0032] Step 5-1: Curve at the Boundary Sampling to obtain the boundary data point set to be fitted ,because At the junction of different blade-like surface patches, the high-order geometric information of the corresponding sampling points is calculated based on the expression of the blade-like surface patch with the largest curvature change;

[0033] Step 5-2: Inside the blade surface patch, that is , sample to obtain the internal data point set to be fitted The high-order geometric information of the corresponding sampling points is based on the expression of the blade surface patch Calculated.

[0034] Furthermore, in step 6, the general fitting process of the PHT spline surface based on the uniformly subdivided control grid is as follows:

[0035] Step 6-1: Based on the blade surface model Geometric feature measurement, introducing the initial approximation error threshold , and evenly subdivide the complete single parameter domain Get the uniform subdivision control grid of the PHT spline surface ;

[0036] Step 6-2: Sampling the uniform subdivision control grid Get the data point set to be fitted from the base point , and parameterized to a complete single parameter domain The corresponding relationship is formed ;

[0037] Step 6-3: Use the value rules of step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-order geometric information is obtained by applying the interpolation theorem to obtain a uniform subdivision control grid. PHT spline surface ;

[0038] Step 6-4: If the control mesh is based on uniform subdivision PHT spline surface Blade surface model In the data point set to be fitted The comprehensive error at Greater than the initial approximation error threshold , alternately iterate and implement steps 6-1 to 6-3 until the control grid is uniformly subdivided PHT spline surface Satisfy the given initial approximation error threshold .

[0039] Furthermore, in step 7, the high-precision fitting process of the PHT spline surface based on the hierarchical subdivision control grid is as follows:

[0040] Step 7-1: Based on the design standards and actual application scenarios of blade-like surfaces, comprehensively consider the segmentation and sampling features and introduce a high-precision approximation error threshold ;

[0041] Step 7-2: Calculate the current PHT spline surface and blade surface model The set of data points to be fitted at the boundary The comprehensive error containing high-order geometric information ;

[0042] Step 7-3: If the comprehensive error obtained in step 7-2 is Greater than the high-precision approximation error threshold , record the corresponding control grid and perform local subdivision to obtain the hierarchical subdivision control grid , supplementary hierarchical subdivision control grid The base point to the data point set to be fitted ;

[0043] Step 7-4: Use the value rules of step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives High-order geometric information and control mesh based on hierarchical subdivision Implementing interpolation theorem to obtain higher precision PHT spline surface ;

[0044] Step 7-5: If the PHT spline surface is of higher precision Blade surface model In the data point set to be fitted The comprehensive error at Greater than the high-precision approximation error threshold , alternately iterate and implement steps 7-2 to 7-4 until the control grid is subdivided based on the hierarchy PHT spline surface Meet the target high-precision approximation error threshold .

[0045] The beneficial effects of the present invention are:

[0046] This invention establishes a global correspondence between the target geometry and a single, complete parameter domain through global reparameterization for engineering metrics. This ensures surface accuracy and continuity, as well as boundary consistency of parameter distribution, when processing complex geometries. Furthermore, by constructing a PHT spline model, the invention maps blade-like surfaces to multiple control grid regions. Each region is defined by a set of spline basis functions and independently optimized, ensuring local design flexibility and improving design efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a globally consistent geometry design method for blade-like surfaces based on PHT splines;

[0048] Figure 2 The input blade surface model diagram based on NURBS representation;

[0049] Figure 3 For cutting surface patches and their boundary curves;

[0050] Figure 4 For cutting parameter domain and its boundary curve graph;

[0051] Figure 5 Schematic diagram of the boundary-consistent reparameterization process;

[0052] Figure 6 Schematic diagram of the globally consistent reparameterization process;

[0053] Figure 7 Schematic diagram of the general fitting process of the initial PHT spline surface based on the uniform subdivision control grid, where (a) is the uniform subdivision control grid , (b) is the boundary data point set to be fitted , (c) is the internal data point set to be fitted , (d) is based on uniform subdivision control grid PHT spline surface ;

[0054] Figure 8 Schematic diagram of the high-precision fitting process of PHT spline surface based on hierarchical subdivision control grid, where (a) is the hierarchical subdivision control grid , (b) is the boundary data point set to be fitted , (c) is the internal data point set to be fitted , (d) is the control grid based on hierarchical subdivision PHT spline surface . DETAILED DESCRIPTION

[0055] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below in conjunction with specific implementation methods.

[0056] The present invention provides a globally consistent geometric design method for blade-like surfaces based on PHT splines, such as Figure 1 The specific implementation steps are as follows:

[0057] Step 1: Input the blade surface model stored in STEP format ,in, Represents a blade surface model Middle A blade-like surface patch based on clipped NURBS representation The parameter variables, Represents a blade surface model Leaf-like surface patches based on clipped NURBS representation the number of

[0058] Step 2: From the blade surface model Get and record each blade-like surface patch based on the clipped NURBS representation The boundary curve And the corresponding clipping parameter domain The parametric boundary curve , among which blade-like surface patches is the curved quadrilateral obtained by clipping, that is ;

[0059] Step 3: Blade-like surface patch Corresponding clipping parameter domain Implementing boundary-consistent reparameterization to meet engineering metrics constraints , get the corresponding rule parameter domain , and ensure different blade surface pieces Corresponding rule parameter domain Continuity of parameter distribution at the splice, where Respectively represent the definitions in the rule parameter domain Parameter variables on ;

[0060] Step 4: Stitching by boundary consistent reparameterization All rule parameter fields obtained , and implement a globally consistent reparameterization , to obtain a complete single parameter domain , as the domain of the PHT spline surface, where Respectively, they are defined in a complete single parameter domain Parameter variables on ;

[0061] Step 5: Blade-like surface patch obtained based on reparameterization , comprehensively considering the fitting target and accuracy, reasonably sampling to obtain the set of data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The set of data points to be fitted by the boundary and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the reparameterized inverse process on the blade surface patch The parameter coordinates on Represents the geometric coordinates of the sampling point, and the superscript -1 represents the inverse operation of the function;

[0062] Step 6: Set the data points to be fitted Parameterized to a complete single parameter domain The corresponding relationship is formed , and use high-order geometric information to interpolate the data point set to be fitted Obtain PHT spline surface based on uniform subdivision grid ;in, Represents the composite operation of functions, ;

[0063] Step 7: Based on the design standards of blade-like surfaces and the engineering indicators that meet boundary consistency, the segmentation and sampling features are comprehensively considered, and the approximation error constraint is introduced to obtain the approximation error of the PHT spline surface. The local subdivision is implemented in the uniform subdivision control grid to generate a hierarchical control grid, and a high-precision approximate blade surface model is obtained based on the hierarchical subdivision control grid. PHT spline surface .

[0064] Example

[0065] The present invention will be described below with reference to specific embodiments.

[0066] Step 1, such as Figure 2 As shown, the blade surface model stored in STEP format is input ;

[0067] Step 2: Get and record the cropped surface patch The boundary curve and its corresponding clipping parameter domain The boundary curve ;

[0068] like Figure 3 As shown, the blade surface model Contains 4 blade surfaces based on clipping NURBS expression and 4 rounded surfaces , and the corresponding boundary curve is and .

[0069] like Figure 4 As shown, the parameter domain of the blade surface patch and is a clipped curved quadrilateral with a parametric boundary curve of and , according to the blade surface patch and In the adjacency relationship of Euclidean space, adjust the parameter direction of the boundary curve and the target complete single parameter domain The parameter direction is consistent; and the corresponding parameter range is obtained as and .

[0070] Step 3: Clip parameter domain Implementing boundary-consistent reparameterization , get the rule parameter domain , the specific implementation method is as follows:

[0071] like Figure 5 As shown: On each blade surface patch Get two sets of opposite edges as and , the four corner points are 、 、 、 ; and achieve boundary consistent reparameterization through bilinear interpolation, ensuring that the geometric boundaries before and after reparameterization are consistent, the isoparameters are approximately evenly distributed, and the regular parameter domain corresponding to all clipped surface patches is guaranteed Continuity of parameter distribution at the splice.

[0072] Step 4: Implement globally consistent reparameterization , splicing all rule parameter fields Get a complete single parameter domain , the specific implementation method is as follows:

[0073] like Figure 6 Shown: According to all blade-like surface patches In the order of arrangement in Euclidean space and the parameter direction after the boundary is consistently reparameterized, all regular parameter domains Arrange them sequentially and reparameterize them to obtain a complete single parameter domain, which serves as the definition domain of the PHT spline surface.

[0074] Step 5: Sample the set of data points to be fitted at the geometric features and calculate the corresponding high-order geometric information. The specific implementation method is as follows:

[0075] like Figure 7 (b) Figure 8 As shown in (b), the boundary curve of the blade surface patch is Sampling to obtain the boundary data point set to be fitted ,The high-order geometric information of the corresponding sampling points is calculated based on the expression of the blade-like surface patch with large curvature variation;

[0076] like Figure 7 (c) Figure 8 As shown in (c), inside the blade-like surface patch, that is, , sample to obtain the internal data point set to be fitted To maintain the unique geometric features of blade-like surfaces such as bending, sweeping, and twisting, the high-order geometric information of the corresponding sampling points is based on the expression of the blade-like surface patch Calculated.

[0077] Step 6: The general fitting process of the PHT spline surface based on the uniform subdivision control grid is as follows:

[0078] like Figure 7 As shown in (a), based on the blade surface model The measurement of geometric features such as bending, sweeping, and twisting, uniformly subdividing the complete single parameter domain Get the control mesh of the PHT spline surface , and obtain the high-order geometric information at the base point according to the value selection rules of step 5, including geometric coordinates , first-order partial derivative and , mixed partial derivatives ;

[0079] like Figure 7 As shown in (d), the interpolation theorem based on uniform subdivision control grid is obtained by using high-order geometric information. PHT spline surface .

[0080] Step 7: The high-precision fitting process of the PHT spline surface based on the hierarchical subdivision control grid is as follows:

[0081] like Figure 8 (a) Figure 8 As shown in (b), if the comprehensive error of the currently obtained PHT spline surface is greater than the target high-precision approximation error threshold , record the corresponding control grid and perform local subdivision to obtain the hierarchical subdivision control grid , and supplement the hierarchical subdivision control grid The base point to the data point set to be fitted ;

[0082] like Figure 8 As shown in (d), the value selection rule of step 5 is used to calculate the high-order geometric information, and the control grid is based on the hierarchical subdivision Implementing interpolation theorem to obtain higher precision PHT spline surface .

[0083] It can be seen that the present invention not only achieves globally consistent geometric design and obtains complex blade-like surfaces using a complete single parameter domain fitting, but also can achieve high-precision fitting of corresponding geometric features and splicing boundaries by local hierarchical subdivision of the control grid.

[0084] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0085] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A globally consistent geometric design method for blade-like surfaces based on PHT splines, characterized in that: The steps include: Step 1: Input the blade surface model stored in STEP format ,in, Represents a blade surface model Middle A blade-like surface patch based on clipped NURBS representation The parameter variables, Represents a blade surface model Leaf-like surface patches based on clipped NURBS representation the number of Step 2: From the blade surface model Get and record each blade-like surface patch based on the clipped NURBS representation The boundary curve And the corresponding clipping parameter domain The parametric boundary curve , among which blade-like surface patches is the curved quadrilateral obtained by clipping, that is ; Step 3: Blade-like surface patch Corresponding clipping parameter domain Implementing boundary-consistent reparameterization to meet engineering metrics constraints , get the corresponding rule parameter domain , and ensure different blade surface pieces Corresponding rule parameter domain Continuity of parameter distribution at the splice, where Respectively represent the definitions in the rule parameter domain Parameter variables on ; Step 4: Stitching by boundary consistent reparameterization All rule parameter fields obtained , and implement a globally consistent reparameterization , to obtain a complete single parameter domain , as the domain of the PHT spline surface, where Respectively, they are defined in a complete single parameter domain Parameter variables on ; Step 5: Blade-like surface patch obtained based on reparameterization , comprehensively considering the fitting target and accuracy, reasonably sampling to obtain the set of data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The set of data points to be fitted by the boundary and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the reparameterized inverse process on the blade surface patch The parameter coordinates on Represents the geometric coordinates of the sampling point, and the superscript -1 represents the inverse operation of the function; Step 6: Set the data points to be fitted Parameterized to a complete single parameter domain The corresponding relationship is formed , and use high-order geometric information to interpolate the data point set to be fitted Obtain PHT spline surface based on uniform subdivision grid ;in, Represents the composite operation of functions, ; Step 7: Based on the design standards of blade-like surfaces and the engineering indicators that meet boundary consistency, the segmentation and sampling features are comprehensively considered, and the approximation error constraint is introduced to obtain the approximation error of the PHT spline surface. The local subdivision is implemented in the uniform subdivision control grid to generate a hierarchical control grid, and a high-precision approximate blade surface model is obtained based on the hierarchical subdivision control grid. PHT spline surface .

2. The method for designing blade-like curved surfaces globally consistent with PHT splines according to claim 1, characterized in that: Step 2 includes: Step 2-1: Record each blade surface The boundary curve ; Step 2-2: On each boundary curve Corresponding clipping parameter domain In the document, the parameter boundary curve based on NURBS is recorded And the corresponding parameter value range ; Step 2-3: Follow the blade surface Adjacency relationship in Euclidean space, adjust boundary curve and parametric boundary curves The parameter direction makes the target complete single parameter domain The parameters of and , the corresponding parameter value range .

3. The method for designing blade-like curved surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 3 includes: Step 3-1: Blade-like surface patch Corresponding clipping parameter domain For a curved quadrilateral, record two sets of opposite sides separately and ,in, The parameter boundary curve obtained by reordering and adjusting the parameter directions in steps 2-3; Step 3-2: Record the cropping parameter fields separately The four corner points of: ， ， ， ， in, is the boundary parameter curve The parameter value range of Step 3-3: Use bilinear interpolation to interpolate each leaf surface patch Corresponding clipping parameter domain Implementing boundary-consistent reparameterization is the corresponding rule parameter domain : 。 4. The method for designing blade-like curved surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 4 comprises: Step 4-1: Follow the blade-like surface patch Initial implementation of globally consistent reparameterization of adjacency relations in Euclidean space ,according to OK Arrange columns and concatenate all rule parameter fields , get the intermediate parameter domain ,in, Respectively represent the definitions in the intermediate parameter domain Parameter variables on ; Step 4-2: Implement global consistent reparameterization again ,Right now , to obtain a complete single parameter domain For the domain of the PHT spline surface, complete the fully consistent reparameterization, ,in, Respectively, they are defined in a complete single parameter domain The parameter variables on the blade surface are recorded as and .

5. The method for designing blade-like curved surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: Step 5 includes: Step 5-1: Curve at the Boundary Sampling to obtain the boundary data point set to be fitted ,because At the junction of different blade-like surface patches, the high-order geometric information of the corresponding sampling points is calculated based on the expression of the blade-like surface patch with the largest curvature change; Step 5-2: Inside the blade surface patch, that is , sample to obtain the internal data point set to be fitted The high-order geometric information of the corresponding sampling points is based on the expression of the blade surface patch Calculated.

6. The method for designing blade-like curved surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 6 comprises: Step 6-1: Based on the blade surface model Geometric feature measurement, introducing the initial approximation error threshold , and evenly subdivide the complete single parameter domain Get the uniform subdivision control grid of the PHT spline surface ; Step 6-2: Sampling the uniform subdivision control grid Get the data point set to be fitted from the base point , and parameterized to a complete single parameter domain The corresponding relationship is formed ; Step 6-3: Use the value rules of step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-order geometric information is obtained by applying the interpolation theorem to obtain a uniform subdivision control grid. PHT spline surface ; Step 6-4: If the control mesh is based on uniform subdivision PHT spline surface Blade surface model In the data point set to be fitted The comprehensive error at Greater than the initial approximation error threshold , alternately iterate and implement steps 6-1 to 6-3 until the control grid is uniformly subdivided PHT spline surface Satisfy the given initial approximation error threshold .

7. The method for designing blade-like curved surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 7 comprises: Step 7-1: Based on the design standards and actual application scenarios of blade-like surfaces, comprehensively consider the segmentation and sampling features and introduce a high-precision approximation error threshold ; Step 7-2: Calculate the current PHT spline surface and blade surface model The set of data points to be fitted at the boundary The comprehensive error containing high-order geometric information ; Step 7-3: If the comprehensive error obtained in step 7-2 is Greater than the high-precision approximation error threshold , record the corresponding control grid and perform local subdivision to obtain the hierarchical subdivision control grid , supplementary hierarchical subdivision control grid The base point to the data point set to be fitted ; Step 7-4: Use the value rules of step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives High-order geometric information and control mesh based on hierarchical subdivision Implementing interpolation theorem to obtain higher precision PHT spline surface ; Step 7-5: If a higher precision PHT spline surface Blade surface model In the data point set to be fitted The comprehensive error at Greater than the high-precision approximation error threshold , alternately iterate and implement steps 7-2 to 7-4 until the control grid is subdivided based on the hierarchy PHT spline surface Meet the target high-precision approximation error threshold .

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