Blade curved surface global consistent geometric design method based on PHT spline

Abstract

The invention relates to a blade-like curved surface global consistent geometric design method based on a PHT spline, and the method comprises the steps: carrying out the high-precision fitting of a blade-like complex curved surface and the geometric features of the blade-like complex curved surface through employing a PHT-spline curved surface. According to the main technical scheme, the method comprises the following steps: splicing and cutting a parameter domain into a globally consistent complete single parameter domain as a definition domain of a PHT spline through a boundary consistency re-parameterization process; geometric features and boundary information are comprehensively considered, a to-be-fitted data point set is obtained through reasonable sampling, and corresponding high-order geometric information is calculated; and performing high-precision fitting by controlling hierarchical subdivision of a grid to obtain a blade curved surface represented based on a PHT spline. According to the method, the problem of discontinuity caused by cutting and splicing in a traditional design method is solved, the global consistency of the overall design is ensured, and meanwhile, the design precision and efficiency are improved.

Description

Technical Field

[0001] The 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 mainly includes surface modeling and solid modeling, among which surface modeling is an important research content of computer-aided geometric design. Non-Uniform Rational B-Splines (NURBS) defined on tensor product grids are widely used in the representation of different geometric objects, which has promoted the vigorous development of modern geometric modeling research. NURBS has an efficient evaluation algorithm and a control network that allows designers to intuitively edit and modify surfaces, and has become a standard geometric representation of industrial models. With the rapid development of modern industry, the topological structure and geometric details of the model have become more and more complex, and the traditional NURBS representation faces challenges, mainly because NURBS is defined on a regular tensor product grid, which cannot be locally refined and is not convenient for multi-piece splicing. Locally refined splines were developed in this context, that is, by introducing T points or hierarchical structures, they have the ability to be locally refined and facilitate the splicing of multiple pieces of arbitrary topology. In essence, they are all considering splines on T grids.

[0003] Blade surfaces present complex geometric features such as bends, sweeps, and twists. Traditional design methods usually rely on local approximation and piece-by-piece design, which is composed of multiple cut NURBS surface pieces. Although this method can meet the design requirements, due to geometric topology limitations, Boolean operations in the cutting and splicing processes lead to discontinuity problems, making it difficult to ensure the consistency of the overall design of the entire surface, increasing the complexity and uncertainty of the design process, and also affecting the processing 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, and high-precision fitting of complex surface geometric features by a single PHT spline (Polynomial Splines over Hierarchical T-meshes, PHT-splines) surface is achieved, and a surface expression oriented to engineering indicators is obtained, which is conducive to the integration of design, manufacturing and CNC machining of blade-like surfaces.

[0005] To achieve the above object, the technical solution adopted by the present invention is: A method for designing blade-like surfaces with global consistent geometry based on PHT splines comprises the following steps: Step 1: Input the blade surface model stored in STEP format ,in, Represents the blade surface model Middle A blade-like surface patch based on a clipped NURBS representation The parameter variables, Represents the blade surface model Blade-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 parameter boundary curve , where blade-like curved surface is the curved quadrilateral obtained by clipping, that is ; Step 3: Blade-like curved surface Corresponding clipping parameter domain Implement boundary-consistent reparameterization towards satisfying engineering metric constraints , get the corresponding rule parameter domain , and ensure that different blade types have curved surfaces 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 through boundary consistent reparameterization Get all rule parameter fields , 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 consider the fitting target and accuracy, and reasonably sample the data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The boundary data point set to be fitted and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the inverse process of reparameterization 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 , and use high-order geometric information to interpolate the set of data points to be fitted Obtain a PHT spline surface based on a uniformly subdivided 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 approximation error constraints are 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 .

[0006] Furthermore, in step 2, the blade-like surface expressed based on NURBS is composed of multiple trimmed NURBS surface patches, and the corresponding parameter domain is a trimmed curved quadrilateral. The specific analysis method is as follows: Step 2-1: Record each blade surface The boundary curve ; Step 2-2: On each boundary curve Corresponding clipping parameter domain In the NURBS representation, the parameter boundary curve 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 .

[0007] Furthermore, in step 3, for each cropped surface patch , 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: Step 3-1: Blade-like curved surface 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 direction in step 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 : .

[0008] Furthermore, in step 4, the method of implementing global consistent reparameterization to obtain a complete single parameter domain is as follows: Step 4-1: Follow the blade surface Initial implementation of globally consistent reparameterization of adjacency relations in Euclidean space ,according to OK Arrange columns to 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 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 obtained by reparameterization are recorded as and .

[0009] 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: Step 5-1: On the boundary curve Sampling to obtain the boundary data point set to be fitted ,because At the joints 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.

[0010] Furthermore, in step 6, the general fitting process of the PHT spline surface based on the uniformly subdivided control grid is as follows: 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 ; Step 6-3: Use the value selection rules in step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-order geometric information is obtained by implementing the interpolation theorem to obtain a uniform subdivision control grid. PHT spline surface ; Step 6-4: If the control grid 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 .

[0011] Furthermore, in step 7, the high-precision fitting process of the PHT spline surface based on the hierarchical subdivision control grid is as follows: Step 7-1: According to the design standards and actual application scenarios of blade-like surfaces, the segmentation and sampling features are comprehensively considered and a high-precision approximation error threshold is introduced ; 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 implement local subdivision to obtain the hierarchical subdivision control grid , add hierarchical subdivision control grid From the base point to the data point set to be fitted ; Step 7-4: Use the value selection rules in step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-level geometric information of the mesh is obtained and the mesh is controlled based on the hierarchical subdivision. Implementing the interpolation theorem to obtain higher precision PHT spline surfaces ; Step 7-5: If the PHT spline surface with 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 , iterate and implement steps 7-2 to 7-4 alternately until the control grid is subdivided based on the hierarchy PHT spline surface Meet the target high-precision approximation error threshold .

[0012] The beneficial effects of the present invention are: The present invention establishes a global correspondence between the target geometry and a single complete parameter domain through global reparameterization for engineering indicators, ensuring that the correctness and continuity of the surface and the boundary consistency of the parameter distribution can be maintained when processing complex geometric shapes. Furthermore, the present invention constructs a PHT spline model to correspond the blade-like surface to multiple control grid areas, each area is defined by a set of spline basis functions and independently adjusted and optimized, ensuring the flexibility of local design and improving design efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of a method for designing blade-like surfaces with global consistent geometry based on PHT splines; Figure 2 The input blade surface model diagram based on NURBS representation; Figure 3 To cut the surface patch and its boundary curve graph; Figure 4 To cut the parameter domain and its boundary curve graph; Figure 5 Schematic diagram of the boundary-consistent reparameterization process; Figure 6 Schematic diagram of the globally consistent reparameterization process; 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 ; 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

[0014] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0015] The present invention provides a globally consistent geometric design method for blade-like surfaces based on PHT splines, such as Figure 1 As shown, the specific implementation steps are as follows: Step 1: Input the blade surface model stored in STEP format ,in, Represents the blade surface model Middle A blade-like surface patch based on a clipped NURBS representation The parameter variables, Represents the blade surface model Blade-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 parameter boundary curve , where blade-like curved surface is the curved quadrilateral obtained by clipping, that is ; Step 3: Blade-like curved surface Corresponding clipping parameter domain Implement boundary-consistent reparameterization towards satisfying engineering metric constraints , get the corresponding rule parameter domain , and ensure that different blade types have curved surfaces 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 through boundary consistent reparameterization Get all rule parameter fields , 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 consider the fitting target and accuracy, and reasonably sample the data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The boundary data point set to be fitted and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the inverse process of reparameterization 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 , and use high-order geometric information to interpolate the set of data points to be fitted Obtain a PHT spline surface based on a uniformly subdivided 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 approximation error constraints are 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 .

[0016] Example The present invention is described below in conjunction with specific embodiments.

[0017] Step 1, such as Figure 2 As shown, the blade surface model stored in STEP format is input ; Step 2: Get and record the cropped surface patch The boundary curve And its corresponding clipping parameter domain The boundary curve ; like Figure 3 As shown, the blade surface model Contains 4 leaf surfaces based on clipping NURBS expression and 4 rounded surfaces , and the corresponding boundary curve is and .

[0018] 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 .

[0019] Step 3: Clip parameter domain Implementing boundary consistent reparameterization , get the rule parameter domain , the specific implementation method is as follows: 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 isoparms are approximately evenly distributed, and the regular parameter domain corresponding to all clipped surface patches is guaranteed Continuity of parameter distribution at the splice.

[0020] Step 4: Implement globally consistent reparameterization , concatenate all rule parameter fields Get the complete single parameter domain , the specific implementation method is as follows: 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 reparameterized, all the regular parameter domains Arrange them sequentially and reparameterize them to get a complete single parameter domain, which is used as the definition domain of the PHT spline surface.

[0021] 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: like Figure 7 (b) Figure 8 As shown in (b), the boundary curve of the blade surface patch splicing 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; like Figure 7 (c) Figure 8As shown in (c), inside the blade-like surface patch, that is, , sample to obtain the internal data point set to be fitted , in order 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.

[0022] Step 6: The general fitting process of PHT spline surface based on uniform subdivision control grid is as follows: 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 ; like Figure 7 As shown in (d), the interpolation theorem is implemented using high-order geometric information to obtain a uniformly subdivided control grid. PHT spline surface .

[0023] Step 7: The high-precision fitting process of the PHT spline surface based on the hierarchical subdivision control grid is as follows: 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 implement local subdivision to obtain the hierarchical subdivision control grid , and add hierarchical subdivision control grid From the base point to the data point set to be fitted ; like Figure 8 As shown in (d), the high-order geometric information is calculated using the value selection rule in step 5, and the control grid is subdivided based on the hierarchy. Implementing the interpolation theorem to obtain higher precision PHT spline surfaces .

[0024] It can be seen that the present invention not only realizes globally consistent geometric design and uses a complete single parameter domain to fit complex blade-like surfaces, but also can achieve high-precision fitting of corresponding geometric features and splicing boundaries by local hierarchical subdivision of the control grid.

[0025] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0026] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description 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 may also be appropriately combined to form other implementation modes 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 the blade surface model Middle A blade-like surface patch based on a clipped NURBS representation The parameter variables, Represents the blade surface model Blade-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 parameter boundary curve , where blade-like surface patches is the curved quadrilateral obtained by clipping, that is ; Step 3: Blade-like curved surface Corresponding clipping parameter domain Implement boundary-consistent reparameterization towards satisfying engineering metric constraints , get the corresponding rule parameter domain , and ensure that different blade types have curved surfaces 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 through boundary consistent reparameterization Get all rule parameter fields , 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 consider the fitting target and accuracy, and reasonably sample the data points to be fitted at the geometric features And calculate the corresponding high-order geometric information, where The boundary data point set to be fitted and the internal set of data points to be fitted composition, represents the region boundary, and Indicates the sampling points calculated by the inverse process of reparameterization 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 , and use high-order geometric information to interpolate the data point set to be fitted Obtain a PHT spline surface based on a uniformly subdivided grid ;in, Represents the composite operation of functions, ; Step 7: According to 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. 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. A method for designing blade-like surfaces globally consistent geometry based on 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 NURBS representation, the parameter boundary curve 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 surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 3 comprises: Step 3-1: Blade-like curved surface 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 direction in step 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 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 surface Initial implementation of globally consistent reparameterization of adjacency relations in Euclidean space ,according to OK Arrange columns to 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 Completely reparameterize 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 obtained by reparameterization are recorded as and .

5. The method for designing blade-like surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: Step 5 includes: Step 5-1: On the boundary curve Sampling to obtain the boundary data point set to be fitted ,because At the joints 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 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 ; Step 6-3: Use the value selection rules in step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-order geometric information is obtained by implementing the interpolation theorem to obtain a uniform subdivision control grid. PHT spline surface ; Step 6-4: If the control grid 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 surfaces globally consistent geometry based on PHT splines according to claim 1, characterized in that: The step 7 comprises: Step 7-1: According to the design standards and actual application scenarios of blade-like surfaces, the segmentation and sampling features are comprehensively considered and a high-precision approximation error threshold is introduced ; 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 implement local subdivision to obtain the hierarchical subdivision control grid , add hierarchical subdivision control grid From the base point to the data point set to be fitted ; Step 7-4: Use the value selection rules in step 5 to calculate the geometric coordinates , first-order partial derivative and , mixed partial derivatives The high-level geometric information of the mesh is obtained and the mesh is controlled based on the hierarchical subdivision. Implementing the interpolation theorem to obtain higher precision PHT spline surfaces ; 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 , iterate and implement steps 7-2 to 7-4 alternately 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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