Topological optimization feature geometric reconstruction method for curved surface blade structure based on coordinate space mapping
By using coordinate space mapping and image processing techniques, the topology optimization results of three-dimensional curved blades are extracted and reconstructed, solving the problems of cumbersome model reconstruction and significant human influence in traditional methods, and achieving high-precision blade manufacturing.
Patent Information
- Application Number
- CN202610199697.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-11
- Publication Date
- 2026-05-12
AI Technical Summary
The complex geometries generated by existing topology optimization methods are difficult to achieve through traditional manufacturing processes, and the reconstruction results are greatly affected by human factors, lacking direct application capabilities.
By using a coordinate space mapping method, the topology optimization results of three-dimensional curved blades are converted into two-dimensional density field images. Image processing techniques are then used to extract key features and reconstruct the three-dimensional model, including boundary tracking, morphological operations, and NURBS curve fitting, to achieve model reconstruction from two-dimensional to three-dimensional.
It achieves high-precision feature extraction and model reconstruction of topology optimization results, solving the problems of cumbersome model reconstruction and large influence of human factors in traditional methods, and supports the efficient manufacturing of three-dimensional curved blades.
Smart Images
Figure CN122020909A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural optimization design and relates to a geometric reconstruction method for topology optimization features of curved blade structures based on coordinate space mapping. Background Technology
[0002] For a long time, the research and development of aero engines, considered the "pearl" of industrial prowess, has represented a nation's overall industrial level and is of great significance to defense, transportation, and other fields. Developing higher-level aero engines has become an inevitable trend in the face of increasingly fierce international technological competition. While ensuring structural reliability and safety, topology optimization design of key aero engine components not only helps achieve lightweighting but also improves performance parameters such as thrust-to-weight ratio. Simultaneously, it reduces material consumption, effectively lowering engine production costs and ultimately generating significant economic benefits.
[0003] Topology optimization, a subcategory of structural optimization, optimizes the material distribution within a given design domain based on load conditions, constraints, and performance indicators. Through technological advancements, topology optimization methods are now widely used in aerospace, automotive, and even construction. With lightweight design playing an increasingly important role in aerospace, topology optimization technology is crucial for reducing material weight. Topology optimization offers high design freedom, directly optimizing the distribution of fluid and solid materials within the design domain to achieve optimal performance. In optimization design, product design often requires balancing various factors to determine the best solution. Because topology optimization can consider various factors in advance, it significantly reduces the possibility of design failure. Secondly, the most attractive aspect of topology optimization is its ability to reduce unnecessary weight, which is critical in aerospace. Every gram of added weight increases design costs considerably, and weight reduction and size reduction translate to lower energy consumption. Furthermore, topology optimization not only minimizes material usage and cost but also improves product performance, reduces costs, increases efficiency, and promotes innovative design by optimizing material distribution and structure. It has wide applications in many fields, including aerospace, automotive, manufacturing, and construction engineering. It is an important way to achieve innovative engine structural configurations and lightweighting. As a key component of the engine, the blade plays a vital role in the safe and reliable operation of the entire engine.
[0004] Early blades mostly used solid structures, but solid blades were heavy and had high fuel consumption, which could not meet the increasingly demanding design requirements of higher thrust-to-weight ratios and lower fuel consumption rates for aero engines. With the advancement of technology and the increasing demands of engine design, lightweight blade design is rapidly developing. Supported by advanced processes, curved blades with three-dimensional lightweight designs that better conform to aerodynamic design are the development direction for the foreseeable future. Topology optimization is an effective way to achieve lightweight blades, as it can achieve optimal material distribution while meeting aerodynamic performance and structural reliability requirements.
[0005] Reconstructing the resulting model after topology optimization has always been a significant challenge. Structures generated by topology optimization methods often exhibit complex porous or mesh-like distributions, and these highly irregular structures are difficult to replicate directly using existing manufacturing technologies. This leads to difficulties in feature extraction, a lack of effective parametric description methods, tedious model reconstruction, and significant susceptibility to human factors in the reconstruction results, posing challenges to subsequent refined design. Many complex geometries generated by topology optimization are often difficult to manufacture using traditional industrial manufacturing methods. However, advancements in additive manufacturing technology have overcome the limitations of traditional manufacturing processes, allowing the design output of topology optimization to be directly processed by 3D printers, greatly accelerating the industrialization of topology optimization. However, topology optimization still faces challenges such as difficulty in feature extraction, tedious model reconstruction, and significant susceptibility to human factors in the reconstruction results, thus requiring post-processing. The inherent contradiction between "ideal design" and "practicality" makes geometric reconstruction technology a crucial link between topology optimization and engineering applications.
[0006] Therefore, a method for feature extraction and model reconstruction based on topology optimization results of curved blade structures in engine components is needed to address the lack of direct application capability of topology optimization results and to more accurately extract model parameters to ensure compliance with engineering requirements. This requires obtaining pixel or mesh information of the topological configuration feature contours to reconstruct the optimization model, ultimately obtaining a parametric CAD geometric model.
[0007] Patent application: A method and device for automatic geometric reconstruction based on three-dimensional topology optimization results: 202410778530.2[P]. 2025-04-04., application number CN202410778530.2. Its main problem is that the patent does not explain in detail how to remove holes in the skeleton position that are not conducive to reconstruction before extracting the skeleton.
[0008] Patent application: A method for geometric reconstruction of topology optimization results, application number CN202011212905.7. Its main problem is that it does not describe a geometric reconstruction method for three-dimensional topology optimization models, and the reconstruction research is mainly in two-dimensional space. Summary of the Invention
[0009] The technical problem this invention aims to solve is to propose a method for reconstructing topology optimization structure models using topology optimization structure images. This method overcomes the difficulties in modeling and studying three-dimensional curved surface topology optimization structures, and can solve technical problems such as dimensionality reduction mapping based on topology optimization density distribution results and extraction of key structural features.
[0010] The technical solution of the present invention is as follows: Based on the topology optimization density distribution results of a certain type of engine's three-dimensional curved blade structure, topology optimization geometric reconstruction is performed on the remaining effective material region in the density topology optimization results. First, the deformation from a three-dimensional mesh to a two-dimensional mesh is implemented in the program. The three-dimensional density optimization results in physical space are mapped onto a rectangular plate at a certain ratio through mesh deformation, while keeping the mesh node connection relationship unchanged.
[0011] Subsequently, based on the density distribution results of the flat surface, the density of each grid region was assigned brightness values ranging from 0 to 255, from smallest to largest. Each grid on the flat surface corresponds to a colored pixel block with a brightness value, ultimately resulting in a two-dimensional density field image in RGB format. Then, key geometric features were captured and the coordinates of corresponding skeleton points were obtained using image morphology processing and skeleton extraction techniques. First, the image was converted to a binary image, and the brightness of the entire image was normalized, with 0 representing the darkest and 1 representing the brightest. By setting a density threshold, a brightness range between 0 and 1 was selected. Then, opening and closing sum operations and median filtering were performed to make the extracted features clearer and more accurate. All contours were retrieved through boundary tracking, and each contour was skeletonized. Finally, the coordinate information of the skeleton points in pixel space was extracted and saved.
[0012] The extracted pixel skeleton is then mapped back to the mesh nodes in the actual 2D model. Based on the 2D mesh nodes, it is then mapped back to the mesh nodes of the original 3D blade. Finally, based on the 3D mesh nodes, line fitting is performed in CAD software. The model of the ribs is gradually constructed from lines to surfaces and from surfaces to volumes. The model is continuously adjusted according to the needs of practicality. Finally, the reconstructed model is imported into the original cavity structure to complete the geometric reconstruction of the topology optimization of the 3D curved surface structure.
[0013] A method for topology optimization feature geometry reconstruction of curved surface structures based on coordinate space mapping includes the following steps: Step 1: First, establish a rectangular plate model. For the topology optimization density distribution result of the three-dimensional curved blade structure, deform the curved mesh that represents the density distribution information on it, map the deformed mesh onto the rectangular plate model, and simultaneously map the topology optimization density distribution result onto the rectangular plate. Then, process the topology optimization density distribution result on the rectangular plate to obtain a two-dimensional density field RGB image. Step 2: Input the two-dimensional density field RGB image into PyCharm software, set the pixel value threshold of the image using the global fixed threshold binarization method to obtain a clear density field feature binarized image, and then invert the colors of the binarized image to obtain a color-inverted binarized image. Step 3: Use morphological opening and closing operations to filter the color-inverted binarized image obtained in the previous step, fill in the small holes in the topological result mapped to the image space and remove discontinuous regions. Step 4: By adjusting the opening and closing mechanism, the kernel size, and the number of operations, determine the size of the small color blocks to be removed and the size of the holes to be filled. Repeat Step 4 and compare the processed images each time. The goal is to minimize the number of remaining holes and discontinuous small color blocks, and finally obtain the binarized image with the least noise. Step 5: For the binarized image processed in the previous step, use nonlinear filtering techniques and a median filter function with a suitable bandwidth to remove the pits and burrs on the boundary, and obtain a binarized image with smooth boundaries. Step 6: For the binarized image after median filtering, use the Suzuki boundary tracing algorithm to retrieve all contours, extract the hierarchical contours, and store all points on the contours. Step 7: Use a morphological thinning algorithm to morphologically thin the contours extracted by each boundary tracing to obtain the skeleton, and then use the Suzuki boundary tracing algorithm to extract and save all skeleton points. Step 8: Map the extracted skeleton points to the mesh nodes on the flat plate obtained by mesh deformation in Step 1, and then map and process them to the surface mesh nodes on the original 3D curved blade model to finally obtain the point coordinates of the remaining effective material area of the blade after topology optimization in the 3D real space. Step 9: Based on the NURBS curve fitting method, select the part of the internal connecting rib in the blade topology optimization result from the point set obtained in the previous step, and perform overall B-spline curve fitting in CAD software to obtain the two-dimensional contour of the internal rib. Step 10: Model based on two-dimensional contour. Use the shelling function of the CAD software to process the original hollow blade model to obtain the inner cavity model. Relying on the inner cavity surface, the rib contour is initially obtained by stretching and surface processing to obtain the three-dimensional rib model. Finally, Boolean operation is performed with the outer solid of the blade left by shelling to obtain the complete hollow blade reconstruction model. In step 1, the mapping of the three-dimensional curved surface to the rectangular plate is achieved by changing the position of the curved surface mesh nodes to deform the mesh without changing the connection method of the nodes or the number of nodes on the boundary, and then mapping it onto the rectangular plate.
[0014] In step 1, the topology optimization density distribution results on the rectangular plate are processed by extracting a two-dimensional density field RGB image from data visualization and analysis software.
[0015] In step 2, the presence / absence of material in the density distribution on the plate is mapped to the image pixel value of 0 / 255. Before color inversion, the pixel value of the area with material is 0, and the pixel value of the area without material is 255.
[0016] The morphological opening and closing operations in step 3 are implemented in PyCharm using OpenCV functions.
[0017] In step 4, the operation is usually repeated twice. The pixel value window selected for removing islands and holes is about 1.5 times the size of the islands and holes themselves.
[0018] In step 6, boundary retrieval can filter effective contours by the number of contour points contained in each contour or the pixel area occupied by the contour in the pixel space, and further remove small contours that are difficult to be reconstructed.
[0019] In step 7, the morphological thinning algorithm gradually removes white pixels that retain the structure through iterative erosion and dilation until no white pixels meet the erosion condition, at which point the iteration stops, resulting in a skeleton image.
[0020] In step 10, the shelling is a function provided by UG. The thickness of the shelling for each surface of the blade can be manually selected according to the actual situation.
[0021] The beneficial effects of this invention are: 1. The method of the present invention directly identifies features and extracts skeleton points from topology optimization structure images, and reconstructs key geometric features through the coordinates of skeleton points; it solves the problem that commonly used topology optimization software directly outputs the structure but cannot model the structure. 2. The method of the present invention obtains the coordinates of all skeleton points. By adjusting the information of the coordinate points, the structure can be modified, and secondary optimization design of the optimized structure can be achieved. Attached Figure Description
[0022] Figure 1 It is the appearance result of topology optimization of the three-dimensional curved blade structure; Figure 2 It is the result of topology optimization density distribution of the central curved surface of the three-dimensional structure; Figure 3 It is a schematic diagram of the actual physical space grid; Figure 4 This is a schematic diagram of a uniform mesh after mesh deformation; Figure 5 This is a diagram illustrating pixel coordinates in image space. Figure 6 This is a schematic diagram of the two-dimensional density distribution results on a gridded flat plate computational domain; Figure 7 It is a mapped two-dimensional density pixel image; Figure 8 This is a binary image showing the density distribution of the optimized structure in two-dimensional space. Figure 9 This is a schematic diagram of the reconstructed rib model; Figure 10 This is a schematic diagram of the reconstructed three-dimensional optimized structural model; Figure 11 It is an image skeleton model; Figure 12 It is the set of skeletal points of the intermediate surface in three-dimensional space; Figure 13 This is a schematic diagram of mapping onto the surface of the inner cavity; Figure 14 This is a schematic diagram of the reconstructed rib model; Figure 15 This is a schematic diagram of the reconstructed structural model after 3D optimization. Detailed Implementation
[0023] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.
[0024] First, the appearance of this type of three-dimensional curved blade after topology optimization is as follows: Figure 1 As shown in the topology optimization results, the topology optimization density distribution of the blade center plane is as follows: Figure 2 As shown, a rectangular plate model is established. The surface mesh representing the density distribution information is deformed using RBF interpolation-based mesh deformation, and the deformed mesh is mapped onto the rectangular plate model. The relationship between the mesh before and after deformation mapping is as follows: Figure 3 and Figure 4 As shown, Figure 3 Each mesh node on the original surface has a unique corresponding node. Figure 4 The mesh nodes on the medium-sized plate, with the same number, are mapped to each other. During this mesh deformation process, the density distribution on the center surface of the curved blade is also mapped onto the plate. Figure 4 Image processing of the results can map the coordinates of grid nodes to spatial coordinates composed of pixels, thus forming a graph like... Figure 5 The image shown.
[0025] The density distribution result mapped from the topology optimization of the blade center plane to the density distribution result on the plate is as follows: Figure 6As shown, this deformation mapping process first reads the original 3D nodes, establishes an RBF relationship between the original control points and the target control points, selects the Gaussian radial basis function as the basis function, sets the RBF parameter influence radius to 0.5, and the polynomial order to 2, calculates the weight relationship, and transforms the coordinates of the surface mesh nodes according to the weight relationship, mapping the mesh node coordinates in the real physical space to the computational domain of the rectangular plate. Simultaneously, it preserves the element connection relationships and the number of nodes on the boundary in terms of structure, and finally outputs new mesh node data. Based on the internal density distribution results mapped on the rectangular plane of the plate surface, pixel values ranging from 0 to 255 are used to represent the density of each feature from small to large. Each 2D mesh on the plate surface corresponds to a colored pixel block with a pixel value, ultimately obtaining a planar density distribution image in RGB form, as shown below. Figure 7 As shown.
[0026] Then, programs or other operations are written to further process the image. Here, the cv2 module of OpenCV in PyCharm is used. The RGB image of the density field mapped onto a flat rectangular plate is used as the input file. A global fixed threshold binarization method is used to set the pixel value threshold of the image. In this image processing, the density corresponds to the normalized pixel value range of 0~1. Typically, 0.3 and 0.8 are chosen as the density thresholds, ensuring that any pixel value other than 255 is 0. Finally, a binarized image with clear density field characteristics is obtained, as shown in the image. Figure 8 As shown in the image, black corresponds to the material portion of the blade after topology optimization, with a pixel value of 0, while white corresponds to the material portion of the blade after topology optimization, with a pixel value of 255. Subsequently, a black-and-white inversion is performed, turning the portion with retained material white and the portion with removed material black.
[0027] In a binarized image, the main structure appears as large, continuous white areas with holes, while the noise structure consists of other small, discontinuous white areas. The image is filtered through opening and closing operations, including erosion and dilation. Dilation expands the bright or white areas of the image, resulting in a larger bright area than the original. Erosion reduces and refines the bright or white areas, filling in small holes and discontinuous areas in the topological structure. The effects of erosion and dilation on the image are as follows: Figure 9As shown; the size of the small color patches to be removed and the size of the holes to be filled can be determined by adjusting the opening and closing kernel size and the number of operations. This operation is repeated, and the processed images are compared each time. The goal is to retain the most continuous white areas and the fewest remaining holes and small color patches, ultimately obtaining a binarized image with minimal noise. This step is usually repeated twice. The pixel structure size is determined based on the size of the holes to ensure hole filling. The closing kernel size is set to a 4×4 pixel value window, and the opening kernel size is selected to eliminate islands, using a 3×3 pixel value window. Median filtering is used to remove pits and burrs on the boundaries, i.e., replacing the pixel with the median of its neighborhood. The filtering bandwidth of the median filtering function is a 4×4 pixel value window, with the goal of obtaining smooth structural boundaries. The processed image is shown below. Figure 10 As shown.
[0028] Boundary tracing was performed using the Suzuki algorithm with the cv2 module to retrieve all boundary contours, extract hierarchical contours, and store all points on each contour. Contours were then filtered based on the number of points they contained, eliminating short contours with 7 points or fewer. A morphological thinning algorithm was then used to create a skeletonization function. Iterative operations of erosion and dilation were performed on the image to open it. The opening result was subtracted from the original image to obtain the skeleton image. At the end of each iteration, the skeleton layers from each iteration were merged into the total skeleton. Iteration stopped when no white pixels satisfied the erosion condition. The final skeleton is shown below. Figure 11 As shown; for the skeleton image, the Suzuki algorithm is used to extract all skeleton pixels by contour.
[0029] Subsequently, still using PyCharm, the grid data from the 2D density distribution result file and the point cloud data extracted after image processing were read. An adaptive distance search was performed based on the Euclidean algorithm, and the KD-tree algorithm was used to accelerate the nearest neighbor search. A minimum distance threshold was set to ensure that skeleton pixels meeting the threshold corresponded to 2D grid nodes. Finally, the skeleton points were mapped from the image back to the grid nodes of the rectangular flat 2D plane. Invalid matching points were then filtered by setting a maximum distance threshold. The row numbers of the matching points and the filtered 2D point set were then output, completing the mapping from 2D pixel coordinates to 2D grid nodes. Next, 3D grid nodes were mapped from the 2D grid nodes. First, the 3D grid nodes were read from the original 3D blade file before mapping. The corresponding points were obtained according to the recorded row numbers. Then, the matching points were grouped into sets of three, and the average coordinate values were converted into tuples for deduplication. This resulted in the output of a high-quality 3D node point set. Finally, the point set of the solid region on the center surface of the corresponding curved blade was obtained, as shown below. Figure 12 As shown.
[0030] Subsequently, a NURBS-based curve fitting method was employed. For the extracted 3D structural point set, the portion of the point set belonging to the internal connecting ribs in the blade topology optimization results was selected for B-spline curve fitting to obtain the 2D structural contour. Then, modeling was performed based on the 2D contour. First, the original blade model surface was artificially separated into an outer shell and an inner cavity model using a shelling function with a certain thickness. The fitted lines were then regularly extended along the normal directions of the upper and lower surfaces of the inner cavity model to map them to the upper and lower surfaces. This step allowed for manual control of the extension width. Figure 13 As shown, a three-dimensional rib model is obtained by thickening and surface processing of the inner cavity surface, which can be manually set. Figure 14 As shown, the length and width of the ribs are then constrained and adjusted by the inner cavity surface to ensure the ribs are located inside the cavity, resulting in a three-dimensional geometric model. This model is then combined with the outer shell model left from the shelling process and Boolean operations are performed to construct a complete model, as shown below. Figure 15 As shown.
[0031] In summary, this invention provides a method for topology optimization and reconstruction of 3D curved surface structures based on pixel grayscale. It directly identifies the skeleton and extracts skeleton points from the topology optimization structure image, and reconstructs the 3D optimized structure using the coordinates of these skeleton points. This solves the problem that commonly used topology optimization software cannot directly output vector structures, thus hindering structure modeling. Through boundary tracing, it can extract the feature contours of numerous 3D curved surface structures. This method obtains the coordinates of all skeleton points, allowing for control over the number of extracted coordinate points by adjusting sampling, or modification of the structure by directly adjusting the coordinate point information, thus enabling secondary optimization design of the optimized structure.
Claims
1. A method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping, characterized in that, Includes the following steps: Step 1: First, establish a rectangular plate model. For the topology optimization density distribution result of the three-dimensional curved blade structure, deform the curved mesh representing the density distribution information on it, map the deformed mesh onto the rectangular plate model, and simultaneously map the topology optimization density distribution result onto the rectangular plate model. Then, process the topology optimization density distribution result on the rectangular plate model to obtain a two-dimensional density field RGB image. Step 2: Input the two-dimensional density field RGB image into PyCharm software, set the pixel value threshold of the image using the global fixed threshold binarization method to obtain a clear density field feature binarized image, and then invert the colors of the binarized image to obtain a color-inverted binarized image. Step 3: Use morphological opening and closing operations to filter the color-inverted binarized image obtained in the previous step, fill in the small holes in the topological result mapped to the image space and remove discontinuous regions. Step 4: By adjusting the opening and closing mechanism, the kernel size, and the number of operations, determine the size of the small color blocks to be removed and the size of the holes to be filled. Repeat Step 4 and compare the processed images each time. The goal is to minimize the number of remaining holes and discontinuous small color blocks, and finally obtain the binarized image with the least noise. Step 5: For the binarized image processed in the previous step, use nonlinear filtering techniques and a median filter function with a suitable bandwidth to remove the pits and burrs on the boundary, and obtain a binarized image with smooth boundaries. Step 6: For the binarized image after median filtering, use the Suzuki boundary tracing algorithm to retrieve all contours, extract the hierarchical contours, and store all points on the contours. Step 7: Use a morphological thinning algorithm to morphologically thin the contours extracted by each boundary tracing to obtain the skeleton, and then use the Suzuki boundary tracing algorithm to extract and save all skeleton points. Step 8: Map the extracted skeleton points to the mesh nodes on the flat plate obtained by mesh deformation in Step 1, and then map and process them to the surface mesh nodes on the original three-dimensional curved blade structure to obtain the point coordinates of the remaining effective material area of the blade after topology optimization in the three-dimensional real space. Step 9: Based on the NURBS curve fitting method, select the part of the internal connecting rib in the blade topology optimization result from the point set obtained in the previous step, and perform overall B-spline curve fitting in CAD software to obtain the two-dimensional contour of the internal rib. Step 10: Model based on the two-dimensional contour. Use the shelling function of the CAD software to process the original hollow blade model to obtain the inner cavity model. Use the surface of the inner cavity model to stretch the rib contour to obtain the three-dimensional rib model. Finally, perform Boolean operation with the outer solid of the blade left by shelling to obtain the complete hollow blade reconstruction model.
2. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 1, mapping is achieved by changing the position of the curved mesh nodes to deform the mesh without changing the connection method of the nodes or the number of nodes on the boundary, and then mapping it onto the rectangular plate model.
3. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 1, the topology optimization density distribution results on the rectangular plate model are processed by extracting a two-dimensional density field RGB image from data visualization and analysis software.
4. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 2, the presence or absence of material in the density distribution on the rectangular plate model is mapped to the image pixel values of 0 or 255; the pixel value of the area with material before color inversion is 0, and the pixel value of the area without material is 255.
5. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 2, the morphological opening and closing operations are implemented in PyCharm software using OpenCV functions.
6. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 4, the operation is repeated twice, and the pixel value window selected for removing islands and holes is 1.5 times the size of the islands and holes themselves.
7. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 6, boundary retrieval filters valid contours by the number of contour points contained in each contour or the pixel area occupied by the contour in the pixel space, and further removes small contours that are difficult to be used for reconstruction.
8. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 7, the morphological thinning algorithm gradually removes white pixels that retain the structure through iterative erosion and dilation until no white pixels meet the erosion condition, at which point the iteration stops, resulting in a skeleton image.
9. The method for topological optimization and geometric reconstruction of curved surface structures based on coordinate space mapping according to claim 1, characterized in that, In step 10, shelling is a function provided by UG. The thickness of the shell for each face of the blade is selected according to the actual situation.