A view point planning method and system for three-dimensional measurement of a blade

Abstract

This invention discloses a viewpoint planning method and system for three-dimensional measurement of blades, belonging to the field of optical three-dimensional measurement technology. The method includes: importing the CAD theoretical model of the blade to be measured; dividing the CAD theoretical model of the blade into a crown region, a blade region, and a root region; generating redundant viewpoint sets based on the characteristics of different regions using different viewpoint sampling methods; converting the CAD theoretical model of the blade to be measured into a uniform triangular mesh model; merging the redundant viewpoint sets generated from different regions; performing visibility evaluation for each viewpoint in the viewpoint sets based on the triangular mesh model of the blade to be measured; merging the visibility evaluation results to obtain a visibility matrix; transforming the viewpoint planning problem into a set coverage problem; solving the set coverage problem to obtain the minimum number of viewpoints required for three-dimensional measurement of the complete blade. This invention can reduce the number of viewpoints required for three-dimensional measurement of a complete blade, ensuring the integrity and efficiency of the measurement data.

Description

Technical Field

[0001] This invention relates to the field of optical three-dimensional measurement technology, and specifically to a viewpoint planning method and system for three-dimensional measurement of blades. Background Technology

[0002] Blades are the core components for energy conversion in heavy-duty gas turbines, aero engines, and steam turbines. They are the most numerous and also the most prone to accidents within the unit. Performing three-dimensional measurements on the blades to verify whether their manufacturing meets design requirements is an important means of ensuring the energy conversion efficiency of turbomachinery meets standards and preventing accidents.

[0003] Three-dimensional measurement of blades, compared to that of other parts, demands higher accuracy and efficiency. Non-contact optical methods, such as structured light 3D measurement, offer a better balance between accuracy and efficiency compared to contact methods like coordinate measuring machines (CMMs). However, due to the discontinuities and complexity of blade surfaces, optical 3D measurement devices cannot obtain a complete blade model in a single scan. Developing a measurement plan for blades with thin walls and freeform surface features remains a challenging task.

[0004] Existing blade 3D measurement systems are still mainly based on manual planning, which makes it difficult to guarantee the integrity and efficiency of the measurement data: poor relative position between the optical 3D measurement device and the blade will seriously affect the acquisition quality, thus failing to guarantee complete blade measurement; a lot of time needs to be spent on experiments and developing measurement plans before actual measurement; and too many unnecessary viewpoints will reduce measurement efficiency during actual measurement.

[0005] Viewpoint planning solves the data integrity and efficiency problems faced by manual planning. Viewpoint planning is defined as: given an imaging environment and a measured object, finding a minimum number of viewpoints in the viewpoint space within an acceptable computational time to achieve a specified detection or reconstruction goal. A viewpoint has at least six degrees of freedom and can be defined as v = (x, y, z, α, β, γ). Therefore, systems employing viewpoint planning typically include a robotic arm.

[0006] Existing literature or data shows that most current viewpoint planning methods for three-dimensional blade measurement only target a single profile, which cannot guarantee the complete measurement of the blade, or are difficult to adapt to the thin-walled and complex free-form surface characteristics of the blade, resulting in redundant viewpoints, missing measurement data, and low efficiency, or relying on pasting marker points on the surface of the target to be measured, which is a cumbersome process. Summary of the Invention

[0007] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a viewpoint planning method and system for three-dimensional blade measurement, ensuring the data integrity and efficiency of three-dimensional blade measurement.

[0008] To achieve the above objectives, the following steps are included:

[0009] A viewpoint planning method for three-dimensional blade measurement includes the following steps:

[0010] Import the CAD theoretical model of the blade to be tested;

[0011] The CAD theoretical model of the leaf to be tested is divided into the crown region, the leaf blade region, and the leaf root region; based on the characteristics of different regions, different viewpoint sampling methods are used to generate a redundant viewpoint set;

[0012] The CAD theoretical model of the blade to be tested is converted into a uniform triangular mesh model;

[0013] Redundant viewpoint sets generated from different regions are merged. Based on the triangular mesh model of the blade under test, visibility is evaluated for each viewpoint in the viewpoint set. The visibility evaluation results are merged to obtain a visibility matrix. Based on the visibility matrix, the viewpoint planning problem is transformed into a set coverage problem.

[0014] Solve the set coverage problem to obtain the minimum set of viewpoints required for a complete three-dimensional measurement of the blade.

[0015] As a further improvement of the present invention, the CAD theoretical model of the blade to be tested is imported based on the interface provided by FreeCAD.

[0016] As a further improvement of the present invention, the division of the CAD theoretical model of the leaf to be tested into the crown region, leaf blade region, and leaf root region is based on area and height as characteristics for dividing the leaf model, specifically including:

[0017] Calculate the area of ​​each NURBS surface in the CAD theoretical model of the blade to be tested, and select the surface with the largest area as the reference surface.

[0018] Calculate the minimum height z of the reference profile. min Maximum height z max ; Calculate h top =z min +(z max -z min )*0.8, h bottom =z min +(z max -z min )*0.2;

[0019] After calculating the bounding boxes of all surfaces, traverse the surfaces. If the z-coordinate value of all corner points of the bounding box of a surface is greater than h... top The surface belongs to the leaf crown region; if the z-coordinate values ​​of all corner points of the bounding box are less than hbottom The surface in question belongs to the leaf root region; the remaining surfaces belong to the leaf body region.

[0020] As a further improvement of the present invention, the step of generating a redundant viewpoint set based on the characteristics of different regions and using different viewpoint sampling methods includes:

[0021] For the leaf crown and leaf root regions, based on the spatial sampling method, the bounding box of each region model is calculated. The center of the bounding box is used as the center of the sphere, and the optimal measurement distance of the optical measurement device is used as the radius to draw a sphere. The viewpoint is obtained by sampling on the surface of the sphere.

[0022] For the blade region, based on the vertex sampling method, the CAD theoretical model of the blade region is converted into a triangular mesh model. Then, the mesh is simplified. The vertices of the simplified triangular mesh model are traversed. Starting from the vertex and with the vertex normal as the direction, the optimal measurement distance of the optical measurement device is offset to obtain the viewpoint.

[0023] As a further improvement of the present invention, the conversion of the CAD theoretical model of the blade to be tested into a uniform triangular mesh model is based on the Mefisto method.

[0024] As a further improvement of the present invention, the visibility evaluation for each viewpoint in the viewpoint set includes:

[0025] For each measuring device in the optical measuring apparatus at this viewpoint, calculate the set of triangular facets that it can measure under the constraints of field of view, depth of field, incident angle, and no obstruction.

[0026] The intersection of the sets of triangular facets that each measuring device can measure is obtained to obtain the set of triangular facets that the optical measuring device can measure from a single viewpoint.

[0027] The triangular patch set represents the combined visibility assessment results of the optical measurement device from a single viewpoint; the visibility assessment results from all viewpoints are combined to obtain the visibility matrix.

[0028] As a further improvement of the present invention, the problem of solving the set coverage problem is solved using a greedy algorithm.

[0029] A viewpoint planning system for three-dimensional blade measurement includes the following steps:

[0030] The import module is used to import the CAD theoretical model of the blade to be tested;

[0031] The generation module is used to divide the CAD theoretical model of the leaf under test into the crown region, leaf blade region, and leaf root region; based on the characteristics of different regions, different viewpoint sampling methods are used to generate a redundant viewpoint set;

[0032] The conversion module is used to convert the CAD theoretical model of the blade under test into a uniform triangular mesh model.

[0033] The transformation module is used to merge redundant viewpoint sets generated from different regions. Based on the triangular mesh model of the blade under test, it performs visibility assessment for each viewpoint in the viewpoint set, merges the visibility assessment results, and obtains a visibility matrix. Based on the visibility matrix, the viewpoint planning problem is transformed into a set coverage problem.

[0034] The solver module is used to solve the set coverage problem and obtain the minimum number of viewpoints required for a complete 3D measurement of the blade.

[0035] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of any of the viewpoint planning methods for three-dimensional measurement of blades.

[0036] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the viewpoint planning method for three-dimensional measurement of blades.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] This invention first imports the CAD theoretical model of the blade to be tested, dividing the model into the crown region, blade region, and root region. For each region, different viewpoint sampling methods are used to generate redundant viewpoint sets. After converting the CAD theoretical model of the blade to be tested into a uniform triangular mesh model, the three redundant viewpoint sets are merged. Based on the triangular mesh model of the blade to be tested, a visibility assessment is performed to obtain a visibility matrix. Finally, the set coverage problem is solved to obtain the minimum number of viewpoints required for the complete 3D measurement of the blade. This invention fully considers the structural characteristics of different parts of the blade when performing viewpoint sampling. For the crown and root regions, a spatial sampling method is used for viewpoint sampling, generating viewpoints that cover the root and crown platform surfaces, reducing measurement blind spots. For the blade region, considering its thin-walled and free-form surface characteristics, a vertex sampling method is used for viewpoint sampling, generating viewpoints that effectively cover its surface. By rationally dividing the blade model and using different methods for viewpoint sampling in different regions, this invention can generate high-quality redundant viewpoint sets, laying the foundation for the final visibility assessment and set coverage problem solution. The invention is simple in principle and highly automated, which can reduce the number of viewpoints required when performing three-dimensional measurements on a complete blade, and ensure the integrity and efficiency of the measurement data. Attached Figure Description

[0039] Figure 1This is a flowchart of the algorithm of the present invention;

[0040] Figure 2 This is a schematic diagram of the blade theoretical model segmentation steps in the embodiment;

[0041] Figure 3 This is a spatial sampling diagram in the embodiment; where (a) is the sampling result of the leaf crown region and (b) is the sampling result of the leaf root region;

[0042] Figure 4 This is a schematic diagram of vertex sampling in the leaf blade region of the embodiment;

[0043] Figure 5 This is a schematic diagram of the viewpoint sampling results of the complete blade in the embodiment;

[0044] Figure 6 This is a schematic diagram of the visibility assessment in the embodiment; where (a) is the visibility assessment result of a single measuring device; and (b) is the visibility assessment result of a surface structured light scanner.

[0045] Figure 7 This is a schematic diagram of the visibility matrix in the embodiment;

[0046] Figure 8 This is a schematic diagram of the viewpoint planning results in the embodiment;

[0047] Figure 9 A block diagram of a viewpoint planning system for three-dimensional blade measurement;

[0048] Figure 10 This is a schematic diagram of an electronic device in one of the embodiments. Detailed Implementation

[0049] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0050] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0051] like Figure 1 As shown, the first objective of this invention is to provide a viewpoint planning method for three-dimensional measurement of blades, comprising the following steps:

[0052] Step 1: Import the CAD theoretical model of the blade to be tested.

[0053] Step 2: Divide the CAD theoretical model of the leaf to be tested into the crown region, leaf blade region, and leaf root region.

[0054] Step 3: For the leaf crown region, leaf blade region, and leaf root region, different viewpoint sampling methods are used based on the characteristics of different regions to generate a redundant viewpoint set.

[0055] Step four: Convert the CAD theoretical model of the blade to be tested into a uniform triangular mesh model.

[0056] Step 5: Merge redundant viewpoint sets generated from different regions. Based on the triangular mesh model of the blade under test, perform visibility evaluation for each viewpoint in the viewpoint set to obtain a visibility matrix. Based on the visibility matrix, transform the viewpoint planning problem into a set coverage problem.

[0057] Step six: Solve the set coverage problem to obtain the minimum set of viewpoints required for a complete three-dimensional measurement of the blade.

[0058] The invention is simple in principle and highly automated, which can reduce the number of viewpoints required when performing three-dimensional measurements on a complete blade, and ensure the integrity and efficiency of the measurement data.

[0059] The invention will now be further described with reference to the accompanying drawings.

[0060] like Figure 1 As shown, the present invention provides a viewpoint planning method for three-dimensional measurement of blades, comprising the following steps:

[0061] 1) Import the CAD theoretical model of the blade to be tested.

[0062] Preferably, the model is imported using the interface provided by FreeCAD.

[0063] 2) Divide the CAD theoretical model of the leaf to be tested into the crown region, leaf body region, and leaf root region.

[0064] Preferably, the area of ​​each NURBS surface in the CAD theoretical model of the blade to be tested is calculated, and the surface with the largest area is selected as the reference profile. The minimum height z of this reference profile is then calculated. min Maximum height z max Calculate h top =z min +(z max -z min )*0.8, h bottom =z min +(z max -z min *0.2. After calculating the bounding boxes of all surfaces, traverse the surfaces. If the z-coordinate value of all corner points of the bounding box of a surface is greater than h... top The surface belongs to the leaf crown region; if the z-coordinate values ​​of all corner points of the bounding box are less than h bottom The first surface belongs to the leaf root region; the remaining surfaces belong to the leaf blade region. The partitioning result is as follows: Figure 2 As shown.

[0065] 3) For the leaf crown region, leaf blade region, and leaf root region, different viewpoint sampling methods are used based on the characteristics of different regions to generate redundant viewpoint sets.

[0066] Preferably, for the leaf crown region and leaf root region, redundant viewpoint sets are generated based on the spatial sampling method: First, the bounding box of each region model is calculated, with the center of the bounding box as the center of the sphere, and the radius of the sphere is 614mm, the optimal measurement distance of the surface structured light scanner. The vertices evenly distributed on the sphere are the viewpoints, and the viewpoint direction points to the center of the sphere.

[0067] Sampling results as follows Figure 3 As shown, the pose of the viewpoint is represented by a coordinate system in the figure.

[0068] For the blade region, a redundant viewpoint set is generated based on a vertex sampling method: First, the CAD theoretical model of the blade region is converted into a triangular mesh model. Then, the mesh is simplified based on a vertex clustering method. The vertices of the simplified triangular mesh model are traversed, and with each vertex as the starting point and the vertex normal as the direction, the optimal measurement distance of the structured light scanner (614 mm) is offset to obtain the viewpoint, with the viewpoint direction pointing towards the vertex. The sampling results are as follows: Figure 4 As shown.

[0069] 4) Convert the CAD theoretical model of the blade to be tested into a uniform triangular mesh model.

[0070] Preferably, the conversion is based on the Mefisto method, and the maximum side length is set to 2mm.

[0071] 5) Merge redundant viewpoint sets generated from different regions, as shown in the following figure. Figure 5 As shown. Based on the triangular mesh model of the blade under test, the visibility is evaluated for each viewpoint in the viewpoint set, and the visibility matrix is ​​obtained.

[0072] Preferably, for each measuring device in the binocular structured light scanner, including the left camera, the projector, and the right camera, the set of triangular facets that the device can measure under the conditions of satisfying the constraints of field of view, depth of field, incident angle, and no occlusion is calculated based on the rasterization method.

[0073] like Figure 6 As shown in (a), the dark area on the blade model is the set of triangular facets that the device can measure. The blade model is located inside the frame model, which has marker points pasted on it to assist in point cloud stitching.

[0074] The intersection of the sets of triangular faces that each measuring device can measure yields the set of triangular faces that the optical measuring device can measure from a single viewpoint, such as... Figure 6 As shown in (b).

[0075] The visibility assessment results from all viewpoints are combined to obtain a visibility matrix. A small-scale visibility matrix is ​​shown below. Figure 7 As shown, v i Indicates the viewpoint, s j This represents a triangular facet, where 1 indicates measurable and 0 indicates unmeasurable.

[0076] 6) Solve the set coverage problem to obtain the minimum set of viewpoints required for a complete three-dimensional measurement of the blade.

[0077] Preferably, a greedy algorithm is used to solve the problem, and the result is as follows: Figure 8 As shown.

[0078] like Figure 9 As shown, the present invention also provides a viewpoint planning system for three-dimensional measurement of blades, comprising:

[0079] The import module is used to import the CAD theoretical model of the blade to be tested;

[0080] The generation module is used to divide the CAD theoretical model of the leaf under test into the crown region, leaf blade region, and leaf root region; based on the characteristics of different regions, different viewpoint sampling methods are used to generate a redundant viewpoint set;

[0081] The conversion module is used to convert the CAD theoretical model of the blade under test into a uniform triangular mesh model.

[0082] The transformation module is used to merge redundant viewpoint sets generated from different regions. Based on the triangular mesh model of the blade under test, it performs visibility assessment for each viewpoint in the viewpoint set, merges the visibility assessment results, and obtains a visibility matrix. Based on the visibility matrix, the viewpoint planning problem is transformed into a set coverage problem.

[0083] The solver module is used to solve the set coverage problem and obtain the minimum number of viewpoints required for a complete 3D measurement of the blade.

[0084] like Figure 10 As shown, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the viewpoint planning method for three-dimensional measurement of blades.

[0085] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the viewpoint planning method for three-dimensional measurement of blades.

[0086] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for view point planning for blade three-dimensional measurement, characterized in that, The method comprises the following steps: Importing a CAD theoretical model of a blade to be measured; Dividing the CAD theoretical model of the blade to be measured into a crown region, a blade body region and a blade root region; based on the characteristics of different regions, different viewpoint sampling methods are adopted to generate a redundant viewpoint set; Converting the CAD theoretical model of the blade to be measured into a uniform triangular mesh model; Merging the redundant viewpoint sets generated in different regions, performing visibility evaluation on each viewpoint in the viewpoint set based on the triangular mesh model of the blade to be measured, merging the visibility evaluation results to obtain a visibility matrix; and converting the viewpoint planning problem into a set covering problem based on the visibility matrix; Solving the set covering problem to obtain a set of the minimum number of viewpoints required for complete three-dimensional measurement of the blade; The method comprises the following steps: For the crown and root regions, based on a space sampling method, the bounding boxes of the model of each region are calculated, a sphere is made with the center of the bounding box as the center and the best measurement distance of the optical measurement device as the radius, and the viewpoints are sampled on the sphere surface; For the blade body region, based on a vertex sampling method, the CAD theoretical model of the blade body region is converted into a triangular mesh model, then the mesh is simplified, the vertices of the simplified triangular mesh model are traversed, the vertices are taken as the starting points and the vertex normals are taken as the directions, and the viewpoints are obtained by offsetting the best measurement distance of the optical measurement device; The visibility evaluation on each viewpoint in the viewpoint set comprises the following steps: For each measurement device in the optical measurement device under the viewpoint, the set of triangular facets that can be measured under the constraint conditions of meeting the field of view angle, the depth of field, the incident angle and no occlusion is calculated respectively; The intersection of the set of triangular facets that can be measured by each measurement device is calculated to obtain the set of triangular facets that can be measured by the optical measurement device under a single viewpoint; The set of triangular facets is the merged visibility evaluation result of the optical measurement device under a single viewpoint; and the visibility evaluation results under all viewpoints are merged to obtain the visibility matrix.

2. The view point planning method for blade three-dimensional measurement according to claim 1, characterized in that, The CAD theoretical model of the blade to be measured is imported based on the interface provided by FreeCAD.

3. The view point planning method for blade three-dimensional measurement according to claim 1, characterized in that, The CAD theoretical model of the blade to be measured is divided into the crown region, the blade body region and the blade root region by taking the area and height as the characteristics, and the division specifically comprises the following steps: The area of each NURBS surface in the CAD theoretical model of the blade to be measured is calculated, and the surface with the largest area is selected as the reference surface; calculating the minimum height of the reference profile z min , maximum height z max ; calculating h top = z min + ( z max - z min ) * 0.8, h bottom = z min + ( z max - z min ) * 0.2; After calculating the bounding box of all surfaces, traverse the surfaces, if the coordinate value of all corner points of the bounding box of the surface is greater than the coordinate value of the corner point of the bounding box of the leaf crown region, the surface belongs to the leaf crown region; if the coordinate value of all corner points of the bounding box of the surface is less than the coordinate value of the corner point of the bounding box of the leaf root region, the surface belongs to the leaf root region; the remaining surfaces belong to the leaf body region. z h top , the surface belongs to the leaf crown region; if the coordinate value of all corner points of the bounding box of the surface is less than the coordinate value of the corner point of the bounding box of the leaf root region, the surface belongs to the leaf root region; the remaining surfaces belong to the leaf body region. z h bottom ,​​ 4. The view point planning method for blade three-dimensional measurement according to claim 1, characterized in that, The CAD theoretical model of the blade to be measured is converted into a uniform triangular mesh model based on the Mefisto method.

5. The view point planning method for blade three-dimensional measurement according to claim 1, characterized in that, The set covering problem is solved by using a greedy algorithm.

6. A viewpoint planning system for three-dimensional measurement of a blade, which implements the viewpoint planning method for three-dimensional measurement of a blade according to any one of claims 1 to 5, and comprises the following steps: An importing module for importing a CAD theoretical model of a blade to be measured; A generating module for dividing the CAD theoretical model of the blade to be measured into a crown region, a blade body region and a blade root region; based on the characteristics of different regions, different viewpoint sampling methods are adopted to generate a redundant viewpoint set; a conversion module configured to convert a CAD theoretical model of the blade to be measured into a uniform triangular mesh model; a conversion module configured to merge the redundant viewpoint sets generated in different regions, perform visibility evaluation for each viewpoint in the viewpoint sets based on the triangular mesh model of the blade to be measured, merge the visibility evaluation results to obtain a visibility matrix, and convert the viewpoint planning problem into a set covering problem based on the visibility matrix; a solution module configured to solve the set covering problem to obtain a set of the minimum number of viewpoints required for complete three-dimensional measurement of the blade. 7.An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the viewpoint planning method for three-dimensional measurement of a blade according to any one of claims 1 to 5 when executing the computer program. 8.A computer readable storage medium storing a computer program, wherein the computer program implements the steps of the viewpoint planning method for three-dimensional measurement of a blade according to any one of claims 1 to 5 when executed by a processor.

Images