CN107330977B - Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method - Google Patents
Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method Download PDFInfo
- Publication number
- CN107330977B CN107330977B CN201710426984.3A CN201710426984A CN107330977B CN 107330977 B CN107330977 B CN 107330977B CN 201710426984 A CN201710426984 A CN 201710426984A CN 107330977 B CN107330977 B CN 107330977B
- Authority
- CN
- China
- Prior art keywords
- subdivision
- point
- curved surface
- root
- grid
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 40
- 239000002775 capsule Substances 0.000 claims abstract description 19
- 238000009499 grossing Methods 0.000 claims description 3
- 238000005259 measurement Methods 0.000 abstract description 5
- 230000002349 favourable effect Effects 0.000 abstract description 2
- 238000012544 monitoring process Methods 0.000 description 5
- 238000003780 insertion Methods 0.000 description 4
- 230000037431 insertion Effects 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008602 contraction Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 235000014594 pastries Nutrition 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
- G06T17/205—Re-meshing
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Computer Graphics (AREA)
- Geometry (AREA)
- Software Systems (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Processing Or Creating Images (AREA)
- Image Generation (AREA)
Abstract
The invention provides a Shepard interpolation-based root-three subdivision airship envelope surface reconstruction method, which is characterized in that after an initial triangular grid is established on the basis of point cloud data obtained by laser radar measurement, grid splitting rules of the root-three subdivision surface reconstruction method are used for calculating newly-inserted grid point coordinates by adopting Shepard interpolation and root-three subdivision alternate reciprocation. The method integrates the phenomena of shrinkage or expansion of the reconstructed curved surface and the like of the Shepard interpolation algorithm, reduces the error between the reconstructed curved surface and the actual curved surface, has the advantages of good curved surface smoothness, slow increase of the number of triangular meshes and the like of the root three-subdivision curved surface reconstruction method, is favorable for curved surface reconstruction, and is particularly suitable for the measurement requirement of the capsule form when the adjacent space is subjected to different wind loads on the ground.
Description
Technical Field
The invention relates to the technical field of aircraft testing.
Background
With the heat tide of the development of the near space in recent years, various novel aircrafts are continuously emerging, wherein the near space airship receives more and more research and attention due to the potential use of the near space airship. The airship in the adjacent space is a soft airship, the appearance of the airship is influenced by factors such as air inflation amount, load, wind load and the like, so that the specific shape of the airship capsule in the ground transferring and flying process is difficult to be displayed according to the original design of the airship, the appearance of the airship capsule directly influences the reliability of equipment attached to the airship capsule, and the deformation of the airship capsule influences the safety of the airship capsule. Therefore, during the ground transfer process, the shape and deformation of the airship capsule are required to be measured. In order to obtain the shape of the airship capsule and further monitor the deformation of the capsule, researchers adopt a laser radar-based capsule scanning method to obtain point cloud data of partial points on the curved surface of the capsule, perform curved surface reconstruction on the airship capsule according to the point cloud data, and monitor the shape of the capsule.
After the laser radar scans the airship envelope to obtain point cloud data, the curved surface of the airship can be reconstructed, and therefore the shape change of the airship envelope can be monitored. The method for performing curved surface reconstruction on the soft airship capsule comprises parameter curved surface reconstruction, subdivision curved surface reconstruction and the like. Subdivision is the limit of a mesh sequence that passes throughUsing a set of rules, new vertices are inserted in a given initial mesh, and this process is repeated. The method overcomes the difficulty of processing any topology by the parametric surface, and only a special subdivision rule is needed to be adopted at the irregular topology, unlike the problem that the parametric surface needs to process very complicated boundary splicing, so that the subdivision surface modeling is suitable for monitoring the shape and deformation of the airship. The most widely applied method in subdivision surface modeling is to insert edge points on the triangle mesh edge for segmentation, such as a Loop subdivision method and a butterfly subdivision method, i.e., a new vertex is directly inserted into an old triangle edge, and the old edge is segmented into two new edges. This way each triangular face is subdivided into four smaller triangular faces. If n-1 points are inserted in the triangle edge, each old edge is divided into n new edges, and the new fixed points and the old vertexes are connected according to a certain topological rule, so that each triangle surface is subdivided into n2A smaller triangular face. Thus, after dividing the primary side into three new sides, the number of resulting triangular meshes increases by a factor of 9. The traditional subdivision method has the advantages that the number of grids is increased quickly, and the original data are subjected to space movement, so that the reconstructed curved surface contracts or expands, a large error is generated between the reconstructed curved surface and an actual curved surface, and the shape and deformation monitoring of the airship are not facilitated.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method suitable for reconstructing the near space airship capsule shape, which has the advantages of high Shepard interpolation subdivision precision, low triangle subdivision speed of the traditional root-number three subdivision algorithm and smooth reconstruction curved surface, and can perform precision reconstruction on the deformation of an stratospheric airship.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
Wherein, R is a parameter selected according to the density degree of the point cloud, so that a set number of points fall into a circle domain which takes the new surface point as the center of the circle and takes R as the radius; r isiThe two-dimensional distance from a point i in the point cloud to the new surface point is obtained; x is an x coordinate component value in the three-dimensional coordinate of the new surface point; x is the number ofiIs the x coordinate component value in the three dimensional coordinates of point i; y is a y coordinate component value in the three-dimensional coordinate of the new surface point; y isiIs the y coordinate component value in the three dimensional coordinate of point i; n is the number of point clouds; f. ofiThe elevation value of the point i is used, and mu is a dimensionless non-negative parameter in the interpolation algorithm;
step 2, subdividing for the second time, firstly subdividing the grid and inserting new face points
Then, smoothing the grid, and correcting the three-dimensional coordinates of each old vertex
Wherein V is the weight of the corresponding old vertex and the adjacent vertex
n is the number of edges with vertex V as the end point; vi2、Vj2、Vk2Indicating △ a certain triangle in the mesh before the last subdivisionijkThree vertices of (V)sThe other end point of the s-th edge taking the vertex V as the end point in the grid is taken as the end point;
and (3) repeating the steps 1 and 2, after each subdivision, connecting a new vertex with a point existing before according to a root three-subdivision rule, dividing each triangle in the previous mesh into three triangles, and stopping the subdivision when the number of the triangles reaches a set upper limit, wherein the triangle subdivision mesh at the moment is the subdivision reconstruction curved surface.
The invention has the beneficial effects that: aiming at the requirement of airship capsule shape measurement, the invention designs a root three-subdivision surface reconstruction method based on Shepad interpolation, which is characterized in that after an initial triangular grid is established on the basis of point cloud data obtained by laser radar measurement, grid splitting rules of the root three-subdivision surface reconstruction method are used for calculating newly-inserted grid point coordinates by adopting Shepad interpolation and root three-subdivision alternate reciprocation. The invention integrates the phenomena of no contraction or expansion of the reconstruction curved surface by the Shepard interpolation algorithm, reduces the error between the reconstruction curved surface and the actual curved surface, and
the subdivision surface reconstruction method has the advantages of good surface smoothness, slow increase of the number of triangular meshes and the like, is favorable for surface reconstruction, and is particularly suitable for the measurement requirement of the capsule form when the adjacent space is subjected to different wind loads on the ground.
Drawings
FIG. 1 is a schematic diagram of the grid subdivision rules of the present invention;
FIG. 2 is a schematic diagram of a reconstructed surface, wherein (a) is a reconstructed surface according to the method of the present invention, and (b) is a reconstructed surface according to a conventional root-number-three subdivision method;
FIG. 3 is a schematic diagram of error analysis, wherein (a) is the method of the present invention to reconstruct surface errors, and (b) is the existing root three subdivision method to reconstruct surface errors.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
The reconstructed initial mesh of the invention is a triangular mesh, and the specific steps are as follows.
(1) Shepard interpolation subdivision: the subdivision rule adopts a root number three subdivision principle, a Shepard interpolation algorithm is adopted in a coordinate calculation method of an interpolation new vertex, and a new triangular mesh can be obtained according to the root number three subdivision rule;
(2) root number three subdivision: and thirdly, subdividing the root number of the new mesh obtained in the first step, and calculating to obtain the coordinates of a new vertex according to a root number trisection algorithm.
And (3) repeating the steps (1) and (2), stopping subdivision when the number of the triangles reaches the set upper limit, wherein the triangular subdivision meshes at the moment are the reconstructed curved surfaces. The method overcomes the defect that the precision of the traditional root-number three-subdivision algorithm is not high, and has the advantages of high Shepard interpolation subdivision precision, low triangle subdivision speed and smooth reconstruction curved surface of the traditional root-number three-subdivision algorithm, so that the method can be used for accurately reconstructing the deformation of the stratospheric airship.
Each step of subdivision comprises two times of step subdivision, and each step of subdivision comprises one Shepard interpolation subdivision and three root subdivisions; and the subdivision and splitting rules are divided twice, namely the subdivision speed follows the root number three subdivision principle, so that the triangular mesh growth speed of the subdivision surface is reduced. The specific steps of each step are as follows.
1. The method adopts Shepard interpolation to calculate the coordinates of the insertion points during the first subdivision, solves the problems that the error between a reconstructed surface and an actual surface obtained by the existing root three subdivision method is large, and the like, and comprises the following specific steps:
1) subdividing the grid, inserting new points with two-dimensional coordinate values, other than elevation, of
In this subdivision, the face-grid splitting speed follows
The splitting speed of the subdivision method, i.e. 1-3 plane splitting.
2) For a smooth curved surface, interpolating a new surface point Shepard to obtain an elevation value thereof
Wherein, R is reasonably selected according to the density degree of the point cloud, so that a proper number of points fall into the corresponding circular domain.
2. The existing root number three subdivision is adopted during the second subdivision, the problem that the reconstructed curved surface is not smooth enough during the first subdivision is solved, and the specific steps are as follows.
1) Subdividing the mesh, inserting new points having three-dimensional coordinate values of
Wherein, VFIs a triangular surface delta (V)i,Vj,Vk) The new vertex of (2).
2) Correcting three-dimensional coordinates of old vertexes for smooth grids
The formula is a weighted sum of the self vertex and the adjacent vertices, wherein the weights α of the adjacent verticesnIs calculated by the formula
The two subdivisions are combined together to form a step subdivision of the method for monitoring the shape and the deformation of the airship based on Shepad interpolation root three subdivision surface reconstruction, and the reconstruction of the shape of the airship capsule can be realized by repeating the step subdivision.
In the embodiment of the invention, after the point cloud data obtained by scanning the laser radar is initialized by the triangular mesh, the initial mesh is subdivided by the root three subdivision rule, and the subdivision rule is shown in figure 1.
In the figure, VFConnecting the new surface point with the vertex of the triangular surface for the new insertion point position, wherein the vertex is shown by a dotted line in the figure; to solve this problem, the old inner edge is removed and the new faces in the two faces adjacent to this edge are point-connected, as shown in the right drawing, since the two triangular faces adjacent to the inner edge (the inner solid line) are too narrow. And repeating the steps to obtain the grid of the subdivision algorithm. Here, in order to reconstruct the accuracy and smoothness of the surface, the technical difficulty lies in the calculation of the three-dimensional coordinates of the new insertion point each time subdivided. The three-dimensional coordinate algorithm for the new insertion point at each subdivision is now expressed as follows.
1. First subdivision:
1) subdividing the grid, inserting new points with two-dimensional coordinate values, other than elevation, of
Wherein Vi1，Vj1，Vk1Three vertices, V, of a triangle of the initial control meshF1Is a new pastry.
2) For a smooth curved surface, interpolating a new surface point Shepard to obtain an elevation value thereof
And R is a distance threshold value to the new surface point, which is set in the xy two-dimensional plane by the user according to different test conditions, namely, points which are lower than the distance threshold value R from the new surface point participate in the solution of the elevation. r is the two-dimensional distance from each point to the new surface point, and ri is the two-dimensional distance from the point i in the point cloud to the new surface point; x is an x coordinate component value in the three-dimensional coordinate of the new surface point; xi is the x coordinate component value in the three-dimensional coordinate of the ith point in the point cloud; y is a y coordinate component value in the three-dimensional coordinate of the new surface point; yi is a y coordinate component value in the three-dimensional coordinate of the ith point in the point cloud; i is the subscript number of the ith point in the point cloud; n is the number of all point clouds; and fi is an elevation value of the point i, mu is a dimensionless non-negative parameter in the interpolation algorithm, and different values are obtained according to different point cloud users.
In this embodiment, R is selected reasonably according to the density of the point cloud, so that more than five points fall into the corresponding circle.
2. And (5) second subdivision:
1) subdividing the mesh, inserting new points having three-dimensional coordinate values of
Wherein, VF2For the triangular surface delta (V) in the triangular mesh obtained after the first subdivisioni2,Vj2,Vk2) The new vertex of (2).
2) Correcting three-dimensional coordinates of old vertexes for smooth grids
Wherein V is the old ceiling, VvThe formula is a weighted sum of the self vertex and the neighboring vertices, wherein the weights α of the neighboring verticesnIs calculated by the formula
n is the number of edges with vertex V as the end point. Vi2、Vj2、Vk2Indicating △ a certain triangle in the mesh before the last subdivisionijkThree vertices of (V)sIs the other end point of the s-th edge of the mesh, which has vertex V as the end point. The above formula is based on Shepard interpolation designed for the invention
And (3) repeating the steps, namely repeating the steps of subdividing for the first time and subdividing for the second time, so as to obtain the subdivided and reconstructed surfaces.
In the embodiment of the invention, the point cloud data of the curved surface is acquired by adopting laser, then the curved surface is reconstructed by adopting the method of the invention and the existing root method III respectively, and the reconstructed curved surface is shown as figure 2. FIG. 3 is an error comparison of two methods to reconstruct a surface. As can be seen from FIG. 3, the root three-subdivision algorithm based on Shepard interpolation designed by the present invention greatly reduces the error of the reconstructed surface: the area of the curved surface with 0.2% of the elevation adduction proportion accounts for about 90% of the whole area, and the area of the curved surface with 0.2% of the elevation adduction proportion of the reconstructed curved surface by the existing root-number three-subdivision algorithm accounts for 70% of the whole area; except for a few curved surface areas, the error of the reconstructed curved surface obtained by the method, namely the height adduction ratio, is less than or equal to 0.4 percent, and the error of the reconstructed curved surface of the existing root-number three-algorithm method is about 10 percent, and the error of the area of the curved surface is more than 0.4 percent.
The embodiment provides a monitoring method suitable for the form and deformation of the airship in the process of transferring and flying in the adjacent space. The Shepard interpolation is used for improving the root number three subdivision method, so that the error of the reconstructed curved surface can be greatly reduced; meanwhile, the grid splitting speed is lower than that of the existing non-root-number three-subdivision algorithm, and the shape and deformation monitoring of the airship is facilitated.
Claims (1)
1. A root-number three-subdivision airship capsule curved surface reconstruction method based on Shepard interpolation is characterized by comprising the following steps:
step 1, subdividing for the first time, firstly subdividing the grid, inserting new surface points, and obtaining two-dimensional coordinate values of the new surface points except for the elevation
Wherein, Vi1、Vj1、Vk1Three vertexes of the initial control grid triangle are respectively; then, smoothing the curved surface, and interpolating the new surface points Shepard to obtain the elevation thereofValue of
Wherein, R is a parameter selected according to the density degree of the point cloud, so that a set number of points fall into a circle domain which takes the new surface point as the center of the circle and takes R as the radius; r isiThe two-dimensional distance from a point i in the point cloud to the new surface point is obtained; x is an x coordinate component value in the three-dimensional coordinate of the new surface point; x is the number ofiIs the x coordinate component value in the three dimensional coordinates of point i; y is a y coordinate component value in the three-dimensional coordinate of the new surface point; y isiIs the y coordinate component value in the three dimensional coordinate of point i; n is the number of point clouds; f. ofiThe elevation value of the point i is used, and mu is a dimensionless non-negative parameter in the interpolation algorithm;
step 2, subdividing for the second time, firstly subdividing the grid and inserting new face points
Then, smoothing the grid, and correcting the three-dimensional coordinates of each old vertex
Wherein V is the weight of the corresponding old vertex and the adjacent vertex
n is the number of edges with vertex V as the end point; vi2、Vj2、Vk2Indicating △ a certain triangle in the mesh before the last subdivisionijkThree vertices of (V)sThe other end point of the s-th edge taking the vertex V as the end point in the grid is taken as the end point;
and (3) repeating the steps 1 and 2, after each subdivision, connecting a new vertex with a point existing before according to a root three-subdivision rule, dividing each triangle in the previous mesh into three triangles, and stopping the subdivision when the number of the triangles reaches a set upper limit, wherein the triangle subdivision mesh at the moment is the subdivision reconstruction curved surface.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710426984.3A CN107330977B (en) | 2017-06-08 | 2017-06-08 | Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710426984.3A CN107330977B (en) | 2017-06-08 | 2017-06-08 | Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107330977A CN107330977A (en) | 2017-11-07 |
| CN107330977B true CN107330977B (en) | 2020-08-11 |
Family
ID=60194865
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710426984.3A Expired - Fee Related CN107330977B (en) | 2017-06-08 | 2017-06-08 | Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107330977B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110426991B (en) * | 2019-07-30 | 2021-10-08 | 苏州行远志成自动化科技有限公司 | Composite position error compensation method and device |
| CN117541747B (en) * | 2023-10-31 | 2024-08-06 | 中国人民解放军总医院 | C-B spline-based subdivision wavelet transformation method, device, equipment and medium |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101639946A (en) * | 2009-08-26 | 2010-02-03 | 北京农业信息技术研究中心 | Plant leaf three-dimensional model geometric description and curved surface reconstruction method and system |
| CN103793939A (en) * | 2013-07-29 | 2014-05-14 | 北京正安融翰技术有限公司 | Local increasing type curved-surface reconstruction method of large-scale point cloud data |
| US8823775B2 (en) * | 2009-04-30 | 2014-09-02 | Board Of Regents, The University Of Texas System | Body surface imaging |
-
2017
- 2017-06-08 CN CN201710426984.3A patent/CN107330977B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8823775B2 (en) * | 2009-04-30 | 2014-09-02 | Board Of Regents, The University Of Texas System | Body surface imaging |
| CN101639946A (en) * | 2009-08-26 | 2010-02-03 | 北京农业信息技术研究中心 | Plant leaf three-dimensional model geometric description and curved surface reconstruction method and system |
| CN103793939A (en) * | 2013-07-29 | 2014-05-14 | 北京正安融翰技术有限公司 | Local increasing type curved-surface reconstruction method of large-scale point cloud data |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107330977A (en) | 2017-11-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105761312B (en) | A kind of mima type microrelief method of surface reconstruction | |
| US20240153123A1 (en) | Isogeometric Analysis Method Based on a Geometric Reconstruction Model | |
| JP5436416B2 (en) | Approximation processing method and approximation processing apparatus | |
| CN103701466A (en) | Scattered point cloud compression algorithm based on feature reservation | |
| CN112632869B (en) | Grid frame-based non-structural boundary layer grid generation method | |
| CN109410342A (en) | A kind of point cloud compressing method retaining boundary point | |
| JP2011054144A (en) | Atmospheric flow field simulation method in consideration of topographical resolution difference | |
| CN102938161B (en) | A kind of 3D shape automatic division method based on Mean Shift | |
| CN107767453A (en) | A kind of building LIDAR point cloud reconstruction and optimization methods of rule-based constraint | |
| CN107330977B (en) | Shepard interpolation-based root-number three-subdivision airship envelope curved surface reconstruction method | |
| Wang et al. | Hole filling of triangular mesh segments using systematic grey prediction | |
| Holdstein et al. | Three-dimensional surface reconstruction using meshing growing neural gas (MGNG) | |
| CN101276484A (en) | Method for generating gridding based on harmonic map | |
| CN108335354A (en) | A kind of greedy projection Triangulation Algorithm list wood method for reconstructing based on Moving Least | |
| Qing et al. | Point cloud simplification algorithm based on particle swarm optimization for online measurement of stored bulk grain | |
| CN106530397A (en) | Geological surface three-dimensional reconstruction method based on sparse profile geological contours | |
| CN113744389B (en) | Point cloud simplifying method for complex part curved surface feature preservation | |
| CN113094964A (en) | Method and device for generating blade machining coordinates | |
| CN110207618B (en) | Surface line data extraction method of three-dimensional scanning measurement data | |
| Lee | Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 1: Construction of underlying geometrical model | |
| CN111797551B (en) | Interpolation method for three-dimensional cloud image display of test strain data | |
| CN112634458A (en) | Oral cavity model point cloud simplification method based on characteristic significance evaluation | |
| CN106056124A (en) | Relief extraction method based on three-dimensional curved surface loop guidance | |
| Shaowen et al. | Algorithm of 3D reconstruction based on point cloud segmentation denoising | |
| He et al. | Adaptive Mesh Subdivision Method Based on Approximation Error of Edge |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| TA01 | Transfer of patent application right | ||
| TA01 | Transfer of patent application right |
Effective date of registration: 20200509 Address after: No. 23, Taiping Road, Haidian District, Beijing 100036 Applicant after: Joint Service College of National Defense University of the people's Liberation Army of China Address before: 21 box 190, box 841700, the Xinjiang Uygur Autonomous Region, Urumqi Applicant before: UNIT 63655 OF PLA |
|
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200811 |