CN115578270A - Star map blind restoration method for elliptic arc track - Google Patents
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Abstract
The invention discloses a method for blindly restoring a star map when a star point track is an elliptic arc track under the condition that a star sensor does not have zero compound motion at three-axis angular velocity, which comprises the following steps: s1: carrying out ellipse fitting on the elliptical arc track of the star points; s2: carrying out projection transformation-based transformation of an elliptical arc track and an arc track; s3: performing circular arc track and straight-line segment track transformation based on polar coordinate transformation; s4: carrying out straight-line segment track restoration based on blind restoration of the motion blurred image; s5: and carrying out coordinate inverse transformation and projective inverse transformation to obtain a final restoration result of the star map with the original track being the elliptic arc track. According to the invention, the elliptic arc track is converted into the circular arc track through projective transformation, the circular arc track is converted into the straight-line track through polar coordinate transformation, and then the star map of the elliptic arc track is restored through straight-line segment restoration and coordinate inverse transformation, so that the blind restoration of the star map of the elliptic arc track is realized.
Description
Technical Field
The invention relates to the technical field of fuzzy restoration of a moving star map, in particular to a star map blind restoration method when a star point track is an elliptic arc track under the condition that a star sensor does not have zero compound motion at three-axis angular velocity.
Background
The star sensor is an instrument for measuring the attitude of a fixed star with high precision, and the star sensor firstly shoots a starry sky image and then calculates the attitude of a spacecraft according to imaging information. When the spacecraft moves at high speed, the imaging star points can produce trailing, and trailing tracks are different when the motion forms are different. At the moment, the star light energy can be dispersed to a plurality of pixels, so that the image signal-to-noise ratio is reduced, the star point extraction precision is reduced, and further the attitude calculation precision is reduced. Therefore, how to eliminate the motion blur of the trailing star point under the high dynamic condition of the spacecraft has important significance on the attitude measurement of the star sensor.
In order to solve the motion blur problem, one method is to reduce the image quality degradation caused by motion blur through hardware optimization before the star sensor is shot, such as using a time delay integration method, a servo tracking platform technology, an electron multiplication charge coupled device, an enhanced charge coupled device, a multi-view-field star sensor and the like. However, these improvements are relatively difficult and costly, and so the second category of methods for resolving motion blur tends to be more common.
The second method is to perform optimization processing on the image through software after the star sensor shoots, so as to eliminate star point trailing. The methods are mainly divided into two types, one is non-blind restoration, namely restoration of motion blurred images under the condition of other measurable spacecraft angular velocity instruments. Wu dawn the Jue of university of aerospace, the Schchen fly of the university of Qinghua, and the like perform degaussing of star point motion blur by deeply integrating data from SINS (strap-down inertial navigation) or MENS (micro electro mechanical system) gyroscopes. The Chen Nan adds EKF (extended Kalman filter) on the basis of the above coupling system. Sunset of the university of Qinghua couples the star sensor with an INS (inertial navigation system) on the basis of Chen Nan. Marilbalance of the national defense science and technology university grows by utilizing a plurality of sub-star point areas, and star point tailing is eliminated through a correlation frame on the basis of integrating MEMS gyroscope data. These methods all require the use of an angular velocity measuring instrument.
Another software-based star map motion restoration method is blind restoration, which is restoration based only on images captured by a star sensor, so that there is no need to know the motion before image motion restoration. For blind restoration of a straight-line segment track, in the conventional method, motion directions are generally obtained by Radon transformation, hough transformation, a structural differential operator method and the like, trailing lengths are obtained by curve fitting, a frequency spectrum method, bispectrum and the like, then a fuzzy kernel function is generated according to the motion directions and the trailing lengths, and finally star point fuzzy restoration of the straight-line segment track is realized based on image restoration algorithms such as L-R filtering, wiener filtering, inverse filtering and the like. In addition, there are a series of optimization and improvement algorithms for angle and length detection of straight line segments and image restoration filtering algorithms.
The existing blind restoration algorithm for the star point images only aims at the condition that the motion track of the star point is a straight line segment, but when the motion condition of the star sensor is complex, particularly when the angular velocity of three axes is not zero, the motion track of the star point image is an ellipse, and the method can not be applied.
Disclosure of Invention
The invention provides a method for blind recovery of star maps of elliptic arc trajectories, which aims to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for blindly restoring a star map aiming at an elliptic arc track comprises the following steps:
s1: carrying out ellipse fitting on the elliptical arc track of the star points;
s2: carrying out projection transformation-based transformation of an elliptical arc track and an arc track;
s3: performing circular arc track and straight-line segment track transformation based on polar coordinate transformation;
s4: carrying out straight-line segment track restoration based on blind restoration of the motion blurred image;
s5: and carrying out coordinate inverse transformation and projective inverse transformation to obtain a final restoration result of the star map with the original track being the elliptic arc track.
Further, the step S1 specifically includes: s101: expressing the elliptic arc track by a general expression, and defining a target function as an algebraic distance from a coordinate point to the elliptic arc track; s102: collecting pixel coordinates on the track; s103: substituting the coordinate values, simplifying the ellipse fitting problem into a problem which can be solved by using a least square method, and solving a general expression of the elliptic arc track.
Further, the specific content of S2 is: s201: projecting the elliptic arc track on the image plane on a plane taking the composite angular velocity as a normal vector, wherein the projection track is changed into an arc track with the eccentricity of 0; meanwhile, the tracks of other fixed stars at different positions on the projection plane are changed into circular arc tracks with eccentricity of 0; s202: collecting coordinates of four groups of corresponding points on any elliptic arc track of the image plane and the circular arc track of the projection plane corresponding to the elliptic arc track; s203: and substituting the coordinate values, and solving a projective transformation matrix from the image plane to the projection plane through least square estimation and singular value decomposition to realize the transformation from the elliptic arc track to the circular arc track.
Further, the specific content of S3 is: s301: selecting an optimal polar coordinate transformation rotation angle quantization unit; s302, the circular arc track in the rectangular coordinate system is converted into a straight-line track in the polar coordinate system through polar coordinate conversion, the problem of light spot deformation in the polar coordinate inverse conversion process is effectively solved, and the recovery precision is guaranteed.
Further, the specific content of S4 is: s401: for the converted straight-line segment star locus, the corresponding motion blur angle is 0, so that only the motion length needs to be detected; extracting light bars by adopting a classic Steger algorithm to further obtain the motion blur length; s402: generating a fuzzy kernel function based on the angle and length information of the motion blur; s403: and restoring the straight-line segment track under the polar coordinate system by adopting a Lucy-Richardson algorithm.
Further, the specific content of S5 is: s501: through polar coordinate inverse transformation, the image pixel information is inversely transformed from the polar coordinate to a rectangular coordinate corresponding to a plane taking a rotating shaft as a normal vector; s502: and performing inverse projective transformation again to transform the rectangular coordinates corresponding to the projection plane to the rectangular coordinates corresponding to the image plane, wherein the corresponding transformation matrix is the inverse matrix of the transformation matrix from the image plane to the projection plane, so as to obtain the final recovery result of the star map with the original track being the elliptic arc track.
The invention has the following advantages:
compared with the prior art, the method has the following beneficial effects:
1. the elliptic arc track is converted into the circular arc track through projective transformation, the circular arc track is converted into the straight-line track through polar coordinate transformation, and then star map restoration of the elliptic arc track is realized through straight-line restoration and coordinate inverse transformation.
2. The invention solves the problem of spot deformation after recovery and ensures the recovery precision by selecting the optimal polar coordinate transformation quantization unit.
3. The provided method is verified and tested through simulation and experiments, and experimental results show that the method is effective, can carry out blind restoration on the star map of the elliptical track, and has the same precision as the existing star map restoration method aiming at the straight-line track.
Drawings
Fig. 1 is a flow chart of a star map blind restoration algorithm of an elliptic arc locus.
Fig. 2 is a schematic diagram of the projection of the star point locus onto a plane with the rotation axis being a normal vector.
Fig. 3 is a schematic diagram of transformation of a rectangular coordinate system to a polar coordinate system.
Fig. 4 is a schematic diagram of a spot after polar coordinate transformation based on a conventional quantization unit.
Fig. 5 is a schematic diagram of a spot after polar coordinate transformation based on an optimal quantization unit.
FIG. 6 is a diagram showing simulation and experimental results after image processing in the steps of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
A method for blind restoration of a star atlas for an elliptic arc trajectory, as shown in fig. 1, comprises the following steps:
s1: carrying out ellipse fitting on the elliptical arc track of the star points;
s2: carrying out projection transformation-based transformation of an elliptical arc track and an arc track;
s3: performing circular arc track and straight-line segment track transformation based on polar coordinate transformation;
s4: carrying out straightness track restoration based on blind restoration of the motion blurred image;
s5: and carrying out coordinate inverse transformation to obtain a final restoration result of the star map with the original track being the elliptic arc track.
Further, the step S1 specifically includes: s101: the elliptic arc trajectory is expressed by a general formula as shown in formula (1):
AX 2 +BXY+CY 2 +DX+EY+F＝0 (1)
in the process of ellipse fitting, the objective function may be defined as the algebraic distance from the input coordinate point to the elliptic arc trajectory, as shown in equation (2):
F(x i ，y i )＝Ax i 2 +Bx i y i +Cy i 2 +Dx i +Ey i +F＝0 (2)
define vector M = [ A, B, C, D, E, F] T ，X＝[x i 2 ，x i y i ，y i 2 ，x i ，y i ，1] T Then the objective function can be written as equation (3):
F(X i )＝X i *M＝0 (3)
s102: collecting pixel coordinates on the track;
s103: substituting the coordinate values to simplify the ellipse fitting problem into a problem which can be solved by using a least square method as shown in formula (4),
and solving a general expression of the elliptic arc locus.
Further, the specific content of S2 is: s201: as shown in fig. 2, the elliptical arc trajectory on the image plane is projected on a plane with the composite angular velocity thereof as a normal vector, and the projected trajectory is changed into an arc trajectory with an eccentricity of 0; meanwhile, the tracks of other fixed stars at different positions on the projection plane are changed into circular arc tracks with eccentricity of 0;
s202: the transformation matrix from the rectangular coordinate system of the image plane to the projected pi-plane with the rotation axis as the normal vector can be represented by a projective transformation matrix H containing 9 parameters, and the relationship between the point on the image plane and the point on the projection plane can be represented by the following formula (5):
wherein the content of the first and second substances,
due to the last row of H [ H ] 31 H 32 H 33 ]And
the multiplication result is 1, an additional conditional constraint equation can be obtained, so that the degree of freedom of the projective transformation parameter matrix is 8, and the matrix can be obtained by collecting coordinates of four groups of corresponding points on any elliptic arc track of the image plane and an arc track of a pi plane corresponding to the elliptic arc track and substituting the coordinates for solving; to improve the accuracy, four sets of corresponding points are preferentially selected on the trajectory of the image plane farther from the center of the image, such as l in fig. 2 3 . Meanwhile, for the accuracy of calculation, special four-point substitution on the elliptical locus of the image plane is preferably selected for solving, for example, l in fig. 2 3 The intersection point of the rotation axis and the image plane is recorded as M, A and C are the track l 3 The intersection point of the ellipse and the major axis thereof; b and D are the line segment passing through M and perpendicular to the long axis of the ellipse and l 3 The intersection of the ellipses. And then, obtaining points A ', B', C 'and D' on the pi plane corresponding to the points A, B, C and D on the image plane according to the projective geometric relation of the star vector.
Substituting four sets of coordinate values, an equation of the form Ah =0 is set up as shown in formula (6):
wherein, the first and the second end of the pipe are connected with each other,
s203: and substituting the coordinate values, and solving a column vector solution H through least square estimation and singular value decomposition, thereby obtaining a projective transformation matrix H for transforming the elliptic arc track into the circular arc track, and realizing the transformation from the elliptic arc track to the circular arc track.
Further, the specific content of S3 is: s301: the abscissa of the polar coordinate system is a rotation angle theta, and the ordinate is a rotation radius r; if the coordinate transformation is performed according to the conventional quantization unit (i.e. the rotation angle is quantized according to 1 °, and the rotation radius is quantized according to the length corresponding to 1 pixel), when the restored light spot is transformed to the rectangular coordinate system, the light spot has obvious tangential stretching deformation, as shown in fig. 3. The reason for this phenomenon is that the spot size after the straight-line trajectory in the polar coordinate system is restored exists, and the transverse width of the spot size represents the rotation angle size. When the quantization unit of the abscissa in the polar coordinate system is larger, the transverse width of the recovered light spot is larger. The larger the transverse width of the recovered light spot is, the longer the arc is formed when the light spot is inversely transformed to a rectangular coordinate system, and the more the difference between the stretching length of the arc and the radial vectorization stretching length is, the more obvious the light spot deformation is. Therefore, the optimal rotation angle quantization unit corresponding to the rotation radius quantization unit is calculated according to the rotation radius quantization unit, so that the problem of light spot deformation in the polar coordinate inverse transformation process is effectively solved, and the restoration precision is ensured.
The invention selects the quantization unit of the rotation radius as 1 pixel and the quantization unit of the rotation angle as delta theta opt . The recovered light spot width under a polar coordinate system is W r Length L of θ The length L of θ Corresponding to N rotation angle quantization units. Under the rectangular coordinate system, the radius r of the light spot is different, the corresponding optimal rotation angle quantization value is different, so that the radius of the selected light spot is half of the rotation radius of the polar coordinate, namely the length value of the image sensor is 1/4, and the corresponding optimal rotation is realizedThe rotation angle quantization unit is used as the optimal rotation quantization unit of the whole transformation, so that the optimal rotation angle quantization unit value delta theta is obtained according to the formula (7) opt 。
In the embodiment of the invention, the width W of the recovered light spot r For 3 pixels, the spot length is 4 quantization units, so N is taken to be 4. The star sensor pixel array in the embodiment of the invention is 2048 × 2048 pixels, so r is 512 pixels. Accordingly, the optimal rotation angle quantization unit determined by the embodiment of the present invention is about 0.1 °.
S302: according to the optimal quantization unit, mapping the pixel value corresponding to the rectangular coordinate in the image to the pixel value corresponding to the polar coordinate, and transforming the circular arc track in the rectangular coordinate system into the straight-line track in the polar coordinate system by the following transformation formula (8):
fig. 5 is a schematic diagram of the light spot after inverse polar coordinate transformation according to the optimal quantization unit, and it can be seen from comparison with fig. 4 that the problem of light spot deformation is significantly improved.
Further, the specific content of S4 is: s401: the motion blur angle corresponding to the converted straight-line segment locus is 0, so that the motion length only needs to be detected; extracting light bars by adopting a classic Steger algorithm to further obtain the motion blur length;
s402: for the blur caused by uniform linear motion, the blur kernel function is shown as the following formula (9):
in the formula, theta is a motion fuzzy angle and represents an included angle between a motion direction and the positive direction of a horizontal shaft; l is a motion blur metric representing the distance a pixel moves in the direction of motion; thus, based on the angle and length information of the motion blur, a blur kernel function is generated;
s403: substituting the fuzzy kernel function into equation (10) using the Lucy-Richardson algorithm:
therefore, the recovery of the straight-line segment track under the polar coordinate system is realized.
Further, the specific content of S5 is: s501: through polar coordinate inverse transformation, the image pixel information is inversely transformed from the polar coordinate to a rectangular coordinate corresponding to a plane taking a rotating shaft as a normal vector; under polar coordinates, each pixel contains three pieces of information: an abscissa rotation angle value theta, an ordinate rotation radius value rho and a corresponding pixel gray value G (theta, rho); therefore, it is necessary to inversely transform the information back to the rectangular coordinate system, and the inverse transformation formula is as follows (11):
s502: after the polar coordinate inverse transformation is finished, performing projective inverse transformation again to transform the rectangular coordinate corresponding to the projection plane to the rectangular coordinate corresponding to the image plane, wherein the corresponding transformation matrix is the inverse matrix of the transformation matrix from the image plane to the projection plane; and obtaining the final recovery result of the star map with the original track being the elliptic arc track after all the transformations are completed.
FIG. 6 is an experimental result of each step of the invention, and an implementation result shows that the invention can effectively restore the star map of the elliptic arc track, the restoration precision is about 0.2pixel, and is equivalent to the restoration precision of the star map of the existing straight-line track.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the protection of the present invention by equivalent or modified technical solutions and their inventive concepts within the technical scope of the present invention.
Claims (11)
1. A star map blind restoration method for an elliptic arc track is characterized by comprising the following steps:
s1: carrying out ellipse fitting on the elliptical arc track of the star points;
s2: carrying out projection transformation-based transformation of an elliptical arc track and an arc track;
s3: carrying out circular arc track and straight-line segment track transformation based on polar coordinate transformation;
s4: carrying out straight-line segment track restoration based on blind restoration of the motion blurred image;
s5: and carrying out coordinate inverse transformation and projective inverse transformation to obtain a final restoration result of the star map with the original track being the elliptic arc track.
2. The method for blind restoration of a star atlas aiming at an elliptic arc trajectory as claimed in claim 1, wherein the step of S1 specifically comprises:
s101: expressing the elliptic arc track by a general expression, and defining a target function as an algebraic distance from a coordinate point to the elliptic arc track;
s102: collecting pixel coordinates on the track;
s103: substituting the coordinate values, and simplifying the ellipse fitting problem into a problem which can be solved by using a least square method, thereby solving a general expression of the elliptic arc track.
3. The method for blind restoration of a star atlas of an elliptic arc trajectory according to claim 1, wherein the specific contents of S2 are:
s201: projecting the elliptic arc track on the image plane on a plane with the composite angular velocity as a normal vector, wherein the projection track is changed into an arc track with the eccentricity of 0; meanwhile, the tracks of other fixed stars at different positions on the projection plane are changed into circular arc tracks with eccentricity of 0;
s202: collecting coordinates of four groups of corresponding points on any elliptical arc track of the image plane and the arc track of the projection plane corresponding to the elliptical arc track;
s203: and substituting the coordinate values, and solving a projective transformation matrix from the image plane to the projection plane through least square estimation and singular value decomposition to realize the transformation from the elliptic arc track to the circular arc track.
4. The method for blind restoration of a star atlas aiming at an elliptic arc trajectory, according to claim 1, wherein the specific contents of S3 are:
s301: the optimal polar coordinate transformation quantization unit is determined, the problem of spot deformation in the polar coordinate inverse transformation process is effectively solved, and the restoration precision is ensured;
s302: and transforming the circular arc track in the rectangular coordinate system into a straight-line track in the polar coordinate system through polar coordinate transformation.
5. The method for blind restoration of a star atlas aiming at an elliptic arc trajectory, according to claim 1, wherein the specific contents of S4 are:
s401: for the converted straight-line segment star locus, the corresponding motion blur angle is 0, so that the motion length only needs to be detected; extracting light bars by adopting a classic Steger algorithm to further obtain the motion blur length;
s402: generating a fuzzy kernel function based on the angle and length information of the motion blur;
s403: and restoring the straight-line segment track under the polar coordinate system by adopting a Lucy-Richardson algorithm.
6. The method for blind restoration of a star atlas of an elliptic arc trajectory according to claim 1, wherein the specific contents of S5 are:
s501: through polar coordinate inverse transformation, the image pixel information is inversely transformed from the polar coordinate to a rectangular coordinate corresponding to a projection plane taking a rotating shaft as a normal vector;
s502: and performing inverse projective transformation again to transform the rectangular coordinates corresponding to the projection plane to the rectangular coordinates corresponding to the image plane, wherein the corresponding transformation matrix is the inverse matrix of the transformation matrix from the image plane to the projection plane, so as to obtain the final recovery result of the star map with the original track being the elliptic arc track.
7. The method for blind star atlas recovery of the elliptic arc trajectory in accordance with claim 2, wherein the elliptic arc trajectory is expressed by a general formula, such as formula (1):
AX 2 +BXY+CY 2 +DX+EY+F＝0 (1)
in the process of ellipse fitting, the objective function can be defined as the algebraic distance from the input coordinate point to the elliptic arc trajectory, as shown in equation (2):
F(x i ，y i )＝Ax i 2 +Bx i y i +Cy i 2 +Dx i +Ey i +F＝0 (2)
define vector M = [ A, B, C, D, E, F] T ，X＝[x i 2 ，x i y i ，y i 2 ，x i ，y i ，1] T Then the objective function can be written as equation (3):
F(X i )＝X i *M＝0 (3)
s102: collecting pixel coordinates on the track;
s103: substituting the coordinate values to simplify the ellipse fitting problem into a problem which can be solved by using a least square method as shown in formula (4),
and solving a general expression of the elliptic arc locus.
8. A method for blind restoration of a star map for an elliptic arc trajectory as claimed in claim 3, characterized by:
s202: the transformation matrix from the rectangular coordinate system of the image plane to the projected pi-plane with the rotation axis as the normal vector can be represented by a projective transformation matrix H containing 9 parameters, and the relationship between the point on the image plane and the point on the projection plane can be represented by the following formula (5):
wherein, the first and the second end of the pipe are connected with each other,
due to the last row of H [ H ] 31 H 32 H 33 ]And
the multiplication result is 1, an additional conditional constraint equation can be obtained, so that the degree of freedom of the projective transformation parameter matrix H is 8, and the matrix can be obtained by acquiring coordinates of four groups of corresponding points on any elliptic arc track of the image plane and an arc track of a pi plane corresponding to the elliptic arc track and substituting the coordinates for solving;
substituting four sets of coordinate values, an equation of the form Ah =0 is listed as shown in formula (6):
wherein the content of the first and second substances,
s203: and substituting the coordinate values, solving a column vector solution H through least square estimation and singular value decomposition, thereby obtaining a projective transformation matrix H for transforming the elliptical arc track into the circular arc track, and realizing the transformation from the elliptical arc track to the circular arc track.
9. The method for blind restoration of a star map for an elliptic arc trajectory according to claim 4, characterized by:
s301: the abscissa of the polar coordinate system isRotating the angle theta, wherein the ordinate is the rotating radius r; selecting the quantization unit of the rotation radius as 1 pixel, and calculating the optimal quantization unit of the rotation angle as delta theta according to the formula (7) opt ；
In the formula, W r And L θ Respectively the width and length of the recovered light spot in a polar coordinate system, W r Typically 3 to 5 pixels, length L θ Corresponding to N rotation angle quantization units, and when the Lucy-Richardson recovery algorithm is based, N is 4; r is the length value of 1/4 of the image sensor;
s302: according to the optimal quantization unit, mapping the pixel value corresponding to the rectangular coordinate in the image to the pixel value corresponding to the polar coordinate, and transforming the circular arc trajectory in the rectangular coordinate system into the straight-line trajectory in the polar coordinate system by the following formula (8):
10. the method for blind restoration of a star map for an elliptic arc trajectory according to claim 5, characterized by:
s402: for the blur caused by uniform linear motion, the blur kernel function is shown as the following formula (9):
in the formula, theta is a motion fuzzy angle and represents an included angle between a motion direction and the positive direction of a horizontal shaft; l is a motion blur metric representing the distance a pixel moves in the direction of motion; thus, based on the angle and length information of the motion blur, a blur kernel function is generated;
s403: substituting the fuzzy kernel function into equation (10) using the Lucy-Richardson algorithm:
therefore, the recovery of the straight-line segment track under the polar coordinate system is realized.
11. The method for blind restoration of a star map for an elliptic arc trajectory according to claim 6, characterized by:
s501: through polar coordinate inverse transformation, the image pixel information is inversely transformed from the polar coordinate to a rectangular coordinate corresponding to a plane taking a rotating shaft as a normal vector; under polar coordinates, each pixel contains three pieces of information: an abscissa rotation angle value theta, an ordinate rotation radius value rho and a corresponding pixel gray value G (theta, rho); therefore, it is necessary to inversely transform the information back to the rectangular coordinate system, and the inverse transformation formula is as follows (11):
s502: after the polar coordinate inverse transformation is finished, performing projective inverse transformation again to transform the rectangular coordinate corresponding to the projection plane to the rectangular coordinate corresponding to the image plane, wherein the corresponding transformation matrix is the inverse matrix of the transformation matrix from the image plane to the projection plane; and obtaining the final recovery result of the star map with the original track being the elliptic arc track after all the transformations are completed.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117078803A (en) * | 2023-10-16 | 2023-11-17 | 北京龙德缘电力科技发展有限公司 | SVG-based primary graph quick drawing method |
| CN117078803B (en) * | 2023-10-16 | 2024-01-19 | 北京龙德缘电力科技发展有限公司 | SVG-based primary graph quick drawing method |
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