Portable multidirectional target and method for three-dimensional laser scanning of long and large tunnel

Abstract

The invention belongs to the technical field of engineering three-dimensional laser scanning, and particularly relates to a portable multidirectional target and method for three-dimensional laser scanning of a long tunnel. A portable multidirectional target for three-dimensional laser scanning of a long tunnel comprises a base and a reflecting panel, a limiting ring is detachably connected to the upper portion of the base, the reflecting panel is rotatably connected with the limiting ring and comprises a reflecting panel front face and a reflecting panel back face, a prism is arranged in the middle of the reflecting panel back face, and the reflecting panel front face and the reflecting panel back face are connected with the limiting ring. The reflection panel front face and the reflection panel back face are coated with black and white. According to the invention, a'scanning-prism 'double-sided measurement mode is adopted by the reflection panel, so that the problem of conflict between target scanning identification distance limitation and coordinate measurement is effectively solved, the functionality of the target is enhanced, and accurate measurement by adopting a total station and a known coordinate control point under a long distance is further realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering three-dimensional laser scanning, and in particular relates to a portable multi-directional target and method for three-dimensional laser scanning of long tunnels. Background Art

[0002] 3D laser scanning technology, a revolutionary breakthrough in surveying and mapping, uses active laser ranging to acquire high-density point cloud data. Compared to traditional surveying methods, it boasts high environmental adaptability, high efficiency, large data volumes, and strong spatial analysis capabilities. 3D laser scanning of long and large tunnels primarily uses densely scanned point cloud data to create a rubbing of the tunnel's existing state. This point cloud data is then used for calculation and analysis to identify structural dimensions, defects, and other issues within the tunnel, enabling monitoring and inspection during construction and after completion. Determining the absolute coordinates of the point cloud is the foundation for this calculation and analysis.

[0003] The current point cloud absolute coordinate solution technology based on targets and total stations has multiple bottlenecks: first, the precise arrangement of targets often requires the centering and leveling of the measuring tripod, which greatly reduces the data collection efficiency in the stand-type scanning mode; second, when using the total station's prism-free coordinate measurement mode, it is easily affected by the incident angle and requires auxiliary measurement methods, resulting in reduced operating efficiency; third, due to the limited target scanning recognition distance and the limitations of on-site coordinate control point layout, the error increases when using coordinate transfer to measure targets, and the inertial navigation-assisted orientation technology of three-dimensional laser scanners has cumulative error problems in long-distance applications, resulting in staggered layers and joints in the collected point cloud data after splicing; fourth, when performing absolute coordinate solution for long tunnel point clouds, the absolute coordinate solution is not accurate enough and the residual value is large because the measured target coordinates are not adjusted during coordinate parameter conversion. Summary of the Invention

[0004] In response to the above problems, the purpose of the present invention is to provide a portable multi-directional target and method for three-dimensional laser scanning of long tunnels, to solve the conflict problem in the prior art between the target scanning and identification distance limit and the distance of the existing coordinate control points on site, to eliminate the phenomenon of no adjustment and large residual in the existing absolute coordinate solution, to achieve accurate target identification at a limited distance and improve the absolute measurement accuracy of the target, and to have an adjustment function when converting known coordinate parameters.

[0005] The technical solution of the present invention is: a portable multi-directional target for three-dimensional laser scanning of long tunnels, including a base and a reflective panel, a restriction ring is detachably connected to the top of the base, the reflective panel is rotatably connected to the restriction ring, the reflective panel includes a front surface of the reflective panel and a back surface of the reflective panel, a prism is provided in the middle of the back surface of the reflective panel, and the front and back surfaces of the reflective panel are painted black and white.

[0006] A connecting rod is fixedly connected to the upper part of the base, a connecting sleeve is provided below the limiting ring, the connecting sleeve is sleeved with the connecting rod, and a locking button is provided on the connecting sleeve.

[0007] The two ends of the reflective panel are respectively provided with reflective panel rotating columns, the outer side of the reflective panel rotating columns is provided with a rubber ring, the reflective panel rotating columns and the limiting ring are respectively provided with rubber ring rotating grooves, and the reflective panel rotating columns and the limiting ring are rotatably connected.

[0008] The base is a magnetic base, the base shell is made of metal, and a fixed tripod or a fixed magnet is provided under the base, and the fixed magnet is made of rubidium magnet.

[0009] The base is a tripod with a connecting rod.

[0010] A method for three-dimensional laser scanning of a long tunnel, using the portable multi-directional target for three-dimensional laser scanning of a long tunnel as described above, comprises the following steps: S1: Press the locking button, insert the fixed connecting rod in the base into the connecting sleeve at the lower end of the reflective panel, and release the locking button; S2: During the tunnel 3D laser scanning process, after the 3D laser scanner is set up, the target is flexibly placed according to the scanning recognition limit distance, and the target is adsorbed to a stable position such as the tunnel track or the transport belt diagonal support through a magnetic base, and the stability is observed; S3: After setting up the total station at a known control point that satisfies line of sight, rotate the limiting ring and reflective panel according to the position of the total station, and point the prism on the back of the reflective panel toward the total station to complete the target coordinate measurement; S4: Rotate the limiting ring and the reflective panel according to the scanning angle, and turn the reflective panel toward the 3D laser scanner to complete the 3D laser point cloud data acquisition; S5: Rotate the limiting ring and the reflective panel according to the position of the total station, and turn the prism on the back of the reflective panel toward the total station to complete the target coordinate verification; S6: Calculate the absolute coordinates of the point cloud. If the error between the two target coordinate measurements is less than the nominal accuracy of the 3D laser scanner, the target position is considered correct. S7: After the 3D laser scanning of this station is completed, press the locking button and separate the base. After storage is completed, proceed to the next 3D laser scanning operation.

[0011] The absolute coordinate solution of the point cloud in step S4 includes the following steps: S41. Calculation and measurement of the center coordinates of the reflective panel, specifically including: S411, the total station measures the collimation prism to perform absolute coordinate measurement, and the absolute coordinate of the prism center point a is obtained; S412. It is known that the nominal distance between the center point a of the prism and the center point b of the reflective panel is L ab , the prism constant of the prism is P , then enter the correction value in the total station when performing absolute measurement of the target P 'Replace the original prism constant value, P 'for P '= P + L ab ; S413, operate the total station to perform coordinate measurement according to the conventional measurement method, and the coordinate value returned at this time is the absolute coordinate of the center point b of the reflection panel; S42, 3D laser scanning point cloud absolute coordinate solution, using 3 or more sets of coordinates to perform 3D laser scanning point cloud absolute coordinate solution, specifically including: S421. Use the total station to measure the absolute coordinates of the prisms at different positions and obtain the absolute coordinates of at least three or more center points b of the reflective panels, which are set as b 1. b 2. b 3; S422, 3D laser scanning point cloud is spliced by pairing target balls between adjacent stations. The corresponding coordinates of 3 or more point cloud space coordinate systems in the spliced point cloud data are set as B 1. B 2. B 3; S423, the positions of the above three groups of corresponding points are the same, that is, b 1- B 1 is the same position point, b 2- B 2 is the same position point, b 3- B 3 represents the same position point. At this time, there is a rigid body transformation relationship between the spaces where the three groups of points are located. The absolute coordinates of the point cloud are solved using Euler transformation.

[0012] Use Euler transformation to solve the absolute coordinates of point cloud. The specific process is as follows: S4231. Assume that the spatial coordinate vector of a point in the point cloud coordinate system is a =[ x 1, y 1, z 1] T , the spatial unit orthogonal basis is e =( e 1, e 2, e 3), the spatial coordinates in the absolute space coordinate system are a '=[ x 1',y 1', z 1'] T ， Assume that the space unit orthogonal basis e After one rotation, it changes to e' =( e 1', e 2', e 3'), since its actual space vector itself does not change, the equation can be obtained according to the coordinate definition: (1) (2) (3) Where, A is an orthogonal matrix, the matrix A It is composed of the inner product of two sets of unit orthogonal bases, which expresses the rotation relationship of the coordinate system of the same vector before and after rotation. R for ; S4232, after the rotation transformation is completed, the translation amount t Perform translation transformation and obtain the following formula according to the coordinate definition: (4) S4233. Combining the above rotation and translation transformations, the spatial coordinate changes are: (5) S4234, use homogeneous coordinates to convert the original n dimensional coordinates n +1 dimensional representation, the above formula can be converted to homogeneous coordinates as follows: (6) (7) S4235, The spatial coordinate system transformation matrix calculated for at least three sets of corresponding points with known point cloud coordinates and absolute coordinates.

[0013] The technical effects of the present invention are: 1. The base of the present invention effectively solves the limitations of target installation by adopting two methods of adaptive magnetic attraction and tripod, thereby realizing arbitrary position fixation through the magnetic attraction base, and precise installation by measuring the known point position of the tripod; 2. The present invention adopts the "scanning-prism" double-sided measurement method, which effectively solves the conflict problem between the target scanning and recognition distance limitation and coordinate measurement, enhances the functionality of the target, and realizes precise measurement of the total station and known coordinate control points at long distances; 3. The present invention adopts the prism constant method to calculate the coordinates of the center point of the black and white reflective panel of the target, effectively solving the conversion problem between the absolute measurement coordinates and the target center point coordinates, thereby realizing simple calculation of the target center point coordinates; 4. The present invention adopts the Euclidean transformation method to effectively solve the problem of absolute coordinate solution of three-dimensional laser scanning point clouds of long tunnels, thereby realizing residual control during absolute coordinate solution.

[0014] The following is a further description with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The diagram is a front structural diagram of a portable multi-directional target for three-dimensional laser scanning of long tunnels according to the present invention.

[0016] Figure 2 The diagram is a schematic diagram of the reverse structure of a portable multi-directional target for three-dimensional laser scanning of long tunnels according to the present invention.

[0017] Figure 3 It is a structural schematic diagram of the base of the present invention.

[0018] Figure 4 It is a structural schematic diagram of the reflective panel of the present invention.

[0019] Figure 5 It is a schematic diagram of the measurement and calculation of the center coordinates of the reflective panel of the present invention.

[0020] Figure 6 This is a flow chart of the use of the portable multi-directional target of the present invention.

[0021] Figure 7 This is a flow chart of the point cloud absolute coordinate solution method of the present invention.

[0022] Figure markings: 1-base, 2-reflection panel, 3-prism, 4-limiting ring, 5-connecting rod, 6-connecting sleeve, 7-locking button, 8-reflection panel rotation column, 9-rubber ring, 21-front side of reflection panel, 22-back side of reflection panel. DETAILED DESCRIPTION Example 1

[0023] like Figures 1 to 4As shown, a portable multi-directional target for three-dimensional laser scanning of long tunnels includes a base 1 and a reflective panel 2. A limiting ring 4 is detachably connected to the top of the base. The reflective panel 2 is rotatably connected to the limiting ring 4. The reflective panel 2 includes a reflective panel front surface 21 and a reflective panel back surface 22. A prism 3 is provided in the middle of the reflective panel back surface 22. The reflective panel front surface 21 and the reflective panel back surface 22 are painted in black and white.

[0024] The present invention adopts a "scanning-prism" double-sided measurement method through a reflective panel, which effectively solves the conflict between the target scanning and recognition distance limitation and coordinate measurement, enhances the functionality of the target, and further realizes accurate measurement over long distances using a total station and known coordinate control points. Example 2

[0025] On the basis of Example 1, in this embodiment, preferably, a connecting rod 5 is fixedly connected to the top of the base 1, a connecting sleeve 6 is provided below the limiting ring 4, the connecting sleeve 6 is sleeved with the connecting rod 5, and a locking button 7 is provided on the connecting sleeve 6.

[0026] The connecting sleeve 6 of the present invention is sleeved with the connecting rod 5. The connecting sleeve 6 is provided with a locking button 7, which can quickly achieve a fixed connection of the reflective panel 2. At the same time, the connecting sleeve 6 can rotate 360° in the horizontal direction on the connecting rod 5, which is convenient for adjusting the position of the reflective panel 2. Example 3

[0027] Based on Example 1 or Example 2, in this embodiment, preferably, a reflection panel rotating column 8 is respectively provided at both ends of the reflection panel 2, a rubber ring 9 is provided on the outside of the reflection panel rotating column 8, and rubber ring rotation grooves are respectively provided on the reflection panel rotating column 8 and the restriction ring 4, and the reflection panel rotating column 8 is rotatably connected to the restriction ring 4.

[0028] The reflective panel 2 described in the present invention is respectively provided with a reflective panel rotating column 8 at both ends, and a rubber ring 9 is provided on the outside of the reflective panel rotating column 8. The reflective panel rotating column 8 and the limiting ring 4 are respectively provided with a rubber ring rotation groove. The reflective panel rotating column 8 and the limiting ring 4 are rotatably connected. The reflective panel can rotate 360° in the vertical direction around the limiting ring, adapting to the environment to meet scanning and coordinate measurement in any direction. Example 4

[0029] On the basis of Example 1 or Example 3, in this embodiment, preferably, the base 1 is a magnetic base, the base shell is made of metal, a fixed magnet is provided under the base 1, and the fixed magnet is made of rubidium magnet.

[0030] The base 1 described in the present invention is a magnetic base, the base shell is made of metal, a fixed magnet is provided under the base 1, and the fixed magnet is made of rubidium magnet. The base adopts an adaptive magnetic method to effectively solve the limitations of target installation, thereby realizing fixation at any position through the magnetic base. Example 5

[0031] On the basis of Example 1 or Example 3, in this embodiment, preferably, the base 1 is a tripod with a connecting rod.

[0032] The base 1 of the present invention is a tripod with a connecting rod, and can be accurately set up by measuring the position of known points on the tripod. Example 6

[0033] like Figure 6 As shown, a method for three-dimensional laser scanning of a long tunnel, using the portable multi-directional target for three-dimensional laser scanning of a long tunnel as described above, comprises the following steps: S1: Press the locking button 7, insert the fixed connecting rod 5 in the base 1 into the connecting sleeve 6 at the lower end of the reflective panel 2, and release the locking button 7; S2: During the 3D laser scanning process in the tunnel, after the 3D laser scanner is set up, the target is flexibly placed according to the scanning recognition limit distance, and is adsorbed on a stable position such as the tunnel track or the transport belt diagonal support by the magnetic base 1, and the stability is observed; S3: After setting up the total station at a known control point that satisfies line of sight, rotate the limiting ring 4 and the reflective panel 2 according to the position of the total station, and turn the prism 3 on the back of the reflective panel 2 toward the total station to complete the target coordinate measurement; S4: Rotate the limiting ring 4 and the reflective panel 2 according to the scanning angle, and turn the reflective panel 2 toward the 3D laser scanner to complete the 3D laser point cloud data acquisition; S5: Rotate the limiting ring 4 and the reflective panel 2 according to the position of the total station, and turn the prism 3 on the back of the reflective panel 2 toward the total station to complete the target coordinate verification; S6: Calculate the absolute coordinates of the point cloud. If the error between the two target coordinate measurements is less than the nominal accuracy of the 3D laser scanner, the target position is considered correct. S7: After the three-dimensional laser scanning of this station is completed, the locking button 7 is pressed and the base 1 is separated. After the storage is completed, the next three-dimensional laser scanning operation is carried out.

[0034] like Figure 5 、 Figure 7 As shown, the absolute coordinate solution of the point cloud in step S4 includes the following steps: S41. Calculation and measurement of the center coordinates of the reflective panel, specifically including: S411: The total station measures and sights the prism 3 to perform absolute coordinate measurement, and the absolute coordinates of the prism center point a are obtained. S412. It is known that the nominal distance between the center point a of the prism and the center point b of the reflective panel 2 is L ab , the prism constant of prism 3 is P , then enter the correction value in the total station when performing absolute measurement of the target P 'Replace the original prism constant value, P 'for P '= P +L ab ; S413, operate the total station to perform coordinate measurement according to the conventional measurement method, and the coordinate value returned at this time is the absolute coordinate of the center point b of the reflection panel 2; S42, 3D laser scanning point cloud absolute coordinate solution, using 3 or more sets of coordinates to perform 3D laser scanning point cloud absolute coordinate solution, specifically including: S421, the total station is used to measure the absolute coordinates of the prisms 3 at different positions, and the absolute coordinates of at least three or more center points b of the reflective panel 2 are obtained, which are set as b 1. b 2. b 3; S422, 3D laser scanning point cloud is spliced by pairing target balls between adjacent stations. The corresponding coordinates of 3 or more point cloud space coordinate systems in the spliced point cloud data are set as B 1. B 2. B 3; S423, the positions of the above three groups of corresponding points are the same, that is, b 1- B 1 is the same position point, b 2- B 2 is the same position point, b 3- B 3 represents the same position point. At this time, there is a rigid body transformation relationship between the spaces where the three groups of points are located. The absolute coordinates of the point cloud are solved using Euler transformation.

[0035] The present invention adopts the prism constant method to calculate the coordinates of the center point of the target black and white reflective panel, which effectively solves the conversion problem between the absolute measurement coordinates and the target center point coordinates, and thus realizes the simple calculation of the target center point coordinates.

[0036] Use Euler transformation to solve the absolute coordinates of point cloud. The specific process is as follows: S4231. Assume that the spatial coordinate vector of a point in the point cloud coordinate system is a =[ x 1, y 1,z 1] T , the spatial unit orthogonal basis is e =( e 1, e 2, e 3), the spatial coordinates in the absolute space coordinate system are a '=[ x 1', y 1', z 1'] T ， Assume that the space unit orthogonal basis e After one rotation, it changes to e' =( e 1', e 2', e 3'), since its actual space vector itself does not change, the equation can be obtained according to the coordinate definition: (1) (2) (3)

[0037] Where, A is an orthogonal matrix, the matrix A It is composed of the inner product of two sets of unit orthogonal bases, which expresses the rotation relationship of the coordinate system of the same vector before and after rotation. R for ; S4232, after the rotation transformation is completed, the translation amount t Perform translation transformation and obtain the following formula according to the coordinate definition: (4) S4233. Combining the above rotation and translation transformations, the spatial coordinate changes are: (5) S4234, using homogeneous coordinates to n dimensional coordinates n +1 dimensional representation, the above formula can be converted to homogeneous coordinates as follows: (6) (7) S4235, The spatial coordinate system transformation matrix calculated for at least three sets of corresponding points with known point cloud coordinates and absolute coordinates.

[0038] The present invention adopts the Euclidean transformation method to effectively solve the problem of absolute coordinate solution of three-dimensional laser scanning point cloud in long tunnels, thereby realizing residual control during absolute coordinate solution.

[0039] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A portable multi-directional target for three-dimensional laser scanning of long tunnels, characterized by: The invention comprises a base (1) and a reflective panel (2); a restriction ring (4) is detachably connected to the top of the base; the reflective panel (2) and the restriction ring (4) are rotatably connected; the reflective panel (2) comprises a reflective panel front surface (21) and a reflective panel back surface (22); a prism (3) is provided in the middle of the reflective panel back surface (22); and both the reflective panel front surface (21) and the reflective panel back surface (22) are painted in black and white.

2. The portable multi-directional target for three-dimensional laser scanning of long tunnels according to claim 1, characterized in that: A connecting rod (5) is fixedly connected to the top of the base (1), a connecting sleeve (6) is provided below the limiting ring (4), the connecting sleeve (6) is sleeved with the connecting rod (5), and a locking button (7) is provided on the connecting sleeve (6).

3. The portable multi-directional target for three-dimensional laser scanning of long tunnels according to claim 2, characterized in that: Reflective panel rotating columns (8) are respectively provided at both ends of the reflective panel (2), a rubber ring (9) is provided on the outside of the reflective panel rotating column (8), and rubber ring rotating grooves are respectively provided on the reflective panel rotating column (8) and the limiting ring (4), and the reflective panel rotating column (8) and the limiting ring (4) are rotatably connected.

4. The portable multi-directional target for three-dimensional laser scanning of long tunnels according to claim 3, characterized in that: The base (1) is a magnetic base, the base shell is made of metal, and a fixed magnet is provided below the base (1), and the fixed magnet is made of rubidium magnet.

5. The portable multi-directional target for three-dimensional laser scanning of long tunnels according to claim 3, characterized in that: The base (1) is a tripod with a connecting rod.

6. A method for three-dimensional laser scanning of long tunnels, using the portable multi-directional target for three-dimensional laser scanning of long tunnels as claimed in claim 4, characterized in that: The following steps are involved: S1: Press the locking button (7), insert the fixed connecting rod (5) in the base (1) into the connecting sleeve (6) at the lower end of the reflective panel (2), and release the locking button (7); S2: During the three-dimensional laser scanning process in the tunnel, after the three-dimensional laser scanner is set up, the target is flexibly placed according to the scanning recognition limit distance, and is adsorbed on a stable position such as the track or the transport belt diagonal support in the tunnel through the magnetic base (1), and the stability is observed; S3: After setting up the total station at a known control point that satisfies line of sight, the limiting ring (4) and the reflective panel (2) are rotated according to the position of the total station, and the prism (3) on the back of the reflective panel (2) is directed toward the total station to complete the target coordinate measurement; S4: rotating the limiting ring (4) and the reflective panel (2) according to the scanning angle, and facing the reflective panel (2) toward the 3D laser scanner to complete the 3D laser point cloud data acquisition; S5: Rotate the limiting ring (4) and the reflective panel (2) according to the position of the total station, and turn the prism (3) on the back of the reflective panel (2) toward the total station to complete the target coordinate verification; S6: Calculate the absolute coordinates of the point cloud. If the error between the two target coordinate measurements is less than the nominal accuracy of the 3D laser scanner, the target position is considered correct. S7: After the three-dimensional laser scanning of this station is completed, the locking button (7) is pressed and the base (1) is separated. After the storage is completed, the next three-dimensional laser scanning operation is carried out.

7. The method for three-dimensional laser scanning of a long tunnel according to claim 5, characterized in that: The absolute coordinate solution of the point cloud in step S4 includes the following steps: S41. Calculation and measurement of the center coordinates of the reflective panel, specifically including: S411, the total station measures the sighting prism (3) to perform absolute coordinate measurement, and at this time, the absolute coordinate of the prism center point a is obtained; S412. It is known that the nominal distance between the center point a of the prism and the center point b of the reflective panel (2) is L ab , the prism constant of prism (3) is P , then enter the correction value in the total station when performing absolute measurement of the target P 'Replace the original prism constant value, P 'for P '= P + L ab ; S413. Use the total station to measure coordinates according to the conventional measurement method. The coordinate value returned at this time is the center point of the reflection panel (2). b Absolute coordinates; S42, 3D laser scanning point cloud absolute coordinate solution, using 3 or more sets of coordinates to perform 3D laser scanning point cloud absolute coordinate solution, specifically including: S421. Use the total station to measure the absolute coordinates of the prisms (3) at different positions and obtain the absolute coordinates of at least three or more center points b of the reflective panels (2). Set them as b 1. b 2. b 3; S422, 3D laser scanning point cloud is spliced by pairing target balls between adjacent stations. The corresponding coordinates of 3 or more point cloud space coordinate systems in the spliced point cloud data are set as B 1. B 2. B 3; S423, the positions of the above three groups of corresponding points are the same, that is, b 1- B 1 is the same position point, b 2- B 2 is the same position point, b 3- B 3 represents the same position point. At this time, there is a rigid body transformation relationship between the spaces where the three groups of points are located. The absolute coordinates of the point cloud are solved using Euler transformation.

8. The method for three-dimensional laser scanning of a long tunnel according to claim 6, characterized in that: Use Euler transformation to solve the absolute coordinates of point cloud. The specific process is as follows: S4231. Assume that the spatial coordinate vector of a point in the point cloud coordinate system is a =[ x 1, y 1, z 1] T , the spatial unit orthogonal basis is e =( e 1, e 2, e 3), the spatial coordinates in the absolute space coordinate system are a '=[ x 1', y 1', z 1'] T ， Assume that the space unit orthogonal basis e After one rotation, it changes to e' =( e 1', e 2', e 3'), since its actual space vector itself does not change, the equation can be obtained according to the coordinate definition: （1） （2） （3） Where, A is an orthogonal matrix, the matrix A It is composed of the inner product of two sets of unit orthogonal bases, which expresses the rotation relationship of the coordinate system of the same vector before and after rotation. R for ; S4232, after the rotation transformation is completed, the translation amount t Perform translation transformation and obtain the following formula according to the coordinate definition: （4） S4233. Combining the above rotation and translation transformations, the spatial coordinate changes are: （5） S4234, use homogeneous coordinates to convert the original n dimensional coordinates n +1 dimensional representation, the above formula can be converted to homogeneous coordinates as follows: （6） （7） S4235, The spatial coordinate system transformation matrix calculated for at least three sets of corresponding points with known point cloud coordinates and absolute coordinates.

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