CN116778077A - Linear voxelization method based on space linear three-dimensional reconstruction - Google Patents
Linear voxelization method based on space linear three-dimensional reconstruction Download PDFInfo
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Abstract
The invention discloses a space linear voxelization method in a global satellite navigation system (Global Navigation Satellite System; GNSS) water vapor inversion process, which consists of two processes of space linear projection pixelization and reconstruction voxelization. Comprising the following steps: space coordinates; spatially voxelizing; projecting all voxel blocks and straight lines in the space range onto XZ, YZ and XY planes in a three-dimensional coordinate system; gradually searching from a projection starting point and acquiring two-dimensional intersection point information (intersection point codes and coordinates) of a voxel block projection grid line and a space straight line projection line on each projection surface; and carrying out coding sequencing, and then combining intersection point information on the two corresponding two-dimensional projection planes through coding matching to obtain the information of the space straight line divided by the voxel blocks. The method reduces the problem in the three-dimensional space to two dimensions to acquire information, and then combines the information to reconstruct the related information of the straight line passing through the voxel block in the three-dimensional space, thereby reducing the difficulty of information acquisition.
Description
Technical Field
The invention relates to the field of global satellite navigation system (Global Navigation Satellite System; GNSS) vapor inversion, in particular to a method for determining three-dimensional relations between GNSS signal lines and voxel blocks in a chromatographic model, which is used in a foundation GNSS three-dimensional vapor inversion process.
Background
In the process of performing ground GNSS water vapor inversion, in order to establish a water vapor chromatographic equation to calculate and obtain the three-dimensional distribution condition of water vapor in the atmosphere, discretizing a chromatographic area, dividing the determined area into a set of regular cubes (hereinafter referred to as voxel blocks), then, obtaining the intercept of the voxel block penetrated by the GNSS signal lines participating in the water vapor inversion test to form a chromatographic matrix A, and obtaining the wet delay amount of each GNSS signal line penetrating through the atmosphere according to a GNSS observation model to form a B matrix to obtain an observation equation A x=B, and solving the chromatographic equation to obtain the water vapor parameter x in each voxel block of the voxel block set in the chromatographic area, thereby grasping the water vapor distribution and change condition of the chromatographic area with higher resolution.
In the traditional foundation GNSS three-dimensional water vapor inversion process, the intercept of a GNSS signal line cut by a voxel block is calculated by a line-surface intersection method, the process needs to respectively calculate the intersection points of the space straight line (the space straight line described below represents the GNSS signal line in the practical application of the field) and all planes parallel to XZ, YZ and XY planes, and the intersection points are ordered according to the Z value, so that the intercept of the space straight line cut by the voxel block is obtained, and the number of the voxel block where a certain section of intercept is located is calculated by the three-dimensional coordinates of the intersection points, and the process is called straight line voxelization. The method is completely carried out in a three-dimensional space, the difficulty of dividing the space straight line is certainly increased, and particularly when a huge amount of space straight lines need to be divided, the real-time performance required by GNSS vapor inversion and forecasting can be challenged due to the defects of the traditional method.
Disclosure of Invention
In view of the problems of the traditional method, a linear voxelization method based on space linear three-dimensional reconstruction is provided, and two-dimensional intersection point information is obtained through projection; and then carrying out intersection sorting and intersection matching according to codes, and then carrying out three-dimensional reconstruction to obtain intersection points of the space straight line passing through the voxel blocks and calculating the intercept and the voxel block number where the intercept is located. Fig. 1 is a general flow of the linear voxelization method based on the spatial linear three-dimensional reconstruction, which comprises two parts of spatial linear projection pixelization and reconstruction voxelization.
Spatial line projection pixelation is a process of projecting and progressively searching for two-dimensional intersection information, as shown in fig. 1 (a): firstly, the selected space is coordinated and further discretized, and the selected space is divided into a set of regular voxel blocks; projecting all voxel blocks in the space straight line and voxel block set to XZ, YZ and XY planes; and gradually searching intersection points of the space straight projection line and grids obtained by the projection of the voxel blocks on the projection plane along the advancing direction of the projection line, coding the intersection points and obtaining coordinates of the intersection points. Reconstruction voxelization is a process of combining two-dimensional intersection information of three projection planes and reconstructing spatial straight-line intersection information, as shown in fig. 1 (b): firstly, sorting and matching two-dimensional intersection points according to coding information acquired on three projection planes, reconstructing three-dimensional coordinates of intersection points of space straight lines and planes forming voxel blocks according to two-dimensional coordinates of two points successfully matched, further obtaining intercept of the space straight lines cut by the voxel blocks, and meanwhile, obtaining numbers of voxel blocks through which the space straight lines pass simply according to the coding information.
The linear voxelization method based on the space linear three-dimensional reconstruction in the GNSS water vapor inversion process is easy to realize, and the process of reducing dimension acquisition information and then integrating the information ensures that the acquisition of the space linear segmentation information is more efficient, and has a certain application value.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will briefly introduce the drawings required to be used in the embodiments or the prior art descriptions, it is obvious that the drawings in the following description are only schematic views of the present invention, and other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a rectilinear voxel method based on spatial rectilinear three-dimensional reconstruction provided by the invention.
FIG. 2 is a schematic diagram of spatial co-ordination and voxel rendering provided by the present invention.
Fig. 3 is a schematic view of projection of a spatial straight line and a voxel block provided by the present invention.
Fig. 4 is a schematic diagram of pixelizing and acquiring intersection information of spatial linear projection provided by the invention.
Fig. 5 is a schematic diagram of spatial linear reconstruction and voxelization provided by the present invention.
FIG. 6 is a schematic diagram illustrating the intersection ordering according to XZ and YZ projection codes provided by the invention.
Fig. 7 is a schematic diagram of voxel block numbering rules provided in the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The following steps are the spatial linear projection pixelized portion:
step 1: and carrying out coordinated and voxelized processing on the selected space. As shown in fig. 2, the selected space is placed in a suitable coordinate system and is coordinated; the selected space is partitioned by a plane perpendicular to the X-axis, Y-axis, and Z-axis as shown in fig. 2 (a), 2 (b), and 2 (c), and the space is discretized into a finite set of voxel blocks, defined herein: the plane parallel to the YZ plane (i.e., the plane perpendicular to the X axis) is a YZ profile, the plane parallel to the XZ plane (i.e., the plane perpendicular to the Y axis) is an XZ profile, and the plane parallel to the XY plane (i.e., the plane perpendicular to the Z axis) is an XY profile.
Step 2: the spatial straight line, voxel block is projected to the XZ, YZ, XY plane. As shown in fig. 3, fig. 3 (a) shows a selected discretized region and one spatial line in the region, and fig. 3 (b), 3 (c), and 3 (d) show projections of the set of voxel blocks and the spatial line constituting the region on XZ, YZ, and XY planes, respectively.
Step 3: the projection lines are pixelized and two-dimensional intersection point information is acquired. As shown in fig. 4, the slope (positive or negative) and the straight line advancing direction (upward or downward) on the projection plane are divided into four cases as shown in fig. 4 (a), 4 (b), 4 (c), and 4 (d). Taking the case shown in FIG. 4 (a) as an example, the process of projection line pixelation and intersection acquisition is performed as followsThe following description: START and END in fig. 4 (a) represent projection points of START and stop points of a spatial straight line on a two-dimensional plane, respectively, and are also performed along the direction from START to END in the subsequent intersection searching process; in the process of searching for the intersection point, the line connecting the starting point with the angular point of the grid where the starting point is located, the line connecting the intersection point with the angular point of the grid where the projection line passes through the intersection point, are all called Del lines, the principle of selecting the angular point of the grid is that the direction of Del lines is consistent with the advancing direction of the projection line (all face to the upper left in FIG. 4 (a)), the above content defines the advancing direction of the search in the graph and the Del line of the judgment line in the process of searching for the intersection point, and the process of searching for the intersection point of the projection line and the grid line on the two-dimensional plane will be specifically described below. Firstly, determining the slope k of a projection line in a projection coordinate system according to the coordinates of a projection line starting point and a projection line stopping point; from the START point, the slope k of the Del line is compared D The relation of the magnitude of k is shown in FIG. 4 (a) where (k<0；END Ordinate of the ordinate >START Ordinate of the ordinate ) In the Del line slope k starting from the START point D >k, it can be determined that the first intersection of the projection line must be created by the intersection of the projection line with the lateral grid line; then continue to judge the slope k of Del line with the first intersection point as the starting point D The relation of the size of k to k is found that D <k, determining that the second intersection of the projection line must be generated for the projection line to intersect the longitudinal grid line, and so on, until the end of the projection line is reached, ending the search process. In the process, the intersection codes obtained by searching are required to be coded, the starting point and the stopping point are both coded to be 3, the intersection code generated by intersecting the transverse grid lines is 1, the intersection code generated by intersecting the longitudinal grid lines is 0, and if the intersection point is just coincident with the grid corner point, the code is 2. According to this rule, the intersection point corresponding to the case shown in fig. 4 (a) is encoded as 3,1,0,1,2,1,0,1,0,3. The intersection point discrimination and encoding method in the three cases shown in fig. 4 (b), 4 (c) and 4 (d) is similar to that in fig. 4 (a). Next, the coordinates of each intersection point can be directly calculated from the code, and in the case shown in fig. 4 (a), the rule for calculating the intersection point from the code is as follows:
in the formula (1), floor is a downward rounding function, ceil is an upward rounding function; k is the slope of the projection line in the projection coordinate system, b is the intercept of the projection line in the projection coordinate system; l is the length of the projection grid, w is the width of the projection grid; x is X i-1 For the transverse coordinates of the i-1 th searched point, Y i-1 Longitudinal coordinates for the i-1 th searched point; x is X i For the transverse coordinates of the ith searching point, Y i Is the longitudinal coordinate of the i-th point being searched.
According to the four different cases of fig. 4 (a), 4 (b), 4 (c), and 4 (d), the calculation formulas for calculating the coordinates of the intersections according to the codes are slightly different, but follow the same rule as a whole.
The following steps are reconstructing the voxelized portion:
step 4: the intersection points are ordered according to the codes and the coordinate information of the XZ and YZ projection planes. As can be seen from fig. 2, the projections of the XY profile on the XZ and YZ projection planes are all a single transverse grid, so it can be seen that when a straight line in the three-dimensional space passes through the XY profile, if the spatial relationship is projected on the XZ and YZ planes, the projection line representing the spatial straight line intersects with the transverse grid line, and the codes are all 1, so that it is obtained that the intersection point represented by 1 in the code string on the XZ projection plane and the intersection point represented by 1 in the code string on the YZ projection plane are the projection points of the same three-dimensional space intersection point on the two different projection planes. As can be seen from the projection code of a certain spatial line shown in fig. 5, the numbers of codes 1 in the projection code strings of the spatial line on the XZ and YZ planes are equal, and 1 in the two code strings are in one-to-one correspondence, but 0 in the middle of each pair of adjacent codes 1 in the two code strings respectively represents a projection point of a different non-XY profile intersection point (that is, the three-dimensional intersection point is not generated by passing the spatial line through the XY profile) on the two projection surfaces in the three-dimensional space (0 in the XZ projection plane code string represents that the spatial line passes through the YZ profile, and 0 in the YZ projection plane code string represents that the spatial line passes through the XZ profile), so after the corresponding ordering of the codes 1 (as shown in fig. 6), if two 0 are in the middle of each pair of adjacent codes 1, the intersection point of 0 in the middle of each pair of adjacent codes 1 is also required to be ordered according to the size of the longitudinal coordinates (because in solving the problem of the related field, the direction of the GNSS signal line always follows the propagation direction from the ground to the air). In the sorting process, the codes 2 on the XZ and YZ projection surfaces are regarded as 1 in the sorting process because the codes 2 on the XZ and YZ projection surfaces represent that a space straight line passes through the intersection line of the two surfaces, namely passes through the two surfaces at the same time, but are sorted according to the ascending direction when being sorted. The case shown in fig. 5 is shown in fig. 6 after the coding order of XZ and YZ planes is completed.
Step 5: and carrying out coordinate matching and three-dimensional reconstruction of space intersection points according to the finished sorting codes. As can be seen from fig. 2, the projection of the XY profile on the XZ projection plane is a lateral grid line, and the projection of the XY profile on the YZ projection plane is also a lateral grid line, so it can be seen that when a straight line in the three-dimensional space passes through the XY profile, the projection line representing the spatial straight line when the spatial relationship is projected on the XZ projection plane intersects with the lateral grid line, and is encoded as 1; when the spatial relation is projected to the YZ projection plane, the projection line which is expressed as the spatial straight line is intersected with the transverse grid line, and the code is 1, so that the intersection point represented by 1 in the code string on the XZ projection plane and the intersection point represented by 1 in the code string on the YZ projection plane are projection points of the same three-dimensional space intersection point on two different projection planes, the two-dimensional coordinate corresponding to the code 1 on the XZ projection plane can provide X, Z value of the three-dimensional space intersection point, the two-dimensional coordinate corresponding to the code 1 on the YZ projection plane can provide Y, Z value of the three-dimensional space intersection point, and the X, Y, Z value of the three-dimensional space intersection point can be obtained by integrating the two-dimensional intersection point coordinate information represented by the corresponding code 1 on the two projection planes (namely, the intersection point that the spatial straight line passes through the XY profile is obtained).
As can be seen from fig. 2, the projection of the YZ profile on the XZ projection plane is a longitudinal grid line, and the projection of the YZ profile on the XY projection plane is also a longitudinal grid line, so it can be seen that when a straight line in the three-dimensional space passes through the YZ profile, the projection line representing the spatial straight line when the spatial relationship is projected on the XZ projection plane intersects with the longitudinal grid line, and the code is 0; when the spatial relation is projected to the XY projection plane, the projection line which is expressed as the spatial straight line is intersected with the longitudinal grid line, and the code is 0, so that the intersection point represented by 0 in the code string on the XZ projection plane and the intersection point represented by 0 in the code string on the XY projection plane are projection points of the same three-dimensional space intersection point on the two different projection planes, the X, Z value of the three-dimensional space intersection point can be provided by the two-dimensional coordinate corresponding to the code 0 on the XZ projection plane, the X, Y value of the three-dimensional space intersection point can be provided by the two-dimensional coordinate corresponding to the code 0 on the XY projection plane, and the X, Y, Z value of the three-dimensional space intersection point can be obtained by combining the two information (namely, the intersection point that the spatial straight line passes through the YZ profile is obtained).
Similarly, the projection of the XZ profile on the YZ projection plane is a longitudinal grid line, and the projection of the XZ profile on the XY projection plane is a transverse grid line, so that when a straight line in the three-dimensional space passes through the XZ profile, the projection line representing the spatial straight line when the spatial relationship is projected on the YZ projection plane intersects with the longitudinal grid line, and the code is 0; when the spatial relation is projected on an XY projection plane, the projection line which shows that the spatial straight line intersects with a transverse grid line and is coded into 1, so that an intersection point represented by 0 in a coding string on a YZ projection plane and an intersection point represented by 1 in a coding string on the XY projection plane are projection points of the same three-dimensional space intersection point on two different projection planes, a Y, Z value of the three-dimensional space intersection point can be provided by two-dimensional coordinates corresponding to the coding 0 on the YZ projection plane, a X, Y value of the three-dimensional space intersection point can be provided by two-dimensional coordinates corresponding to the coding 1 on the XY projection plane, and X, Y, Z values of the three-dimensional space intersection point can be obtained by combining the two pieces of information (namely, the intersection point that the spatial straight line passes through an XZ profile is obtained).
According to the above-described matching principle, the following matching rule (taking fig. 6 as an example) can be obtained: if the code 1 is encountered in the ordered intersection code chain, it is indicated that the three-dimensional intersection coordinates of the space straight line corresponding to the code and the voxel block are formed by combining two-dimensional intersection coordinates represented by two corresponding codes 1 on the XZ and YZ projection planes. If code 0 is encountered in the sorted intersection code chain, it is necessary to distinguish whether the code 0 is from the XZ projection plane (0 without underline in fig. 6) or from the YZ projection plane (0 with underline in fig. 6); if the code 0 is determined to come from the XZ projection plane, the three-dimensional intersection point coordinates of the space straight line corresponding to the code 0 in the code chain after the sorting and the voxel block are indicated to be formed by combining two-dimensional intersection point coordinates represented by two corresponding codes 0 on the XZ projection plane and the XY projection plane; if it is determined that code 0 comes from the YZ projection plane, it is indicated that the three-dimensional intersection point coordinates of the voxel block and the space straight line corresponding to 0 in the code chain after sorting should be combined by the two-dimensional intersection point coordinates represented by code 0 on the corresponding YZ projection plane and code 1 on the XY projection plane.
In the process of matching the intersection codes, because the codes 2 on the projection surface represent the intersection lines of the space straight lines passing through the two profiles, namely, the two profiles can be regarded as 1 or 0, and in the process of matching, the codes 2 on the projection surface are all regarded as 1 to be matched in the same processing mode in the sorting process.
Step 6: and calculating the number of the voxel block penetrated by the space straight line according to the ordered codes. The voxel block numbering rules are shown in fig. 7, so the following method for calculating voxel block numbers from codes will also be divided into two parts: calculating the layer number of the intersection point codes; and calculating the grid number where the intersection point code is projected onto the XY plane.
The case shown in fig. 5 will be described as an example. As can be seen from the description in Step5, in the ordered intersection codes shown in FIG. 6, all codes 1 represent that a spatial line passes through an XY profile, that is, the spatial line passes through the intersection represented by code 1 and then enters the next layer, so that it can be determined when the spatial line passes through the intersection to enter the next layer according to the position where code 1 occurs; in the ordered intersection codes, all codes 0 indicate that the space straight line intersects with the XZ and YZ profiles, and projection lines of the space straight line intersect with the horizontal axis and the vertical axis in the projection grid when projected onto the XY plane, so that after the space straight line passes through the intersection represented by the codes 0 in the ordered code string, the space straight line can pass through which voxel block in the layer continuously according to the intersection codes on the XY projection plane. The rule for calculating the grid number from the projection code on the XY plane is shown in equation 2.
In formula 2, n i+1 A grid number representing the grid number to be traversed after the straight line passes through the intersection represented by the code; n is n i A grid number indicating the position of the space straight projection line before crossing the intersection point represented by the code; l represents the number of voxel blocks in a row (in the X-axis direction) in a layer, in the case shown in fig. 7 l=6. When the code is 0, the straight projection line passes through the vertical axis, namely the space straight line passes through the YZ profile along the X axis in the negative direction and enters adjacent voxel blocks in the same layer, so the code is increased or decreased by 1 on the original basis; when the code is 1, the straight projection line passes through the transverse axis, namely the space straight line passes through the XZ profile along the Y axis forward direction and enters the voxel blocks of the adjacent rows in the same layer, so the number is added with l on the original basis; when the code is 2, the space straight line passes through the XZ and YZ profiles at the same time, and the number is added with l-1 on the original basis.
The formula represented by formula 2 is shown in FIG. 5 (k shown in FIG. 4a<0；END Ordinate of the ordinate >START Ordinate of the ordinate The case of (b) as an example, the encoding calculation formula in the case shown in fig. 4b is shown as formula 3; the encoding calculation formula in the case shown in fig. 4c is as formula 4; the encoding calculation formula in the case shown in fig. 4d is as formula 5.
Therefore, as long as the number of the voxel block where the starting point projection point is located is known, the number of the voxel block where the spatial straight line passes through the layer can be calculated according to the rule in the above formula in different cases.
Through the two steps, the grid number n and the layer number k of each section of intercept on the XY projection plane, which are intercepted by the voxel blocks, are obtained, and the voxel block number corresponding to the intercept to be calculated is k x m+n on the assumption that the voxel block number of each layer is m.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (3)
1. A rectilinear voxel method based on spatial rectilinear three-dimensional reconstruction, comprising:
s1: the space is coordinated; dividing the regular cubes and voxelizing the regular cubes;
s2: projecting a space straight line to be voxelized and all voxel blocks onto XZ, YZ and XY planes in a coordinate system respectively;
s3: gradually advancing from a projection line starting point, respectively searching intersection points of space straight projection lines on three projection planes and grids obtained by the projection of the voxel blocks, and coding;
s4: ordering the intersection codes according to the sequence from the starting point to the end point according to the corresponding relation between different types of intersection codes on the XZ and YZ projection planes and the ordinate size relation in a small range;
s5: matching and combining the two-dimensional intersection point information obtained by calculation on the two projection surfaces according to the corresponding relation of the intersection point codes on each two projection surfaces to obtain the three-dimensional coordinates of the intersection point of the space straight line passing through each profile, and further obtaining the intercept;
s6: and (3) combining the coding chain with the sorting completed in the step (S4) and coding chain information on the XY projection plane to obtain the number of the voxel block where the intercept obtained in the step (S5) is located.
2. The method for linear voxel forming based on space straight line three-dimensional reconstruction according to claim 1, wherein in step S3, intersection points are searched step by comparing the relationship between the slope of the Del line and the slope of the space straight line projection line, so as to obtain the coordinate information of the intersection points between the space straight line projection line and the voxel block projection grid on the two-dimensional plane, and encode the intersection points of different types.
3. The method for linear voxel forming based on space straight line three-dimensional reconstruction according to claim 1, wherein in the steps S4 to S6, the order of the space straight line crossing the crossing points of each voxel block is determined according to the corresponding relation between different types of crossing points on the two-dimensional projection surface and the ordinate size relation in a small range, then the three-dimensional coordinates of the crossing points generated by the space straight line crossing different types of molded surfaces are obtained by combining two-dimensional crossing point coordinate information on the two-dimensional projection surfaces with related relation, so as to obtain the intercept of the voxel block crossed by the space straight line, finally the number of layers of the intercept of a certain section is determined according to the coding chain information which completes the sorting in the step S4, the position of the intercept of the section in the layer is determined by combining the coding chain information of the XY projection surface, and finally the serial numbers of the voxel blocks of the section are obtained by combining the two pieces of information.
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