CN110413714B - Vector element gridding method in global discrete grid system with topology fidelity - Google Patents
Vector element gridding method in global discrete grid system with topology fidelity Download PDFInfo
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Abstract
The invention discloses a vector element gridding method in a global discrete grid system with topology fidelity. The invention can effectively maintain the topological relation between the original vector data and ensure the correct integration of the vector data in the global discrete grid system.
Description
Technical Field
The invention relates to a geographic information technology, in particular to a vector element gridding method in a global discrete grid system with topology fidelity.
Background
The global discrete grid divides the earth surface into continuous seamless multi-layer regional unit sets, is used for fitting the earth surface under different resolutions, has the characteristics of nesting hierarchy and global continuity, and can be used for normatively integrating and analyzing mass data with any resolution in the global range. The integration of the vector data, namely discretizing the vector data into grid cells with corresponding scales according to a certain criterion, realizes the grid expression of the geographic object. This is the core problem of global discrete grid research.
In vector data, the grid formation of point data is simple, and the point data can be expressed by a grid element with the resolution corresponding to the proportional scale. For line data, it is necessary to determine all cells on the path of the line through the mesh. A plurality of vector line gridding methods exist in a traditional plane grid, a vertex-to-vertex line generation algorithm, an adjacent sequence line generation algorithm, a shortest path searching algorithm along a grid element boundary and the like for a triangular grid, a digital differential method, a midpoint drawing method, a Bresenham algorithm, a Wu algorithm and the like for a quadrilateral grid, a multidimensional discrete line mathematical model with Vince (2006) for a hexagonal grid and a corresponding algorithm are adopted. On the basis, related scholars transplant vector data gridding algorithm in a plane space to a global discrete grid of a spherical space. Meanwhile, dutton utilizes the multi-resolution hierarchical characteristics of the QTM grid to provide a simplified line algorithm for drawing synthesis, and performs precision control on the gridded expression of vector line data in the text rate and the like, so that the vector drawing method on the planar grid can perform high-precision drawing on the spherical grid. For face data, it is then necessary to determine the grid region that intersects the face. Tong et al propose a reasonable sphere expansion method, which realizes the meshing of vector surface data on a spherical hexagonal mesh by subdividing and repeatedly transforming vector data of different expansion areas.
In the current global discrete grid system, the existing vector data grid method needs to determine a specific grid level required for ensuring the expression precision of original vector data according to the corresponding relation between a map scale and the grid level, and then integrate the vector data by using various grid methods. The existing gridding method mainly considers the expression precision of vector data in grids and strives to accurately express the geometric characteristics of entity objects in geographic space. However, because of the difference between vector data and grid systems for position expression, gridding is a lossy process, and necessarily results in distortions in areas, side lengths, shapes, and topology. Relative to other aspects, the topological relationships characterize spatial relationships between geographic entities, and a misinterpretation of a topological relationship would lead to a wrong spatial awareness. During the gridding of vector data in a global discrete grid, changes in topological relationships may occur.
Disclosure of Invention
The invention aims to: the invention aims to solve the defects in the prior art, provides a vector element gridding method in a global discrete grid system with topology fidelity, and realizes the correct integration of vector data in the global discrete grid system.
The technical scheme is as follows: the invention relates to a vector element gridding method in a global discrete grid system with topology fidelity, which sequentially comprises the following steps:
(1) Inputting original vector data needing gridding, and then determining the type of the original vector data; here, the original vector data type includes vector point data, vector line data, and vector plane data;
(2) Respectively providing vector point data, vector line data and topological distortion which may occur in the process of gridding vector surface data based on a nine-intersection model;
(3) And respectively carrying out the following processing on each original vector data type: initial grid formation, topology distortion detection and topology distortion repair;
(4) Outputting a final grid result according to the model format;
the initial grid meshing determines an initial grid level through a map scale of original vector data, and then determines all grid elements expressing entity geometry for vector point data, vector line data and vector surface data according to different strategies respectively; the topological distortion detection determines the topological relation after initial grid meshing according to the spatial relation of the grid elements, finds out the object with the changed topological relation and records the related grid elements causing distortion; and the topological distortion repair utilizes the multi-resolution hierarchical characteristic of the grid system, replaces the grid cells recorded in the last step with the grid cells with higher resolution, confirms the attribution of the grid cells and detects the topological distortion again, and recursively repairs until all the topological distortions disappear.
Further, the topological distortion in the step (2) includes the following cases:
(A) According to the nine-intersection model, the points are zero-dimensional objects without boundaries, and the topological relations between the points are Equal (Equal, T) and separated (Disjoint, F); if the space coordinates of the two original vector points are completely the same, the two vector points are equal in topology, otherwise, the two vector points are separated; after the vector points are subjected to grid meshing, if the original two separated vector points are converted into the same grid cell, the topological relation of the point object is changed from phase separation to equal;
(B) According to the nine-intersection model, the topological relationship between the line objects has two types of departure (FF and FF) and Overlap (Overlap, FF and FF (F) and ('!' symbol represents a logical non-operation); if the straight line segments forming the two vector lines have intersection points, the two vector lines are overlapped, otherwise, the two vector lines are separated; after the vector lines are meshed, if the cell string converted from the originally separated two vector lines contains the same cell, the topological relation of the line objects is changed from separation to overlapping.
(C) In the vector data set in practical application, the vector surfaces are not overlapped usually, and the topological relations between the surface images are only two types of connection (Meet, F, T, FF, etc.); after gridding, the vector surface data has 5 types of topological changes, namely: in the case where a single surface is meshed, the surface disappears completely, and one surface is divided into a plurality of surfaces, and in the case where two surfaces originally connected are separated from each other, the two surfaces originally separated are also connected to each other, and in the case where the surrounding relationship between the three surfaces is lost.
Further, in the step (3), each vector point includes an x coordinate value and a y coordinate value, the point object is represented by a single cell at a specific grid level, and the specific step of gridding the vector point data is as follows:
1) And initial gridding: converting the geographic coordinates expressing the space positions of the vector points into corresponding grid element codes, wherein the grid elements identified by the grid element codes are the spherical grid area where the vector points are located;
2) After the initial grid is screened, the geometric position information of the original vector points is converted into a form representation of spherical cells, but when the change of the topological relation is likely to occur at the moment to detect the topological distortion, all point objects are traversed, and the topological relations of the current point object and other point objects after the original vector data and the initial grid are compared, that is: assume the original spatial coordinates of points i and j to be (x) i ，y i ) And (x) j ，y j ) And the cells after the initial grid formation are coded into code i And code j If x i ≠x j ||y i ≠y j And code i ＝code j If so, indicating that the point i and the point j generate topological relation distortion after initial grid formation, and changing the phase separation into the equality;
3) After the topological distortion detection is carried out on the initial grid result, all relevant point objects with the topological distortion are found, when the topological distortion is repaired, because the grid system has the multi-resolution hierarchical characteristic, all the point objects with the topological distortion are described by using grid elements of a higher level, so that the geometric expression precision of the point objects in the grid system is improved, if the topological distortion exists, the grid elements of the higher level are used, and the process is recursed until all the topological distortion is eliminated.
Further, in the step (3), each vector line object is represented by a group of consecutive adjacent cells at a specific grid level, and the specific step of gridding the vector line data is as follows:
1) And recording the original vector line data to form straight line segment end points, and determining the grid cell string passed by the straight line segment according to the two end points of the straight line segment during initial grid formation. In the planar triangular grid, a plurality of straight line segment gridding algorithms exist, wherein the vertex-to-vertex straggling algorithm screens grid elements according to the distances from the grid element vertexes to the straight line segments, the generated grid element string path is unique, the fitting effect is good, the implementation is simple and the efficiency is high, the planar straight line distance is expanded into the spherical great arc distance, and the vertex-to-vertex straggling algorithm on the planar triangular grid is applied to the spherical triangular grid by combining with the adjacent search algorithm of the spherical grid elements;
2) After vector line initial grid meshing, the topological relation is probably changed into overlapping by phase separation, when detecting this topological distortion, only need compare line object initial grid meshing before and after the topological relation can, promptly: if the original vector line k and t have no intersection point, the code set of cell strings expressing k and t after the initial grid meshing k And codeSet t The intersection not being empty, i.e.
The fact that the lines k and t generate topological relation distortion after initial grid formation is shown, and the phase separation is changed into overlapping;
3) And when the topological distortion is repaired, similar to point objects, for all related line objects with the topological distortion, the geometric expression precision of the line objects in the grid system is improved, the position form of the line objects is described by using a higher-level lattice element, and recursion is carried out until the topological relation among all the line objects is repaired.
Further, when the vector line data is initially gridded, all straight line segments constituting the vector line are gridded by adopting the following method:
step 1: inputting two end points of the straight line segment, and converting the two end points into cell representation to determine a starting cell startCell and an ending cell of the cell string.
Step 2: and establishing a space cell string list, and initializing the current cell curCell as an initial cell startCell.
And 3, step 3: if the current cell curCell is a termination cell endCell, outputting a cell string list, and ending the algorithm; otherwise, the next step is carried out.
And 4, step 4: the current cell curCell is added to the list of cell strings.
And 5: obtaining three edge adjacent cells adjCell of current cell curCell according to adjacent search algorithm of spherical cell 1 、adjCell 2 And adjCell 3 。
And 6: and for adjacent cells which are not in the cell string list, calculating the distance between each vertex and the spherical surface great circle of the straight line segment, obtaining the farthest distance between each adjacent cell and the straight line segment, taking the adjacent cell with the smallest farthest distance as the next current cell curCell, and returning to the step 3.
Further, the specific step of gridding the vector plane data in the step (3) is as follows:
1) After gridding, directly reflecting the topological adjacency relation between the surface objects by the grid cells intersected with the boundary of the original vector surface, easily generating topological distortion after gridding the narrow region of the vector surface, and directly determining whether the topological relation between the surfaces can be reserved by the division of the grid cells intersected with the narrow region; in order to identify the cells, the cells are classified into three types according to the position relation between the original vector plane and the cells:
(1.1) stabilizing cells: for a vector plane, the cells completely contained by the range between the inner ring and the outer ring are the stable cells of the plane. Because the stable cells are only intersected with a single vector plane, if the stable cells of a certain vector plane can only be attributed to the plane according to the area dominance principle, no other possibility exists.
(1.2) unstable neurons: for a vector plane, the cells intersected with the outer ring or the inner ring of the vector plane are unstable cells of the plane. Because unstable cells may intersect multiple vector planes, unstable cells of a vector plane may be attributed to the plane and may also be attributed to other planes intersecting the unstable cells according to the area dominance principle.
(1.3) Key cells: for a certain vector plane, the cells intersected with its narrow region (i.e. the region with width smaller than the length of one cell edge in the original vector plane) are the key cells of the plane. The key cells also intersect the vector plane boundaries and are special unstable cells. Since the vector is a region in which unstable cells are concentrated, the key cell part of a vector plane is easily divided by mistake, and the topological relation of the plane may change.
2) And initial gridding: because the attribution of the stable cells is only possible, the most critical in the initial grid networking is the determination of the attribution of the unstable cells, the attribution of the unstable cells is determined by using an area optimization principle, and the topological adjacency relation between original vector planes is recorded at the same time, so that the subsequent topological distortion detection and restoration are facilitated, and three non-repeated lists are created for each plane for recording the stable cells, the unstable cells and the key cells of each plane: for a certain face, if a certain cell is a stable cell of the face, adding the code of the cell into a stable cell code list of the face; if a certain cell is an unstable cell of the surface, adding the code of the cell into an unstable cell code list of the surface; if a certain cell is the key cell of the face, adding the code of the cell into a key cell code list of the face;
3) After the initial grid formation according to the area dominance principle, the original vector surface has been converted into the spherical cell set expression, but the topological relation between the surfaces may have been changed. Before repairing the topological distortion, the topological distortion needs to be detected firstly according to two adjacent matrixes M o And M g To detect topological distortion, M o And M g Is an n × n contiguous matrix, nFor the number of original vector surfaces, when surface r is adjacent to surface s, M [ r [ [ r ]][s]＝M[s][r]=1, otherwise M [ r)][s]＝M[s][r]＝0；
Matrix M for recording topological adjacency relation of original vector plane o Obtained by querying the topological relation of the original vector data, and for M recording the topological adjacency relation among the surfaces after the initial grid formation g If it is assumed that an unstable bin is assigned as a face r and an adjacent bin is assigned as a face s (r ≠ s), then it is known that the faces r and s are adjacent after gridding, and M is juxtaposed g [r][s]＝M g [s][r]=1, traversing all unstable grid elements, and obtaining the topological relation adjacency matrix M between all surfaces after grid meshing g ；
Using a adjacency matrix M o And M g Detecting four types of topological distortion after gridding: if for the surface r, it is not adjacent to any other surface after being reticulated, i.e.
The surface r disappears after the gridding; if M is o [r][s]1, and M g [r][s]=0, the topological relation of the planes r and s changes from adjacent to separated; if M is o [r][s]=0, and M g [r][s]=1, the topological relationship of the planes r and s changes from phase separation to adjacency; if for face r, it has one and only one face s after it is meshed with M o [r][s]=1, and there is more than one face h for M g [r][h]=1, the plane r is originally surrounded by the plane s, but the surrounding relation disappears after the grid formation;
for another type of topological distortion, namely the vector surface is divided after being gridded, the boundary of the surface is divided into a plurality of disconnected parts. The boundary of the surface is either an unstable cell or an adjacent cell of the unstable cell, so that for each surface, the boundary of the surface after gridding is firstly found through the unstable cell: if a certain unstable cell of the face object is attributed to the face, the boundary cell is the boundary of the face, otherwise, the adjacent cell attributed to the face is the boundary of the face; traversing the boundary cells by using a flood filling algorithm with one cell of the boundary as a starting point, wherein if the cells in the boundary are not filled, the boundary is not communicated, and the surface cells are divided after being meshed;
4) After various topological distortions are detected, all surfaces of which the topological relations change after gridding are found; because the key cells of a plane are cells intersecting with the narrow region (i.e. the region with the width smaller than the size of one cell in the original plane) according to the definition of the key cells, the narrow region where the topology distortion plane occurs is expressed by finer cells, that is, the key cells of the plane are replaced by the cells of a higher level. Then, determining attribution of all new cells according to an area optimization principle, similar to the initial grid formation process, wherein in the new cells, if a certain cell is completely contained by a certain face, the new cell is attributed to a stable cell of the face, otherwise, the new cell is attributed to an unstable cell of the face, and then determining a key cell of the face according to the unstable cell; and finally, returning to the topological distortion detection step, and if the distortion still exists, recursively repairing until all the topological distortions disappear.
Has the advantages that: the invention effectively repairs the topological distortion generated after gridding, and can completely avoid the topological relation change after the entity object gridding by increasing the resolution of the object with the changed topological relation by means of the multi-resolution hierarchical characteristic of the global discrete grid system and performing the recursive repair of the topological distortion.
Drawings
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic diagram of vector point initial gridding according to the present invention;
FIG. 3 is a schematic diagram of vector point topological distortion repair according to the present invention;
FIG. 4 is a schematic diagram of the meshing of straight line segments of vector lines in accordance with the present invention;
FIG. 5 is a schematic diagram of vector line topology distortion repair according to the present invention;
FIG. 6 is a schematic diagram of an initial gridding process for vector planes in accordance with the present invention;
FIG. 7 is a schematic diagram of vector surface topology distortion repair according to the present invention.
Detailed Description
The technical solution of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiments.
As shown in fig. 1, the vector element gridding method in a global discrete grid system with topology fidelity of the present invention sequentially includes the following steps:
(1) Inputting original vector data needing gridding, and then determining the type of the original vector data; here, the original vector data type includes vector point data, vector line data, and vector plane data;
(2) Respectively providing vector point data, vector line data and topological distortion which may occur in the process of gridding vector surface data based on a nine-intersection model;
(3) And respectively carrying out the following processing on each original vector data type: initial grid formation, topology distortion detection and topology distortion repair;
(4) Outputting a final grid result according to a model format;
in the step (3), each vector point comprises an x coordinate value and a y coordinate value, the point object is represented by a single grid cell at a specific grid level, and the specific step of grid-meshing the vector point data is as follows:
1) And initial gridding: as shown in fig. 2, the geographic coordinates expressing the spatial position of the vector point are converted into corresponding grid cell codes, and the grid cell identified by the grid cell codes is the spherical grid region where the vector point is located;
2) When detecting the topological distortion, only all point objects need to be traversed, and the topological relation between the current point object and other point objects after the original vector data and the initial grid are compared, namely: suppose the original spatial coordinates of points i and j are (x) i ，y i ) And (x) j ，y j ) And the cells after the initial grid formation are coded into code i And code j If x i ≠x j ||y i ≠ y j And code i ＝code j If so, indicating that the point i and the point j generate topological relation distortion after the initial grid formation, and changing the phase separation into the equality;
3) And when the topological distortion is repaired, describing the position information of all point objects with the topological distortion by using the grid cells of a higher level, if the topological distortion still exists, reusing the grid cells of the higher level, and repeating the process until all the topological distortion is eliminated.
As shown in fig. 3, in 3 (a) of fig. 3, the original two vector points are separated, but the original grid is transformed into the same cell after being subjected to the initial grid formation, and the topological relationship is changed from the separation to the equality. When the distortion is repaired, firstly, two original vector points are gridded by using a higher-level cell, but at the moment, the two vector points are still positioned in the same cell, as shown in 3 (b) of fig. 3, so that a higher-level sub-cell is used again, at the moment, the original two vector points are converted into different cells, as shown in 3 (c) of fig. 3, the topological relation is restored to be separated, and the repair is completed.
In the step (3), each vector line object is represented by a group of continuous adjacent cells at a specific grid level, and the specific step of gridding the vector line data is as follows:
1) The original vector line data records straight line segment end points, and when the initial grid is meshed, grid cell strings passed by the straight line segments are determined according to the two end points of the straight line segments: expanding the plane straight-line distance into a spherical great arc distance, and applying a vertex-to-vertex dispersion line algorithm on the plane triangular grid to the spherical triangular grid by combining an adjacent search algorithm of spherical grid elements;
as shown in fig. 4, in initially gridding the vector line data, all straight line segments constituting the vector line are gridded by the following method:
step 1: inputting two end points of the straight line segment, and converting the two end points into cell representation to determine a starting cell startCell and an ending cell of the cell string.
Step 2: and (5) establishing a space element string list, and initializing the current cell curCell as an initial cell startCell.
And step 3: if the current cell curCell is a termination cell endCell, outputting a cell string list, and ending the algorithm; otherwise, the next step is carried out.
And 4, step 4: the current cell curCell is added to the list of cell strings.
And 5: three edge adjacent cells adjCell of current cell curCell are obtained according to adjacent search algorithm of spherical cells 1 、adjCell 2 And adjCell 3 。
Step 6: and (4) for adjacent cells which are not in the cell string list, calculating the distance from each vertex to the spherical surface great circular arc of the straight line segment, obtaining the farthest distance from each adjacent cell to the straight line segment, taking the adjacent cell with the smallest farthest distance as the next current cell curCell, and returning to the step 3.
2) When detecting this topological distortion, only need contrast line object initial grid meshing before and after the topological relation can, promptly: if the original vector line k and t have no intersection point, the code set of cell strings expressing i and j after the initial grid meshing k And codeSet t The intersection not being empty, i.e.
Then indicating that the lines k and t generate topological relation distortion after initial gridding and change from phase separation into overlapping;
3) And when the topological distortion is repaired, describing the position form of all related line objects with the topological distortion by using the grid cells of a higher level, and recursing until the topological relation among all the line objects is repaired. As shown in fig. 5, when repairing the topological distortion in fig. 5 (a), the initial gridding method is also used for two vector lines, but at this time, by using a higher level of cells, it can be found that there is no intersection part after the two vector lines are gridded, the topological relation is restored from intersection to phase separation, and the repairing result is shown in fig. 5 (b).
The specific steps for gridding the vector surface data are as follows:
1) And classifying the cells intersected by the boundary of the original vector plane into three types according to the position relation between the original vector plane and the cells:
(1.1) stable cells: for a vector plane, the cells completely contained by the range between the inner ring and the outer ring are the stable cells of the plane. Because the stable cells are only intersected with a single vector plane, if the stable cells of a certain vector plane can only be attributed to the plane according to the area dominance principle, other possibilities do not exist.
(1.2) unstable neurons: for a vector plane, the cells intersected with the outer ring or the inner ring of the vector plane are unstable cells of the plane. Because unstable cells may intersect multiple vector planes, unstable cells of a vector plane may be attributed to the plane and may also be attributed to other planes intersecting the unstable cells according to the area dominance principle.
(1.3) Key cells: for a certain vector plane, the cells intersected with its narrow region (i.e. the region with width smaller than the length of one cell edge in the original vector plane) are the key cells of the plane. The key cells are also intersected with the boundary of the vector plane, and are special unstable cells, and because the unstable cells are concentrated and gathered regions, the key cells of a certain vector plane are easily divided by errors, so that the topological relation of the plane may be changed.
2) And initial gridding: as shown in fig. 6, the area dominance principle is used to determine the attribution of unstable cells, and simultaneously, the topological adjacency relation between the original vector planes is recorded, and meanwhile, for recording the stable cells, unstable cells, and key cells of each plane, three non-repeating lists are created for each plane: for a certain face, if a certain cell is a stable cell of the face, adding the code of the cell into a stable cell code list of the face; if a certain cell is an unstable cell of the surface, adding the code of the cell into an unstable cell code list of the surface; if a certain cell is the key cell of the face, adding the code of the cell into a key cell code list of the face;
3) Detecting topological distortion: first according to two adjacency matrices M o And M g To detect topological distortion, M o And M g Is n × n adjacency matrix, n is the number of original vector planes, when a plane r is adjacent to a plane s, M [ r [ [ r ]][s]＝M[s][r]=1, otherwise M [ r)][s]＝M[s][r]＝0；
Matrix M for recording topological adjacency relation of original vector plane o Obtained by querying the topological relation of the original vector data, and for M recording the topological adjacency relation among the surfaces after the initial grid formation g Then need to record again according to the initial grid processJudging the unstable cell, if it is assumed that the unstable cell is attributed to the face i and some adjacent cell is attributed to the face s (r ≠ s) for some unstable cell, then it is known that the subsequent i and the face j are adjacent to each other after gridding, and juxtaposing M g [r][s]＝M g [s][r]=1, traversing all unstable grid elements, and obtaining the topological relation adjacency matrix M between all surfaces after grid meshing g ；
Using a adjacency matrix M o And M g Detecting four types of topological distortion after grid meshing: if for the face r, it is not adjacent to any other face after being meshed, i.e. it is meshed
The surface r disappears after the gridding; if M is o [r][s]1, and M g [r][s]=0, the topological relation of the planes r and s changes from adjacent to separated; if M is o [r][s]=0, and M g [r][s]=1, the topological relationship of the planes r and s changes from phase separation to adjacency; if for face r, it has one and only one face s after it is meshed with M o [r][s]=1, and there is more than one face h for M g [r][h]If =1, the surface r is originally surrounded by the surface s, but the surrounding relationship disappears after the gridding;
for another type of topological distortion, namely that a vector surface is divided after being subjected to gridding, the boundary of the surface is divided into a plurality of disconnected parts, and for each surface, the boundary of the surface after being subjected to gridding is firstly found through an unstable lattice: if some unstable cell of the face object is attributed to the face, the boundary cell is the boundary of the face, otherwise, the adjacent cell attributed to the face is the boundary of the face; traversing the boundary cells by using a flood filling algorithm with one cell of the boundary as a starting point, wherein if the cells in the boundary are not filled, the boundary is not communicated, and the surface cells are divided after being meshed;
4) After detecting various topological distortions, finding out all the surfaces of which the topological relations change after gridding; then determining attribution of all new cells according to an area dominance principle, wherein in the new cells, if a certain cell is completely contained by a certain face, the certain cell is attributed as a stable cell of the face, otherwise, the new cell is attributed as an unstable cell of the face, and then determining a key cell of the face according to the unstable cell; finally, returning to the topological distortion detection step, if there is still distortion, recursively repairing until all topological distortion disappears, as shown in fig. 7, where 7 (a) in fig. 7 is an example of plane-vanishing repair, 7 (b) in fig. 7 is an example of plane-divided repair, 7 (c) in fig. 7 is an example of phase-to-phase-change repair, 7 (d) in fig. 7 is an example of phase-to-phase-change repair, and 7 (e) in fig. 7 loses the example of bounding repair.
Example 1:
in this embodiment, the step of meshing the vector data with a partial scale of 1: 110,000,000 downloaded from Natural Earth based on the regular icosahedron triangle eighth layer mesh is as follows:
(1) Inputting original vector data needing gridding;
(2) Determining the type of original vector data;
(3) According to the type of the original vector data, carrying out initial grid formation by using a point, line or plane method in the invention content;
(4) According to the type of original vector data, carrying out topology distortion detection by using a point, line or plane method in the invention content;
(5) And performing topology distortion recursive restoration by using a point, line or plane method in the invention contents according to the type of the original vector data.
Claims (5)
1. A vector element gridding method in a global discrete grid system with topology fidelity is characterized in that: the method sequentially comprises the following steps:
(1) Inputting original vector data needing gridding, and then determining the type of the original vector data; here, the original vector data type includes vector point data, vector line data, and vector plane data;
(2) Respectively providing vector point data, vector line data and topological distortion which may occur in the process of gridding vector surface data based on a nine-intersection model;
(3) And respectively carrying out the following processing on each original vector data type: initial grid formation, topology distortion detection and topology distortion repair;
(4) Outputting a final grid result according to a model format;
the initial grid meshing determines an initial grid level through a map scale of original vector data, and then determines all grid cells expressing entity geometry for vector point data, vector line data and vector surface data respectively;
the topological distortion detection determines the topological relation after initial grid meshing according to the spatial relation of the grid elements, finds out the object with the changed topological relation and records the related grid elements causing distortion;
the topological distortion repair replaces the grid cells recorded in the last step with the grid cells with higher resolution by utilizing the multi-resolution hierarchical characteristic of the grid system, confirms the attribution of the grid cells and detects the topological distortion again, carries out recursive repair until all the topological distortions disappear,
the topological distortion in the step (2) comprises the following conditions:
(A) According to the nine-intersection model, points are zero-dimensional objects without boundaries, and the topological relation between the points is equal and separated; if the space coordinates of the two original vector points are completely the same, the two vector points are equal in topology, otherwise, the two vector points are separated; after the vector points are subjected to grid meshing, if the original two separated vector points are converted into the same grid cell, the topological relation of the point object is changed from phase separation to equal;
(B) According to the nine-intersection model, the topological relation between the line objects has two types of separation and overlapping; if the straight line segments forming the two vector lines have intersection points, the two vector lines are overlapped, otherwise, the two vector lines are separated; after the vector lines are subjected to grid formation, if the cell string formed by converting the originally separated two vector lines contains the same cell, the topological relation of the line objects is changed from separation into overlapping;
(C) According to the nine-intersection model, the topological relation between the face objects is connected and separated; after gridding, the vector surface data has 5 types of topological changes, namely: in the case of a single surface, the surface completely disappears after the gridding and one surface is divided into a plurality of surfaces, and in the case of two surfaces originally connected, if the two surfaces become separated, the two surfaces originally separated also become connected, and in the case of three surfaces, the surrounding relationship is lost.
2. The method for vector element gridding in a topologically true global discrete grid system according to claim 1, wherein: in the step (3), each vector point comprises an x coordinate value and a y coordinate value, the point object is represented by a single grid cell at a specific grid level, and the specific step of grid-meshing the vector point data is as follows:
1) And initial gridding: converting the geographic coordinates expressing the space positions of the vector points into corresponding grid element codes, wherein the grid elements identified by the grid element codes are the spherical grid area where the vector points are located;
2) When detecting the topological distortion, only all point objects need to be traversed, and the topological relation between the current point object and other point objects after the original vector data and the initial grid are compared, namely: assume the original spatial coordinates of points i and j to be (x) i ，y i ) And (x) j ，y j ) And the cells after the initial grid meshing are coded into codei and code j If x i ≠x j ||y i ≠y j Code, and code i ＝code j If so, indicating that the point i and the point j generate topological relation distortion after the initial grid formation, and changing the phase separation into the equality;
3) And when the topological distortion is repaired, describing the position information of all point objects with the topological distortion by using the grid cells of a higher level, if the topological distortion still exists, reusing the grid cells of the higher level, and repeating the process until all the topological distortion is eliminated.
3. The method of vector element gridding in a topologically true global discrete grid system according to claim 1, wherein: in the step (3), each vector line object is represented by a group of continuous adjacent cells at a specific grid level, and the specific step of gridding the vector line data is as follows:
1) The original vector line data records straight line segment end points, and when the initial grid is meshed, grid cell strings passed by the straight line segments are determined according to the two end points of the straight line segments: expanding the plane straight-line distance into a spherical great arc distance, and applying a vertex-to-vertex dispersion line algorithm on the plane triangular grid to the spherical triangular grid by combining an adjacent search algorithm of spherical grid elements;
2) When detecting the topological distortion, only the topological relation before and after the initial grid meshing of the line object needs to be compared, namely: if the original vector line k and t have no intersection, the code set of the cell string expressing k and t after the initial grid meshing k And codeSet t The intersection not being empty, i.e.
Then the lines k and t are shown to generate topological relation distortion after the initial grid formation, and the phase separation is changed into the overlapping;
3) And when the topological distortion is repaired, describing the position form of all related line objects with the topological distortion by using the cells at a higher level, and recursing until the topological relation among all the line objects is repaired.
4. The method of vectorial element meshing in a topologically true global discrete mesh system as claimed in claim 3, wherein: when the vector line data is initially gridded, all straight line segments forming the vector line are gridded by adopting the following method:
step 1: inputting two end points of the straight line segment, and converting the two end points into cell representation to determine a starting cell startCell and an ending cell of the cell string;
step 2: establishing a space element string list, and initializing the current cell curCell as an initial cell startCell;
and step 3: if the current cell curCell is a termination cell endCell, outputting a cell string list, and ending the algorithm; otherwise, entering the next step;
and 4, step 4: adding a current cell curCell into a cell string list;
and 5: obtaining three edge adjacent cells adjCell of current cell curCell according to adjacent search algorithm of spherical cell 1 、adjCell 2 And adjCell 3 ；
Step 6: and for adjacent cells which are not in the cell string list, calculating the distance between each vertex and the spherical surface great circle of the straight line segment, obtaining the farthest distance between each adjacent cell and the straight line segment, taking the adjacent cell with the smallest farthest distance as the next current cell curCell, and returning to the step 3.
5. The method of vector element gridding in a topologically true global discrete grid system according to claim 1, wherein: the specific step of gridding the vector surface data in the step (3) is as follows:
1) And classifying the cells intersected by the boundary of the original vector plane into three types according to the position relation between the original vector plane and the cells:
(1.1) stabilizing cells: for a certain vector plane, cells completely contained by the range between the inner ring and the outer ring of the certain vector plane are stable cells of the plane, and as the stable cells are only intersected with a single vector plane, if the stable cells of the certain vector plane can only be attributed to the plane according to the area dominance principle, other possibilities do not exist;
(1.2) unstable neurons: for a certain vector plane, the lattice intersecting with the outer ring or the inner ring of the certain vector plane is the unstable lattice of the plane, and because the unstable lattice may intersect with a plurality of vector planes, if the unstable lattice of the certain vector plane is attributed to the plane according to the area dominance principle, the unstable lattice of the certain vector plane may be attributed to other planes intersecting with the unstable lattice;
(1.3) Key cells: for a certain vector plane, a cell intersected with a narrow region of the certain vector plane is a key cell of the plane, the key cell is also intersected with the boundary of the vector plane and is a special unstable cell, and because the unstable cell is a region in which the unstable cells are gathered in a concentrated manner, the key cell part of the certain vector plane is easily divided by mistake, so that the topological relation of the plane can be changed;
2) And initial gridding: determining attribution of unstable cells by using an area domination principle, simultaneously recording topological adjacency relation between original vector planes, and simultaneously creating three non-repeated lists for each plane for recording stable cells, unstable cells and key cells of each plane: for a certain face, if a certain cell is a stable cell of the face, adding the code of the cell into a stable cell code list of the face; if a certain cell is an unstable cell of the surface, adding the code of the cell into an unstable cell code list of the surface; if a certain cell is the key cell of the face, adding the code of the cell into a key cell code list of the face;
3) Detecting topological distortion: first according to two adjacency matrices M o And M g To detect topological distortion, M o And M g Is n × n adjacency matrix, n is the number of original vector planes, when a plane r is adjacent to a plane s, M [ r][s]＝M[s][r]=1, otherwise M [ r)][s]＝M[s][r]＝0；
Matrix M for recording topological adjacency relation of original vector plane o Obtained by querying the topological relation of the original vector data, and for M recording the topological adjacency relation among the surfaces after the initial grid formation g If it is assumed that an unstable bin is attributed to a face r and an adjacent bin is attributed to a face s, where r is not equal to s, then it is known that the faces r and s are adjacent to each other after gridding, and M is juxtaposed g [r][s]＝M g [s][r]=1, traversing all unstable grid elements, and obtaining the topological relation adjacency matrix M between all surfaces after grid meshing g ；
Using a adjacency matrix M o And M g Detecting four types of topological distortion after gridding: if for the face r, it is not adjacent to any other face after being meshed, i.e. it is meshed
Wherein s is more than or equal to 0 and less than n, the surface r disappears after gridding; if M is o [r][s]1, and M g [r][s]=0, the topological relationship of the planes r and s changes from adjacent to separated; if M is o [r][s]=0, and M g [r][s]=1, the topological relationship of the planes r and s changes from phase separation to adjacency; if for face r, it has one and only one face s after it is meshed with M o [r][s]=1, and there is more than one face h for M g [r][h]If =1, the surface r is originally surrounded by the surface s, but the surrounding relationship disappears after the griddingLosing;
for another type of topological distortion, namely that a vector surface is divided after being subjected to gridding, the boundary of the surface is divided into a plurality of disconnected parts, and for each surface, the boundary of the surface after being subjected to gridding is firstly found through an unstable lattice: if a certain unstable cell of the face object is attributed to the face, the boundary cell is the boundary of the face, otherwise, the adjacent cell attributed to the face is the boundary of the face; traversing the boundary cells by using a flood filling algorithm with one cell of the boundary as a starting point, wherein if the cells in the boundary are not filled, the boundary is not communicated, and the surface cells are divided after being meshed;
4) After various topological distortions are detected, all surfaces of which the topological relations change after gridding are found; then determining attribution of all new cells according to an area dominance principle, wherein in the new cells, if a certain cell is completely contained by a certain face, the certain cell is attributed as a stable cell of the face, otherwise, the new cell is attributed as an unstable cell of the face, and then determining a key cell of the face according to the unstable cell; and finally, returning to the topological distortion detection step, and if the distortion still exists, recursively repairing until all the topological distortions disappear.
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