A method for calculating the topological relationship between buildings and green spaces based on V-TMM

Abstract

The present invention discloses a method for calculating the topological relationship between buildings and green spaces based on V-TMM, including four technical links: trapezoidal grid construction of surface elements, point-trapezoidal grid determination, topological relationship model definition, and calculation of polygonal topological relationship using V-TMM. The surface geometric object is divided into trapezoidal facets by horizontal scanning lines, and a trapezoidal connectivity graph is constructed; the point-trapezoidal grid determination is defined for the uniqueness of the row and column numbers and the horizontal and vertical coordinate intervals of the trapezoidal facets; a formalized definition of the topological relationship of the surface geometric object is given, and a vertex-trapezoidal grid model (V-TMM) is established; and a polygonal topological relationship calculation process based on V-TMM is designed. The present invention can realize the efficient calculation of the topological relationship of surface elements.

Description

Technical Field

[0001] The present invention relates to the fields of geographic information system (GIS), computer-aided design (CAD), computer cartography (CAC), navigation maps, electronic maps, and in particular to a method for calculating the topological relationship between buildings and green spaces based on V-TMM. Background Art

[0002] Topological relationships are the most basic and important spatial relationships in GIS, and they play an important role in GIS spatial reasoning and applications. In recent years, topological relationship conceptual models have been studied in depth, including the N-intersection model, the RCC model, the 2DString model, etc. Although there are many studies on the formal expression of topological relationships, there is little research progress in the calculation methods of topological relationships. There is a relative lack of research on the calculation algorithms combined with the topological relationship conceptual model, as well as the efficiency and stability of the algorithms.

[0003] Current methods for calculating topological relationships include analytic geometry algorithms, planar graph algorithms, and plane sweep conversion methods. The analytic geometry method establishes the parametric equation of a line and solves the positional relationships between points and line segments, line segments and line segments, and line segments and surfaces to achieve topological relationship judgment of spatial objects. Analytical geometry algorithms often have high operating efficiency and are easy to perform comprehensive calculations with spatial relationships such as measurement and orientation, but are difficult to integrate with topological concept models such as the 4 / 9-intersection model to calculate complex topological predicates. The planar graph method converts geometric objects such as points, lines, and surfaces into a planar graph through preprocessing of geometric relationships such as intersection, marks the nodes and edges in the graph as the interior, boundary, and exterior of the geometric object, and marks the surface as the left and right of the edge. Then, the 4 / 9 intersection model and its extensions (such as the dimensional model) are used to solve complex topological predicates. However, the plane graph method involves a large number of intersection operations when converting geometric objects into plane graphs, which is inefficient. In addition, information such as distance and orientation is lost during the conversion process, making it difficult to perform mixed spatial relationship calculations. The scan conversion method converts 2D topological relationship calculations into 0D pixel points, or 1D scan lines, or 2D polygons for calculation. After the conversion, the algorithm complexity can be significantly reduced, and higher computational efficiency can be achieved. However, this type of algorithm is often proposed for the calculation of topological relationships between a certain type of objects. A general and efficient method for calculating topological relationships has not yet been formed.

[0004] To solve the above problems, a new method is needed to realize the rapid calculation of GIS topological relationships. The Chinese patent entitled "A method, device and system for confirming regional water network topological relationships", application number CN201910145895.0, publication number CN111626460A, relates to the technical field of water network topological relationships in water supply systems, and provides a method, device and system for confirming regional water network topological relationships. The method includes determining one or more areas where water network topological relationships may potentially be incorrectly assigned; obtaining water flow data of each flow metering device contained in the one or more areas; and confirming one or more flow metering devices in the one or more areas that are in a state of incorrect water network topological relationships according to the water flow data. The present invention proposes a method for determining one or more areas where water network topological relationships may potentially be incorrectly assigned, and determining the probability of one or more flow metering devices in the one or more areas that are in a state of incorrect water network topological relationships through water flow data, thereby greatly saving the manpower cost of field investigation staff and improving the efficiency of investigation. The Chinese patent entitled "A method, device and storage medium for obtaining topological relationships based on spatial positions", with application number CN202110253348.1 and publication number CN112632399A, discloses a method, device and storage medium for obtaining topological relationships based on spatial positions, wherein the method includes: obtaining the WGS84 historical coordinate point data of the target object, and using the WGS84 historical coordinate point data to generate a real geographic projection coordinate surface under the Web Mercator coordinate system; obtaining the WGS84 real-time coordinate point data of the target object, and projecting the WGS84 real-time coordinate point data to the Web Mercator coordinate system to obtain the geographic projection coordinates of the target object; performing topological calculation on the geographic projection coordinates of the target object and the real geographic projection coordinate surface to obtain the topological relationship. This method effectively improves the accuracy of topological relationship calculation, can give full play to the value of historical scattered point data, and is conducive to monitoring the accuracy of decision-making plans made by decision makers. Both of the above two patent applications involve methods for calculating topological relationships, but neither of them discloses an efficient method for calculating topological relationships based on trapezoidal grids. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of topological relationship calculation and efficiency of surface elements, and to provide a topological relationship calculation method based on a trapezoidal grid to achieve efficient and stable calculation of topological relationships between surface elements.

[0006] The overall idea of ​​the present invention is to geometrically transform the surface elements into polygons, and through horizontal line scanning, divide the polygons into several trapezoidal facets and construct trapezoidal chains one by one to form a trapezoidal connectivity graph. Using the uniqueness of the row and column numbers and the horizontal and vertical coordinate intervals of the trapezoidal facets, the point-trapezoidal grid judgment is defined, and on this basis, the definition of the polygon topological relationship matrix is ​​given. Furthermore, for two arbitrary polygons, a polygon topological relationship calculation process is designed. This method is highly applicable and targeted for the calculation of the topological relationship of surface elements, and can achieve a high calculation efficiency.

[0007] The present invention provides a method for calculating the topological relationship between buildings and green spaces based on V-TMM, comprising the following steps:

[0008] Step 1, horizontal scanning line segmentation of the surface element to obtain a trapezoidal chain, construct a trapezoidal connectivity graph, and further construct a trapezoidal grid based on the trapezoidal connectivity graph;

[0009] Step 2, point-trapezoidal grid determination;

[0010] Step 3, formal definition of topological relations of surface geometric objects, and establishment of Vertex-Trapezoidal Mesh Model (V-TMM);

[0011] Step 4: Calculate the topological relationship between buildings and green spaces based on V-TMM to detect whether there is any illegal building land.

[0012] The above step 1 specifically includes: (1) geometrically transforming the surface element into a polygon, making a horizontal scan line from each vertex and forming an intersection with the polygon edge, and each two adjacent scan lines constitute a scan line, matching the intersection points between the scan lines and the polygon vertices to obtain a set of intersecting edges; (2) pairing the intersecting edges located in the same scan line from left to right to form a trapezoidal patch, and distinguishing the backbone trapezoid and the detail trapezoid in the trapezoidal patch according to the adjacency relationship and number of adjacencies between the trapezoidal patches; (3) finding the head of the trapezoid chain, which is either a triangle at the top of the polygon or a triangle following the backbone trapezoid. The detailed trapezoid below; starting from each trapezoid chain head, scan the lines one by one downward until the first backbone trapezoid is encountered and stop to build a trapezoid chain; after all the trapezoid chains are built, they are combined into a trapezoidal connectivity graph; (4) After steps (1), (2) and (3), a trapezoidal connectivity graph representing the polygon can be obtained; the trapezoidal facets are the basic units that make up the polygon, and the trapezoidal connectivity graph is an advanced and complete polygon decomposition form after the trapezoidal facets are classified and regularized, which is aimed at various calculation, analysis and visualization needs based on the trapezoidal grid data structure.

[0013] The above step 2 specifically includes: (1) in the trapezoidal connected graph constructed in step 1, traverse the trapezoidal chain one by one for the point to be determined, and determine whether the point falls within the current trapezoidal chain; (2) determine whether the point is located between the first and last trapezoids of the trapezoidal chain. If so, locate the detail trapezoidal row where the point is located, otherwise the point is outside the polygon; (3) determine whether the point is located in a detail trapezoid of the detail trapezoidal row. If so, the point is inside the polygon, otherwise the point is outside the polygon; (4) after steps (1), (2) and (3), it can be determined whether the point is within the trapezoidal grid formed by polygonal decomposition, that is, whether the point is within the polygon. This determination is called point-trapezoidal grid determination.

[0014] The above step 3 specifically includes: for the two polygons A and B whose topological relationship is to be calculated, construct a trapezoidal connectivity graph of the two. Using the point-trapezoidal grid judgment, the number of vertices of polygon B in polygon A is obtained, and the eight basic topological relationships are divided into three categories according to the number. Then, combined with the auxiliary judgment corresponding to each major category of topological relationship, a deterministic topological relationship matrix is ​​formed. This topological relationship model is called the vertex-trapezoidal grid model (V-TMM).

[0015] The above step 4 specifically includes: inputting the coordinate data of the building and the green space, and geometrically transforming the two into polygons. After the horizontal line scanning and segmentation in step 1, a trapezoidal connected graph is used to represent any building or green space, and then a vertex set P of a building A is obtained. A , and obtain P through step 2 A The number of points in a green space B is substituted into the topological relationship matrix defined in step 3. According to the matrix values, the topological relationship between the building and the green space is calculated to complete the detection of whether there is any violation of the building occupying the green space.

[0016] Beneficial effects: The present invention can efficiently and stably calculate the topological relationship between any two surface elements. The topological relationship definition is compatible with the eight types of topological relationships defined by the simple element specification released by the Open Geographic Information System Association, and can be freely expanded. Compared with the topological relationship calculation method of analytic geometry, this method has a deterministic topological relationship matrix and the calculation process is clear and efficient; compared with the topological relationship calculation of the plane graph, this method avoids a large number of intersection operations and significantly reduces the complexity of the algorithm; compared with other existing plane scan line topological relationship calculation methods, this method is highly targeted and applicable to surface elements, and improves the calculation efficiency of the topological relationship of surface elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flow chart of the method of the present invention;

[0018] Figure 2 Schematic diagram of trapezoidal decomposition of a single polygon;

[0019] Figure 3 Schematic diagram of a trapezoidal patch;

[0020] Figure 4 Schematic diagram of basic topological relationships of polygons. DETAILED DESCRIPTION

[0021] The present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0022] The present invention divides the surface elements by horizontal scanning lines and constructs a trapezoidal connectivity graph. The unique horizontal and vertical coordinate intervals of each trapezoidal face piece are used to perform point-trapezoidal grid judgment, and a deterministic topological relationship matrix is ​​defined on this basis. Finally, the topological relationship between the two polygons is obtained according to the topological relationship matrix of the two polygons.

[0023] Example 1

[0024] like Figure 1 As shown in the figure, the calculation of the topological relationship between building land and green space within a certain range in my country includes the following steps:

[0025] Step 1: horizontal scanning line segmentation of the surface element to construct a trapezoidal grid;

[0026] Step 2, point-trapezoidal grid determination;

[0027] Step 3, formal definition of topological relations of surface geometric objects, and establishment of Vertex-Trapezoidal Mesh Model (V-TMM);

[0028] Step 4: Calculate the topological relationship between buildings and green spaces based on V-TMM to detect whether there is any illegal building land.

[0029] More specific implementation steps are as follows:

[0030] Area element division and trapezoidal grid construction

[0031] The present invention uses horizontal scanning lines to perform trapezoidal subdivision on surface elements to quickly realize spatial operations between surface elements. The surface elements are geometrically transformed into polygons. If the surface element is P, the surface element can be geometrically transformed into a point sequence P1, P2, ..., P n-1 , P n =P1, P1P2, P2P3, ..., P n-1 P n =P n P1 forms the edge of the polygon, P i (i=1, 2, ..., n) are vertices of the polygon.

[0032] The horizontal scan lines emitted from each vertex of the polygon break each edge of the polygon (including the outer boundary and the inner boundary) to form a group of small line segments; Figure 2, in the same row, two adjacent small line segments from left to right serve as hypotenuses and the scan line to form trapezoidal patches.

[0033] In the specific implementation, first open a floating point array Polygon_Vertex_Y[] to store the vertices P1, P2, ..., P 11 ( Figure 2 The Y coordinate value of the array (represented by a solid circle in the figure) is sorted by the quick sort method from small to large, and the elements with the same value are eliminated; a horizontal scan line S1, S2, ..., S is drawn from each element in the array. n (Represented by dotted lines) Break the edges of polygon P.

[0034] Taking edge P1P2 as an example, the Y coordinate values ​​of its endpoints are two elements in the ordered array Polygon_Vertex_Y[]. In the figure, P1 and P2 are located on scan lines S1 and S4 respectively. It can be inferred that edge P1P2 intersects with scan lines S2 and S3 between S1 and S4 (the intersection is represented by a hollow circle). At this time, P1P2 is broken into three small line segments connected end to end. When all the edges of polygon P are broken, a set of small line segments organized in rows can be obtained. In the same row, these small line segments are matched in pairs from left to right, and the trapezoidal units can be extracted one by one, which realizes the trapezoidal decomposition of the polygon. It should be pointed out that triangular facets may appear in the decomposition result ( Figure 2 The top and bottom of the polygon in the figure are respectively the top and bottom of the polygon, which can be regarded as special trapezoids with degenerated bases.

[0035] The trapezoidal patches obtained by scanning line segmentation will be stored in a pair of data structures TrapMesh_Row and TrapMesh_Unit. The row trapezoidal patch linked list structure TrapMesh_Row is used to organize the trapezoidal patches in a scan line, and the pointers *Begin and *End of the TrapMesh_Unit type point to the first and last trapezoidal patches in the row respectively; in this way, all the trapezoidal patches in the same row are connected in series, which is convenient for insertion, deletion, search and other operations.

[0036] The trapezoidal patch structure TrapMesh_Unit records the position coordinates, attributes, adjacent trapezoidal patches and other information of a trapezoidal patch unit. Figure 3 As an example, the trapezoidal patch is composed of the outer boundary vertex P2 and the inner boundary vertex P 10 and P 11, the intersection of scan line S5 and edge P2P3. The Y coordinate values ​​of the four vertices are the same as the Y coordinate values ​​of scan line S4S5, so there is no need to record them repeatedly. Therefore, the trapezoid patch structure only stores the X coordinate values ​​of the four vertices UpLeft, UpRight, DownLeft, DownRight, the attribute PolygonID of the polygon to which the trapezoid patch belongs, and the pointer *Next pointing to the adjacent trapezoid patch in the same row.

[0037] Point-trapezoidal grid determination

[0038] One of the characteristics of the trapezoidal grid inherited from the grid is that each sub-region obtained by dividing the polygon by the horizontal scan line, that is, each trapezoidal face that constitutes the trapezoidal grid, has a unique row and column number and a unique horizontal and vertical coordinate interval. Utilizing this characteristic, the computational efficiency of the image can be greatly improved. The present invention uses this to determine whether a point is within a polygon.

[0039] Current determination methods include cross multiplication method, area method, angle sum method, number of horizontal / vertical intersection points, etc. However, no matter which method is used, it involves complex and tedious calculations. Under the structure of the trapezoidal grid, by using the unique horizontal and vertical coordinate interval of each trapezoidal face, it is only necessary to traverse row by row and column by column, and compare the horizontal and vertical coordinate values ​​of the point to be determined with the left and right endpoint values ​​of the horizontal and vertical coordinate interval of the current trapezoidal face to complete the determination of whether the point is inside the polygon. That is, a simple size comparison is used to replace tedious cross multiplication, intersection and other calculations to obtain higher computing efficiency. The present invention refers to this determination method as point-trapezoidal grid determination, and the specific process of the algorithm can be described as:

[0040] 1) Let the horizontal and vertical coordinates of the point P to be determined be X p , Y p Traverse the ladder chain in the ladder connection graph and extract the first and last ladders T of the current ladder chain p , T r , get the first trapezoid T p The ordinate of the upper parallel side maxy(T p ) and the ordinate miny(T p ), if miny(T p )≤Y p ≤maxy(T p ), then proceed to the next step, otherwise the point is not within the polygon.

[0041] 2) Traverse the trapezoidal patches in the trapezoidal chain and extract the current trapezoidal patch T i The ordinate maxy(T i ) and miny(T i ), if miny(T i )≤Y p ≤maxy(Ti ), the point to be determined may be located within the trapezoidal patch, so the traversal is stopped and the next step of determination is entered.

[0042] 3) Get the trapezoidal patch T i The horizontal and vertical coordinates of the four vertices, namely the coordinates of the upper left corner (ULx, ULy), the lower left corner (DLx, DLy), the upper right corner (URx, URy), and the lower right corner (DRx, DRy) of the trapezoidal face.

[0043] 4) Determine whether point P is located on the trapezoidal patch T i In the inscribed matrix of , that is, whether the following conditions are satisfied

[0044] max(ULx,DLx)≤X p ≤min(URx,DRx)

[0045] If yes, the point is inside the polygon and the determination ends; otherwise, proceed to the next step.

[0046] 5) Determine whether point P is located on the trapezoidal patch T i The left hypotenuse area, that is, whether the following two conditions are met

[0047] min(ULx,DLx)≤X p ≤max(ULx,DLx)

[0048]

[0049] If yes, the point is inside the polygon and the determination ends; otherwise, proceed to the next step.

[0050] 6) Determine whether point P is located on the trapezoidal patch T i The right hypotenuse area, that is, whether the following two conditions are met

[0051] min(URx,DRx)≤X p ≤max(URx,DRx)

[0052]

[0053] If yes, the point is inside the polygon and the determination ends; otherwise, the point is not inside the polygon.

[0054] Topological relationship matrix definition

[0055] To facilitate description of the positional relationship between a point and a polygon, in the present invention, a point inside and on the boundary of a polygon is referred to as being contained by the polygon, and a point only inside the polygon is referred to as being included by the polygon.

[0056] The present invention calculates the topological relationship between two polygons (including simple and complex polygons) based on the trapezoidal grid. For two polygons A and B, first construct the trapezoidal grids of the two, and use the point-trapezoidal grid judgment to obtain the number of vertices of B included in A. Based on this number and combined with the corresponding auxiliary judgment, a deterministic topological relationship matrix is ​​formed, which is called the vertex-trapezoidal mesh model (V-TMM) in the present invention. The topological relationship matrix R (A, B) can be described as:

[0057]

[0058] Where N is the number of vertices of polygon B contained in A. According to the theory of Egenhofer et al., any polygon I, with its interior I° and boundary It can be expressed in two parts; all vertices of I form a point set P I ; C represents the entire plane area. It should be pointed out that the determination of whether each point set intersects with the area is realized through point-trapezoidal grid determination.

[0059] Regarding the values ​​of each element in the matrix, N∈[0,N B ] and N∈Z, Z is an integer set, N B is the number of vertices of polygon B. The remaining elements correspond to a judgment, and the value range is {0,1}. If a point in the point set is located in the judgment area, it takes 1, and if it is not, it takes 0. At the same time, in order to express the matrix concisely, * is introduced to indicate that the element is irrelevant to the topological relationship calculation of the current situation and is ignored.

[0060] The eight basic spatial topological relationships of polygons expressed by V-TMM can be described as:

[0061]

[0062]

[0063] Using V-TMM to detect illegal building sites

[0064] The two polygons whose topological relationships are to be calculated are denoted as A and B. According to the result of point-trapezoidal grid determination, that is, the value of N in the topological relationship matrix R, the present invention divides the eight basic topological relationships into the following three categories:

[0065] {included, separated} N=0

[0066] {overlap, covered, connected} N∈[1, N A -1]

[0067] {equal, covering, including} N=N A

[0068] 1) N is 0

[0069] None of B's ​​vertices are contained by A, that is, all of B's ​​vertices are outside A. There are two possibilities. First, if Figure 4 As shown in (a), all vertices of A are outside of B, and A and B are disjoint. Figure 4 As shown in (b), all vertices of A are contained within B, and A is included (Within) by B.

[0070] According to the above analysis, when N is 0, the topological relationship between A and B ranges from {separate, contained}. The present invention uses the elements of the first row of the topological relationship matrix to calculate the topological relationship and determine whether there is a vertex in A that is contained in B. If so, P A ∈B° takes 1, then A is contained by B (Within), the calculation ends, and the topological relationship matrix is ​​described as:

[0071]

[0072] Otherwise, P A ∈B° takes 0, then A and B are separated (Disjoint), the calculation ends, and the topological relationship matrix is ​​described as:

[0073]

[0074] 2) N is between 1 and N B -1

[0075] For the convenience of matrix expression, let n∈[1, N B -1] and n∈Z, Z is an integer set. That is, in this case, N is n, and some but not all of B's ​​vertices are included in A. There are three possibilities. One is, Figure 4 (c) There are vertices of B that are included in A, and A and B overlap.

[0076] If none of B's ​​vertices are contained by A, it means that some of B's ​​vertices are contained by A but not contained by A. Then these vertices all fall on the boundary of A, that is, the boundaries of A and B overlap. There are two other possibilities in this case. First, if Figure 4 (d) A borders B from the inside, and A is covered by B (CoveredBy); second, Figure 4 (e) A borders B from the outside, and A and B are in contact (Touch).

[0077] According to the above analysis, when N is n, the topological relationship between A and B ranges from {overlapping, covered, connected}. The present invention uses N and the elements in the second row of the topological relationship matrix to calculate the topological relationship. First, it is determined whether there is a vertex in B that is included in A. If so, PB ∈A° takes 1, then A and B overlap (Overlap), the calculation ends, and the topological relationship matrix is ​​described as:

[0078]

[0079] Otherwise, P B ∈A° takes 0, and then determines whether there is a vertex in A that is included in B. If so, then P A ∈B° takes 1, then A is covered by B (CoveredBy), the calculation ends, and the topological relationship matrix is ​​described as:

[0080]

[0081] Otherwise, P A ∈B° takes 0, then A and B are connected (Touch), the calculation ends, and the topological relationship matrix is ​​described as:

[0082]

[0083] 3) N is N B

[0084] All vertices of B are contained by A. At this time, there are three possibilities. Figure 4 (f) There is no vertex of A that is outside B, that is, all the vertices of A are also included in B, which means that the vertices of A and B are exactly the same, and A and B are equal.

[0085] Otherwise, there are two other possibilities. Figure 4 (g) The vertices of B are either contained in A or on the boundary of A, and A covers B (Cover); secondly, Figure 4 (h) All vertices of B are contained in A, and A contains B (Contain).

[0086] According to the above analysis, N is N B When , the topological relationship value range of A and B is {equal, inclusive, covering}. The present invention uses N and the elements of the third row of the topological relationship matrix to calculate the topological relationship. First, it is determined whether there is a vertex in A that is outside B. If not, If 0 is taken, A and B are equal (Equal), the calculation ends, and the topological relationship matrix is ​​described as:

[0087]

[0088] otherwise, Take 0, and then determine whether there is a vertex in B that is not included in A. If so, P B ∈(CA°) takes 1, then A covers B (Cover), the calculation ends, and the topological relationship matrix is ​​described as:

[0089]

[0090] Otherwise, P B ∈(CA°) takes 0, then A contains B (Contain), the calculation ends, and the topological relationship matrix is ​​described as:

[0091]

[0092] In the detection of illegal construction land, the coordinate data of the building and green space are first input, and the two are geometrically transformed into polygons. Then, the polygons are segmented using horizontal scanning lines, and the corresponding trapezoidal connectivity graph is constructed. The building is then taken as polygon A and the green space as polygon B. The result of the point-trapezoidal grid judgment is substituted into the corresponding topological relationship matrix in the corresponding V-TMM to calculate the topological relationship between A and B.

[0093] Through the above process, the topological relationship between each building and each green space is calculated one by one. Only when the calculation result is separation (Disjoint) or connection (Touch), the building does not occupy the green space. The building ID number in other cases is recorded, and all buildings that illegally occupy green space can be extracted to complete the detection of illegal building land.

Claims

1. A method for calculating the topological relationship between buildings and green spaces based on V-TMM, characterized in that: The steps include: Step 1, horizontal scanning line segmentation of the surface element to obtain a trapezoidal chain, construct a trapezoidal connectivity graph, and further construct a trapezoidal grid based on the trapezoidal connectivity graph; Step 2, point-trapezoidal grid determination; specifically includes: (1) In the ladder-shaped connected graph constructed in step 1, traverse the ladder chains for the points to be determined one by one to determine whether the points fall within the current ladder chain; (2) Determine whether the point is located between the first and last trapezoids of the trapezoid chain. If so, locate the detail trapezoid row where the point is located; otherwise, the point is outside the polygon; (3) Determine whether the point is located in a detail trapezoid of the detail trapezoid row. If so, the point is inside the polygon; otherwise, the point is outside the polygon. (4) After steps (1), (2) and (3), determine whether the point is within the trapezoidal grid formed by polygonal division, that is, whether the point is within the polygon. This determination is called point-trapezoidal grid determination; Step 3, formal definition of the topological relationship of the face geometric objects, and establishment of a vertex-trapezoidal mesh model (V-TMM); specifically, for two polygons A and B whose topological relationship is to be calculated, construct a trapezoidal connectivity graph of the two, use point-trapezoidal mesh judgment to obtain the number of vertices of polygon B in polygon A, and divide the eight basic topological relationships into three categories according to the number, and then combine the auxiliary judgment corresponding to each major category of topological relationship to form a deterministic topological relationship matrix. This topological relationship model is called a vertex-trapezoidal mesh model (V-TMM); Step 4: Calculate the topological relationship between buildings and green spaces based on V-TMM to detect whether there is any illegal building land; specifically, the following steps are performed: Input the coordinate data of buildings and green spaces, and transform them into polygons. After horizontal line scanning and segmentation in step 1, use a trapezoidal connectivity graph to represent any building or green space, and then obtain a vertex set P of building A. A , and obtain P through step 2 A The number of points in a green space B is substituted into the topological relationship matrix defined in step 3. According to the matrix values, the topological relationship between the building and the green space is calculated to complete the detection of whether there is any violation of the building occupying the green space.

2. The method for calculating the topological relationship between buildings and green spaces based on V-TMM according to claim 1, characterized in that: The step 1 specifically includes: (1) Geometrize the surface element into a polygon, draw a horizontal scan line from each vertex of the polygon and form an intersection with the polygon edge. Every two adjacent scan lines constitute a scan line. Match the intersection points between the scan lines with the polygon vertices to obtain the intersection edge set; (2) The intersecting edges on the same scan line are paired from left to right to form trapezoidal patches. The backbone trapezoids and detail trapezoids in the trapezoidal patches are distinguished according to the adjacency relationship and number of adjacencies between the trapezoidal patches. (3) Find the head of the trapezoid chain, which is either the triangle at the top of the polygon or the detail trapezoid below the backbone trapezoid; Starting from each ladder chain head, traverse the ladder face patches downward one by one until you encounter the first backbone ladder and stop, thus constructing a ladder chain; After all ladder chains are constructed, they are combined into a ladder-connected graph; (4) After steps (1), (2) and (3), a trapezoidal connectivity graph representing the polygon is obtained; the trapezoidal face is the basic unit of the polygon, and the trapezoidal connectivity graph is an advanced and complete polygon decomposition form after the trapezoidal face set is classified and regularized, which is suitable for various calculation, analysis and visualization needs based on the trapezoidal grid data structure.

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