Step modeling method for urban rainfall flood simulation based on point cloud data

Abstract

The invention discloses an urban rainfall flood simulation-oriented step modeling method based on point cloud data, and belongs to the technical field of urban hydrological modeling, and the method comprises the steps: setting grids, laying the grids on step point cloud data, and traversing the point cloud data of each grid unit to obtain large step surface points; arc-shaped step edge points or linear step edge points are fitted according to the step edge shapes of the large step surface points, and small steps between the large steps are interpolated according to the preset small step number and the elevation difference of the large step surface points; when the vertical surface of the small step is interpolated, a preset offset is set in the positive direction of the Y axis of the edge of the step above the vertical surface of the small step to obtain a small step surface point; the large step surface points and the small step surface points are merged and then recovered to the initial direction and the geographic coordinate system, and an irregular triangulation network is constructed based on Delaunay triangulation to complete step modeling. According to the method, the problem of artificial surface modeling distortion caused by insufficient DEM data precision in traditional urban rainfall flood simulation is solved.

Description

Technical Field

[0001] The invention relates to a step modeling method for urban rain and flood simulation based on point cloud data, belonging to the technical field of urban hydrological modeling. Background Art

[0002] In the urban stormwater simulation technology system, elevation models are the fundamental data carrier for simulation and analysis. By digitally representing the three-dimensional morphology of urban surfaces, they provide the computational foundation for shallow water equations and hydrological models. Current urban stormwater simulations primarily rely on traditional digital elevation model (DEM) technology to construct surface elevation datasets. This technology uses regular grids or irregular triangulated networks (TINs) to obtain surface elevation sampling points through aerial photogrammetry and satellite remote sensing, and then uses spatial interpolation algorithms to generate continuous elevation surfaces. To meet the needs of artificial surface modeling, the industry has developed two mainstream technical approaches: parametric modeling based on CAD software. By inputting geometric parameters such as step height, width, and slope, the DEM generates a 3D solid model using tools such as feature modeling and surface extrusion. Collaborative modeling based on BIM platforms integrates information from the entire building lifecycle to achieve a geometrically and semantically integrated representation of step models. Both approaches are widely used in architectural design and engineering, accurately reproducing the geometric morphology and spatial position of steps, effectively supporting 3D urban visualization and engineering quantity analysis.

[0003] Traditional urban stormwater simulation technology suffers from significant data deficiencies in artificial surface modeling, manifested in a structural conflict between DEM data accuracy and the complexity of surface features. First, traditional 2.5D DEM data suffers from insufficient vertical sampling density, resulting in significant distortion in the representation of artificial surface features such as steps, which have millimeter-scale geometric features. Experimental data shows that when step heights are less than 0.5 meters, conventional DEM grid resolution cannot effectively capture their vertical variations, resulting in elevation errors of up to 30%-50% of the actual height in the step area. This geometric distortion directly leads to anomalies in hydrodynamic simulations, such as misidentifying steps as gently sloping terrain, resulting in flow path deviations and miscalculation of ponded depths. Second, traditional hydrological models further exacerbate simulation distortions by simplifying complex terrain. Existing models often use empirical formulas such as the Manning equation to describe surface roughness. However, factors such as the angular structure and material variations of step surfaces cannot be represented by a single parameter, leading to systematic deviations in the calculation of flow resistance. Furthermore, traditional technology systems underutilize new data sources such as 3D point clouds. While step point cloud data acquired through 3D laser scanning offers millimeter-level accuracy and centimeter-level resolution, existing hydrodynamic models lack the ability to directly process these massive amounts of point cloud data and must be converted to a DEM format through dimensionality reduction. This conversion inevitably results in a loss of detailed information. These deficiencies collectively result in a 20%-40% decrease in the prediction accuracy of urban flood simulations in areas with dense step density, severely hindering the scientific nature of waterlogging risk assessment and emergency response planning. Summary of the Invention

[0004] The purpose of the present invention is to provide a step modeling method for urban stormwater simulation based on point cloud data. By constructing an irregular triangulated network through high-precision point cloud data rasterization clustering, geometrically constrained edge fitting and multi-level step topology interpolation technology, step modeling is completed to solve the problem of artificial surface modeling distortion caused by insufficient DEM data accuracy in traditional urban stormwater simulation.

[0005] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions.

[0006] The present invention provides a step modeling method for urban stormwater simulation based on point cloud data, comprising:

[0007] Obtain point cloud data of steps on the urban surface;

[0008] Correct the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system;

[0009] Set the grid and tile it on the step point cloud data, and merge the step point cloud data in the same grid unit as the grid unit point cloud data;

[0010] Traverse each grid cell and merge all grid cell point cloud data with the same X-axis coordinate value as the current grid cell point cloud data and the difference in Z-axis coordinate value less than a first preset threshold into a group. If the cumulative number of step point cloud data in the group is greater than a second preset threshold, the grid cell point cloud data in the group is regarded as a large step surface point;

[0011] If the step edge shape of the large step surface point is arc-shaped, the X-axis coordinates of the large step surface point are sequentially traversed, the arc-shaped step edge points of the large step surface point are extracted in sequence, and the arc-shaped step edge points of the large step surface point are fitted using a third-order B-spline curve;

[0012] If the step edge shape of the large step surface point is a straight line, construct a straight line point parallel to the positive direction of the X axis and with a length equal to the width of the large step surface as the straight line step edge point of the large step surface point;

[0013] Using arc-shaped or straight-line step edge points, small steps between large steps are interpolated based on the preset number of small steps and the elevation difference between the large step surface points. When interpolating the vertical surface of the small step, a preset Y-axis offset is applied to the step edge above the vertical surface of the small step to obtain the small step surface points.

[0014] After merging the large step surface points and the small step surface points, the step point cloud data is restored to the initial direction and geographic coordinate system, and an irregular triangulated network is constructed based on Delaunay triangulation to complete the step modeling.

[0015] Furthermore, the method of correcting the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system includes:

[0016] Get the initial direction of the step point cloud data, use any point in the step point cloud data as a reference point, and transform the step point cloud data from the geographic coordinate system to a relative coordinate system with the reference point as the origin;

[0017] Perform principal component analysis on the step point cloud data to extract the direction vector of the plane formed by the X-axis and Y-axis of the relative coordinate system;

[0018] The geometric center of the step point cloud data is obtained by averaging the X-axis coordinate and Y-axis coordinate of the step point cloud data;

[0019] According to the angle between the positive direction of the Y-axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center, and the step point cloud data that deviates from the positive direction of the Y-axis in the relative coordinate system is corrected to the positive direction of the Y-axis in the relative coordinate system based on the translation matrix and the rotation matrix.

[0020] Furthermore, the translation matrix and the rotation matrix are respectively expressed as:

[0021] ;

[0022] Where, Represents the translation matrix. The 1s and 0s in the first three rows and first three columns represent the unit matrix. This transformation does not perform scaling or rotation. The 0 in the third column of the fourth row indicates that the Z axis does not participate in the translation. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinates will not affect other dimensions. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinates after the transformation remains 1. Indicates the X-axis coordinate of the geometric center of the step point cloud data. Indicates the Y-axis coordinate of the geometric center of the step point cloud data. Represents a rotation matrix. The 0 in the third column of the first two rows indicates that the Z axis does not participate in the Y direction calculation. The 0 in the first two columns of the third row indicates that the X-axis and Y-axis coordinates do not participate in the Z direction calculation. The 1 in the third row indicates that the Z axis coordinate remains unchanged. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinate does not affect other dimensions. The 0 in the fourth row indicates that the applied translation is 0. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinate after the transformation is kept as 1. Indicates the angle between the positive direction of the Y axis and the direction vector The cosine value of Indicates the angle between the positive direction of the Y axis and the direction vector The sine value of .

[0023] Furthermore, the X-axis coordinate and Y-axis coordinate of the grid unit point cloud data are the center coordinates of the grid unit, and the Z-axis coordinate of the grid unit point cloud data is the average Z coordinate of all step point cloud data in the same grid unit.

[0024] Furthermore, the resolution of the grid is 0.01 m, and the side length of the grid unit is less than or equal to 1 / 3 of the depth of the small step.

[0025] Furthermore, the edge points of the arc-shaped steps need to satisfy edge constraints, which are expressed as:

[0026] ;

[0027] Where, Indicates the mathematical symbol "arbitrary", Represents the mathematical symbol "or", , , Respectively represent the X-axis coordinate, Y-axis coordinate and Z-axis coordinate of the edge point of the arc step, Indicates that all X-axis coordinates are equal to the X-axis coordinates of the arc step edge point And the Z-axis coordinate is the same as the Z-axis coordinate of the edge point of the arc step The difference is less than the first preset threshold The big step pastry collection, Represents a large step surface point set, The X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the step point cloud data.

[0028] Furthermore, the objective function of the third-order B-spline curve is expressed as:

[0029] ;

[0030] Where, Indicates the total number of edge points of the front arc step fitted using a third-order B-spline curve. Indicates that before using the third-order B-spline curve fitting, The coordinates of the edge points of the arc steps, Indicates the third-order B-spline curve after fitting The edge point of the arc step on The square of the distance between two points, Indicates the smoothing factor, the value is 1.

[0031] Furthermore, the method of using arc-shaped step edge points or straight-line step edge points to interpolate small steps between large steps according to a preset number of small step steps and the elevation difference of large step surface points includes:

[0032] Calculate the average elevation of each large step based on the surface points of each group of large steps, then calculate the elevation difference between adjacent large steps based on the average elevation of each large step, and divide it by the preset number of small steps to obtain the unit elevation of the small steps;

[0033] Calculate the Y-axis distance between the inner edges of adjacent large steps based on each group of large step surface points, and divide it by the preset number of small steps to obtain the unit depth of the small steps;

[0034] Starting from the inner edge of the large step surface with the lowest average elevation, insert an arc-shaped step edge point or a straight step edge point every time you move forward by the unit depth of a small step in the positive direction of the Y axis and move up by the unit elevation of a small step in the positive direction of the Z axis.

[0035] Furthermore, the preset offset value is 0.001m.

[0036] Furthermore, after merging the large step surface points and the small step surface points, restoring the step point cloud data to the initial direction and geographic coordinate system includes:

[0037] Merge the large step surface points and the small step surface points to obtain the merged step point cloud data;

[0038] According to the angle between the positive direction of the Y-axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center, and the merged step point cloud data is converted into step point cloud data with the initial direction in the relative coordinate system based on the translation matrix and the rotation matrix;

[0039] Based on the reference point and the initial orientation of the step point cloud data in the relative coordinate system, the step point cloud data is restored to the geographic coordinate system.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. The present invention traverses the grid unit point cloud data, identifies the large step surface points based on the Z-axis coordinate difference and the cumulative number threshold, and effectively distinguishes the step structures of different height levels. For the edge processing of the large step surface points, different processing methods are adopted according to the edge shape. When the step edge is arc-shaped, the X-axis coordinates are traversed sequentially and the arc-shaped step edge points are extracted, and then the third-order B-spline curve is used for fitting. It can accurately restore the smooth curve characteristics of the arc edge, avoid the distortion caused by the simplified processing of the arc edge by the traditional method, greatly improve the accuracy of the step edge modeling, and ensure that in the urban rain and flood simulation, the flow simulation of water along the step edge is more in line with the actual situation. When the step edge is a straight line, the straight line points parallel to the positive direction of the X-axis and with a width equal to the large step surface are directly used as the straight line step edge points, which simply and efficiently handles the straight line edge situation, taking into account both processing speed and accuracy.

[0042] 2. This invention interpolates small steps by utilizing the preset number of small steps and the elevation difference between the large step surface points. This method of generating small steps based on actual elevation relationships makes the step structure more consistent with the characteristics of real urban terrain and enhances the fidelity of the actual scene. In addition, when interpolating the vertical surface of the small step, a preset offset is set in the positive Y-axis direction for the step edge above the vertical surface of the small step. This fully considers the possible small protrusions or irregularities in the vertical direction of the actual step, avoids the rainstorm simulation deviation caused by over-idealization of the vertical surface, and further improves the reliability of the model.

[0043] 3. The present invention completes the step modeling by merging the large step surface points and the small step surface points and restoring them to the initial direction and geographic coordinate system, and constructing an irregular triangulated network based on Delaunay triangulation. It not only completely retains the geographical location and various detailed features of the steps, but also the constructed irregular triangulated network has a good topological structure, which can efficiently perform subsequent stormwater simulation calculations, providing an accurate, reliable and efficient step model for urban stormwater simulation, supplementing the deficiencies of centimeter-level precision urban artificial surface models in stormwater simulation, and helping to more accurately predict the water flow movement, water accumulation distribution, etc. in cities under stormwater conditions, providing a scientific basis for urban flood control and drainage planning, emergency response, etc., and has important practical application value and social significance.

[0044] 4. By calibrating the urban surface step point cloud data to the positive Y-axis of the relative coordinate system, this method effectively unifies the data orientation benchmark, providing a standardized data foundation for subsequent processing. This avoids modeling errors caused by differences in coordinate orientation and significantly improves data usability and processing efficiency. Secondly, by setting a grid and tiling it over the step point cloud data, point cloud data within the same grid cell is merged, achieving reasonable data aggregation. This reduces data volume while preserving key spatial features. While ensuring data accuracy, it also reduces the computational complexity of subsequent processing and improves overall modeling speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a step modeling method for urban stormwater simulation based on point cloud data provided by an embodiment of the present invention;

[0046] Figure 2 This is a schematic diagram of a process for correcting step point cloud data to the positive direction of the Y-axis of the relative coordinate system provided by an embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of the result of correcting the step point cloud data to the positive direction of the Y axis in the relative coordinate system provided by an embodiment of the present invention;

[0048] Figure 4 This is a schematic diagram of the principle of generating grid cell point cloud data provided by an embodiment of the present invention;

[0049] Figure 5 Schematic diagram of the result of grid cell point cloud data provided by an embodiment of the present invention;

[0050] Figure 6 This is a schematic diagram of the large step surface point extraction result of the straight-edge step provided by an embodiment of the present invention;

[0051] Figure 7 This is a schematic diagram of the large step surface point extraction result of the arc-edge step provided by an embodiment of the present invention;

[0052] Figure 8 2 is a schematic diagram of the arc-shaped step edge point extraction result provided by an embodiment of the present invention;

[0053] Figure 9 Schematic diagram of the result of fitting the arc-shaped step edge points with a third-order B-spline curve provided by an embodiment of the present invention;

[0054] Figure 10 Schematic diagram of the process of interpolating small steps provided by an embodiment of the present invention;

[0055] Figure 11 This is a schematic diagram of the interpolation result of a small step provided by an embodiment of the present invention;

[0056] Figure 12 This is a schematic diagram of the point cloud reconstruction result of a straight-edge step provided by an embodiment of the present invention;

[0057] Figure 13 This is a schematic diagram of the point cloud reconstructed from an arc-edge step according to an embodiment of the present invention;

[0058] Figure 14 This is a schematic diagram of the modeling result of constructing an irregular triangulated network based on Delaunay triangulation of straight-edge step reconstructed point cloud data provided by an embodiment of the present invention;

[0059] Figure 15 This is a schematic diagram of the modeling result of constructing an irregular triangulated network based on Delaunay triangulation of arc-edge step reconstructed point cloud data provided by an embodiment of the present invention;

[0060] Figure 16 This is a schematic diagram of the water flow simulation effect using the ANUGA model based on the straight-edge step modeling result provided by an embodiment of the present invention;

[0061] Figure 17 This is a schematic diagram of the modeling results of the steps in the North Square of Nanjing Normal University provided by an embodiment of the present invention;

[0062] Figure 18 Schematic diagram of the rain flood simulation results of the North Square of Nanjing Normal University under uniform rainfall intensity provided by an embodiment of the present invention;

[0063] Figure 19 It is a schematic diagram comparing the modeling results of the irregular triangulated network constructed based on the original step point cloud data and the reconstructed step point cloud data provided by an embodiment of the present invention based on Delaunay triangulation. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0065] Example 1

[0066] like Figure 1 As shown, this embodiment introduces a step modeling method for urban stormwater simulation based on point cloud data, which is characterized by including:

[0067] Step 1: Obtain point cloud data of steps on the urban surface.

[0068] The present invention simulates steps on the urban surface through step point cloud data.

[0069] Step 2: Correct the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system.

[0070] This invention converts point cloud data from the original geographic coordinate system into a spatial rectangular coordinate system by converting it into a relative coordinate system, facilitating subsequent traversal of the X and Y coordinates of the point cloud data. By correcting the initial direction of the step point cloud data to the positive Y-axis, all steps are unified into a single type of step with a positive Y-axis orientation, simplifying the process and providing a data foundation for subsequent extraction of arc-shaped step edge points and interpolation of small steps along the positive Y-axis.

[0071] Step 3: Set the grid and tile it on the step point cloud data, and merge the step point cloud data in the same grid unit as the grid unit point cloud data.

[0072] This invention uses grid normalization to normalize the originally chaotic point cloud data into grid unit point cloud data. This not only removes most of the noise point cloud and reduces the impact of the noise point cloud on subsequent operations such as extracting large step surfaces, but also ensures that all grid unit point cloud data are within the X-axis and Y-axis coordinate network with fixed scale intervals, allowing the originally chaotic point cloud data to be arranged in a regular pattern. This allows the point cloud data to be processed using grid-based methods, providing the data foundation for the subsequent extraction of large step surfaces and curved step edges based on the gridded X coordinates.

[0073] Step 4: Traverse each grid cell and merge all grid cell point cloud data whose X-axis coordinate values are equal to the current grid cell point cloud data and whose Z-axis coordinate value difference is less than the first preset threshold into a group. If the cumulative number of step point cloud data in the group is greater than the second preset threshold, the grid cell point cloud data in the group is regarded as a large step surface point.

[0074] The present invention utilizes the characteristic advantage of the regular arrangement of grid point cloud data by setting the condition of equality on the X axis, and gradually groups the grid unit point cloud data by column along the X axis; by setting a threshold condition on the Z axis, it ensures that the points in each group after grouping belong to the same step surface; by setting a quantity threshold, based on the geometric feature that "on each straight line perpendicular to the X axis, that is, on the straight line where the step extends, the points according to the large step surface must be far more than the points on the small step surface", the point cloud data group storing the large step surface points is screened out, thereby extracting the large step surface, setting the X axis to provide a data basis for the subsequent operations of determining the step edge shape and extracting the arc step edge, providing a data basis for the steps of calculating the unit depth and unit height in the subsequent operation of interpolating the small step, and providing start and end conditions for the steps of interpolating the arc step edge and the straight step edge;

[0075] Step 5: Determine the edge shape of the steps of the large step pasta:

[0076] If the step edge shape of the large step surface point is arc-shaped, the X-axis coordinates of the large step surface point are traversed sequentially, and the arc-shaped step edge points of the large step surface point are extracted in sequence. The arc-shaped step edge points of the large step surface point are fitted using a third-order B-spline curve; wherein, the arc-shaped step edge point extraction result is as follows: Figure 8 As shown in the figure, the result of fitting the arc-shaped step edge points using the third-order B-spline curve is as follows: Figure 9 shown.

[0077] The present invention sets boundary constraints based on the geometric characteristic that "the step edge point satisfies all points with a similar elevation difference, and all points must be larger or smaller than it in the Y direction", and initially extracts the arc edge points of the large step surface points. However, because the grid unit point cloud data is regularly arranged, sharp corners often appear at the arc segments, making it impossible to form smooth arc points. Therefore, the present invention uses B-spline curve fitting to the initially extracted arc edge points to increase the density and smoothness of the arc edge points, providing interpolation elements for the subsequent interpolation of small steps, and ensuring that the arc edges can be accurately modeled when the irregular triangulation network is subsequently constructed based on Delaunay triangulation.

[0078] If the step edge shape of the large step surface point is a straight line, construct a straight line point parallel to the positive direction of the X-axis and with a length equal to the width of the large step surface as the straight line step edge point of the large step surface point.

[0079] This method directly generates straight line points parallel to the X-axis and with a width equal to that of the large step surface as the straight step edge points. This ensures that the small step edges subsequently interpolated and modeled are standard straight lines without curvature or noise. This provides interpolation elements for subsequent interpolation of small steps and improves the efficiency of extracting and fitting step edge points.

[0080] Step 6: Use arc-shaped step edge points or straight-line step edge points to interpolate small steps between large steps according to the preset number of small steps and the elevation difference of large step surface points. When interpolating the vertical surface of the small step, apply a preset offset in the Y-axis direction to the step edge above the vertical surface of the small step to obtain the small step surface points.

[0081] The present invention uses arc-shaped step edge points or straight-line step edge points to interpolate small steps between large steps according to unit height and unit depth calculated based on large step surface points and a preset number of steps, thereby ensuring that when an irregular triangulated network is subsequently constructed based on Delaunay triangulation, the small step surface can be accurately modeled, thereby allowing the entire step model to have the geometric form of a real step; the present method applies a preset offset in the Y direction to avoid the occurrence of two points with different Z coordinates having the same X and Y coordinates after interpolating the small steps, thereby avoiding the occurrence of degenerate triangles when constructing an irregular triangulated network using the Delaunay triangulation algorithm, thereby ensuring the reasonable construction of the subsequent irregular triangulated network and the normal progress of the hydrodynamic simulation.

[0082] Step 6: After merging the large step surface points and the small step surface points, restore the step point cloud data to the initial direction and geographic coordinate system, and construct an irregular triangulated network based on Delaunay triangulation to complete the step modeling.

[0083] The present invention generates complete reconstructed step point cloud data by merging large step surface points with interpolated small step surface points, ensuring that the reconstructed step point cloud data incorporates the geometric features of both large and small step surfaces. The reconstructed step point cloud data is then restored to its original orientation and geographic coordinate system, ensuring that the geographic location and area of the step point cloud data remain unchanged after reconstruction. This not only supports stormwater simulation for a single step, but also allows it to be integrated with the surrounding area, thereby constructing a high-precision surface model for the entire area and achieving high-precision stormwater simulation for the entire area.

[0084] Example 2

[0085] Based on the same inventive concept as Example 1, this example introduces the implementation steps of a step modeling method for urban stormwater simulation based on point cloud data, including:

[0086] Step 1: Obtain the step point cloud data of the urban surface and correct the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system.

[0087] In this embodiment, the initial direction of the step point cloud data is corrected to the positive direction of the Y axis in the relative coordinate system, including:

[0088] Step 1.1: Get the initial orientation of the step point cloud data. Using any point in the step point cloud data as a reference point, transform the step point cloud data from the geographic coordinate system to a relative coordinate system with the reference point as the origin.

[0089] Step 1.2: Perform principal component analysis on the step point cloud data to extract the direction vector of the plane formed by the X-axis and Y-axis of the relative coordinate system, such as Figure 2 Shown as solid line.

[0090] Step 1.3: Get the geometric center of the step point cloud data by averaging the X-axis and Y-axis coordinates of the step point cloud data. Figure 2 In the figure, the geometric center coordinates of the step point cloud data are (13.7212, -14.4237).

[0091] Step 1.4: Based on the angle between the positive direction of the Y axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center. Based on the translation matrix and the rotation matrix, the step point cloud data that deviates from the positive direction of the Y axis in the relative coordinate system is corrected to the positive direction of the Y axis in the relative coordinate system, as shown in the following example: Figure 2 As shown, the original step point cloud data is rotated 30 degrees clockwise to the dotted line direction, and the step point cloud data is corrected to the positive direction of the Y axis in the relative coordinate system. Figure 3 shown.

[0092] In some embodiments, the translation matrix and the rotation matrix are respectively expressed as:

[0093] ;

[0094] Where, Represents the translation matrix. The 1s and 0s in the first three rows and first three columns represent the unit matrix. This transformation does not perform scaling or rotation. The 0 in the third column of the fourth row indicates that the Z axis does not participate in the translation. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinates will not affect other dimensions. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinates after the transformation remains 1. Indicates the X-axis coordinate of the geometric center of the step point cloud data. Indicates the Y-axis coordinate of the geometric center of the step point cloud data. Represents a rotation matrix. The 0 in the third column of the first two rows indicates that the Z axis does not participate in the Y direction calculation. The 0 in the first two columns of the third row indicates that the X-axis and Y-axis coordinates do not participate in the Z direction calculation. The 1 in the third row indicates that the Z axis coordinate remains unchanged. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinate does not affect other dimensions. The 0 in the fourth row indicates that the applied translation is 0. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinate after the transformation is kept as 1. Indicates the angle between the positive direction of the Y axis and the direction vector The cosine value of Indicates the angle between the positive direction of the Y axis and the direction vector The sine value of .

[0095] In this embodiment, the translation matrix and the rotation matrix are respectively expressed as:

[0096] ;

[0097] Where, Indicates the X-axis coordinate of the geometric center of the step point cloud data. Indicates the Y-axis coordinate of the geometric center of the step point cloud data Represents the cosine value of the angle between the positive direction of the Y axis and the direction vector, Indicates the sine of the angle between the positive Y-axis and the direction vector.

[0098] Step 2: Set the grid and tile it on the step point cloud data, and merge the step point cloud data in the same grid unit as the grid unit point cloud data.

[0099] In this embodiment, the resolution of the grid is 0.01 m, and the side length of the grid unit is less than or equal to 1 / 3 of the depth of the small step.

[0100] In this embodiment, the X-axis coordinate and Y-axis coordinate of the grid cell point cloud data are the center coordinates of the grid cell, and the Z-axis coordinate of the grid cell point cloud data is the average Z coordinate of all step point cloud data in the same grid cell, such as Figure 4 As shown, the grid unit point cloud data generation result of the whole step is as follows Figure 5 shown.

[0101] Step 3: Traverse each grid cell and merge all grid cell point cloud data whose X-axis coordinate values are equal to the current grid cell point cloud data and whose Z-axis coordinate value difference is less than the first preset threshold into a group. If the cumulative number of step point cloud data in the group is greater than the second preset threshold, the grid cell point cloud data in the group is regarded as a large step surface point.

[0102] In this embodiment, the first preset threshold is 0.05, the second preset threshold is 15, and the large step surface point extraction result of the straight-edge step is as follows: Figure 6 As shown in the figure, the results of large step surface point extraction of circular edge steps are as follows Figure 7 shown.

[0103] Step 4: Determine the edge shape of the large step surface:

[0104] If the step edge shape of the large step surface point is arc-shaped, the X-axis coordinates of the large step surface point are sequentially traversed, the arc-shaped step edge points of the large step surface point are extracted in sequence, and the arc-shaped step edge points of the large step surface point are fitted using a third-order B-spline curve;

[0105] In this embodiment, the edge points of the arc-shaped steps need to satisfy edge constraints, which are expressed as:

[0106] ;

[0107] Where, Indicates the mathematical symbol "arbitrary", Represents the mathematical symbol "or", , , Respectively represent the X-axis coordinate, Y-axis coordinate and Z-axis coordinate of the edge point of the arc step, Indicates that all X-axis coordinates are equal to the X-axis coordinates of the arc step edge point And the Z-axis coordinate is the same as the Z-axis coordinate of the edge point of the arc step The difference is less than the first preset threshold The large step pastry collection, Represents a large step surface point set, The X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the step point cloud data.

[0108] In this embodiment, the objective function of the third-order B-spline curve is expressed as:

[0109] ;

[0110] Where, Indicates the total number of edge points of the front arc step fitted using a third-order B-spline curve. Indicates that before using the third-order B-spline curve fitting, The coordinates of the edge points of the arc steps, Indicates the third-order B-spline curve after fitting The edge point of the arc step on The square of the distance between two points, Indicates the smoothing factor, the value is 1.

[0111] If the step edge shape of the large step surface point is a straight line, construct a straight line point parallel to the positive direction of the X-axis and with a length equal to the width of the large step surface as the straight line step edge point of the large step surface point.

[0112] Step 5: Use arc-shaped step edge points or straight-line step edge points to interpolate small steps between large steps according to the preset number of small steps and the elevation difference of the large step surface points. When interpolating the vertical surface of the small step, apply a preset offset in the Y-axis direction to the step edge above the vertical surface of the small step to obtain the small step surface points.

[0113] In this embodiment, arc-shaped step edge points or straight-line step edge points are used to interpolate small steps between large steps according to the preset number of small steps and the elevation difference of the large step surface points, including:

[0114] Step 5.1: Calculate the average elevation of each large step based on the surface points of each group of large steps. Then calculate the elevation difference between adjacent large steps based on the average elevation of each large step, and divide it by the preset number of small steps to obtain the unit elevation of the small steps.

[0115] Step 5.2: Calculate the Y-axis distance between the inner edges of adjacent large steps based on each group of large step surface points, and divide it by the preset number of small step levels to obtain the unit depth of the small step.

[0116] Step 5.3: Starting from the inner edge of the large step surface with the lowest average elevation, move forward in the positive direction of the Y axis by the unit depth of a small step and move forward in the positive direction of the Z axis by the unit elevation of a small step, and insert an arc-shaped step edge point or a straight step edge point. The interpolation process is as follows: Figure 10 As shown, the result of interpolating small steps is as follows Figure 11 shown.

[0117] In this embodiment, the preset offset value is 0.001m.

[0118] Step 6: After merging the large step surface points and the small step surface points, restore the step point cloud data to the initial direction and geographic coordinate system, and construct an irregular triangulated network based on Delaunay triangulation to complete the step modeling.

[0119] In this embodiment, after merging the large step surface points and the small step surface points, the step point cloud data is restored to the initial direction, and the following steps are included:

[0120] Step 6.1: Merge the large step surface points and the small step surface points to obtain the merged step point cloud data. The merged result of the straight-edge step is as follows: Figure 12 As shown, the merging result of the circular edge steps is as follows Figure 13 As shown;

[0121] Step 6.2: Based on the angle between the positive direction of the Y-axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center, and the merged step point cloud data is converted into step point cloud data in the geographic coordinate system based on the translation matrix and the rotation matrix.

[0122] Step 6.3: Based on the reference point and the step point cloud data in the geographic coordinate system, restore the step point cloud data to the initial orientation and geographic coordinate system.

[0123] After restoring the step point cloud data to the initial orientation and geographic coordinate system, an irregular triangulated network is constructed based on the Delaunay triangulation to complete the step modeling. Figure 14 , the circular edge step visualization results are as follows Figure 15 , Figure 14 and Figure 15 The small and medium steps have clear edges and corners, distinct layers, the large steps are flat, and the curved steps have smooth edges, which conform to the real step geometry. It can be seen that the modeling results of single steps by this method are accurate.

[0124] In this embodiment, the modeling results of the straight-edge steps are used to simulate the rainstorm using the ANUGA model with uniform rainfall intensity. Figure 16 This is a schematic diagram showing the modeling results of a straight-sided staircase using the ANUGA model to simulate water flow. The process of rainwater gradually flowing down the staircase is clearly simulated, accurately reflecting the actual rainfall process. This shows that this method accurately simulates rainfall flooding on a single staircase.

[0125] In this embodiment, all the steps in the North Square of Nanjing Normal University are modeled using this method. Figure 17 This is a schematic diagram of the modeling results of the steps in the North Square of Nanjing Normal University provided by an embodiment of the present invention. The large multi-layer steps, small steps, rounded steps, and inclined steps on the square are all carefully modeled, and the geographical location remains unchanged after modeling, with a high degree of integration with the surrounding regional environment. The ANUGA model is used to set a uniform rainfall intensity for rainstorm simulation. Figure 18 This diagram illustrates the simulated flooding results for the North Plaza of Nanjing Normal University under uniform rainfall intensity, as provided by an embodiment of the present invention. Rainwater flows from the upper long steps to the middle platform, where it disperses. It then flows down the lower, diagonal steps and rounded steps to the large platform at the bottom. Only a small amount of water accumulates on the small steps, reflecting a realistic urban flooding scenario. This demonstrates that applying this method to an entire urban area yields equally accurate modeling and simulation results.

[0126] In this embodiment, the reconstruction and modeling effect of the step point cloud data using the above process is significant. The modeling results of the irregular grid constructed based on Delaunay triangulation using the original point cloud data and the point cloud data reconstructed using this method are compared. Figure 19 As shown in the figure, the noise and precision defects in the original point cloud data only model large steps, while small steps are ignored and treated as slopes, which does not conform to the actual geometric characteristics of the steps. However, the step model generated by the reconstructed point cloud data is much more accurate, modeling the small steps with distinct layers, thus faithfully restoring the step geometry and accurately simulating the hydrodynamic processes in the city.

[0127] Example 3

[0128] Based on the same inventive concept as other embodiments, this embodiment introduces a computer-readable storage medium on which computer instructions are stored. When the computer instructions are executed by a processor, the steps of the method of the above-mentioned embodiment 1 or 2 are implemented.

[0129] Example 4

[0130] Based on the same inventive concept as other embodiments, this embodiment introduces a computer program product, including computer instructions. When the computer instructions are executed by a processor, the steps of the method in the above-mentioned embodiment 1 or 2 are implemented.

[0131] In summary, the present invention traverses the X-axis coordinates of grid cell point cloud data and identifies large step surface points based on the Z-axis coordinate difference and cumulative number threshold, effectively distinguishing step structures of different height levels. For edge processing of large step surface points, different processing methods are adopted depending on the edge shape. When the step edge is curved, the X-axis coordinates are sequentially traversed and the curved step edge points are extracted. A third-order B-spline curve is then used for fitting. This accurately restores the smooth curve characteristics of the curved edge, avoiding the distortion caused by the simplified processing of curved edges in traditional methods. This greatly improves the accuracy of step edge modeling and ensures that the simulation of water flow along the step edge in urban stormwater simulations is more realistic. When the step edge is a straight line, straight line points parallel to the positive direction of the X-axis and with a width equal to the large step surface are directly used as straight step edge points. This simple and efficient processing of straight edge cases balances processing speed and accuracy.

[0132] This invention interpolates small steps by utilizing the difference in elevation between the preset number of small steps and the large step surface. This method of generating small steps based on actual elevation relationships makes the step structure more consistent with the characteristics of real urban terrain and enhances the fidelity of the actual scene. Furthermore, when interpolating the vertical surface of the small step, a preset offset is set in the positive Y-axis direction for the step edge above the vertical surface of the small step. This fully accounts for the possible small protrusions or irregularities in the vertical direction of the actual step, avoids the rainstorm simulation deviation caused by over-idealization of the vertical surface, and further improves the reliability of the model.

[0133] The present invention completes the step modeling by merging the large step surface points and the small step surface points and restoring them to the initial direction and geographic coordinate system, and constructing an irregular triangulated network based on Delaunay triangulation. It not only completely retains the geographical location and various detailed features of the steps, but also the constructed irregular triangulated network has a good topological structure, which can efficiently perform subsequent stormwater simulation calculations, providing an accurate, reliable and efficient step model for urban stormwater simulation, and helping to more accurately predict the water flow movement, water accumulation distribution and other conditions in the city under stormwater conditions, providing a scientific basis for urban flood control and drainage planning, emergency response, etc., and has important practical application value and social significance.

[0134] By calibrating the urban surface step point cloud data to the positive Y-axis of the relative coordinate system, this method effectively unifies the data direction benchmark, providing a standardized data foundation for subsequent processing, avoiding modeling errors caused by differences in coordinate direction, and significantly improving data availability and processing efficiency. Secondly, by setting a grid and tiling it on the step point cloud data, point cloud data within the same grid cell are merged, achieving reasonable data aggregation. This reduces the data volume while retaining key spatial features. While ensuring data accuracy, it also reduces the computational complexity of subsequent processing and improves overall modeling speed.

[0135] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0137] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0138] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0139] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

Claims

1. A step modeling method for urban stormwater simulation based on point cloud data, characterized in that: include: Obtain point cloud data of steps on the urban surface; Correct the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system; Set the grid and tile it on the step point cloud data, and merge the step point cloud data in the same grid unit as the grid unit point cloud data; Traverse each grid cell and merge all grid cell point cloud data with the same X-axis coordinate value as the current grid cell point cloud data and the difference in Z-axis coordinate value less than a first preset threshold into a group. If the cumulative number of step point cloud data in the group is greater than a second preset threshold, the grid cell point cloud data in the group is regarded as a large step surface point; If the step edge shape of the large step surface point is arc-shaped, the X-axis coordinates of the large step surface point are sequentially traversed, the arc-shaped step edge points of the large step surface point are extracted in sequence, and the arc-shaped step edge points of the large step surface point are fitted using a third-order B-spline curve; If the step edge shape of the large step surface point is a straight line, construct a straight line point parallel to the positive direction of the X axis and with a length equal to the width of the large step surface as the straight line step edge point of the large step surface point; Using arc-shaped or straight-line step edge points, small steps between large steps are interpolated based on the preset number of small steps and the elevation difference between the large step surface points. When interpolating the vertical surface of the small step, a preset Y-axis offset is applied to the step edge above the vertical surface of the small step to obtain the small step surface points. After merging the large step surface points and the small step surface points, the step point cloud data is restored to the initial direction and geographic coordinate system, and an irregular triangulated network is constructed based on Delaunay triangulation to complete the step modeling.

2. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The method for correcting the initial direction of the step point cloud data to the positive direction of the Y axis in the relative coordinate system includes: Get the initial direction of the step point cloud data, use any point in the step point cloud data as a reference point, and transform the step point cloud data from the geographic coordinate system to a relative coordinate system with the reference point as the origin; Perform principal component analysis on the step point cloud data to extract the direction vector of the plane formed by the X-axis and Y-axis of the relative coordinate system; The geometric center of the step point cloud data is obtained by averaging the X-axis coordinate and Y-axis coordinate of the step point cloud data; According to the angle between the positive direction of the Y-axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center, and the step point cloud data that deviates from the positive direction of the Y-axis in the relative coordinate system is corrected to the positive direction of the Y-axis in the relative coordinate system based on the translation matrix and the rotation matrix.

3. The step modeling method for urban stormwater simulation based on point cloud data according to claim 2 is characterized in that: The translation matrix and the rotation matrix are respectively expressed as: ； Where, Represents the translation matrix. The 1s and 0s in the first three rows and first three columns represent the unit matrix. This transformation does not perform scaling or rotation. The 0 in the third column of the fourth row indicates that the Z axis does not participate in the translation. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinates will not affect other dimensions. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinates after the transformation is kept at 1. Indicates the X-axis coordinate of the geometric center of the step point cloud data. Indicates the Y-axis coordinate of the geometric center of the step point cloud data. Represents a rotation matrix. The 0 in the third column of the first two rows indicates that the Z axis does not participate in the Y direction calculation. The 0 in the first two columns of the third row indicates that the X-axis and Y-axis coordinates do not participate in the Z direction calculation. The 1 in the third row indicates that the Z axis coordinate remains unchanged. The 0 in the fourth column indicates that the fourth dimension of the original homogeneous coordinate does not affect other dimensions. The 0 in the fourth row indicates that the applied translation is 0. The 1 in the fourth column indicates that the fourth dimension of the homogeneous coordinate after the transformation is kept as 1. Indicates the angle between the positive direction of the Y axis and the direction vector The cosine value of Indicates the angle between the positive direction of the Y axis and the direction vector The sine value of .

4. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The X-axis coordinate and Y-axis coordinate of the grid unit point cloud data are the center coordinates of the grid unit, and the Z-axis coordinate of the grid unit point cloud data is the average Z coordinate of all step point cloud data in the same grid unit.

5. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The resolution of the grid is 0.01m, and the side length of the grid unit is less than or equal to 1 / 3 of the depth of the small step.

6. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The edge points of the arc-shaped steps must satisfy edge constraints, which are expressed as: ； Where, Indicates the mathematical symbol "arbitrary", Represents the mathematical symbol "or", , , Respectively represent the X-axis coordinate, Y-axis coordinate and Z-axis coordinate of the edge point of the arc step, Indicates that all X-axis coordinates are equal to the X-axis coordinates of the arc step edge point And the Z-axis coordinate is the same as the Z-axis coordinate of the edge point of the arc step The difference is less than the first preset threshold The big step pastry collection, Represents a large step surface point set, The X-axis coordinate, Y-axis coordinate, and Z-axis coordinate of the step point cloud data.

7. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The objective function of the third-order B-spline curve is expressed as: ； Where, Indicates the total number of edge points of the front arc step fitted using a third-order B-spline curve. Indicates that before using the third-order B-spline curve fitting, The coordinates of the edge points of the arc steps, Indicates the third-order B-spline curve after fitting The edge point of the arc step on represents the square of the distance between two points, Indicates the smoothing factor, the value is 1.

8. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The method of using arc-shaped step edge points or straight-line step edge points to interpolate small steps between large steps according to the preset number of small steps and the elevation difference of large step surface points includes: Calculate the average elevation of each large step based on the surface points of each group of large steps, then calculate the elevation difference between adjacent large steps based on the average elevation of each large step, and divide it by the preset number of small steps to obtain the unit elevation of the small steps; Calculate the Y-axis distance between the inner edges of adjacent large steps based on each group of large step surface points, and divide it by the preset number of small steps to obtain the unit depth of the small steps; Starting from the inner edge of the large step surface with the lowest average elevation, insert an arc-shaped step edge point or a straight step edge point every time you move forward by the unit depth of a small step in the positive direction of the Y axis and move up by the unit elevation of a small step in the positive direction of the Z axis.

9. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: The preset offset value is 0.001m.

10. The step modeling method for urban stormwater simulation based on point cloud data according to claim 1 is characterized in that: After merging the large step surface points and the small step surface points, restoring the step point cloud data to the initial direction and geographic coordinate system includes: Merge the large step surface points and the small step surface points to obtain the merged step point cloud data; According to the angle between the positive direction of the Y-axis in the relative coordinate system and the direction vector, the geometric center of the step point cloud data is used as the rotation center, and the merged step point cloud data is converted into step point cloud data with the initial direction in the relative coordinate system based on the translation matrix and the rotation matrix; Based on the reference point and the initial orientation of the step point cloud data in the relative coordinate system, the step point cloud data is restored to the geographic coordinate system.

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