A terrain cross-section interpolation method suitable for any curved river course

Abstract

This invention discloses a topographic cross-section interpolation method applicable to arbitrarily curved rivers. It constructs a scatter plot of all points for the cross-section to be interpolated using equal division and the Pythagorean theorem. The distance between each interpolated cross-section and the measured cross-section is calculated, and adjacent cross-sections are extracted. Then, based on the Pythagorean theorem, the elevation points of the measured cross-section are assigned to adjacent cross-sections. A distance-weighted method is used to interpolate the elevations of the remaining unassigned cross-sections, obtaining the cumulative distance of the cross-section scatter points and the distances between the left, center, and right banks of the cross-sections. This achieves rapid interpolation of any river topographic cross-section. This invention addresses the limitation of scattered river boundaries and limited topographic elevation cross-section data in meeting the requirements of mathematical modeling. It employs equal division, the Pythagorean theorem, and distance-weighted methods, fully considering the curvature and topographic variations of natural rivers, thus achieving rapid interpolation of river topographic cross-sections and providing effective technical support for river numerical simulation research and hydraulic science.

Description

Technical Field

[0001] This invention belongs to the field of river numerical simulation technology, specifically relating to a topographic cross-section interpolation method applicable to arbitrarily curved river channels. Background Technology

[0002] Numerical simulation of rivers has become one of the core methods in water conservancy research, relying on topography, grids, and boundaries to complete modeling and calculate results. However, the density and detail of river channel topography cross-sections are key factors determining the feasibility of river numerical simulation modeling. While significant progress has been made in river topography measurement using advanced instruments and remote sensing, even with today's advanced measurement techniques, large-scale, high-precision field measurements of underwater river topography remain challenging. Measurements are often conducted only at a few typical cross-sections, resulting in spatially sparse and discontinuous data. Relying on limited measured topographic data to construct numerical simulation models, especially for highly meandering rivers, may prevent the model from achieving detailed topographic interpolation, ultimately leading to model failure. Therefore, rapidly interpolating detailed river channel topographic data from limited measured cross-section data, addressing issues such as the inability to interpolate along highly meandering rivers, the inability to perpendicular interpolation cross-sections to the flow direction, large topographic errors, and slow generation speed, is a crucial technical challenge for river numerical simulation.

[0003] In recent years, several methods for densifying and interpolating topographic elevation data points of natural river channels have been published both domestically and internationally. Patent CN108010103B discloses a method for rapidly and accurately generating complex river channel topography. This method unifies the spatial relationships of boundary points in complex terrain by dividing, classifying, and numbering them. It then fits scattered boundary points to the natural river channel's direction to generate new river channel boundaries. Based on a weighted interpolation method, it generates topography through river channel interpolation, using changes in the distance and gradient between the section to be supplemented and the known sampled elevation sections of the river channel to achieve supplementation. Patent CN113656852A discloses a method for rapidly generating refined river channel topography. This method sets the horizontal cross-section spacing and the number of vertical cross-sections, interpolating and supplementing cross-sections in the order from upstream to downstream and from left bank to right bank. Following the same order, it interpolates and calculates the riverbed elevation at intersection nodes between adjacent measured cross-sections, encoding and matching the node coordinates with the riverbed elevation to achieve refined interpolation calculation of river channel topography. Patent CN108986222A discloses a method for generating digital terrain of a channelless river. This method obtains the planar coordinate data of several control points on the characteristic longitudinal control line of the selected channelless target river segment, including the river boundary line. It constructs a planar grid by methods such as fixed number division and fixed distance division, calculates the planar coordinates of the intersection points of each cross section and each longitudinal grid line, and then uses the planar coordinate data and elevation data of each measuring point on the cross section to perform elevation interpolation on the intersection points of each cross section and each longitudinal grid line using the distance weighting method, thereby realizing the generalization of the terrain of the cross section. Patent CN109960838A discloses an automatic method for generating river topography that reflects the basic characteristics of a river. This method uses measured cross-sectional data of the river channel combined with high-resolution remote sensing images or existing river vector data to extract the left and right bank (levee) lines and the thalweg line, which reflect the basic characteristics of the river. By densifying the median line between the left and right bank (levee) lines and the thalweg line and intersecting it with the measured cross-sectional line of the river channel, a directional interpolation line segment of the river channel is formed. Further directional interpolation generates river elevation points that reflect the basic characteristics of the three lines of the river, thereby realizing the automatic generation of river topography.

[0004] Existing methods for river topographic interpolation still have considerable room for improvement. These methods generally suffer from drawbacks such as strict data requirements, difficulty in obtaining data, cumbersome procedures, slow interpolation speed, or even inability to perform interpolation or extrapolation. Some methods are only effective for simple, smooth rivers, and cannot be used for topographic interpolation of complex, meandering rivers. This is because most methods do not consider the requirement that the interpolation cross-section should be as perpendicular as possible to the river flow direction. In addition, the results of previous methods are only applicable to modeling in a three-dimensional coordinate system (XYZ) and cannot be applied to modeling cumulative elevation. Therefore, it is necessary to develop a topographic cross-section interpolation method that is applicable to rivers with arbitrary bends and simultaneously meets the requirements for XYZ and cumulative elevation modeling.

[0005] This addresses the problems of being unable to interpolate along the river's direction, resulting in large errors, high computational load, and slow generation speed when constructing refined river topography using limited measured data from river cross-sections. Summary of the Invention

[0006] To address the above problems, this invention provides a topographic cross-section interpolation method applicable to arbitrarily curved river channels.

[0007] The present invention adopts the following technical solution:

[0008] A topographic cross-section interpolation method applicable to arbitrarily curved river channels includes the following steps:

[0009] Step 1: Collect measured cross-sections and left and right bank boundary data files of the upstream and downstream of the river, and digitize the water and land boundaries of the left and right banks along the river. Generate evenly spaced scattered points from the digitized left and right bank boundary data.

[0010] Step 2: Scattered points and supplementary points for the left and right bank boundaries of the river interpolation section: Based on the required number of interpolation section results, calculate the straight-line distance between the left bank endpoints of all the interpolation sections determined in the left bank scatter points and the right bank boundary scatter points. Select the right bank boundary scatter point with the shortest corresponding straight-line distance as the right bank endpoint of the interpolation section. Complete the sampling of all right bank endpoints one by one. Finally, complete the supplementary points from the left bank to the right bank and number the interpolation sections.

[0011] Step 3: Assign and interpolate the topographic elevation of the interpolation sections: Locate the interpolation sections adjacent to the upstream and downstream measured sections, assign the measured elevation scatter points of the upstream and downstream sections to the interpolation sections, and linearly interpolate the elevations of the scatter points in the sections that have not been assigned elevations to determine the topographic elevations of all scatter points in the adjacent interpolation sections. Finally, complete the topographic elevations of the other unassigned interpolation sections to obtain the numerical topography of the river channel suitable for XYZ format modeling.

[0012] Step 4: Based on the interpolated river topographic cross-sections, calculate the cumulative distance from the scattered points in each interpolated cross-section to the left bank, as well as the distances between the left, middle, and right banks of each interpolated cross-section, to obtain a numerical topographic representation of the river suitable for cumulative distance elevation format modeling.

[0013] Furthermore, step 1 includes the following steps:

[0014] S11 collects measured cross-sectional data of the upstream and downstream of the river channel, including the topography of two measured cross-sections, upstream and downstream. The cross-sectional data includes digitized x-coordinate, y-coordinate and elevation z; and obtains uniformly scattered coordinate files of the left and right bank boundaries.

[0015] S12 collects the boundary files of the left and right banks of the river channel, and delineates the boundary of the left and right banks of the river channel that needs to be interpolated in the digital map. The boundary range is not limited by the measured cross-section range. The left and right bank boundaries need to maintain similar lengths, and the vectorized left and right bank boundary files are exported.

[0016] S13 transforms the coordinate system of the boundary files, imports the vectorized left and right bank boundary files into the geographic information system software, converts them into a recognizable format file through the software, and uses the software's coordinate transformation function to convert the coordinate system of the left and right bank boundary files into a coordinate system consistent with the measured cross section;

[0017] The left and right bank boundaries of the S14 river channel are generated with uniformly spaced scattered points. Using the constant number division method, the left and right bank files are split into uniformly scattered points by software.

[0018] Furthermore, step 2 includes the following steps:

[0019] S21 extracts the left bank endpoints from the aforementioned left bank scatter file and assigns the corresponding x and y coordinates of the left bank scatter points to the left bank endpoints.

[0020] S22 calculates the distance of each left bank endpoint to the nearest right bank boundary point and assigns the x and y coordinates of the right bank boundary points to the right bank endpoint.

[0021] S23 fills in the horizontal and vertical coordinates of the interpolated scattered points in the cross section to be interpolated.

[0022] Furthermore, step 3 includes the following steps:

[0023] S31 uses the sum of the straight-line distances between the two endpoints and the endpoints of the measured section to find the section to be interpolated adjacent to the upstream measured section, and determines the sequence number of the adjacent section to be interpolated as a. 上 and a 下 ;

[0024] S32 calculates the scatter point of the upstream measured section closest to the left bank endpoint of the interpolated section, and assigns the topographic elevation of this scatter point to the section number a. 上 The left bank endpoint; numbered a 下 The same applies to the left bank endpoint;

[0025] S33 calculates the scattered points of the upstream measured cross-sections closest to the right bank endpoint of the interpolated cross-section, and assigns the topographic elevation of the scattered points to the right bank endpoint of the cross-section with serial number a; the same applies to the right bank endpoint of the cross-section with serial number a.

[0026] The lowest point of the measured elevation of the upstream section of S34 is p. Calculate the scatter plot of this point and the point with the serial number a. 上 The straight-line distance between the sections to be interpolated is calculated, and the elevation is assigned to the scatter point with the shortest distance, with the index 'a'. 下 The assignment is similar;

[0027] S35 for serial number a 上 and a 下 Elevation values ​​are assigned to the scattered points from the left bank endpoint to the thalweg point in the interpolated cross section;

[0028] After S36 is assigned, the scattered points in the interpolation section whose elevation has not been assigned are linearly interpolated from the scattered points on both sides that have been assigned.

[0029] S37 obtains the sequence number a after assignment and interpolation. 上 and a 下 After obtaining the cross-sectional topographic elevation file, the elevation of the remaining cross-sections is interpolated using the distance-weighted method.

[0030] Furthermore, step 4 includes the following steps:

[0031] S41 calculates the cumulative distance from each scattered point in each interpolation section to the left bank endpoint;

[0032] S42 calculates and derives the straight-line distances between the left, middle, and right banks of the interpolated cross-sections.

[0033] Furthermore, the construction method is applicable to topographic cross-section interpolation models of arbitrarily curved river channels.

[0034] Furthermore, the interpolation model is applied to river numerical simulation modeling.

[0035] The beneficial effects of this invention are:

[0036] 1. This invention provides a topographic cross-section interpolation method applicable to arbitrarily curved rivers. The main purpose is to solve the problem that the terrain cannot be interpolated when data modeling is performed due to the limited measured data of the river. The method described in this invention is applicable to topographic interpolation of arbitrarily curved rivers and can also be used for underwater topographic interpolation of reservoirs, lakes and other water bodies.

[0037] 2. The method provided by this invention uses scattered points on the left bank boundary to select points, and uses the Pythagorean theorem to determine the scattered points on the right bank boundary with the shortest distance. Points are then added between the two points to complete the scattered point interpolation of the cross section. The data required by this method is easy to obtain, and the interpolation has strong autonomous selectivity. The number of cross sections and the number of scattered points in the cross section can be arbitrarily selected according to its own needs, and the interpolated cross section is perpendicular to the river flow direction. It is suitable for any complex curved river channel.

[0038] 3. This invention makes full use of measured terrain data to assign terrain elevation to adjacent cross sections. It completes the elevation assignment by identifying the interpolation cross sections with the closest distance and performs linear interpolation in the cross sections, thereby improving the accuracy of terrain interpolation results.

[0039] 4. The method provided by this invention can perform internal interpolation between two measured topographic cross sections, and can also perform external interpolation outside the measured cross sections, thus enabling topographic interpolation of river channels of arbitrary length.

[0040] 5. This invention considers the modeling requirements of both XYZ format and cumulative elevation format, meaning that the generated river topography results have wide applicability and can provide basic topographic data support for most modeling software. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below. Obviously, the drawings described below only relate to some embodiments of the present invention and are not intended to limit the present invention.

[0042] Figure 1 This is a schematic diagram of the technical process of the interpolation method for river channel topographic cross-sections according to the present invention;

[0043] Figure 2 This is a schematic model of the vectorization of the left and right bank boundaries of the river channel and the generation of a uniformly scattered coordinate file for the present invention.

[0044] Figure 3 A schematic diagram showing the point taken at the left bank endpoint of the interpolated section and the right bank endpoint calculated in this invention.

[0045] Figure 4 A schematic diagram showing the interpolation of scattered points in the cross-section to be interpolated according to the present invention.

[0046] Figure 5 This is a schematic diagram showing the assignment of elevation values ​​to the interpolation sections of adjacent measured terrain in this invention.

[0047] Figure 6 This invention provides elevation interpolation for the missing data points of adjacent measured terrain sections to be interpolated.

[0048] Figure 7 This is a scattered elevation interpolation of the cross section to be interpolated for non-adjacent measured terrain in this invention;

[0049] Figure 8 This is a schematic diagram illustrating the calculation of the cumulative distance from the left bank and the distances between the left, middle and right banks of the interpolated cross sections in this invention.

[0050] Figure 9 This is a schematic diagram comparing the interpolation results of the present invention without and with the interpolation results of the present invention;

[0051] Figure 10 This is a schematic diagram comparing the modeling effects of the present invention before and after the interpolation results of this method are imported into the model. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0054] like Figure 1 As shown, a topographic cross-section interpolation method applicable to arbitrarily curved river channels includes the following steps:

[0055] Step 1: Collect measured cross-sections of the upstream and downstream of the river and the boundary files of the left and right banks. Digitize the land and water boundaries of the left and right banks along the river. Import the digitized boundary files of the left and right banks into the geographic information system software to generate evenly spaced scattered points.

[0056] Data collection of measured cross-sections of the S11 river channel, including topographic data of two measured cross-sections upstream and downstream. The cross-section data includes digitized x-coordinate, y-coordinate, and elevation z; and uniformly distributed scatter coordinate files of the left and right bank boundaries are obtained.

[0057] S12 River channel left and right bank boundary files are collected. The left and right bank boundaries of the river channel that need to be interpolated are delineated in the digital map. The boundary range is not limited by the measured cross-section range. The left and right bank boundaries need to be similar in length and are exported as vectorized left and right bank boundary files in ".kml" or ".kmz" format.

[0058] S13 Boundary File Coordinate System Transformation: The vectorized left and right bank boundary files are imported into the geographic information system software, converted into a recognizable ".shp" format file by the software, and the coordinate system of the left and right bank boundary files is converted to a coordinate system consistent with the measured cross section using the software's coordinate transformation function.

[0059] The S14 river channel's left and right bank boundaries are generated with uniformly spaced scattered points. Using the constant division method, the software splits the left and right bank shapefiles into uniformly spaced scattered points (the number of scattered points n can be set according to the accuracy requirements). In other words, the left and right bank boundaries are converted from line files to point files. The x-coordinate (X) and y-coordinate (Y) of each scattered point are obtained through an attribute table, and the attribute table is exported to Excel format to obtain the uniformly spaced scattered point coordinate file of the left and right bank boundaries.

[0060] Step 2: Scattered points and supplementary points for the left and right bank boundaries of the river interpolation section. Based on the required number of interpolation section results, determine the left bank endpoints of all sections to be interpolated from the scattered points on the left bank. Calculate the straight-line distance between each determined left bank endpoint and the scattered points on the right bank boundary. Select the right bank boundary scattered point with the shortest corresponding straight-line distance as the right bank endpoint of the interpolation section. Complete the sampling of each right bank endpoint one by one. Finally, complete the supplementary points from the left bank to the right bank and number the interpolation sections.

[0061] S21 uses the equidistant point sampling method to extract the desired m left bank endpoints from the above left bank scatter file, and assigns the corresponding horizontal and vertical coordinates of the left bank scatter points to the left bank endpoints. The extraction formula is as follows.

[0062]

[0063]

[0064] In the formula, n is the number of scattered points on the left bank boundary; m is the number of cross-sections to be interpolated, which is also the number of scattered points to be taken from the left bank; X 左,1+[n / m×(1-1)] X represents the x-coordinate of the first point selected from the scattered points on the left bank boundary; considering that n / m may be non-integer, "[...]" indicates rounding; 1,1 X is the x-coordinate of the left bank endpoint of the first section to be interpolated. 1,m Let X be the x-coordinate of the left bank endpoint of the m-th section to be interpolated; the calculation of Y is the same as that of X.

[0065] S22 uses the Pythagorean theorem to calculate the distance of each left bank endpoint to the nearest right bank boundary point, and assigns the x and y coordinates of the right bank boundary points to the right bank endpoints. The calculation formula is as follows:

[0066]

[0067] In the formula, d 1,1 d is the straight-line distance between the left bank endpoint of the first section to be interpolated and the first scattered point on the right bank; 1,n Let D1 be the straight-line distance between the left bank endpoint of the first section to be interpolated and the nth scattered point on the right bank. Find the right bank boundary scattered point that is closest to the left bank endpoint of the first section to be interpolated and denote it as D1. Similarly, we can find the right bank boundary scattered points corresponding to all sections to be interpolated one by one, which are the right bank endpoints.

[0068] The method for calculating the straight-line distance between the left bank endpoint of the m-th interpolation section and each scattered point on the right bank is the same as described above.

[0069]

[0070]

[0071] In the formula, The x-coordinate is the closest right bank boundary scatter point to the left bank boundary scatter point of the first interpolated section; X is the x-coordinate of the right bank boundary scatter point that is closest to the left bank boundary scatter point of the m-th interpolation section; k,1 Let be the x-coordinate of the right bank endpoint of the first interpolation section, where k is the number of interpolation points required for each interpolation section, set according to the requirements; the calculation of Y is the same as that of X.

[0072] Based on linear interpolation theory, S23 fills in the abscissa and ordinate of the interpolated scattered points in the cross-section to be interpolated. The calculation formula for the fill in the points of the first cross-section to be interpolated is as follows:

[0073]

[0074]

[0075] In the formula, X 2,1 Y is the x-coordinate of the second scattered point from the left bank to the right bank in the first cross-section to be interpolated; the calculation of Y is the same as that of X.

[0076] The interpolation points for the m-th section to be interpolated are calculated in the same way as those for the 1st section to be interpolated.

[0077] Step 3: Assign and interpolate the topographic elevation of the interpolation sections. Find the interpolation sections adjacent to the upstream and downstream measured sections, and assign the measured elevation scatter points of the upstream and downstream sections to the interpolation sections. The elevation of the scatter points in the section that have not been assigned is linearly interpolated with the elevation of the scatter points already assigned in the section, thereby determining the topographic elevation of all scatter points in the adjacent interpolation sections. Finally, complete the topographic elevation of other unassigned interpolation sections to obtain the numerical topography of the river channel suitable for XYZ format modeling.

[0078] Step S31: Locate the interpolation section adjacent to the upstream measured section, and calculate the straight-line distance L between the first point of the left bank endpoint of the interpolation section and the left bank of the upstream measured section. 1,1 , ..., L 1,m Calculate the straight-line distance L between the first point on the right bank endpoint of the section to be interpolated and the right bank of the upstream measured section. k,1 , ..., L k,m The section to be interpolated whose sum of straight-line distances at both ends is minimized is denoted as a. 上 .

[0079] Step S32: The measured elevation of the upstream section is given to the adjacent section (serial number a). 上 The elevation of the left bank endpoint of the section to be interpolated is assigned. Using the Pythagorean theorem, the scatter point of the upstream measured section closest to the left bank endpoint of the interpolated section is calculated, and the topographic elevation of this scatter point is assigned to the left bank endpoint. The number of scatter points in the upstream measured section is 0. The calculation formula is as follows:

[0080]

[0081] In the formula, X 1,上 X is the x-coordinate of the first scatter point of the upstream measured section. o,上 Y is the x-coordinate of the 0th scatter point of the upstream measured section; Y is the y-coordinate. For serial number a 上 The straight-line distance between the left bank endpoint of the section to be interpolated and the first point of the upstream measured elevation scatter plot. For serial number a 上 Find the straight-line distance between the left bank endpoint of the section to be interpolated and the 0th point of the upstream measured elevation scatter points; find the point among the extracted upstream measured elevation scatter points that is closest to the left bank endpoint, and assign the elevation of this point to the index a. 上 The formula for the left bank endpoint of the section to be interpolated is as follows:

[0082]

[0083] Step S33: The measured elevation of the upstream section is given to the adjacent section (serial number a). 上 The elevation of the right bank endpoint of the section to be interpolated is assigned. Using the Pythagorean theorem, the scatter plot of the upstream measured section closest to the right bank endpoint of the interpolated section is calculated, and the topographic elevation of this section is assigned to the right bank endpoint. The calculation formula is as follows:

[0084]

[0085] In the formula, For serial number a 上 The straight-line distance between the right bank endpoint of the section to be interpolated and the first point of the upstream measured elevation scatter plot. For serial number a 上 Find the straight-line distance between the right bank endpoint of the section to be interpolated and the 0th point of the upstream measured elevation scatter plot; find the point among the extracted upstream measured elevation scatter plots that is closest to the right bank endpoint, and assign the elevation of this point to the index a. 上 The formula for the right bank endpoint of the section to be interpolated is as follows:

[0086]

[0087] Step S34: The measured elevation of the upstream section is given to the adjacent section (serial number a). 上 The elevation of the endpoint of the deep channel of the section to be interpolated is assigned, and the lowest point of the measured elevation of the section is obtained as p, that is, the x-coordinate of the point is X. p,上 The vertical axis is Y p,上 Elevation Z p,上 Calculate the scatter plot and the index a. 上 The straight-line distance between the sections to be interpolated is calculated, and the elevation is assigned to the scatter point with the shortest distance. The calculation formula is as follows:

[0088]

[0089]

[0090] In the formula, is the straight-line distance between the scatter point with the lowest measured elevation in the upstream and the scatter point numbered a 上 at the first scatter point of the cross-section to be interpolated.

[0091] Step S35: Assign elevations to the scatter points from the left-bank endpoint to the thalweg point in the interpolation cross-section numbered a 上 . Let the number of scatter points from the left-bank endpoint to the thalweg point in the interpolation cross-section be q, and the number of scatter points from the scatter point assigned a value at the left-bank endpoint in the upstream measured cross-section to the measured thalweg point be r. Then there are two interpolation cases in this step. If q < r, the elevation assignment calculation is as follows:

[0092]

[0093]

[0094] In the formula, S is the serial number of the scatter point in the upstream measured cross-section whose elevation needs to be assigned to the cross-section to be interpolated; is the serial number of the scatter point in the upstream measured cross-section whose elevation needs to be assigned to the second scatter point numbered a 上 in the cross-section to be interpolated, and "[…]" indicates taking the integer.

[0095] If q ≥ r, the elevation assignment calculation formula is as follows:

[0096]

[0097] In the formula, S is the serial number of the scatter point in the cross-section to be interpolated whose elevation needs to be assigned by the upstream measured cross-section; 1 + [q / r] × 1 is the corresponding serial number of the second scatter point in the cross-section numbered a 上 in the cross-section to be interpolated that needs to be assigned an elevation by the upstream measured cross-section, and "[…]" indicates taking the integer. Finally, for the scatter points in the cross-section numbered a 上 in the cross-section to be interpolated whose elevations have not been assigned, linear interpolation is performed by the scatter points on both sides that have been assigned values to obtain the elevation file of all scatter points in the cross-section numbered a 上 in the cross-section to be interpolated.

[0098] Step S36: The elevation interpolation calculation method for the scatter points from the thalweg point to the right-bank endpoint in the interpolation cross-section numbered a 上 is the same as that in Step S35.

[0099] Step S37: Locate the cross-section to be interpolated adjacent to the downstream measured cross-section, and successively calculate the straight-line distance L 1,1 , …, L 1,m, calculate the straight-line distance L between the first point of the right bank endpoint of the to-be-interpolated section and the right bank of the upstream measured section one by one k,1 , …, L k,m , record the serial number of the to-be-interpolated section with the smallest sum of the straight-line distances at both ends as a 下 . Assign elevation values to the left bank endpoints of the to-be-interpolated sections adjacent to (with serial number a 下 ) of the downstream measured section elevation. The steps are the same as S32; the steps for right bank section assignment are the same as S33; the steps for assigning elevation values to the thalweg endpoints of the to-be-interpolated sections adjacent to (with serial number a 下 ) of the downstream measured section elevation are the same as S34; the calculation steps for the scattered points that have not been assigned elevation values further are the same as S35 and S36.

[0100] Step S38: Obtain the cross-section topographic elevation file with the assigned and interpolated serial numbers a 上 and a 下 . For the elevation interpolation of the remaining sections, there are 3 cases. Let the serial number of the remaining sections be t. If 1 ≤ t < a 上 , the elevation interpolation formula for each scattered point in the section is as follows:

[0101]

[0102] If a 上 < t < a 下 , the elevation interpolation formula for each scattered point in the section is as follows:

[0103]

[0104] If a 下 < t ≤ m, the elevation interpolation formula for each scattered point in the section is as follows:

[0105]

[0106] In the formula, Z <00​​​​​​​​​​​​​​

[0110]

[0111] In the formula, B k,1 The cumulative distance is the distance from the kth scatter point to the first scatter point in the first interpolation section; the cumulative distance for the remaining interpolation sections is calculated in the same way.

[0112] S42: Calculate the straight-line distances between the left, middle, and right banks of the interpolated sections. Taking the first and second interpolated sections as examples, the calculation formula is as follows:

[0113]

[0114] In the formula, C 左,2 The straight-line distance from the second interpolation section to the left bank endpoint of the first interpolation section is given; the straight-line distances between the left, middle, and right banks of the remaining sections are obtained in the same way.

[0115] Therefore, completing step 4 will yield a numerical topography of the river channel suitable for cumulative elevation modeling.

[0116] Example

[0117] This invention proposes a topographic cross-section interpolation method applicable to arbitrarily curved river channels. The overall interpolation process is as follows: Figure 1 As shown, the main steps include:

[0118] Step 1: Collect basic river channel data and generate uniform scatter plots of left and right bank boundary files.

[0119] Two measured upstream and downstream topographic cross-sections were collected from a major meandering river section in Zhejiang Province, primarily for topographic cross-section interpolation. The geographic coordinate system is CGCS2000. Each topographic cross-section contains 13 elevation points. The collected data are as follows: Figure 1 As shown in the steps, data acquisition methods typically include self-measurement, support from other technical departments, and acquisition via elevation-based geographic information systems.

[0120] Obtain the left and right bank boundaries of the target river channel using Google Earth. Use the "Path" function to outline the left and right bank boundaries of the river segment, exporting two boundary files in ".kml" format. Using ArcGIS software as an example, import the files using the "Convert from kml" function in the "Convert" menu, and then right-click to export and save them as ".shp" line files. Use the "Projection and Transformation" function in the "Data Management Tools" to convert the coordinates of the boundary files from WGS1984 to CGCS2000. Use the "Construct Points" function in the "Editor" to construct two point files containing 200 evenly distributed boundary points from the left and right bank boundary line files. Finally, use the "Table to Excel" function in the "Convert" menu to export the data as an Excel spreadsheet. The overall operation steps are as follows: Figure 1 As shown.

[0121] Step 2: Taking points on the left and right bank sections of the section to be interpolated and filling points within the section.

[0122] By selecting 50 cross-sections to be inserted, and using the equidistant point sampling method, the desired 50 left bank endpoints are extracted from the aforementioned left bank boundary scatter point file. The horizontal and vertical coordinates of the left bank scatter points are then assigned to the corresponding left bank endpoints. The extraction formula is as follows:

[0123]

[0124]

[0125] Determine and assign values ​​to the right bank endpoint of the section to be interpolated, and then apply the Pythagorean theorem, such as... Figure 3 As shown, the distance to the nearest right bank boundary point is calculated for each left bank endpoint, and the x and y coordinates of the right bank boundary point are assigned to the right bank endpoint. The calculation formula for the first left bank endpoint is as follows:

[0126]

[0127] The x and y coordinates of the interpolated scattered points in the cross-section to be interpolated are interpolated to fill in the missing points, such as... Figure 4 As shown, the number of scattered points in each interpolation section is set to 30. Taking the interpolation points of the first section to be interpolated as an example, the calculation formula is as follows:

[0128]

[0129]

[0130] The interpolation points for the 2nd to 50th interpolation sections are calculated in the same way as the 1st interpolation section.

[0131] Step 3: Assigning values ​​to the cross-section to be interpolated and performing internal and external interpolation.

[0132] By identifying the adjacent interpolation sections to be interpolated to the upstream measured section, the straight-line distance L between the first point of the left bank endpoint of the interpolation section and the left bank of the upstream measured section is calculated one by one. 1,1 , ..., L 1,m Calculate the straight-line distance L between the first point on the right bank endpoint of the section to be interpolated and the right bank of the upstream measured section. k,1 , ..., L k,m The section to be interpolated whose sum of straight-line distances at both ends is minimized is denoted as a. 上 , Figure 5 The diagram shows the second section to be interpolated.

[0133] The measured elevation of the upstream section is assigned to the left bank endpoint of the second interpolated section. Using the Pythagorean theorem, the scatter points of the upstream measured section closest to the left bank endpoint of the interpolated section are calculated, and the topographic elevation of these points is assigned to the left bank endpoint. There are 13 scatter points in the upstream measured section. The calculation formula is as follows:

[0134]

[0135] The point closest to the left bank endpoint among the extracted upstream measured elevation scatter points is taken as the first scatter point. The elevation of this point is then assigned to the left bank endpoint of the second interpolation section, as shown in the following formula:

[0136] Z 1,2 =Z 1,上 (28)

[0137] The measured elevation of the upstream section is assigned to the right bank endpoint of the second interpolated section. Using the Pythagorean theorem, the 12th point of the upstream measured section closest to the right bank endpoint of the interpolated section is calculated, and the topographic elevation of this section is assigned to the right bank endpoint. The calculation formula is as follows:

[0138] Z 30,2 =Z 12,上 (29)

[0139] The measured elevation of the upstream section is used to assign an elevation value to the endpoint of the deep channel of the second section to be interpolated. The lowest point of the measured section elevation is then determined as the sixth scattered point, with the x-coordinate of this point being X. 6,上 The vertical axis is Y 6,上 Elevation Z 6,上 Calculate the straight-line distance between the scatter point and the second interpolated section, and assign the elevation value to the scatter point with the shortest distance. The calculation formula is as follows:

[0140]

[0141] The 6th scatter point of the upstream measured elevation is closest to the 12th scatter point of the 2nd interpolation section. The elevation of this point is then assigned to the 12th scatter point of the 2nd interpolation section, as shown in the following formula:

[0142] Z 12,2 =Z 6,上 (31)

[0143] Elevation values ​​are assigned to the scattered points from the left bank endpoint to the thalweg point in the second interpolation section. As mentioned above, the number of scattered points from the left bank endpoint to the thalweg point is 10. In the upstream measured section, the number of scattered points from the left bank endpoint to the measured thalweg point that are assigned values ​​is 4. Therefore, in this step, q≥r is satisfied. The elevation assignment calculation is as follows:

[0144]

[0145]

[0146] Finally, the scatter points whose elevations were not assigned in the second cross section to be interpolated were linearly interpolated from the scatter points on both sides that had been assigned elevations. The scatter points with empty values ​​included the 2nd, 3rd, 5th, 7th, 8th and 10th scatter points, resulting in the elevation file of all scatter points in the second cross section to be interpolated.

[0147] The elevation interpolation calculation for the scatter points of the deep water point in the second section to be interpolated to the right bank endpoint is performed in the same way as the steps described above. The calculation diagram is shown below. Figure 6 As shown.

[0148] Identify the sections to be interpolated that are adjacent to the downstream measured section, and calculate the straight-line distance L between the first point of the left bank endpoint of the section to be interpolated and the left bank of the upstream measured section. 1,1 , ..., L 1,m Calculate the straight-line distance L between the first point on the right bank endpoint of the section to be interpolated and the right bank of the upstream measured section. k,1 , ..., L k,m The section to be interpolated with the smallest sum of straight-line distances at both ends is number 46. Assign elevation values ​​to the left bank endpoint of the 46th section to be interpolated using the measured elevation of the downstream section, following the same steps as in S32; assign values ​​to the right bank section using the same steps as in S33; assign elevation values ​​to the deep-water endpoint of the 46th section to be interpolated using the measured elevation of the downstream section, following the same steps as in S34; further calculate the scattered points that have not been assigned elevation values ​​using the same steps as in S35 and S36.

[0149] After obtaining the topographic elevation files for the 2nd and 46th cross sections after assignment and interpolation, the elevation interpolation for the remaining cross sections presents three possibilities, such as... Figure 7 As shown, let the sequence number of the remaining cross-sections be t. If 1 ≤ t < 2, then t is 1. The elevation interpolation formula for each scattered point in the first cross-section to be interpolated is as follows:

[0150]

[0151] If 2 < t < 46, the elevation interpolation formula for each scatter point in the cross-section is as follows:

[0152]

[0153] If 46 < t ≤ 50, the elevation interpolation formula for each scatter point in the cross-section is as follows:

[0154]

[0155] Thus, completing step S3 will obtain a numerically modeled river channel terrain suitable for XYZ format modeling. The comparison of the number of cross-sections before and after interpolation is as Figure 9 shown.

[0156] Step 4: Calculate the cumulative distance of scatter points in the cross-section to be interpolated and the left, middle, and right bank distances between cross-sections

[0157] Calculate the cumulative distance of each scatter point in each interpolated cross-section to the left bank endpoint. As Figure 8 shown, taking the first interpolated cross-section as an example, the calculation formula is as follows:

[0158]

[0159] Calculate the straight-line distances of the left, middle, and right banks between interpolated cross-sections. As Figure 8 shown, taking the second and third interpolated cross-sections as an example, the calculation formula is as follows:

[0160]

[0161] Thus, completing step S4 will obtain a numerically modeled river channel terrain suitable for cumulative distance elevation format modeling.

[0162] After copying and pasting the interpolated data, export it to the terrain file format required by the modeling software, and complete terrain interpolation in the model. The modeling effect without this method and the modeling effect with this method are compared as Figure 10 shown.

[0163] The above terrain cross-section interpolation method applicable to arbitrarily curved river channels can be developed based on computer languages such as Visual Basic for Applications and Python. It has high application value and is applicable to a wide range of fields such as geographic information, numerical simulation, and water conservancy science.

[0164] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

[0165] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A topographic cross-section interpolation method applicable to arbitrarily curved river channels, characterized in that, Includes the following steps: Step 1: Collect measured cross-sections and left and right bank boundary data files of the upstream and downstream of the river, and digitize the water and land boundaries of the left and right banks along the river. Generate evenly spaced scattered points from the digitized left and right bank boundary data. Step 2: Scattering and supplementing points for the left and right bank boundaries of the river interpolation section: Based on the required number of interpolation section results, calculate the straight-line distance between the left bank endpoints of all the interpolation sections determined in the left bank scatter points and the right bank boundary scatter points. Select the right bank boundary scatter point with the shortest corresponding straight-line distance as the right bank endpoint of the interpolation section. Complete the sampling of all right bank endpoints one by one. Finally, complete the supplementing points from the left bank to the right bank and number the interpolation sections. Step 3: Assign and interpolate the topographic elevation of the interpolation cross sections: Locate the interpolation cross sections adjacent to the upstream and downstream measured cross sections, assign the measured elevation scatter points of the upstream and downstream to the interpolation cross sections, and linearly interpolate the elevation of the scatter points in the cross section that have not been assigned with the elevation of the scatter points already assigned in the cross section to determine the topographic elevation of all scatter points in the adjacent interpolation cross sections. Finally, complete the topographic elevation of other unassigned interpolation cross sections to obtain the numerical topography of the river channel suitable for XYZ format modeling. Step 3 includes the following steps: S31 uses the sum of the straight-line distances between the two endpoints and the endpoints of the measured section to find the section to be interpolated adjacent to the upstream measured section, and determines the sequence number of the adjacent section to be interpolated as a. 上 and a 下 ; S32 calculates the scatter point of the upstream measured section closest to the left bank endpoint of the interpolated section, and assigns the topographic elevation of this scatter point to the section number a. 上 The left bank endpoint; numbered a 下 The same applies to the left bank endpoint; S33 calculates the scattered points of the upstream measured cross-section closest to the right bank endpoint of the interpolated cross-section, and assigns the topographic elevation of the scattered points to the cross-section number a. 上 The right bank endpoint; numbered a 下 The same applies to the right bank endpoint; The lowest point of the measured elevation of the upstream section of S34 is p. Calculate the scatter plot of this point and the point with the serial number a. 上 The straight-line distance between the sections to be interpolated is calculated, and the elevation is assigned to the scatter point with the shortest distance, with the index 'a'. 下 The assignment is similar; S35 for serial number a 上 and a 下 Elevation values ​​are assigned to the scattered points from the left bank endpoint to the thalweg point in the interpolated cross section; After S36 is assigned, the scattered points in the interpolation section whose elevation has not been assigned are linearly interpolated from the scattered points on both sides that have been assigned. S37 obtains the sequence number a after assignment and interpolation. 上 and a 下 After obtaining the cross-sectional topographic elevation file, the elevation of the remaining cross sections is interpolated using the distance-weighted method. Step 4: Based on the interpolated river topographic cross-sections, calculate the cumulative distance from the scattered points in each interpolated cross-section to the left bank, as well as the distances between the left, middle, and right banks of each interpolated cross-section, to obtain a numerical topographic representation of the river suitable for cumulative distance elevation format modeling.

2. The topographic cross-section interpolation method applicable to arbitrarily curved river channels according to claim 1, characterized in that, Step 1 includes the following steps: S11 collects measured cross-sectional data of the upstream and downstream of the river channel, including the topography of two measured cross-sections, upstream and downstream. The cross-sectional data includes digitized x-coordinate, y-coordinate and elevation z; and obtains uniformly scattered coordinate files of the left and right bank boundaries. S12 collects the boundary files of the left and right banks of the river channel, and delineates the boundary of the left and right banks of the river channel that needs to be interpolated in the digital map. The boundary range is not limited by the measured cross-section range. The left and right bank boundaries need to maintain similar lengths, and the vectorized left and right bank boundary files are exported. S13 transforms the coordinate system of the boundary files, imports the vectorized left and right bank boundary files into the geographic information system software, converts them into a recognizable format file through the software, and uses the coordinate transformation function of the software to convert the coordinate system of the left and right bank boundary files into a coordinate system consistent with the measured cross section. The left and right bank boundaries of the S14 river channel are generated with uniformly spaced scattered points. Using the constant number division method, the left and right bank files are split into uniformly scattered points by software.

3. The topographic cross-section interpolation method applicable to arbitrarily curved river channels according to claim 1, characterized in that, Step 2 includes the following steps: S21 extracts the left bank endpoints from the aforementioned left bank scatter file and assigns the corresponding x and y coordinates of the left bank scatter points to the left bank endpoints. S22 calculates the distance of each left bank endpoint to the nearest right bank boundary point and assigns the x and y coordinates of the right bank boundary points to the right bank endpoint. S23 fills in the horizontal and vertical coordinates of the interpolated scattered points in the cross section to be interpolated.

4. The topographic cross-section interpolation method applicable to arbitrarily curved river channels according to claim 1, characterized in that, Step 4 includes the following steps: S41 calculates the cumulative distance from each scattered point in each interpolation section to the left bank endpoint; S42 calculates and derives the straight-line distances between the left, middle, and right banks of the interpolated cross-sections.

5. A topographic cross-section interpolation method applicable to arbitrarily curved river channels according to any one of claims 1-4, characterized in that, The interpolation method is applicable to topographic cross-section interpolation models of arbitrarily curved river channels.

6. The topographic cross-section interpolation method applicable to arbitrarily curved river channels according to claim 5, characterized in that, The interpolation model is applied to river numerical simulation modeling.

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