A fast terrain cross-section interpolation method based on proportional relationship

Abstract

The present invention discloses a rapid terrain cross-section interpolation method based on proportional relationships, which belongs to the field of water conservancy engineering. Based on the provided original cross-section profile, the coordinates of the left and right end points of the cross-section, the cross-section spacing, and other information, the cross-section coordinate information is used to convert the cross-section profile into scattered point information. The coordinates of the left end point of the interpolated cross-section are obtained by calculating the proportional relationship between the interpolated spacing and the cross-section spacing. The coordinates of the right end point of the interpolated cross-section are then obtained by solving the linear equation. The elevations of the left and right end points and the lowest point elevation are calculated using proportional relationships. Based on the width ratio and elevation ratio within the original cross-section, the position and elevation of each point on the interpolated cross-section are calculated. The present invention overcomes the deficiency of existing cross-section interpolation technologies in lacking position information, and the interpolated cross-section can better reflect the direction of the river.

Description

Technical Field

[0001] The invention belongs to the field of water conservancy projects, and in particular relates to a rapid terrain section interpolation method based on proportional relationships, which belongs to general water conservancy methods. Background Art

[0002] During the planning and design phase of water conservancy projects, topographic cross-sections are one of the important basic data, especially in reservoir flood control calculations, water surface line simulations, and even more complex two-dimensional and three-dimensional hydraulic model studies. Topographic cross-sections are indispensable data, and the quality of cross-section data affects the accuracy of the research.

[0003] In actual terrain section measurements, affected by factors such as cost and terrain, the spacing between measurement sections is often large, ranging from 1 km to 5 km. In one-dimensional hydraulic water surface line research, a large section spacing may result in reduced simulation accuracy or even simulation failure. Appropriate section spacing is one of the key factors for the success of numerical simulation.

[0004] Among existing cross-section interpolation technologies, HEC-RAS software offers the ability to interpolate river topography cross sections. However, this software requires numerous input parameters, which must be formatted in a format the software can recognize. Furthermore, exporting HEC-RAS-interpolated cross sections is difficult, requiring manual programming to identify the data format and export each cross section individually. However, if the cross-section data format changes or the HEC-RAS topography file is encrypted, manual export of the interpolated cross sections becomes impossible, limiting their usefulness. Furthermore, some existing cross-section interpolation methods only interpolate cross-section shape and lack information about river channel direction. While sufficient for one-dimensional applications, these methods are insufficient in two- and three-dimensional applications, lacking positional information for each point within the interpolated cross section. Summary of the Invention

[0005] The purpose of the present invention is to provide a rapid terrain section interpolation method based on proportional relationship to solve the problem of missing interpolation section position information in the prior art.

[0006] The technical solution of the present invention is a rapid terrain section interpolation method based on proportional relationship, comprising the following steps:

[0007] Step 1: Collect the terrain section data required for interpolation;

[0008] Step 2: Calculate the coordinates of each point on the cross section based on the coordinates of the endpoints at both ends of the cross section;

[0009] Step 3, calculate the proportional relationship between the cumulative distance of each point in the section and the section width;

[0010] Step 4: Take the lowest point of the cross section as the reference point, subtract the elevation of the lowest point from the elevation of each point on the cross section to obtain the relative elevation, and then divide it by the relative elevation value of the first point on the cross section to obtain the ratio of the relative elevation of each point on the cross section to the first point on the cross section;

[0011] Step 5: Calculate the number of interpolated sections between the two sections based on the original adjacent i-th and i+1-th section spacings and the interpolation distance, and then calculate the endpoint coordinates of the two ends of the interpolated section using the endpoint coordinates of the two ends of the original section;

[0012] Step 6: Calculate the width of the interpolation section based on the coordinates of the endpoints at both ends of the interpolation section. Divide the interpolation section into the first and second half interpolation sections, based on the number n of interpolation sections and with n / 2 as the dividing line. Using the proportional relationship obtained in step 3, the first half interpolation section uses the cumulative distance-width proportional relationship of each point in the i-th section to calculate the cumulative distance of each interpolation point in the section. The second half interpolation section uses the cumulative distance-width proportional relationship of each point in the i+1-th section to calculate the cumulative distance of each interpolation point in the section.

[0013] Step 7: Based on the coordinates of the endpoints of the interpolation section obtained in step 5 and the cumulative distance of the interpolation points of the section obtained in step 6, similar to step 2, calculate the horizontal and vertical coordinates of each point of the interpolation section;

[0014] Step 8: Find the lowest point of the i-th and i+1-th sections, and use linear interpolation to obtain the elevation of the lowest point of the interpolated section;

[0015] Step 9, calculate the elevation value and relative elevation of the first point of the interpolated section, and multiply it by the ratio of the relative elevation of each point of the i-th section to the first point of the section obtained in step 4 to obtain the relative elevation of each point of the first half of the interpolated section; similarly, calculate the relative elevation of each point of the second half of the interpolated section;

[0016] In step 10, the relative elevation of each point on the interpolated section is added to the elevation of the lowest point on the interpolated section to obtain the elevation of each point on the interpolated section. The coordinate data of the interpolated section is merged with the coordinate data of the original section obtained in step 2 to obtain the complete section coordinate data after interpolation.

[0017] Furthermore, the terrain section data in step 1 includes: section spacing L i , cumulative distance of cross section d i,j , elevation z i,j , the left endpoint coordinate (x i,1 ,y i,1 ), right endpoint coordinates The subscript i represents the section number, j represents the jth point of the section, i = 1, 2, ... m, j = 1, 2, ... n i , m represents the number of sections, n iIndicates the number of points in the i-th section.

[0018] Preferably, in step 5, the distance between the two sections is divided by the interpolation distance and rounded to the nearest integer to obtain the number of interpolation sections between the two sections; the left endpoint coordinates (x s,1 ,y s,1 ),

[0019] According to the coordinates of the left and right endpoints of the i-th and i+1-th sections, calculate the angle θ between the two sections and the horizontal direction. i ,θ i+1 , according to the number of interpolation sections n, i to θ i+1 The angle interval is divided into equal parts and gradually changed to obtain the angle θ between the s-th interpolation section and the horizontal direction s ,

[0020]

[0021] Using the left endpoint coordinates of the sth interpolation section (x s,1 ,y s,1 ) and the angle θ between the sth interpolation section and the horizontal direction s Find the equation of the line of the sth interpolation section, using the coordinates of the right endpoint of the ith section and the coordinates of the right endpoint of the i+1th section Obtain the equation of the line between the two points, combine the equation of the line of the sth interpolation section with the equation of the line of the right endpoints of the i-th and i+1-th sections, and obtain the coordinates of the right endpoint of the s-th interpolation section

[0022] The beneficial effects of the present invention include: (1) The present invention provides a method for performing interpolation calculation based on the surveyed terrain section to generate an interpolation section that is consistent with the terrain and geomorphic characteristics and is highly close to the original terrain section.

[0023] (2) When the measured cross-sectional spacing is too large to meet the use requirements, the present invention can set an interpolation spacing to obtain a cross-sectional profile of appropriate scale.

[0024] (3) The present invention converts terrain section data into scattered point data, which not only retains the section contour information but also stores the section scattered point information. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The present invention will be further described below with reference to the accompanying drawings and examples.

[0026] Figure 1 A flow chart of a method provided in an embodiment of the present invention.

[0027] Figure 2a This is a cross-sectional view No. 1 provided for an embodiment of the present invention.

[0028] Figure 2b This is a cross-sectional view No. 2 provided for an embodiment of the present invention.

[0029] Figure 2c This is a cross-sectional view No. 3 provided for an embodiment of the present invention.

[0030] Figure 3 This is a coordinate data diagram of sections 1-3 provided in an embodiment of the present invention.

[0031] Figure 4 This is a distribution diagram of the interpolation section of an embodiment of the present invention.

[0032] Figure 5 This is a schematic diagram of the cross-sectional profile obtained by interpolation of Section No. 1 according to an embodiment of the present invention.

[0033] Figure 6 This is a schematic diagram of the calculation for converting cross-section cumulative distance and elevation into coordinates in an embodiment of the present invention.

[0034] Figure 7 Schematic diagram of calculating the coordinates of the left endpoint of the interpolation section in an embodiment of the present invention.

[0035] Figure 8 Schematic diagram of calculating the right endpoint of the interpolation section in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] like Figure 1 As shown in FIG, the rapid terrain section interpolation method based on proportional relationship includes the following steps:

[0037] Step 1: Collect the terrain section data required for interpolation. The direction of the river flowing downstream is the positive direction. The left bank of the section is the left side, and the right bank is the right side. The terrain section data includes: section spacing (L i ), cumulative distance of cross section (d i，j ), elevation (z i，j ), left endpoint coordinates (x i，1 ,y i，1 ), right endpoint coordinates The subscript i represents the section number, i = 1, 2, ... m, and j represents the number of section points, j = 1, 2, ... n i ;

[0038] The embodiment provides 3 original sections, such as Figure 2a 、 2b , 2c, the coordinates of the left and right endpoints of each section and the section distance are shown in Table 1.

[0039] Table 1 Coordinate data of sections 1 to 3 of the embodiment

[0040] Section name left end x Left end y Right end x Right end y Section spacing (m) No. 1 439842.735 3170843.895 439298.239 3170049.387 2200 No. 2 438382.417 3171264.079 438479.429 3170207.238 1160 No. 3 437410.455 3171104.558 437006.594 3170354.923 0

[0041] Step 2: Calculate the coordinates of each point on the cross section based on the coordinates of the left and right endpoints of the cross section;

[0042] Taking section i as an example, it specifically includes:

[0043] From the coordinates of the left end point of the section (x i,1 ,y i,1 ) and the right endpoint coordinates Using the triangle similarity principle, such as Figure 6 As shown, establish the relationship Obtain Then we can get the horizontal coordinate x of the calculation point i,c , similarly, we can get the vertical coordinate y i,c ,Right now:

[0044]

[0045]

[0046] Where: x i,c ,y i,c To calculate the horizontal and vertical coordinates of the point; is the total width of the section; d i,c is the cumulative distance between the calculation points; dx is the projection length of the distance between the left endpoint and the interpolation point on the x-axis; the coordinates of each point on the cross section are obtained using formula (1) and formula (2);

[0047] The coordinates of sections 1-3 of the embodiment are as follows: Figure 3 shown.

[0048] Step 3, calculate the proportional relationship between the cumulative distance of each point in the section and the section width;

[0049] Divide the cumulative distance of each point on the cross section by the cross section width to obtain the proportional relationship between each point and the cross section width;

[0050]

[0051] Where: dp i,j is the ratio of the cumulative distance of point j in section i to the section width;

[0052] Step 4: Taking the lowest point of the cross section as the standard, subtract the elevation of the lowest point from the elevation of each point on the cross section to obtain the relative elevation, and then divide it by the relative elevation value of point 1 to obtain the ratio of the relative elevation of each point relative to point 1, specifically including:

[0053] Find the elevation of the lowest point of the section, subtract the elevation of the lowest point from the elevation of each point to obtain the relative elevation of each point relative to the lowest point, then divide the relative elevation of each point by the relative elevation of the first point to obtain the ratio of the relative elevations of each point relative to the first point.

[0054] dz i,j =z i,j -min z i (4)

[0055]

[0056] Where: minz i is the elevation of the lowest point of the section; dz i,j is the relative elevation of the jth point of the section relative to the lowest point; dzp i,j is the ratio of the relative elevation of the jth point to the 1st point on the cross section;

[0057] Step 5: Calculate the number of interpolated sections between the two original adjacent sections (denoted as section i and section i+1) based on the spacing and interpolation distance. Then, use the left and right endpoint coordinates of the two sections to calculate the left and right endpoint coordinates of the interpolated section. Specifically, the calculation includes:

[0058] Divide the distance between the two sections by the interpolation distance and round it up to get the number of interpolation sections between the two sections; Figure 7 The geometric relationship is similar to Equation 1 and Equation 2. The coordinates of the left endpoints of the two sections before and after are used to obtain the coordinates of the left endpoint of the interpolation section. The relationship is as follows:

[0059] n=int(L i / Δd) (6)

[0060]

[0061]

[0062] Where: n is the number of interpolation sections; Δd is the interpolation interval, which indicates the distance from the first interpolation section; c is the interpolation section number, c = 1, 2…n; x c,1 ,y c,1 is the coordinate of the left endpoint of the interpolation section;

[0063] According to the coordinates of the left and right endpoints of section i and section i+1, calculate the angle θ between the two sections and the horizontal direction i ,θ i+1 , according to the number of interpolation sections, i to θ i+1 The angle interval is divided into equal parts and gradually changed to obtain the angle θ between the interpolation section and the horizontal direction c , using x c,1 ,y c,1 and θ cFind the equation of the interpolation section line, using x i+1,n ,y i+1,n Obtain the equation of the line at the end point, and jointly interpolate the equation of the cross-section line with the equation of the line at the end point to obtain the interpolation coordinates of the right endpoint. like Figure 8 As shown;

[0064] Step 6: Calculate the width of the interpolation section based on the coordinates of the left and right endpoints of the interpolation section. Then, based on the number of interpolation sections n, divide the interpolation section into two parts with n / 2 as the dividing line. Using the proportional relationship in step 3, the cumulative distances of each point on the interpolation section are calculated using the proportional relationship of the width of section i for interpolation sections 1 to n / 2, and the cumulative distances of each point on the interpolation section are calculated using the proportional relationship of the width of section i+1 for interpolation sections n / 2+1 to n. Specifically, the following steps are performed:

[0065] Calculate the interpolation section width based on the left and right endpoint coordinates of the interpolation section in step 5. Divide the interpolation section into two parts with n / 2 as the dividing line. When n is an even number, 1 to n / 2 is the first half, and n / 2+1 to n is the second half. When n is an odd number, 1 to int(n / 2)+1 is the first half, and int(n / 2)+2 to n is the second half.

[0066] The first half of the section adopts the width ratio of section i, multiplied by the interpolation section width, to obtain the interpolation section point cumulative distance; the second half of the section adopts the width ratio of section i+1, multiplied by the interpolation section width, to obtain the interpolation section point cumulative distance; the formula is as follows:

[0067]

[0068]

[0069] Where: n i is the number of points on section i; n i+1 is the number of cross-section points i+1; d c,j is the cumulative distance of the interpolation section;

[0070] Step 7: Using the coordinates of the left and right endpoints of the interpolation section obtained in step 5 and the cumulative distances of the interpolation points of the section obtained in step 6, calculate the horizontal and vertical coordinates of each point of the interpolation section according to formula (1) and formula (2);

[0071] Step 8, finding the lowest point of section i and section i+1, and using linear interpolation method to obtain the elevation of the lowest point of the interpolated section; specifically including:

[0072] Find the lowest point minz of section i i 、i+1 section lowest point minz i+1 , the distance between the two sections L iWith the interpolation spacing Δd, the elevation of the lowest point of the interpolation section is obtained according to the linear interpolation method. The formula is as follows:

[0073]

[0074] Where: minz c is the lowest point of the interpolation section c;

[0075] Step 9, calculate the elevation value of the left endpoint of the interpolation section. According to the interpolation section division scheme in step 6, multiply the elevation value of the left endpoint of the first half of the interpolation section by the relative elevation ratio obtained in step 4 to obtain the relative elevation of each point in the first half of the interpolation section. The elevation of the second half of the interpolation section is calculated using the same method, specifically including:

[0076] Use the elevation z of the left end point of section i i,1 、i+1 section left endpoint elevation z i+1,1 , similar to formula (11), the elevation value of the left endpoint of the interpolation section is obtained,

[0077]

[0078] Where z c,1 represents the elevation of the first point of the interpolation section c;

[0079] Calculate the relative elevation dz of the first point of the interpolation section c,1 :

[0080] dz c,1 =z c,1 -minz c

[0081] According to the interpolation section division scheme in step 6, the elevation value of the left endpoint of the first half of the interpolation section is multiplied by the relative elevation ratio of section i in step 4 to obtain the relative elevation of each point in the first half of the interpolation section. The elevation value of the left endpoint of the second half of the interpolation section is multiplied by the relative elevation ratio of section i+1 in step 4 to obtain the relative elevation of each point in the second half of the interpolation section.

[0082] dz c,j =dzp i,j ·dz c,1 ,(j=1,2,…n i ) (c belongs to the front half section) (12)

[0083] dz c,j =dzp i+1,j ·dz c,1 ,(j=1,2,…n i+1 ) (c belongs to the second half of the section) (13)

[0084] Where: dz c,jis the relative elevation of the jth point of the interpolation section c;

[0085] Step 10, adding the interpolation section relative elevation to the lowest elevation of the interpolation section to obtain the elevation of each point on the interpolation section, saving the section coordinates and the interpolation section coordinates of step 2 to obtain the original section coordinates and the interpolation section coordinates; specifically including:

[0086] The relative elevation of each point on the interpolated section in step 9 is added to the elevation of the lowest point on the interpolated section in step 8 to obtain the elevation of each point on the interpolated section. The section coordinates and the interpolated section coordinates in step 2 are saved to obtain the original section coordinates and the interpolated section coordinates.

[0087] z c,j =min z c +dz c,j (14)

[0088] Where: z c,j is the elevation of each point on the interpolated section.

[0089] The original cross-section and interpolation cross-section coordinates of the embodiment are as follows: Figure 4 As shown, Section 1 and Interpolation Section 1 and Interpolation Section 2 are as follows Figure 5 shown.

Claims

1. A rapid terrain section interpolation method based on proportional relationship, characterized in that: The following steps are involved: Step 1: Collect the terrain section data required for interpolation; Step 2: Calculate the coordinates of each point on the cross section based on the coordinates of the endpoints at both ends of the cross section; Step 3, calculate the proportional relationship between the cumulative distance of each point in the section and the section width; Step 4: Take the lowest point of the cross section as the reference point, subtract the elevation of the lowest point from the elevation of each point on the cross section to obtain the relative elevation, and then divide it by the relative elevation value of the first point on the cross section to obtain the ratio of the relative elevation of each point on the cross section to the first point on the cross section; Step 5: Calculate the number of interpolated sections between the two sections based on the original adjacent i-th and i+1-th section spacings and the interpolation distance, and then calculate the endpoint coordinates of the two ends of the interpolated section using the endpoint coordinates of the two ends of the original section; Step 6: Calculate the width of the interpolation section based on the coordinates of the endpoints at both ends of the interpolation section. Divide the interpolation section into the first and second half interpolation sections, based on the number n of interpolation sections and with n / 2 as the dividing line. Using the proportional relationship obtained in step 3, the first half interpolation section uses the cumulative distance-width proportional relationship of each point in the i-th section to calculate the cumulative distance of each interpolation point in the section. The second half interpolation section uses the cumulative distance-width proportional relationship of each point in the i+1-th section to calculate the cumulative distance of each interpolation point in the section. Step 7: Based on the coordinates of the endpoints of the interpolation section obtained in step 5 and the cumulative distance of the interpolation points of the section obtained in step 6, similar to step 2, calculate the horizontal and vertical coordinates of each point of the interpolation section; Step 8: Find the lowest point of the i-th and i+1-th sections, and use linear interpolation to obtain the elevation of the lowest point of the interpolated section; Step 9, calculate the elevation value and relative elevation of the first point of the interpolated section, and multiply it by the ratio of the relative elevation of each point of the i-th section to the first point of the section obtained in step 4 to obtain the relative elevation of each point of the first half of the interpolated section; similarly, calculate the relative elevation of each point of the second half of the interpolated section; In step 10, the relative elevation of each point on the interpolated section is added to the elevation of the lowest point on the interpolated section to obtain the elevation of each point on the interpolated section. The coordinate data of the interpolated section is merged with the coordinate data of the original section obtained in step 2 to obtain the complete section coordinate data after interpolation.

2. The fast terrain section interpolation method according to claim 1, characterized in that: The terrain section data in step 1 include: section spacing L i , cumulative distance of cross section d i,j , elevation z i,j , the left endpoint coordinate (x i,1 ,y i,1 ), right endpoint coordinates The subscript i represents the section number, j represents the jth point of the section, i = 1, 2, ... m, j = 1, 2, ... n i , m represents the number of sections, n i Indicates the number of points in the i-th section.

3. The fast terrain section interpolation method according to claim 2, characterized in that: In step 2, the specific process of calculating the coordinates of point C of the i-th section includes: From the coordinates of the left end point of the section (x i,1 ,y i,1 )Right end face coordinates Using the triangle similarity principle, establish the relationship Get the horizontal coordinate x i,c The calculation formula is: Similarly, we get the vertical coordinate y i,c The calculation formula is: Where x i,c ,y i,c are the horizontal and vertical coordinates of point C respectively; is the total width of the i-th section; d i,c is the cumulative distance from point C of the i-th section; dx is the projection length of the distance between the calculation point and the left endpoint of the section on the x-axis; the coordinates of each point on the section are obtained using formula (1) and formula (2).

4. The fast terrain section interpolation method according to claim 3, characterized in that: In step 3, the calculation of the proportional relationship between the cumulative distance of each point in the section and the section width specifically includes: Divide the cumulative distance of each point on the cross section by the cross section width to obtain the proportional relationship between each point on the cross section and the cross section width. The calculation formula is as follows Where dp i,j It represents the ratio of the cumulative distance of the jth point of the i-th section to the section width.

5. The fast terrain section interpolation method according to claim 4, characterized in that: Step 4 specifically includes: Find the elevation of the lowest point of the section, subtract the elevation of the lowest point from the elevation of each point to get the relative elevation of each point relative to the lowest point, then divide the relative elevation of each point by the relative elevation of the first point to get the ratio of the relative elevation of each point to the first point. dz i,j =z i,j -minz i (4) Where minz i is the elevation of the lowest point of the i-th section; dz i,j Indicates the relative elevation of the jth point of the section relative to the lowest point; dzp i,j It is the ratio of the relative elevation of each point on the section to the first point.

6. The fast terrain section interpolation method according to claim 5, characterized in that: In step 5, the number of interpolated sections between the two sections is calculated based on the spacing between the original i-th and i+1-th sections and the interpolated distance. Then, the left and right endpoint coordinates of the interpolated section are calculated using the left and right endpoint coordinates of the two sections. Specifically, the calculation includes: Divide the distance between two cross-sections by the interpolation distance and round down to obtain the number of interpolation cross-sections between the two cross-sections; according to the geometric relationship between the left endpoints of the interpolation cross-section, the left endpoints of the \(i\)th and \((i + 1)\)th cross-sections, and the \(X\) and \(Y\) axes, obtain the coordinates of the left endpoints of the interpolation cross-section. The calculation formula is as follows: n=int(L i / Δd) (6) Where n is the number of interpolation sections; Δd represents the interpolation spacing, which is the distance between the left endpoints of adjacent interpolation sections; s represents the subscript number of the interpolation section, s = 1, 2…n; x s,1 ,y s,1 Indicates the horizontal and vertical coordinates of the left endpoint of the interpolation section; According to the coordinates of the left and right endpoints of the i-th and i+1-th sections, calculate the angle θ between the two sections and the horizontal direction. i ,θ i+1 , according to the number of interpolation sections n, i to θ i+1 The angle interval is divided into equal parts and gradually changed to obtain the angle θ between the s-th interpolation section and the horizontal direction s , Using the left endpoint coordinates of the sth interpolation section (x s,1 ,y s,1 ) and the angle θ between the sth interpolation section and the horizontal direction s Find the equation of the line of the sth interpolation section, using the coordinates of the right endpoint of the ith section and the coordinates of the right endpoint of the i+1th section Obtain the equation of the line between the two points, combine the equation of the line of the sth interpolation section with the equation of the line of the right endpoints of the i-th and i+1-th sections, and obtain the coordinates of the right endpoint of the s-th interpolation section 7. The fast terrain section interpolation method according to claim 6, characterized in that: Step 6 specifically includes: Calculate the width of the interpolation cross-section according to the coordinates of the left and right endpoints of the interpolation cross-section obtained in Step 5. Divide the interpolation cross-section into the first half interpolation cross-section and the second half interpolation cross-section with \(n / 2\) as the boundary. When \(n\) is even, the cross-sections with subscript \(1\leq s\leq int(n / 2)\) belong to the first half interpolation cross-section, and the interpolation cross-sections with \(int(n / 2)\lt s\leq n\) belong to the second half interpolation cross-section; when \(n\) is odd, the cross-sections with \(1\leq s\leq int(n / 2)+1\) belong to the first half interpolation cross-section, and the cross-sections with \(int(n / 2)+1\lt s\leq n\) belong to the second half interpolation cross-section; For the first half interpolation cross-section, use the cumulative distance-width ratio relationship of each point of the \(i\)th cross-section and multiply it by the width of the interpolation cross-section to obtain the cumulative distance of the interpolation cross-section points; for the second half cross-section, use the cumulative distance-width ratio relationship of each point of the \((i + 1)\)th cross-section and multiply it by the width of the interpolation cross-section to obtain the cumulative distance of the interpolation cross-section points. The calculation formula is as follows: Where n i is the number of points in the i-th section; n i+1 is the number of points in the i+1th section; d s,j Represents the cumulative distance of the jth point of the sth interpolation section.

8. The fast terrain section interpolation method according to claim 7, characterized in that: Step 8 specifically includes: Find the lowest point minz of the i-th section i,j and the lowest point minz of the i+1 section i+1,j , the distance between the two sections L i With the interpolation spacing Δd, the linear interpolation method is used to obtain the elevation of the lowest point of the interpolation section. The calculation formula is as follows: Where minz s,j Indicates the elevation of the lowest point of the sth interpolation section.

9. The fast terrain section interpolation method according to claim 8, characterized in that: Step 9 specifically includes: Similar to formula (11), using the elevation z of the first point of the i-th section i,1 and the elevation z of the first point of the i+1th section i+1,1 , the distance between the two sections L i With the interpolation spacing Δd, the linear interpolation method is used to obtain the elevation of the first point of the interpolation section. The calculation formula is as follows: Where z s,1 Indicates the elevation of the first point of the s-th interpolation section; Calculate the relative elevation dz of the first point of the interpolation section s,1 : dz s,1 =z s,1 -minz s,j For the first half interpolation cross-section, multiply the relative elevation of the first point of each interpolation cross-section by the ratio of the relative elevation of each point of the \(i\)th cross-section to the first point obtained in Step 4 to obtain the relative elevation of each point of the first half interpolation cross-section; For the second half interpolation cross-section, multiply the relative elevation of the first point of each interpolation cross-section by the ratio of the relative elevation of each point of the \((i + 1)\)th cross-section to the first point obtained in Step 4 to obtain the relative elevation of each point of the second half interpolation cross-section; dz s,j =dzp i,j ·dz s,1 ,(j=1,2,…n i ), the sth interpolation section belongs to the first half of the section (12) dz s,j =dzp i+1,j ·dz s,1 ,(j=1,2,…n i+1 ), the sth interpolation section belongs to the second half of the section (13) Where: dz s,j Indicates the relative elevation of the jth point of the sth interpolation section; n i is the number of points in the i-th section; n i+1 is the number of points in the i+1th section.

10. The fast terrain section interpolation method according to claim 9, characterized in that: Step 10 specifically includes; 1) Add the relative elevation of each point of the interpolation cross-section obtained in Step 9 to the lowest elevation of the interpolation cross-section obtained in Step 8 to obtain the elevation of each point of the interpolation cross-section, With s,j =minz s,j +dz s,j (14) Where: z s,j represents the elevation of the jth point of the sth interpolation section; 2)汇总 the coordinate data of each point of the interpolation cross-section and the coordinate data of the original cross-section obtained in Step 2 to obtain the coordinate data of the original cross-section and the interpolation cross-section and save them. It should be noted that there is an unclear expression "汇总" in the original text. It might be a typo or a specific term that needs further clarification. Here it is tentatively translated as "aggregate". If there is a more accurate meaning, the translation should be adjusted accordingly.

Images