Automatic compilation method based on underwater isobath

Abstract

The invention provides an automatic compilation method based on an underwater isobath, and the method comprises the following steps: S1, extracting three-dimensional coordinate data from a data file, generating a threshold sequence through determining a Z value range and an isobath distance, and dividing a first curve and a calculation curve in the threshold sequence; s2, discrete data points are converted into continuous grid data through bilinear interpolation, intersection points with the same elevation value are connected in a constructed triangulation network to form isobath segments, and the isobath segments are connected end to end to obtain a complete initial isobath; s3, for the point of each isobath on the triangulation network, calculating and generating two control points which are respectively positioned on two sides of the initial isobath point; and S4, respectively constructing polygons by the generated control points, then carrying out iterative optimization on a central polygon, and ensuring that a smooth curve is kept between boundary polygons and original topographic features can be kept through multiple iterations. Through the method, the working efficiency is remarkably improved, the accuracy of a drawing result is ensured, and diversified working environments and requirements can be effectively adapted.

Description

Technical Field

[0001] The invention relates to the field of water conservancy projects, and in particular to an automatic compilation method based on underwater depth contours. Background Art

[0002] Underwater depth contours are an indispensable and important tool in water conservancy projects and are widely used in water surveying, channel planning and other fields. Traditional underwater depth contour drawing methods mainly rely on manual operations, which have problems such as low efficiency, unstable accuracy, and difficulty in processing large-scale data. With the advancement of surveying technology, the amount of underwater terrain data collected has increased dramatically, and manual processing methods can no longer meet the needs of modern water conservancy projects.

[0003] In recent years, the application of computer technology in underwater depth contour drawing has become increasingly widespread. The emergence of some computer-aided drawing software has improved the efficiency and accuracy of depth contour drawing to a certain extent. However, these software still require a lot of manual intervention and cannot achieve true automation. In addition, existing automation methods are often difficult to adapt to complex underwater terrain, and there are problems such as insufficient accuracy or inaccurate actual terrain features.

[0004] The dynamic changes in underwater topography also bring new challenges to the drawing of depth contours. Due to factors such as natural erosion and human engineering, underwater topography may continue to change. Traditional depth contour drawing methods are difficult to reflect these changes in a timely manner, resulting in insufficient timeliness of depth contour maps and failure to provide accurate and timely basis for water conservancy project decision-making.

[0005] In addition, different application scenarios have different requirements for depth contour maps. For example, waterway planning may require large-scale detailed depth contour maps, while reservoir management may require small-scale overview depth contour maps. Existing drawing methods are difficult to flexibly cope with such multi-scale requirements and often require repeated tedious manual adjustments.

[0006] Therefore, developing a method that can automatically, accurately and efficiently draw underwater depth contours can not only improve the work efficiency of water conservancy projects, but also provide more reliable data support for the planning, design and management of water conservancy projects. This has important practical significance and application value for improving the overall level of water conservancy projects and promoting the sustainable development of water conservancy undertakings. Summary of the invention

[0007] In order to solve the technical problems in the above background, the present invention provides an automatic compilation method based on underwater depth contours, comprising the following steps:

[0008] S1, extracting three-dimensional coordinate data from the data file, generating a threshold sequence by determining the range of water depth elevation values ​​and the spacing of isobaths, and dividing the first curve and the counting curve in the threshold sequence;

[0009] S2, converting the data points preprocessed in step 1 into continuous grid data by bilinear interpolation, connecting the intersection points with the same elevation value in the constructed triangulated network to form isobath segments, and connecting these segments end to end to obtain a complete initial isobath;

[0010] S3. For each point of the isobath on the triangulated network, calculate and generate the control points and the center point on both sides thereof;

[0011] S4. Use all control points A generated in step 3 to construct an outer polygon, all control points B to construct an inner polygon, and the center point to construct a central polygon. Iterate and optimize the central polygon, and ensure that the smooth curve is maintained between the boundary polygons and the original terrain features are retained through multiple iterations.

[0012] In a preferred solution, step S1 specifically includes the following steps:

[0013] S11, read the original data line by line from the data file, use the string splitting function to parse each line of data into numerical X, Y, Z coordinate values, and store them in the corresponding data structure;

[0014] S12, traversing all data points, continuously updating the current maximum and minimum value records, and determining the threshold range required for generating isobaths;

[0015] S13, increasing the given depth contour interval within the minimum and maximum Z value range, to obtain a threshold sequence;

[0016] S14. When generating a threshold sequence, mark every five intervals in the sequence as counting curves, and the rest as head curves.

[0017] In a preferred embodiment, step S2 further comprises the following steps:

[0018] S21, interpolating discrete data points into continuous grid data using a bilinear interpolation method;

[0019] S22, using the continuous mesh data obtained in step S21 to generate a triangulated network by using a point-by-point interpolation method to perform Delaunay triangulation;

[0020] S23, optimizing the insertion of new points into the triangulated network according to a given maximum edge length threshold;

[0021] S24. Connect the intersection points with the same elevation value inside each triangle to form isobath segments, and then connect the isobath segments in adjacent triangles end to end to finally form initial isobaths.

[0022] In a preferred solution, the bilinear interpolation method in step S21 is specifically:

[0023] Assume that the coordinates of the target point are P(x,y), find the four integer coordinates closest to point P:

[0024] Z11(x1,y1), Z12(x1,y2), Z21(x2,y1), Z22(x2,y2).

[0025] Calculate the interpolated value in the X direction:

[0026]

[0027]

[0028] Calculate the interpolation in the Y direction and get the final result:

[0029]

[0030] The above method is executed in a loop to perform bilinear interpolation on all discrete points in the data file to obtain continuous grid data.

[0031] In a preferred solution, the Delaunay triangulation operation in step S22 includes the following steps:

[0032] Assume that a new node D is inserted;

[0033] S221, draw a circumscribed circle for each triangle, and find out the triangle whose circumscribed circle includes point D;

[0034] S222, deleting the common edges of the triangles whose circumscribed circles include point D, to form a Delaunay cavity;

[0035] S223, connecting point D and each vertex of the Delaunay cavity, thereby completing the insertion of point D into the Delaunay triangle list and forming a new set of Delaunay triangles.

[0036] In a preferred solution, step S23 further includes:

[0037] Assume that the coordinates of the two endpoints of the triangle side are (x1, y1, z1) and (x2, y2, z2).

[0038] x=x1+((x2-x1) / count)*j;

[0039] y=y1+((y2-y1) / count)*j;

[0040] z=z1+((z2-z1) / count)*j;

[0041] In the formula, count represents the total number of points to be inserted, and j represents the index of the current insertion point.

[0042] In a preferred solution, step S3 specifically includes the following steps:

[0043] For each point of the isobath on the triangulated network, two control points are calculated and generated;

[0044] Assuming the original triangulated mesh is triangle ABC, traverse each isobath polygon to obtain the three vertices A, B, and C of the original triangulated mesh;

[0045] When point C does not coincide with A or B, calculate the movable control points newPointA and newPointB.

[0046] distance=canMoveDistance / (zDiff / originalDistance)

[0047] newPoint=destination(from,distance,bearing)

[0048] Among them, canMoveDistance represents the maximum distance allowed to move determined by the custom residual value, zDiff represents the elevation difference between two points, originalDistance represents the original distance between the two points, and the destination function calculates the control point position based on the starting point, distance and azimuth.

[0049] Calculate the center point coordinates:

[0050] X_center=(X_A+X_B) / 2

[0051] Y_center=(Y_A+Y_B) / 2

[0052] Among them, (X_A, Y_A) and (X_B, Y_B) represent the x and y coordinates of newPointA and newPointB respectively.

[0053] In the preferred solution, when C coincides with A or B, the coincident point is directly used as the control point and the center point;

[0054] Add the calculated control points and center points to the corresponding polygon array.

[0055] In a preferred solution, step S4 specifically includes the following steps:

[0056] Use all control points A to construct polygon A, use all control points B to construct polygon B, and use all center points to construct the center polygon;

[0057] The central polygon is first initially smoothed based on the Chaikin algorithm. For each edge of the polygon, new vertices are generated at 1 / 4 and 3 / 4 of the distance from the starting point. These two points divide one of the original edges of the polygon into three equal parts. Assuming that the newly generated vertices are P1 and P2, and the polygon edge is AB, the newly generated vertices are calculated according to the following formula:

[0058]

[0059] Detect the intersection of the newly generated smooth polygon and the original center polygon;

[0060] Find the nearest point of each detected intersection on the central polygon as a new control point. The formula for generating the new control point is:

[0061] P_nearest=nearestPointOnLine(L_center,P_intersect);

[0062] Use the nearestPointOnLine function in the turf.js library to calculate the nearest point, where P_nearest represents the new control point on the center polygon, L_center represents the line segment of the center polygon, and P_intersect represents the detected intersection point;

[0063] Update the center polygon using the newly generated control points.

[0064] In a preferred solution, the step of generating new control points in step S4 is repeated several times, and the current number of iterations is continuously compared with the maximum allowed number of iterations to determine whether to continue iterating, until a preset upper limit of iterations is reached.

[0065] The beneficial effects of the present invention are as follows: the underwater bathymetric automatic drawing method proposed in the present invention improves the efficiency and quality of bathymetric drawing through automated processing and innovative algorithms, has good adaptability and can handle conditions of different scales and complex terrains, strictly maintains the position of fixed points to ensure accurate reflection of terrain features, and is integrated into a visualization software system for practical application, providing reliable technical support for water conservancy project construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Schematic diagram of Delaunay triangulation according to an embodiment of the present invention.

[0067] Figure 2 Schematic diagram of initial isobaths according to an embodiment of the present invention.

[0068] Figure 3 It is a schematic diagram of isobaths automatically drawn according to an embodiment of the present invention.

[0069] Figure 4 It is a depth contour comparison map automatically drawn by the embodiment of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] Example 1

[0072] To achieve the goal of automated depth contour mapping, three key issues need to be resolved: first, how to process complex underwater terrain data and construct an irregular triangulated network model that can accurately express terrain features; second, how to ensure the smoothness and accuracy of depth contours, eliminating irregular protrusions while maintaining important terrain features; third, how to adapt to different scales and application requirements to achieve multi-scale expression of depth contours. The embodiment of the present invention proposes a complete solution to the above problems, which specifically includes four key steps: first, data preprocessing is performed to extract three-dimensional coordinate data from the data file and generate a threshold sequence; second, the initial depth contour is constructed by bilinear interpolation; two control points are generated for each depth contour point, and a polygon structure is constructed on this basis to iteratively smooth the polygon; finally, the final optimization of the depth contour is achieved by moving the control points and smoothing the polygons. The combination of these four steps not only realizes high-quality automatic mapping of underwater depth contours, but also solves the problems of insufficient precision and inaccurate mapping effects existing in the prior art. The detailed principle of each step is described as follows:

[0073] Step 1: The core of data preprocessing is to ensure the quality of original data through normalization. By setting the threshold, outliers can be eliminated. The quality of original data can be improved to provide a reliable data basis for subsequent contour line generation.

[0074] In step 1, read the original data line by line from the data file, use the string splitting function to parse each line of data into numerical X, Y, and Z coordinate values, and store them in the corresponding data structure. Traverse all data points, continuously update the current maximum and minimum value records, determine the threshold range required for isobath generation, and improve data reliability. According to the given isobath spacing increasing within the minimum and maximum Z value range, the threshold sequence can be obtained. In order to improve the readability of the contour map, the expression method of first curve-counting curve is adopted. When generating the threshold sequence, the value of every 5 intervals in the sequence is marked as the counting curve, that is, starting from the starting point, one of every four contour lines is selected as the counting curve and marked in red, and the rest are first curves, thereby forming a clearly layered contour effect. This systematic preprocessing method lays the foundation for the accurate generation and clear visualization of subsequent contour lines.

[0075] Step 2: Convert the discrete data into a continuous grid through bilinear interpolation, then use Delaunay triangulation to generate a triangulated network and optimize it. Finally, connect the equal-elevation points inside the triangle and connect them end to end to form a complete isobath.

[0076] In step 2, the bilinear interpolation method is used to interpolate discrete data points into continuous mesh data, which provides the necessary continuous data source for constructing the triangulation network. Assuming the coordinates of the target point are P(x, y), find the four integer coordinate points closest to point P: Z11(x1, y1), Z12(x1, y2), Z21(x2, y1), Z22(x2, y2).

[0077] Calculate the interpolated value in the X direction:

[0078]

[0079] Calculate the interpolation in the Y direction and get the final result:

[0080]

[0081] The above method is executed in a loop to perform bilinear interpolation on all discrete points in the data file to obtain continuous grid data.

[0082] These continuous mesh data are used to generate a triangulated network by using the Delaunay triangulation method using the point-by-point interpolation method.

[0083] Assuming that a new node D is inserted, the steps of segmentation are as follows:

[0084] 1. Draw a circumscribed circle for each triangle and find the triangle whose circumscribed circle contains point D.

[0085] 2. Delete the common edges of the triangles whose circumscribed circles contain point D to form a Delaunay cavity.

[0086] 3. Connect point D and the vertices of the Delaunay cavity to complete the insertion of point D into the Delaunay triangle list and form a new set of Delaunay triangles.

[0087] In order to improve the quality of the triangulated network, the insertion of new points in the triangulated network is optimized according to the given maximum edge length threshold. Assume that the coordinates of the two endpoints of the triangle edge are (x1, y1, z1) and (x2, y2, z2).

[0088] x=x1+((x2-x1) / count)*j (4)

[0089] y=y1+((y2-y1) / count)*j (5)

[0090] z=z1+((z2-z1) / count)*j (6)

[0091] In the formula, count represents the total number of points to be inserted, and j represents the index of the current insertion point.

[0092] Isobaths are formed by connecting the intersection points with the same elevation value inside each triangle, and then these isobaths in adjacent triangles are connected end to end to form the initial isobaths.

[0093] Step 3, the process of generating isobath control points: traverse the isobath polygons in the triangulation network, calculate the position of the control points according to the vertex coincidence, use the residual value and elevation difference to determine the movable distance, and finally calculate the control points and center points.

[0094] In step 3, for each point of the isobath on the triangulated network, two control points are calculated and generated.

[0095] Assuming that the original triangulated mesh is triangle ABC, traverse each isobath polygon to obtain the three vertices A, B, and C of the original triangulated mesh.

[0096] Determine whether point C coincides with point A or point B, and calculate the control point according to different situations:

[0097] If point C does not coincide with A or B, calculate the movable control points newPointA and newPointB.

[0098] distance=canMoveDistance / (zDiff / originalDistance) (7)

[0099] newPoint=destination(from,distance,bearing) (8)

[0100] Among them, canMoveDistance represents the maximum distance allowed to move determined by the custom residual value, zDiff represents the elevation difference between two points, originalDistance represents the original distance between the two points, and the destination function calculates the control point position based on the starting point, distance and azimuth.

[0101] Calculate the center point coordinates:

[0102] X_center=(X_A+X_B) / 2 (9)

[0103] Y_center=(Y_A+Y_B) / 2 (10)

[0104] Among them, (X_A, Y_A) and (X_B, Y_B) represent the x and y coordinates of newPointA and newPointB respectively.

[0105] If C coincides with A or B, the coincident points are directly used as control points and center points.

[0106] Add the calculated control points and center points to the corresponding polygon array.

[0107] Step 4, the final smoothing process of the depth contour: construct a polygon with control points, then perform preliminary Chaikin algorithm smoothing on the central polygon, detect the intersection of the smoothed polygon and the original polygon, and generate new control points based on these intersections to update the central polygon, and iterate repeatedly until the preset number of times is reached to complete the depth contour drawing.

[0108] In step 4, polygon A is constructed using all control points A, polygon B is constructed using all control points B, and the central polygon is constructed using all center points.

[0109] The smoothing process of the center polygon is an iterative optimization process. The center polygon is first initially smoothed based on the Chaikin algorithm. For each edge of the polygon, new vertices are generated at 1 / 4 and 3 / 4 of the distance from the starting point. These two points divide one of the original edges of the polygon into three equal parts. Assuming that the newly generated vertices are P1 and P2, and the polygon edge is AB, the newly generated vertices are calculated according to the following formula:

[0110]

[0111] Detect the intersection of the newly generated smoothed polygon with the original center polygon.

[0112] Generate new control points for the central polygon: For each detected intersection, find its nearest point on the central polygon as a new control point. The formula for generating new control points is as follows:

[0113] P_nearest=nearestPointOnLine(L_center,P_intersect) (13)

[0114] This function is implemented using the nearestPointOnLine function in the turf.js library, where P_nearest represents the new control point on the center polygon, L_center represents the line segment of the center polygon, and P_intersect represents the detected intersection point.

[0115] Update the center polygon using the newly generated control points.

[0116] The above process is repeated as many times as needed, and the current number of iterations is constantly compared with the maximum allowed number of iterations to decide whether to continue iterating until the preset iteration limit is reached.

[0117] At this point, the automatic compilation of underwater depth contours is completed.

[0118] Example 2

[0119] The waterway near the Yichang section of the Yangtze River was selected to verify the method of the present invention. The specific implementation steps are as follows:

[0120] (1) Select the depth contour file to be drawn, set the depth contour spacing to be equal, and distinguish and mark the first curve and the counting curve to ensure that the depth contours of different depths are clearly expressed.

[0121] (2) The maximum edge length threshold of the triangulated network is set to 50. Based on this parameter, the triangulated network of the underwater terrain is constructed and the initial isobaths are generated.

[0122] (3) Set the error range to 0.5, calculate the movable range of each underwater elevation point, generate corresponding control points, and ensure accurate expression of water depth.

[0123] (4) According to the set maximum number of iterations, the underwater depth contour smoothing iteration is performed to optimize the depth contour shape.

[0124] (5) At this point, the automatic compilation of underwater depth contours has been completed, forming an accurate and beautiful expression of the underwater terrain.

[0125] The method for automatically compiling underwater depth contours proposed in the present invention has two advantages. First, the efficiency and quality of depth contours are improved through automated processing and innovative algorithms. It has good adaptability and can handle different scales and complex terrain conditions. The depth contours automatically compiled by the present invention are shown in FIG. Figure 3 As shown; secondly, strictly maintaining the position of fixed points ensures accurate reflection of terrain features, and integration into the visualization software system facilitates practical application, providing reliable technical support for water conservancy project construction.

[0126] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An automatic compilation method based on underwater depth contours, characterized by: The following steps are involved: S1, extracting three-dimensional coordinate data from the data file, generating a threshold sequence by determining the range of water depth elevation values ​​and the spacing of isobaths, and dividing the first curve and the counting curve in the threshold sequence; S2, converting the data points preprocessed in step S1 into continuous grid data by bilinear interpolation, connecting the intersection points with the same elevation value in the constructed triangulated network to form isobath segments, and connecting the isobath segments end to end to obtain a complete initial isobath; S3, for each point of the isobath on the triangulated network, calculate and generate control points and center points; S4, using all control points A generated in step 3 to construct an outer polygon, all control points B to construct an inner polygon, and the center point to construct a center polygon; The central polygon is iteratively optimized, and multiple iterations are performed to ensure that the smooth curve is maintained between the boundary polygons while retaining the original terrain characteristics.

2. The automatic compilation method based on underwater depth contours according to claim 1 is characterized by: Step S1 specifically includes the following steps: S11, read the original data line by line from the data file, use the string splitting function to parse each line of data into numerical X, Y, Z coordinate values, and store them in the corresponding data structure; S12, traverse all data points, update the current maximum and minimum value records, and determine the threshold range required for generating isobaths; S13, increasing the given depth contour interval within the range of minimum and maximum Z values ​​to obtain a threshold sequence; S14. When generating a threshold sequence, mark every five intervals in the sequence as counting curves, and the rest as head curves.

3. The automatic compilation method based on underwater depth contours according to claim 1 is characterized by: Step S2 also includes the following steps: S21, using a bilinear interpolation method to interpolate discrete data points into continuous grid data; S22, using the continuous mesh data obtained in step S21 to generate a triangulated network by using a point-by-point interpolation method to perform Delaunay triangulation; S23, optimizing the insertion of new points into the triangulated network according to a given maximum edge length threshold; S24. Connect the intersection points with the same elevation value inside each triangle to form isobath segments, and then connect the isobath segments in adjacent triangles end to end to finally form initial isobaths.

4. The automatic compilation method based on underwater depth contours according to claim 3 is characterized by: The bilinear interpolation method in step S21 is specifically as follows: Assuming the coordinates of the target point are P(x,y), find the four integer coordinate points closest to point P: Z11(x1,y1), Z12(x1,y2), Z21(x2,y1), Z22(x2,y2); Calculate the interpolated value in the X direction: Calculate the interpolation in the Y direction and get the final result: The above method is executed in a loop to perform bilinear interpolation on all discrete points in the data file to obtain continuous grid data.

5. The automatic compilation method based on underwater depth contours according to claim 3 is characterized by: The Delaunay triangulation operation in step S22 includes the following steps: Assume that a new node D is inserted; S221, draw a circumscribed circle for each triangle, and find out the triangle whose circumscribed circle includes point D; S222, deleting the common edges of the triangles whose circumscribed circles include point D, to form a Delaunay cavity; S223, connecting point D and each vertex of the Delaunay cavity, thereby completing the insertion of point D into the Delaunay triangle list and forming a new set of Delaunay triangles.

6. The automatic compilation method based on underwater depth contours according to claim 3 is characterized by: Step S23 also includes: Assume that the coordinates of the two endpoints of the triangle side are (x1, y1, z1) and (x2, y2, z2). x=x1+((x2-x1) / count)*j; y=y1+((y2-y1) / count)*j; z=z1+((z2-z1) / count)*j; In the formula, count represents the total number of points to be inserted, and j represents the index of the current insertion point.

7. The automatic compilation method based on underwater depth contours according to claim 1 is characterized by: Step S3 specifically includes the following steps: For each point of the isobath on the triangulated network, two control points are calculated and generated; Assuming the original triangulated mesh is triangle ABC, traverse each isobath polygon to obtain the three vertices A, B, and C of the original triangulated mesh; When point C does not coincide with point A or B, calculate the movable control points newPointA and newPointB; distance=canMoveDistance / (zDiff / originalDistance); newPoint=destination(from,distance,bearing); Among them, canMoveDistance represents the maximum distance allowed to move determined by the custom residual value. zDiff represents the elevation difference between two points, originalDistance represents the original distance between the two points, The destination function calculates the control point location based on the starting point, distance and azimuth; Calculate the center point coordinates: X_center = (X_A + X_B) / 2; Y_center = (Y_A + Y_B) / 2; Among them, (X_A, Y_A) and (X_B, Y_B) represent the x and y coordinates of newPointA and newPointB respectively.

8. The automatic compilation method based on underwater depth contours according to claim 7 is characterized by: When C coincides with A or B, the coincident point is directly used as the control point and center point; Add the calculated control points and center points to the corresponding polygon array.

9. The automatic compilation method based on underwater depth contours according to claim 1 is characterized by: Step S4 The specific steps include: Use all control points A to construct polygon A, use all control points B to construct polygon B, and use all center points to construct the center polygon; The central polygon is first initially smoothed based on the Chaikin algorithm. For each edge of the polygon, new vertices are generated at 1 / 4 and 3 / 4 of the distance from the starting point. These two points divide one of the original edges of the polygon into three equal parts. Assuming that the newly generated vertices are P1 and P2, and the polygon edge is AB, the newly generated vertices are calculated according to the following formula: Detect the intersection of the newly generated smooth polygon and the original center polygon; Find the nearest point of each detected intersection on the central polygon as a new control point. The formula for generating the new control point is: P_nearest=nearestPointOnLine(L_center,P_intersect); Use the nearestPointOnLine function in the turf.js library to calculate the nearest point, where P_nearest represents the new control point on the center polygon, and L_center represents the line segment of the center polygon. P_intersect represents the detected intersection point; Update the center polygon using the newly generated control points.

10. The automatic compilation method based on underwater depth contours according to claim 9 is characterized by: The step of generating new control points in step S4 is repeated several times, and the current number of iterations is continuously compared with the maximum allowed number of iterations to determine whether to continue iterating, until a preset upper limit of iterations is reached.

Images