Segmented smoothing interpolation method and device based on DLG contour lines and computer readable storage medium

Abstract

The application discloses a segmented smooth interpolation method and device based on DLG contour lines and a computer readable storage medium, belongs to the field of geographic information technology, and can generate an interpolated initial curve conforming to actual geographic conditions. The method comprises the following steps: selecting adjacent count curves A and B, setting equal-length trend step points on the count curves A and B at a trend step length s, constructing a line-in-triangle network between the count curves A and B, optimizing Z-shaped line clusters, performing segmented processing, interpolating across line segments, and generating an initial curve C. The application improves operation efficiency and smoothness by segmenting the count curves according to the trend and performing smooth interpolation on the segmented areas. The application has a clever concept, fully excavates feature points in geographic information, conforms to actual geographic characteristics, generates smooth and beautiful interpolated initial curves, and has a high running efficiency when the method is loaded on a computer and runs, and has a wide application prospect.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geographic information, and particularly relates to improvement of DLG graphic editing algorithm technology. BACKGROUND

[0002] In the editing process of DLG contour lines, it is necessary to interpolate a first curve between adjacent count curves. However, interpolation of the first curve by software often leads to distortion, non-smoothness or complicated operation due to algorithm problems, resulting in low work efficiency and complicated operation.

[0003] Specifically, there are two common interpolation algorithms. One is a triangulation interpolation algorithm, which has the advantages of quickly interpolating a whole first curve and the disadvantage of being dependent on node distribution, resulting in poor node distribution and non-smooth transition of the curve due to Z-type and V-type interpolation, as shown in the first curve in FIG. 16. The interpolated line formed after connection is not smooth and hard, and there are many abrupt points, which do not conform to the actual geographical conditions.

[0004] The other is an EPS interpolation algorithm, which generates a first curve by segmenting and cutting according to different curvatures. The first curve is smooth, but the line needs to be interpolated multiple times, which is inefficient due to frequent and redundant operations.

[0005] Therefore, how to design a smooth interpolation first curve that conforms to the actual geographical conditions and is convenient for computer system to generate efficiently has become a technical problem to be solved in the field. SUMMARY

[0006] The present application provides a segmented smooth interpolation method and device based on DLG contour lines and a computer readable storage medium, which can generate an interpolation first curve that conforms to the actual geographical conditions without manual segmentation, thereby improving operation efficiency and smoothness.

[0007] The technical solution of the present application is as follows:

[0008] S1), selecting adjacent count curves A and B,

[0009] selecting two adjacent count curves A and B from DLG contour lines as a basis;

[0010] S2), setting equal-length trend step points on the count curves A and B with a trend step length s,

[0011] i trend step points are set on the count curve A, i≥0; j trend step points are set on the count curve B, j≥0;

[0012] S3), constructing inner triangular network between the curve A and the curve B,

[0013] S3.1), connecting the first trend step point A0 on the curve A with the first trend step point B0 on the curve B to get the net line L0,

[0014] S3.2), generating subsequent net lines L1~L n ;

[0015] to get the net line set L, in which there are Z-shaped and V-shaped line clusters;

[0016] S4), optimizing the Z-shaped line cluster,

[0017] optimizing the Z-shaped line cluster in the net line set L obtained in step 3) by deleting the even sequence net line in the Z-shaped line cluster from the net line set L to get the H-shaped line cluster;

[0018] S5), segment processing,

[0019] dividing the curve A and the curve B into several trend segments based on the H-shaped line cluster;

[0020] S6), interpolating across-line segments,

[0021] interpolating several distance-adapted across-line segments in each trend segment so as to generate several distance-adapted across-line segments between the curve A and the curve B;

[0022] S7), generating the first curve C,

[0023] 2-m equidividing the across-line segments and connecting them from the head to the tail by using multi-segment lines to generate the interpolation first curve C1~C m-1 .

[0024] Further, the trend step length s in step S2) is set within 2-10 mm according to the details of the drawing, which needs to reflect the characteristic details of the curve A or the curve B.

[0025] Further, the step 3.2) is:

[0026] S3.2.1) connecting the line based on i≥0, j≥0 as the inter-line net line (L 1~n ) of the inner triangular network, wherein i, j are the sequence numbers of the characteristic points of the curves A and B on the curves;

[0027] S3.2.2) judging whether i and j are both 0, if yes, jumping to step S3.2.3), if not, jumping to step S3.2.4),

[0028] S3.2.3) judge whether the quadrangle formed by A(i), B(j), B(j+1) and A(i+1) is self-intersecting;

[0029] If not, jump to step S3.2.5);

[0030] If yes, end;

[0031] S3.2.4) judge whether the quadrangle formed by A(i+1), B(j+1) and the last triangular mesh is self-intersecting;

[0032] If yes, jump to step S3.2.3);

[0033] If not, jump to step S3.2.6);

[0034] S 3.2.5) in the quadrangle formed by A(i), B(j), B(j+1) and A(i+1), add the diagonal line meeting the Delauney empty circle feature to the set L as an effective line mesh, if the feature point is on the curve A, then i++, otherwise j++;

[0035] Then jump to step S3.2.1);

[0036] S 3.2.6) judge whether the point A(i+1), B(j+1) in step S3.2.4) meets the condition;

[0037] If yes, jump to step S3.2.7);

[0038] If not, end;

[0039] S3.2.7) add the line as an effective triangular mesh to the set L, if the feature point is on A, then i++, otherwise j++; jump to step S3.2.1).

[0040] Further, the step S5) is segmented with the mesh lines at the two edges of the H-shaped line cluster as boundaries; after segmentation, the remaining V-shaped line cluster and H-shaped line cluster are deleted;

[0041] Further, when the H-shaped line cluster is one, it itself is the segmentation basis.

[0042] Further, in the step 6), when the cross-line segment is inserted in the trend segment,

[0043] First, set the density step t, which is set according to the accuracy requirement of the drawing, and the value range is 0.2-2mm;

[0044] After setting the density step t, calculate the number of cross-line segments inserted according to p=(a+b) / (2xt), and take the integer.

[0045] Wherein a is the curve segment length on the trend segment A curve, b is the curve segment length on the trend segment B curve.

[0046] The device for implementing the DLG contour line segment smoothing interpolation method comprises:

[0047] The adjacent contour curve A and contour curve B selection module selects two adjacent contour curves A and B from the DLG contour lines.

[0048] The trend step point generation module sets trend step points on the contour curve A and contour curve B with a trend step length S.

[0049] The inner triangular net construction module constructs an inner triangular net with the empty circle characteristic between the contour curve A and contour curve B.

[0050] The Z-type line cluster optimization module deletes the even sequence of the cross line segments in the Z-type line cluster from the inner triangular net lines.

[0051] The segment processing module divides the contour curve A and contour curve B into several trend segments according to the H-type line cluster.

[0052] The interpolation cross line segment module inserts several cross line segments with adaptive spacing into each trend segment.

[0053] The first curve C generation module divides the cross line segments into 2-m equal parts, and connects the parts from the beginning to the end to generate the interpolation first curves C1-C m-1 .

[0054] A computer readable storage medium, which stores a computer program, the program is executed by a processor to implement the method of any one of claims 1 to 6.

[0055] The present application changes the technical mode of the prior art interpolation algorithm, and after constructing the inner triangular net, a series of technical treatments are performed, so that the generated first curve is smooth and beautiful, and conforms to the actual geographical conditions.

[0056] Specifically, in the present application, first, trend step points are set on the basis contour curves A and B with a trend step length s, which objectively reflects the trend characteristics of the geographical elevation.

[0057] Secondly, an inner triangular net is constructed between the contour curves A and B, and in this step, the Delaunay empty circle characteristic is adopted as a technical measure to obtain the diagonal line, so that the diagonal line obtained by the present application can conform to the properties of the actual geographical characteristics.

[0058] Thirdly, after obtaining the inner triangular net, the Z-type and V-type line clusters are taken as the basis, and after optimization of the Z-type line cluster, the segment processing is performed, so that the "knee point" characteristics between the adjacent contour lines are obtained.

[0059] Fourthly, after the segmentation, according to the actual plane situation, a plurality of span line segments with adaptive spacing are inserted by setting the density step in the segment, thereby forming the basis for outlining the smooth interpolation curve;

[0060] Finally, the equal division span line segment is connected by the multi-segment line from the head to the tail to generate the interpolation curve.

[0061] The method of the present application is based on selecting two adjacent contour curves A and B in the DLG contour line, segmenting by calculating the trend of the curve, and performing smooth interpolation on the segmented area. The technical scheme of the present application is ingenious, fully excavates the feature points in geographic information, conforms to the actual geographic characteristics, and generates smooth and beautiful interpolation curves. Moreover, the method of the present application has high running efficiency when loaded on a computer and has wide application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is a flowchart of the present application,

[0063] Figure 2 is a specific flowchart of step 3) in the flowchart of the present application;

[0064] Figure 3 is a schematic diagram of setting the trend step in step 2) of the present application,

[0065] Figure 4 is a schematic diagram of constructing the inner triangular net in step 3) of the present application,

[0066] Figure 5 is a schematic diagram of obtaining the diagonal line with the empty circle characteristic in step 3.2.5 of step 3) of the present application,

[0067] Figure 6 is a schematic diagram of the self-intersecting quadrilateral in step 3.2.3 of step 3) of the present application,

[0068] Figure 7 is a judgment diagram in step 3.2.6 of step 3) of the present application,

[0069] Figure 8 is a judgment diagram in step 3.2.4 of step 3) of the present application,

[0070] Figure 9 is a judgment diagram in step 3.2.7 of step 3) of the present application,

[0071] Figure 10 is a schematic diagram of the Z-shaped net line obtained in step 3) of the present application,

[0072] Figure 11 is a schematic diagram of optimizing the Z-shaped net line in step 4) of the present application,

[0073] Figure 12 is the schematic diagram of the step 5) segment processing of the present application,

[0074] Figure 13 is the schematic diagram of the step 6) interpolation across the line segment of the present application,

[0075] Figure 14 is the schematic diagram of the step 7) generation of the first curve of the present application,

[0076] Figure 15 is the schematic diagram of the step 7) completion of the first curve generation of the present application,

[0077] Figure 16 is the schematic diagram of the step 7) completion of the first curve generation of the present application,

[0078] Figure 17 is the schematic diagram of the step 7) completion of the first curve generation of the present application, DETAILED DESCRIPTION

[0079] Before the technical solution of the present application is explained, several professional concepts involved in the present application are defined as follows:

[0080] First curve: also called basic contour line, is a thin solid line measured according to a specified contour interval, used to show the basic form of the landform;

[0081] Count curve: also called thickened contour line, is a thick solid line obtained by thickening the first curve every five contour intervals from the specified elevation, so as to facilitate the interpretation and calculation of elevation on the map;

[0082] Z-shaped net line: a set of three or more auxiliary lines connected at the beginning and end;

[0083] V-shaped net line: a set of two or more adjacent auxiliary lines with the same starting point and different ending points;

[0084] Delaunay empty circle property: Delaunay triangulation is unique (any four points cannot be circumcircle), and there is no other point in the circumcircle of any triangle in the Delaunay triangulation;

[0085] Line-to-line net line (or simply net line): the connecting line between the two count curves.

[0086] The technical solution of the present application will be further explained below with reference to the accompanying drawings. Figures 1-16

[0087] The present application selects two adjacent count curves A and B as the basis in the DLG contour line, and performs the following steps to achieve the technical task of interpolating 1-m first curves between the count curve A and the count curve B, as shown in Figures 1-2 , ​

[0088] S1)、Select the adjacent contour curve A and contour curve B,

[0089] Select two adjacent contour curves A and B as the basis from the DLG contour lines; for example, Figure 16 Select any two adjacent contour curves as the basis for interpolation from the basis DLG contour lines. Figure 16 The elevation between the adjacent contour curves in the middle is 5 meters, and the number of interpolated contour curves is set according to the requirements, such as one interpolated contour curve, the elevation after interpolation is 2.5 meters; four interpolated contour curves, the elevation after interpolation is 1 meter.

[0090] S2)、On contour curve A and contour curve B, respectively, set trend step points with trend step length s,

[0091] Set i+1 trend step points on contour curve A, i≥0; set j+1 trend step points on contour curve B, j≥0; for example, Figure 3 As shown in the figure, it should be noted that in Figure 3 For the sake of clarity, the technical measures will be described as the characteristic points of curve A, trend step points A0, A1, A2… are calculated as the trend characteristics. The trend step points are set on the contour curve A with the trend step length s, and the trend step length s is set according to the details of the drawing, such as 2-10mm, the basic requirement is that the set value of the trend step length should reflect the characteristic details on the curve, such as inflection points, concave points, convex points and other characteristics.

[0092] S3)、Construct a linear triangular network between contour curve A and contour curve B, for example, Figures 4-9 ,

[0093] S3.1)、Connect the first trend step point A0 on contour curve A with the first trend step point B0 on contour curve B to get the net line L0, which is considered as the starting net line of the inner triangular network, and is also the basis for constructing subsequent net lines;

[0094] S3.2)、Based on the previous net line, generate subsequent net lines L1~ L n ;

[0095] Get the net line set L (including L0 and L1~ L n ), there are Z-shaped and V-shaped line clusters in the net line set L, for example, Figure 9 ;

[0096] For the specific process of step S3.2) to generate net lines L1~L n , combined with the detailed description in the attached Figure 2 、 4 -8, as follows,

[0097] S3.2.1)Based on the connection line of i≥0, j≥0 as the interline net line (L 1~n), where i, j are the serial numbers of the characteristic points of curves A, B on the curve (i, j are cyclically accumulated until all the points are used, and the flow of this step will not be described here);

[0098] S3.2.2) whether i, j are both 0, if yes, jump to step S3.2.3), if not, jump to step S3.2.4),

[0099] S3.2.3) whether the quadrilateral formed by A(i), B(j), B(j+1), A(i+1) is self-intersecting;

[0100] if not, jump to step S 3.2.5);

[0101] if yes, end; Figure 6 When i=2, j=2, the quadrilateral formed by A2, B2, B3, A3 in sequence is self-intersecting;

[0102] S3.2.4) whether the two points A(i+1), B(j+1) are both not self-intersecting with the quadrilateral formed by the previous triangular net, this step is to judge the two subsequent points at the same time;

[0103] if yes, jump to step S3.2.3);

[0104] if not, jump to step S3.2.6);

[0105] if Figure 8 , i=3, j=2, the previous generated net line L4 is in the triangular net (A3A2B2). The task of this step is to judge whether A4, B3 are both not self-intersecting with the quadrilateral formed by the previous triangular net.

[0106] The specific judgment process is:

[0107] connect A4 with the triangular net (A3A2B2) to form the quadrilateral A4A3A2B2, which is not self-intersecting;

[0108] connect B3 with the triangular net (A3A2B2) to form the quadrilateral A3A2B2B3, which is not self-intersecting;

[0109] S 3.2.5) in the quadrilateral formed by A(i), B(j), B(j+1), A(i+1), the diagonal line meeting the Delauney empty circle characteristic is added to the set L as an effective line-to-line net line, such as Figure 5 if the characteristic point is on curve A, then i++, otherwise j++;

[0110] then jump to step S3.2.1);

[0111] S 3.2.6)Judge whether the A(i+1), B(j+1) points in step S3.2.4)have a trend step point satisfying the condition, that is, whether one of the two points satisfies, i.e. the trend step point does not form a self-intersection with the previous triangular net;

[0112] If yes, jump to step S3.2.7);

[0113] If Figure 9 , i=3, j=2, the net line L4 is generated before, and the triangular net of the net line L4 is (A3A2B2). The task of this step is to judge whether only one of A4 and B3 forms a self-intersection with the quadrilateral formed by the previous triangular net.

[0114] The specific judgment process is:

[0115] Connect A4 and the triangular net (A3A2B2) into a quadrilateral A4A3A2B2, and there is no self-intersection; then B2A4 is an effective net line,

[0116] Connect B3 and the triangular net (A3A2B2) into a quadrilateral A3A2B2B3, and there is a self-intersection;

[0117] If no, end;

[0118] If Figure 7 , i=3, j=2, the net line L4 is generated before, and the triangular net of the net line L4 is (A3A2B2). The task of this step is to judge whether only one of A4 and B3 forms a self-intersection with the quadrilateral formed by the previous triangular net.

[0119] The specific judgment process is:

[0120] Connect A4 and the triangular net (A3A2B2) into a quadrilateral A4A3A2B2, and there is a self-intersection;

[0121] Connect B3 and the triangular net (A3A2B2) into a quadrilateral A3A2B2B3, and there is a self-intersection;

[0122] S3.2.7)Add the line to the set L as an effective triangular net line, if the feature point is on A, then i++, otherwise j++; jump to step S3.2.1);

[0123] S4)、Optimize Z-type line clusters, such as Figure 11 ,

[0124] Optimize the Z-shaped line cluster obtained in step 3): delete the even sequence net line in the Z-type line cluster from the net line set L, and obtain an H-type line cluster; at this time, there are V-shaped line clusters and H-type line clusters between the two curves A and B.

[0125] S5)、Segment processing, such asFigure 12 ,

[0126] With H type line cluster as segmentation basis, the count curve A and the count curve B are divided into several trend sections; Specifically, the edge net line on both sides of the H type line cluster is taken as the boundary for segmentation; When the H type line cluster is one, it is the segmentation basis itself. After segmentation, the remaining V-shaped line cluster and H-shaped line cluster are deleted;

[0127] S6), interpolation of cross-line segments, such as Figure 13 ,

[0128] In each trend section, a plurality of cross-line segments with adaptive spacing are interpolated, so that a plurality of cross-line segments with adaptive spacing are generated between the count curve A and the count curve B;

[0129] When interpolating the cross-line segments, the density step t needs to be set first, and the density step t is also set by the designer according to the drawing accuracy requirement, and the value range is generally 0.2-2mm.

[0130] After setting the density step t, calculate how many cross-line segments are inserted in this section. The following will explain this process in combination with the attached Figure 12 , such as the second section in Figure 12 , that is, A D1 ~B D1 curve segment length a, B D2 ~A D2 curve segment length b, the number of inserted roots p=(a+b) / (2×t), and the number is rounded.

[0131] Then, the A D1 ~B D1 curve segment and the B D2 ~A D2 curve segment are divided into p+1 equal parts, and the equal division points are connected one by one, that is, the interpolation of the cross-line segments is completed.

[0132] S7), generate the first curve C, such as Figures 14-15 ,

[0133] The cross-line segments are divided into 2-m equal parts, and the first interpolation curve C1-C m-1 is generated by connecting the head to the tail with a plurality of line segments. The value range of m is set according to the use requirement, as described above.

[0134] The device for the segmentation smoothing interpolation method of DLG contour lines provided by the application comprises:

[0135] An adjacent count curve A and a count curve B selection module selects two adjacent count curves A and B from the DLG contour lines;

[0136] A trend step point generation module sets trend step points on the count curve A and the count curve B with a trend step length S.

[0137] The inner triangle net construction module constructs the inner triangle net with the empty circle characteristic between the count curve A and the count curve B;

[0138] The Z-shaped line cluster optimization module deletes the cross line segment of even sequence in the Z-shaped line cluster from the inner triangle net line;

[0139] The segmentation processing module divides the count curve A and the count curve B into a plurality of trend segments with the H-shaped line cluster as the segmentation basis;

[0140] The interpolation cross line segment module inserts a plurality of cross line segments with distance adaptation in each trend segment;

[0141] The first curve C generation module divides the cross line segment into 2-m equal parts, and connects the plurality of line segments from the head to the tail to generate the interpolation first curve C1-C m-1 .

[0142] The application is not limited to the above-mentioned embodiments, and the skilled in the art can make some substitutions and deformations to some technical features according to the disclosed technical content without creative labor on the basis of the technical solutions disclosed in the application, and the substitutions and deformations are all within the protection scope of the application.

Claims

1. A piecewise smooth interpolation method based on DLG contour lines, characterized in that, Includes the following steps, S1) Select adjacent counting curves A and B. Two adjacent curves, A and B, are selected from the DLG contour lines as the basis; S2) Set trend step points of equal length with trend step length s on both the calculation curve A and the calculation curve B. On the calculation curve A, set i trend points, i≥0; on the calculation curve B, set j trend points, j≥0. S3) Construct an in-line triangular network between calculation curve A and calculation curve B. S3.1) Connect the first trend step point A0 on the counting curve A with the first trend step point B0 on ​​the counting curve B to obtain the grid line L0. S3.2) Based on the previous network cable, generate subsequent network cables L1~L in a loop. n ; A set of network cables L is obtained, wherein the set of network cables L contains Z-shaped and V-shaped cable clusters; S4) Optimize Z-type line clusters Optimize the Z-shaped wire clusters in the wire set L obtained in step 3): delete the even-numbered sequences of wires in the Z-shaped wire clusters from the wire set L to obtain H-shaped wire clusters; S5), segmented processing Based on the H-shaped line cluster, the counting curve A and the counting curve B are divided into several trend segments; S6), interpolation across line segments. Within each of the aforementioned trend segments, several cross segments with appropriate spacing are interpolated, thereby generating several cross segments with appropriate spacing between the counting curve A and the counting curve B. S7) Generate the first curve C. Divide the transverse line segment into equal parts of 2 to m, and connect them from beginning to end using multiple line segments to generate interpolation start curves C1 to C2. m-1 .

2. The segmented smooth interpolation method based on DLG contour lines according to claim 1, characterized in that, In step S2), the trend step length s is set within 2-10mm according to the details of the graph, and it needs to reflect the characteristic details of the calculation curve A or calculation curve B.

3. The segmented smooth interpolation method based on DLG contour lines according to claim 1, characterized in that, Step 3.2) is as follows: S3.2.1) Lines connecting i≥0 and j≥0 are used as inter-line wires (L) to construct the inner triangular network. 1~n ), where i and j are the sequence numbers of the trend points of curves A and B on the curve; S3.2.2) Determine if i and j are both 0. If yes, proceed to step S3.2.3; otherwise, proceed to step S3.2.

4. S3.2.3) Determine whether the quadrilateral formed by the four trend points A(i), B(j), B(j+1), and A(i+1) is self-intersecting; (If not, proceed to step S 3.2.5). Thus, the end; S3.2.4) Determine whether points A(i+1) and B(j+1) do not have any self-intersections with the quadrilateral formed by the previous triangular mesh; If so, proceed to step S3.2.3). If not, proceed to step S3.2.6). S 3.2.5) Within the quadrilateral formed by A(i), B(j), B(j+1), and A(i+1), add the diagonals that satisfy the Delauney empty circle property as valid inter-line grid lines to the set L. If the trend step point is on the calculation curve A, then i++, otherwise j++. Then proceed to step S3.2.1). S 3.2.6) Determine whether there exists a trend step point that satisfies the conditions between points A(i+1) and B(j+1) in step S3.2.4); If so, proceed to step S3.2.7). If not, end; S3.2.7) Add this line as a valid triangular network line to set L. If the trend step point is on A, then i++, otherwise j++. Jump to step S3.2.1).

4. The segmented smooth interpolation method based on DLG contour lines according to claim 1, characterized in that, In step S5), the network lines at the outermost edges on both sides of the H-shaped wire cluster are used as boundaries to divide the wire cluster into segments; after segmentation, the remaining V-shaped and H-shaped wire clusters are deleted.

5. The segmented smooth interpolation method based on DLG contour lines according to claim 4, characterized in that, When there is only one H-shaped line cluster, it serves as the basis for segmentation.

6. The segmented smooth interpolation method based on DLG contour lines according to claim 1, characterized in that, In step 6), when inserting a cross-segment within a trend segment... First, set the density step size t. The density step size t is set according to the accuracy requirements of the drawing, and the value range is 0.2-2mm. After setting the density step size t, calculate the number of insertions across the line segment using p = (a + b) / (2 × t), and round the result to the nearest integer. Where a is the length of the curve segment on trend segment A, and b is the length of the curve segment on trend segment B.

7. An apparatus for implementing any of the segmented smooth interpolation methods based on DLG contour lines according to claims 1-6, comprising: The module for selecting adjacent measurement curves A and B selects two adjacent measurement curves A and B from the DLG contour lines. The trend step point generation module sets trend step points on both curve A and curve B with a trend step length S. The inner triangulation construction module constructs an inner triangulation between counting curve A and counting curve B using the characteristics of an empty circle. The Z-type wire cluster optimization module removes even-numbered sequence cross segments from the inner triangular wire cluster. The segmentation module uses the H-shaped line cluster as the segmentation basis to divide the counting curve A and the counting curve B into several trend segments; The interpolation cross-segment module inserts several cross-segments with appropriate spacing during each time period; The module for generating the first curve C divides the transverse line segment into equal parts of 2 to m, and then connects them using polylines from beginning to end to generate interpolated first curves C1 to C2. m-1 .

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method described in any one of claims 1 to 6.

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