A method for smoothing exposure patterns

Abstract

A method for smoothing an exposure pattern, setting a short edge threshold Leps and an OBB bounding box short edge threshold Oeps; obtaining a continuous short edge set according to information of an initial exposure pattern and the set short edge threshold Leps; fitting each continuous short edge set to obtain an OBB bounding box corresponding to the continuous short edge set, comparing the short edge length value of the OBB bounding box with the short edge threshold Oeps of the OBB bounding box, screening out the bounding box whose short edge length value is less than or equal to the short edge threshold Oeps of the bounding box as the OBB bounding box to be smoothed; obtaining the vertices at both ends of the main axis of the OBB bounding box to be smoothed, connecting the vertices at both ends of the main axis of the OBB bounding box to be smoothed, and the connecting line of the vertices at both ends of the main axis constitutes a smoothed pattern contour line, and using the smoothed pattern contour line to replace the continuous short edges in the continuous short edge set. Redundant noise points are eliminated, and the processing speed of subsequent exposure patterns is improved.

Description

Technical Field

[0001] The invention relates to the technical field of graphic processing, in particular to a method for smoothing an exposure graphic. Background Art

[0002] In the field of laser direct writing technology, the problem of constantly updating the mask corresponding to different exposure patterns is solved by digitizing the exposure pattern. However, if the exposure pattern data volume is too large, the processing speed will be greatly reduced, thus affecting the production capacity; at the same time, if there are many tiny burrs in the exposure pattern, it will seriously affect the quality of industrial production, and during the exposure process, the loading and processing of the exposure pattern will become slow, and the use of such exposure pattern data for exposure will also make the exposed pattern not smooth enough, which will affect both the production capacity and the exposure quality. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a method for smoothing an exposure pattern, which reduces the data volume of the exposure pattern and improves the production capacity.

[0004] In order to achieve the above-mentioned purpose, the present invention provides a method for smoothing an exposure pattern, S1. setting a short edge threshold Leps and an OBB bounding box short edge threshold Oeps; S2. obtaining a continuous short edge set according to information of an initial exposure pattern and the set short edge threshold Leps, wherein the continuous short edge set includes a pattern contour line whose length is less than or equal to the short edge threshold Leps at no less than two positions; S3. fitting each continuous short edge set to obtain data information of an OBB bounding box corresponding to the continuous short edge set, comparing the short edge length value of the OBB bounding box with the short edge threshold Oeps of the OBB bounding box, screening out a bounding box whose short edge length value of the OBB bounding box is less than or equal to the short edge threshold Oeps of the bounding box, as an OBB bounding box to be smoothed for continued smoothing; S4. based on the data information of the OBB bounding box to be smoothed, obtaining the vertices at both ends of the main axis of the OBB bounding box to be smoothed, connecting the vertices at both ends of the main axis of the OBB bounding box to be smoothed, the connecting line of the vertices at both ends of the main axis constitutes a smoothed pattern contour line, and the smoothed pattern contour line is used to replace the pattern contour line in the continuous short edge set.

[0005] In one embodiment, the short edge threshold Leps and the OBB bounding box short edge threshold Oeps are determined according to the tolerance allowed by the product to be exposed.

[0006] In one embodiment, the OBB bounding box short edge threshold Oeps is the same as the tolerance, and the short edge threshold Leps is several times the tolerance.

[0007] In one embodiment, the short edge threshold Leps is set to 5-15 times of the tolerance.

[0008] In one embodiment, the method steps of fitting the data information of the OBB bounding box corresponding to the continuous short edge set in step S3 are as follows: S31. Obtain the x-coordinate component and the y-coordinate component of the vertices in the continuous short edge set in the initial coordinate system, and obtain the covariance matrix of the continuous short edge set; S32. Solve the covariance matrix of the continuous short edge set to obtain the eigenvalue group of the corresponding covariance matrix and the eigenvector group corresponding to the eigenvalue group; S33. Establish an eigenvector coordinate system with the eigenvector of the covariance matrix to obtain the data information of the OBB bounding box, and the eigenvector P corresponding to the maximum eigenvalue in the eigenvalue group 1 is the X direction, and the eigenvector P corresponding to the other eigenvalue 2 is the point in the Y direction corresponding to the average value of the x-coordinate component and the y-coordinate component (u x ,u y ) is the coordinate origin; S34. Obtain the coordinates of each vertex in the continuous short edge set in the eigenvector coordinate system (X i , Y i )(i=1,2,3…n), according to the coordinates of the vertices in the continuous short edge set in the eigenvector coordinate system, the length of the short side of the OBB bounding box is obtained.

[0009] In one of the embodiments, the coordinates of the vertices at both ends of the main axis of the OBB bounding box in the eigenvector coordinate system are obtained according to the maximum and minimum values ​​of the X-coordinate component of the OBB bounding box in the eigenvector coordinate system; the coordinates of the vertices at both ends of the main axis of the OBB bounding box in the eigenvector coordinate system are converted into coordinates in the initial coordinate system, and a straight line is used to connect the vertices at both ends of the main axis of the OBB bounding box to form a smooth graphic contour line, and the continuous short edges in the continuous short edge set are replaced, thereby completing the smoothing of the short edge set.

[0010] In one embodiment, the method for smoothing the exposure graphic further includes setting a slope threshold Seps. After the smoothed graphic contour replaces the continuous short edges in the continuous short edge set, the slope threshold Seps is used to determine whether the slope difference between adjacent graphic contours meets the conditions for further smoothing.

[0011] In one embodiment, the slope threshold Seps is the same as the value of the tolerance allowed for the product to be exposed.

[0012] In one of the embodiments, the exposure graphic after the smoothed graphic contour line replaces the continuous short edges in the continuous short edge set is divided into a plurality of smoothing processing line groups, each smoothing processing line group includes adjacent graphic contour lines, the slope of each graphic contour line in the smoothing processing line group is calculated, and the slopes of adjacent graphic contour lines are compared. If the absolute value of the slope difference of adjacent edges is within the range of a given slope threshold Seps, that is, the absolute value of the slope difference of adjacent edges is less than or equal to the slope threshold Seps, the common vertex of the pair of adjacent graphic contour lines is eliminated, and the two end points of the adjacent graphic contour lines are connected by a straight line to obtain the smoothed graphic contour line.

[0013] Compared with the prior art, the exposure pattern smoothing method of the present invention eliminates redundant noise points, reduces the exposure pattern file size by several times, greatly reduces the complexity of the exposure pattern file within the exposure accuracy range, and improves the processing speed of subsequent exposure patterns. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a partial schematic diagram of the initial exposure pattern of the present invention.

[0015] Figure 2 It is an enlarged schematic diagram of a section of the outline of the initial exposure pattern of the present invention.

[0016] Figure 3 It is a block diagram of an embodiment of a smoothing method of the present invention.

[0017] Figure 4 It is a schematic diagram of a block diagram of an OBB bounding box fitting method of the present invention.

[0018] Figure 5 It is a schematic diagram of a continuous short edge set fitting OBB bounding box in an initial coordinate system according to an embodiment of the present invention.

[0019] Figure 6 It is a schematic diagram of a continuous short edge set fitting OBB bounding box in a feature vector coordinate system according to an embodiment of the present invention.

[0020] Figure 7 FIG. 5 is a schematic diagram of a smoothing processing line group according to another embodiment of the smoothing processing method of the present invention.

[0021] Figure 8 It is a schematic diagram of smoothing a line group in another embodiment of the smoothing method of the present invention.

[0022] Fig. 9 It is a partial schematic diagram of a smoothed exposure pattern obtained by the smoothing method of the present invention.

[0023] Fig.10 It is a partially enlarged schematic diagram of a smoothed exposure pattern obtained by the smoothing method of the present invention. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is described below by means of specific embodiments shown in the accompanying drawings.

[0025] like Figure 1 and Figure 2 As shown in the figure, it is a partial picture of some graphic lines in the input initial exposure pattern. The graphic lines in the figure contain many small short edges. Figure 2 In the enlarged image shown in , the length of some line segments in the graphic lines is only about 0.3 microns, which is caused by redundant noise points, resulting in rough lines. In addition, these redundant noise points slow down the loading and processing of the exposure graphics, and the exposed graphics are rough, which affects both the production capacity and the quality of exposure. Therefore, it is necessary to process the initial exposure graphics to remove the redundant noise points.

[0026] In order to improve the processing speed of the exposure pattern, remove redundant noise points, smooth the initial exposure pattern, obtain a smooth exposure pattern, and reduce the amount of data for subsequent image processing. Figures 3 to 10 As shown, the exposure pattern smoothing method first sets threshold parameters, namely, the short edge threshold Leps and the OBB (Oriented Bounding Box) bounding box short edge threshold Oeps, as smoothing processing parameters. The short edge threshold Leps is used to determine the short edge caused by redundant noise points; the OBB bounding box short edge threshold Oeps is used to determine the OBB bounding box that can meet the smoothing processing requirements.

[0027] According to all vertex data of the input initial exposure graphic, the side length used to determine the graphic contour line in the initial exposure graphic is calculated, and the graphic contour line is connected between two vertices. The obtained side length of the graphic contour line is compared with the short edge threshold Leps. The shorter graphic contour lines whose length is less than or equal to the short edge threshold Leps and whose positions are continuous constitute a continuous short edge set. Each continuous short edge set includes no less than two continuous graphic contour lines whose length is less than or equal to the short edge threshold Leps. For each continuous short edge set, the OBB bounding box is calculated to obtain the short side length data of the OBB bounding box, and the short side length data of the OBB bounding box is compared with the short side threshold Oeps of the bounding box to screen out the bounding box whose short side length is less than or equal to the short side threshold Oeps of the bounding box as the OBB bounding box to be smoothed; the vertex coordinates of the two ends of the main axis of the OBB bounding box to be smoothed are obtained, and the vertices at both ends of the main axis are connected to obtain the smoothed graphic contour line of the continuous short edge set group corresponding to the bounding box.

[0028] The specific steps of the exposure pattern smoothing method are described in detail below.

[0029] S1. Set the short edge threshold Leps and the OBB bounding box short edge threshold Oeps. The short edge threshold Leps and the OBB bounding box short edge threshold Oeps are determined according to the tolerance allowed by the product to be exposed. The short edge threshold Leps is several times the tolerance. Preferably, the short edge threshold Leps is set to 5-15 times the tolerance, which can screen out short edges that can be processed smoothly while avoiding too many short edges to be screened, which increases the processing time. The OBB bounding box short edge threshold Oeps is the same as the tolerance.

[0030] S2. Obtain a continuous short edge set according to the information of the initial exposure figure and the set short edge threshold Leps, the continuous short edge set including at least two figure contour lines whose positions are continuous and whose length is less than or equal to the short edge threshold Leps. Specifically, first obtain a set of all vertex data of the initial exposure figure in the initial coordinate system, calculate the side lengths of all figure contour lines, compare the side lengths of the figure contour lines with the short edge threshold Leps, and obtain multiple groups of figure contour lines whose lengths are less than or equal to the short edge threshold Leps and whose positions are continuous to form a continuous short edge set.

[0031] S3. Fit each continuous short edge set to obtain data information of the OBB bounding box corresponding to the continuous short edge set, compare the short edge length value of the OBB bounding box with the short edge threshold value Oeps of the OBB bounding box, and select the bounding box whose short edge length value is less than or equal to the short edge threshold value Oeps of the bounding box as the OBB bounding box to be smoothed. The data information includes the short edge length of the OBB bounding box and the position information of the short edge midpoint of the OBB bounding box.

[0032] The OBB bounding box corresponding to the set of continuous short edges may be fitted using the following exemplary method or other methods.

[0033] S31. Obtain the x-coordinate component and the y-coordinate component of the vertices in the continuous short edge set in the initial coordinate system, and obtain the covariance matrix of the continuous short edge set. The covariance matrix is ​​shown in formula (3-1).

[0034] (3-1)

[0035] The calculation formula for each element in the covariance matrix is ​​as follows:

[0036] (3-2)

[0037] (3-3)

[0038] (3-4)

[0039] (3-5)

[0040] (3-6)

[0041] Among them, x i is the x-coordinate component of each vertex in the continuous short edge set, and y i is the y-coordinate component of each vertex in the continuous short edge set, n is the number of vertices in the continuous short edge set, u x is the average value of the x-coordinate components of the n vertices in the continuous short edge set, u y It is the average value of the y-coordinate components of the n vertices in the set of continuous short edges.

[0042] S32. Solve the covariance matrix of the continuous short edge set to obtain the eigenvalue group of the corresponding covariance matrix and the eigenvector group corresponding to the eigenvalue group. The eigenvalue group includes the first eigenvalue λ 1 and the second eigenvalue λ 2 , where the first eigenvalue λ 1 Greater than the second eigenvalue λ 2 , with the first eigenvalue λ of the covariance matrix 1 Get the corresponding eigenvector P 1 , with the second eigenvalue λ of the covariance matrix 2 Get the corresponding eigenvector P 2 , denoted as vector P 1 =[ b 0 b 1 ], vector P 2 =[ b 2 b 3 ], where the largest eigenvalue λ in the eigenvalue group 1 The corresponding eigenvector P 1 The main axis direction of the OBB bounding box of the continuous short edge set.

[0043] S33. Establish an eigenvector coordinate system with the eigenvector of the covariance matrix to obtain the data information of the OBB bounding box. The eigenvector coordinate system is based on the main axis direction vector P of the OBB bounding box. 1 is the X direction, the eigenvector P 2 is the point in the Y direction corresponding to the average value of the x-coordinate component and the y-coordinate component (u x ,u y ) is the coordinate origin O.

[0044] S34. Get the coordinates of each vertex in the continuous short edge set in the eigenvector coordinate system (X i , Y i )(i=1,2,3…n), according to the coordinates of the vertices in the continuous short edge set in the eigenvector coordinate system, the length of the short side of the OBB bounding box is obtained.

[0045] The coordinates of the vertices in the set of continuous short edges in the new coordinate system can be calculated using formula 3-7.

[0046] (3-7)

[0047] Get the maximum and minimum values ​​of the X-coordinate component and Y-coordinate component of the vertex coordinates in the continuous short edge set in the eigenvector coordinate system, which are recorded as , , k=0,1, where k=0 corresponds to the X coordinate component and k=1 corresponds to the Y coordinate component. The side length L of the OBB bounding box is obtained according to formula 3-8. k , respectively, the length of the long side L 0 and the short side length L 1 .

[0048] (3-8)

[0049] is the minimum value of the X-coordinate component in the eigenvector coordinate system, is the maximum value of the X-coordinate component in the eigenvector coordinate system, is the minimum value of the Y coordinate component in the eigenvector coordinate system, is the maximum value of the Y coordinate component in the eigenvector coordinate system.

[0050] Set the short side length L of the OBB bounding box to 1 Compared with the OBB bounding box short edge threshold Oeps, when L 1 ≤Oeps, that is, when the short side length of the OBB bounding box is less than or equal to the short side threshold Oeps of the bounding box, the OBB bounding box is recorded as the OBB bounding box to be smoothed and continued to be smoothed.

[0051] S4. Based on the data information of the OBB bounding box to be smoothed, obtain the vertices at both ends of the main axis of the OBB bounding box to be smoothed, connect the vertices at both ends of the main axis of the OBB bounding box to be smoothed, and the connecting line of the vertices at both ends of the main axis constitutes a smooth graphic contour line. The smooth graphic contour line is used to replace the graphic contour line in the continuous short edge set.

[0052] Based on the data information of the OBB bounding box to be smoothed, the vertices at both ends of the main axis of the OBB bounding box to be smoothed are obtained. An exemplary method is as follows, and other methods may also be used to obtain the vertices.

[0053] The maximum value of the X coordinate component of the OBB bounding box according to the eigenvector coordinate system and minimum value , obtain the coordinates of the vertices at both ends of the main axis of the OBB bounding box in the eigenvector coordinate system, respectively .

[0054] Place the vertices at both ends of the main axis of the OBB bounding box (left vertex T 1 , right vertex T 2 ) The coordinates in the eigenvector coordinate system are converted to the coordinates in the initial coordinate system, which can be calculated using formula 3-9.

[0055] Left vertex of the main axis of the OBB bounding box

[0056] Right vertex of the main axis of the OBB bounding box (3-9)

[0057] A straight line connects the left vertex T of the main axis of the OBB bounding box 1 and right vertex T 2 A smooth graphic contour is formed, and continuous short edges in a continuous short edge set are replaced to complete smoothing of the short edge set.

[0058] Obtain smoothed graphic contours of all OBB bounding boxes to be smoothed, and obtain exposure graphics after the OBB bounding boxes are smoothed.

[0059] In order to improve the smoothing effect of the exposure pattern, the exposure pattern smoothing method further includes setting a slope threshold Seps. After completing the above initial smoothing, the slope threshold Seps is used to judge whether the slope difference between adjacent pattern contours meets the conditions for further smoothing. The exposure pattern after the OBB bounding box smoothing is further smoothed. The slope threshold Seps is the same as the value of the tolerance.

[0060] During further smoothing, the exposure figure after the OBB bounding box smoothing is first divided into multiple smoothing line groups, each smoothing line group includes adjacent figure contour lines, the slope of each figure contour line in the smoothing line group is calculated, and the slopes of adjacent figure contour lines are compared. If the absolute value of the slope difference of adjacent edges is within the range of a given slope threshold Seps, that is, the absolute value of the slope difference of adjacent edges is less than or equal to the slope threshold Seps, the common vertex of the pair of adjacent figure contour lines is eliminated, and the two end points of the adjacent figure contour lines are connected by a straight line to obtain the smoothed figure contour line.

[0061] The slope k of the graph contour line can be obtained by formula 3-10.

[0062] (3-10)

[0063] Where k is the slope of the contour line of the graph; x i is the x-coordinate of one of the endpoints of the contour line of the figure, y i is the y coordinate of one of the endpoints of the contour line of the figure; i-1is the x-coordinate of the other end point of the contour line of the figure, y i-1 The y coordinate corresponding to the other endpoint of the figure contour line.

[0064] like Figure 8 In the example shown, a smoothing line group includes adjacent graphic contour lines Q 1 Q 2 and the graphic contour line Q 2 Q 3 , graphic contour line Q 1 Q 2 The endpoint Q 1 The coordinates of (x 1 ′,y 1 ′), endpoint Q 2 The coordinates of (x 2 ′,y 2 ′), the contour line Q 1 Q 2 The corresponding slope is , graphic contour line Q 2 Q 3 The endpoint Q 3 The coordinates of (x 3 ′,y 3 ′), the corresponding slope is If the adjacent contour line Q 1 Q 2 The slope k 1 and the graphic contour line Q 2 Q 3 The slope k 2 The absolute value of the difference is less than or equal to the slope threshold Seps, that is, |k 1 -k 2 |≤Seps, then the contour line Q 1 Q 2 and the graphic contour line Q 2 Q 3 The common vertex Q 2 Eliminate and remove the adjacent graphic contour line Q 1 Q 2 and the graphic contour line Q 2 Q 3 It becomes the graphic contour line Q1Q3.

[0065] Compare adjacent graphic contours in sequence, such as for graphic contour line Q 1 Q 2 、Graphic contour line Q 2 Q 3 , compared with the contour line Q 1 Q 2 The slope is k 1 and the graphic contour line Q 2 Q3 The slope is k 2 , determine the slope k 1 and the slope is k 2 Is the absolute value of the difference less than or equal to the slope threshold Seps? If the condition is met, the contour line Q of the graph is 1 Q 2 、Graphic contour line Q 2 Q 3 Smoothing is performed. The slopes of the adjacent graphic contour lines of each smoothing line group are compared to complete further smoothing of the exposure graphic after the OBB bounding box smoothing.

[0066] like Figure 9-10 As shown in the figure, the effect after smoothing processing, the blue line in the figure is the local enlarged line of the original figure, and the green line is the effect after algorithm processing.

[0067] After the above-mentioned smoothing process, redundant noise points are eliminated, and the size of the exposure graphic file is reduced several times. Within the exposure accuracy range, the complexity of the exposure graphic file is greatly reduced, and the processing speed of subsequent exposure graphics is improved.

Claims

1. A method for smoothing an exposure pattern, characterized in that: S1. Set the short edge threshold Leps and the OBB bounding box short edge threshold Oeps; S2. Obtaining a continuous short edge set according to the information of the initial exposure pattern and the set short edge threshold Leps, wherein the continuous short edge set includes at least two positions of continuous pattern contour lines whose length is less than or equal to the short edge threshold Leps; S3. Fit each continuous short edge set to obtain data information of the OBB bounding box corresponding to the continuous short edge set, compare the short edge length value of the OBB bounding box with the short edge threshold value Oeps of the OBB bounding box, and select the bounding box whose short edge length value of the OBB bounding box is less than or equal to the short edge threshold value Oeps of the bounding box as the OBB bounding box to be smoothed; S4. Based on the data information of the OBB bounding box to be smoothed, obtain the vertices at both ends of the main axis of the OBB bounding box to be smoothed, connect the vertices at both ends of the main axis of the OBB bounding box to be smoothed, and the connecting line of the vertices at both ends of the main axis constitutes a smooth graphic contour line. The smooth graphic contour line is used to replace the graphic contour line in the continuous short edge set.

2. The method for smoothing an exposure pattern according to claim 1, characterized in that: The short edge threshold Leps and the OBB bounding box short edge threshold Oeps are determined according to the tolerance allowed by the product to be exposed.

3. The method for smoothing an exposure pattern according to claim 2, wherein: The OBB bounding box short edge threshold Oeps is the same as the value of the tolerance, and the short edge threshold Leps is several times the tolerance.

4. The method for smoothing an exposure pattern according to claim 3, characterized in that: The short edge threshold Leps is set to 5-15 times of the tolerance.

5. The method for smoothing an exposure pattern according to claim 1, characterized in that: The method steps for fitting the data information of the OBB bounding box corresponding to the continuous short edge set in step S3 are as follows: S31, obtaining x-coordinate components and y-coordinate components of vertices in a continuous short edge set in an initial coordinate system, and obtaining a covariance matrix of the continuous short edge set; S32. Solving the covariance matrix of the continuous short edge set to obtain the eigenvalue group of the corresponding covariance matrix and the eigenvector group corresponding to the eigenvalue group; S33. Establish an eigenvector coordinate system with the eigenvector group of the covariance matrix to obtain the data information of the OBB bounding box. The eigenvector P1 corresponding to the maximum eigenvalue in the eigenvalue group is in the X direction, and the eigenvector P2 corresponding to the other eigenvalue is in the Y direction. The point corresponding to the average value of the x-coordinate component and the y-coordinate component (u x ,u y ) is the coordinate origin; S34. Get the coordinates of each vertex in the continuous short edge set in the eigenvector coordinate system (X i , Y i )(i=1,2,3…n), according to the coordinates of the vertices in the continuous short edge set in the eigenvector coordinate system, the length of the short side of the OBB bounding box is obtained.

6. The method for smoothing an exposure pattern according to claim 5, characterized in that: According to the maximum and minimum values ​​of the X-coordinate component of the OBB bounding box in the eigenvector coordinate system, the coordinates of the vertices at both ends of the main axis of the OBB bounding box in the eigenvector coordinate system are obtained; The coordinates of the vertices at both ends of the main axis of the OBB bounding box in the eigenvector coordinate system are converted to the coordinates in the initial coordinate system; a straight line connects the vertices at both ends of the main axis of the OBB bounding box to form a smooth graphic contour line, replaces the continuous short edges in the continuous short edge set, and completes the smoothing of the short edge set.

7. The method for smoothing an exposure pattern according to claim 1, characterized in that: The method for smoothing the exposure pattern also includes setting a slope threshold Seps. After the smoothed pattern contour replaces the continuous short edges in the continuous short edge set, the slope threshold Seps is used to determine whether the slope difference between adjacent pattern contours meets the conditions for further smoothing.

8. The method for smoothing an exposure pattern according to claim 7, characterized in that: The slope threshold value Seps is the same as the value of the tolerance allowed for the product to be exposed.

9. The method for smoothing an exposure pattern according to claim 7, characterized in that: The exposure graphic after the smoothed graphic contour line replaces the continuous short edges in the continuous short edge set is divided into multiple smoothing line groups, each smoothing line group includes adjacent graphic contour lines, the slope of each graphic contour line in the smoothing line group is calculated, and the slopes of adjacent graphic contour lines are compared. If the absolute value of the slope difference of adjacent edges is within the range of a given slope threshold Seps, that is, the absolute value of the slope difference of adjacent edges is less than or equal to the slope threshold Seps, the common vertex of the pair of adjacent graphic contour lines is eliminated, and the two end points of the adjacent graphic contour lines are connected by a straight line to obtain the smoothed graphic contour line.

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