JP3324589B2 - Contour line drawing method, drawing system using this method, and recording medium recording the drawing method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention particularly relates to a contour line drawing method capable of drawing contour lines at high speed, a drawing system using the method, and a recording medium recording the drawing method.

[0002]

2. Description of the Related Art (First Prior Art)
No. 2 based on mesh data disclosed in JP-A-343182
The two-dimensional color tone diagram display device performs a two-dimensional display by obtaining a display area for a specified color boundary value for each element, displaying the display area in each specified color, and repeating for all elements.

[0003] Referring to FIG.
Conventional example 1) will be described. FIG. 16 is a flowchart showing the operation of this conventional technique. FIG.
Whether or not a line segment on a certain element as shown in (A) has an intersection with a color tone boundary value, or nodes larger than the color tone boundary value are sequentially examined, and a point sequence examined as shown in FIG. The configured area is set as a display area and is filled with a specified color. As shown in FIG. 15C, the above procedure is repeated from the one with the lowest color tone boundary value to realize the display of the two-dimensional color tone map. (Second Prior Art) In addition, a method of displaying a color tone diagram connecting contour lines disclosed in Japanese Patent Application Laid-Open No. 9-185725 discloses a method of connecting contour line coordinate points and taking in an outline when an outline is reached. The two-dimensional display is performed collectively.

[0004] Referring to FIG.
Conventional example 2) will be described. FIG. 18 is a flowchart of this conventional technique. FIG. 17 shows a case where an intersection with a color tone boundary value exists for an outline of a certain element.
As in (A), the intersections are connected to generate contour lines in the element. Do this for all elements. Further, as shown in FIG. 17 (B), a certain contour line is selected, and when the contour line reaches the outline, a node having a value higher than the intersection of the outline and the color tone boundary value on the outline is connected along the outline. Go. By repeating this process, a closed curve is formed. As shown in FIG. 17C, when a plurality of closed spaces are formed, a closed curve serving as a reference is selected, and the start of this closed curve is connected to the start of another closed curve, and the end is connected to the end of another closed space in order. Thus, a combined closed curve as shown in FIG. 17D is formed. By painting this closed curve with the designated color at a time, a two-dimensional tone map of the entire tone boundary value is created.

However, these conventional techniques have the following problems. In the first prior art, processing time is required. The reason is that display processing is performed for each element, so that the processing time becomes longer in proportion to the number of elements.

A first problem of the second prior art is that:
Processing time is required. The reason for this is that the determination of the combination is made at the coordinate position, so that the processing time becomes longer in proportion to the factorial of the contour segment.

As a second problem, when a contour line comes into contact with an external boundary, the connection process takes a long time. The reason is that there is a process of obtaining a polygonal line along the outer boundary from the contact position and the value at the outer boundary, and forming a contour line cut at the outer boundary into a loop.

Further, as a third problem, when peaks and valleys are present simultaneously in the contour region, the valley portions disappear when the color tone diagram is drawn in ascending order, and the ridge portions disappear when drawn in descending order. . The reason is that it is impossible to represent the contour line in one of the contour line regions and the outer boundary without performing the inside / outside judgment.

[0009]

SUMMARY OF THE INVENTION It is an object of the present invention to improve the above-mentioned drawbacks of the prior art and, in particular, to provide a new contour drawing method which enables high-speed drawing, a drawing system using this method, and a drawing system. A recording medium on which a method is recorded is provided.

[0010]

SUMMARY OF THE INVENTION The present invention basically employs the following technical configuration to achieve the above object.

That is, in a first aspect of the contour drawing method according to the present invention, a first step of generating a connection table for a triangular element for drawing and a first step of determining a contour are generated in the first step. Using a connection table, the closed curve determining the contour is cut out as polygonal line data by classifying it as a line segment pattern of each element, and the cut-out polygonal line data is stored in a memory allocated to the element. And the third step of creating one closed curve by sequentially connecting the polygonal line data constituting the contour obtained in the second step, and configuring the contour to draw contour lines. Using the connection table, cut out the closed curve as a line segment at each element,
A fourth step of storing in a memory allocated to the element, and a fifth step of drawing contour lines by sequentially connecting the line segments obtained in the fourth step. In a second aspect, the connection table generated in the first step includes, for each node of each of the elements, an element number of an element including the node or an element number of an element formed by the node. A table, a table of line segment numbers of element sides constituting the element for each element, a node number of two nodes which are end points for each element side, and two nodes facing each other via the element side A table of element numbers of elements and node numbers of nodes facing each other via the respective element sides is included, and the third embodiment is characterized in that in the second step or the fourth step, , Without performing the connection determination using the position coordinates, And characterized in that to detect the data of the connection destination by line number or node number,
In a fourth aspect, in the second step, the polygonal line data for determining the contour is classified based on a pattern obtained in advance, and as a result, the obtained line segment is assigned to each element. In a fifth aspect, the polygonal line data for determining contours obtained in the second step includes a boundary line which is an end of a drawing area. Is what you do.

Further, in a sixth aspect, the pattern includes a state in which each element side of the triangular element is the boundary line, and a line segment for determining a contour drawn in the triangular element. In the seventh mode, the line segment that determines the contour has a predetermined direction of counterclockwise or counterclockwise. The eighth aspect is characterized in that the third step includes:
After forming a large polygon in which the start point and the end point of the series of polygonal line data for determining the contour coincide with each other, one start point is added to this large polygon, and the next large polygon is created. According to a ninth aspect, in the fourth step, a contour line is selected from a line segment pattern obtained in advance, and the large polygon is selected and obtained. It is characterized by,
A tenth aspect is characterized in that, in the fourth step, the direction of the contour line is determined based on the magnitude relation of the node values of the triangular elements. When the element side to be matched with the contour line, a pair of nodal values is checked with respect to the surrounding side, a line segment different from the contour line value is set as a contour line, and the matching line segment is excluded. Things.

The contour line drawing system according to the present invention comprises a first means for generating a connection table for a triangle element for drawing, and a connection table generated by the first means for determining a contour. A second means for classifying the closed curve determining the contour as a line segment pattern of each element and cutting it out as broken line data, and storing the cut out broken line data in a memory allocated to the element; And third means for creating one closed curve by sequentially linking the polygonal line data constituting the contour obtained by the second means, and the contour for drawing a contour line. From the closed curve, using the connection table, cut out as a line segment in each element,
A fourth means for storing in a memory allocated to the element, and a fifth means for drawing contour lines by sequentially connecting the line segments obtained by the fourth means. Is what you do.

The aspect of the recording medium in which the contour drawing method according to the present invention is recorded is a first step of generating a connection table for a drawing triangle element, and the first step of determining a contour. Using the connection table generated in the step, the closed curve determining the contour is cut out as polygonal line data by classifying it as a line segment pattern in each element, and the cut out polygonal line data is stored in the memory assigned to the element. A second step of storing, a third means for creating one closed curve by sequentially connecting the polygonal line data constituting the contour obtained in the second step, and a method for drawing a contour line, From the closed curve constituting the contour, using the connection table,
A fifth step of extracting contour lines by cutting out a line segment of each element and storing the obtained data in a memory allocated to the element in a fourth step, and sequentially connecting the line segments obtained in the fourth step. In order to cause a computer to execute a series of processes including steps, the processing program is recorded.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A contour drawing method according to the present invention comprises a first step (FIG. 2) for generating a connection table for drawing triangular elements, and a first step for determining contours. Using the generated connection table, the closed curve determining the contour is cut out as polygonal line data by classifying it as a line segment pattern of each element, and the extracted polygonal line data is stored in a memory allocated to the element. A second step (FIG. 3), a third step (FIG. 4) of creating one closed curve by sequentially connecting the polygonal line data forming the contour obtained in the second step, A fourth step of cutting out the closed curve forming the contour from the closed curve constituting the contour as a line segment for each element using the connection table, and storing the line segment in a memory allocated to the element; And FIG. 5), by connecting the line segments obtained in the fourth process step by step and is characterized in that it comprises a fifth step of drawing a contour line (6), the.

[0016]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing a drawing method of a contour line according to the present invention, a drawing system using the method, and a recording medium on which the drawing method is recorded.

FIG. 1 is a block diagram showing a configuration for drawing contour lines according to the present invention, FIG. 2 is a flowchart showing preprocessing of mesh data according to the present invention, and FIG.
ontour; contour of a region surrounded by contour lines and having the same altitude, also referred to as a contour line region).
5 is a flowchart illustrating a process of connecting line segment data to contours, FIG. 5 is a flowchart illustrating a process of extracting line segment data from contour lines, FIG. 6 is a flowchart illustrating a process of connecting line segment data to contour lines,
FIG. 7 is a classification diagram of a contour cutting pattern,
(A) is used for the calculation order, (B) is used for the cutout pattern, and (C) is used for the center line.

FIG. 8 is a classification diagram of contour line data, and FIG. 9 is a classification diagram of contour lines.

In these figures, a first step (FIG. 2) for generating a connection table for a triangular element for drawing and a connection table generated in the first step for determining contours are used. Then, the closed curve that determines the contour is cut out as polygonal line data by classifying the closed curve as a line segment pattern of each element, and the extracted polygonal line data is stored in a memory allocated to the element (FIG. 3) and the third step (FIG. 4) of creating one closed curve by sequentially connecting the polygonal line data constituting the contour obtained in the second step, and drawing contour lines. From the closed curve constituting the contour, using the connection table, cut out as a line segment in each element,
A fourth step (FIG. 5) of storing in a memory allocated to the element and a fifth step (FIG. 6) of drawing contour lines by sequentially connecting the line segments obtained in the fourth step. When,
And a drawing system using the method.

Hereinafter, the present invention will be described in more detail step by step. (1) FIG. 1 is a block diagram showing the configuration of the present invention.

Referring to FIG. 1, in the present invention, a mesh data pre-processing unit A1, a drawing setting unit A2, a line segment data cutout unit A3, and a line segment data connection unit A
4, a drawing command A5, a display A6 which is a drawing output device, and data A8 serving as a drawing base. (2) Description of the preprocessing unit A1 The data input unit B2 reads the node numbers and coordinate positions of the elements that are the mesh data. Here, the coordinate position is read in order to create a drawing triangle element (nodes are arranged counterclockwise).

First, in B3 and B4, if the element is not a triangle, the element is divided into triangles. This processing is not required if the processing is configured only with the triangular elements in advance. In the next B4, B5, and B10, a table of nodes of the triangular element whose node arrangement is counterclockwise is created. here,
The reason why the data is unified counterclockwise is that the direction as a broken line in the element is unified with respect to the contour line.

Next, at B6, it is determined whether three element sides of the triangular element have been used. At B7, for each node, a table of element numbers of elements including the node, and for each element, A table of element side numbers of element sides constituting the element, a node number of two nodes which are end points of each element side, a node number of two nodes opposed via the element side, and the element side. A table is created with the element numbers of two elements that face each other. In B5, B7, and B10, the generated connection data table is stored in the memory.

FIG. 19 shows a mesh after element preprocessing having 50 × 5 × 2 and 50 triangular elements, and FIG. 20 shows a part of the connection data table generated in the preprocessing. The triangular element for drawing includes not only nodes but also element sides. For example, the element T1 is composed of nodes P1, P8, P7 and element sides S3, S1, S2. Each node is
It spans multiple elements. For example, the node P1 is included in two elements T1 and T2, while the node P8 is
The elements are included in six elements T1, T2, T3, T12, T13, and T14. If each line segment is inside, like element side S2, there are two facing elements and two facing nodes, but if it is in contact with the outside like element side S1, there is one facing element and one facing node. I have no choice.

By creating the connection data table shown in FIG. 20, processing can be performed regardless of the complexity of the boundary line with the outside. (3) Description of Drawing Setting Unit A2 The drawing setting unit A2 is divided into scale processing and viewpoint processing.

In the scale processing, the value at each node is calculated by setting the maximum value, the minimum value of the contour display, the number of divisions, and the designation of linear or log.

In the viewpoint processing, in the case of two dimensions, the coordinates of the nodes only change due to size, movement or rotation, and there is no need to reconstruct the preprocessing unit A1. In the processing, it is necessary to regenerate the mesh data and perform the preprocessing unit A1 again. (4) Drawing contours A method of drawing contours will be specifically described with reference to FIGS. 7, 8, and 19 to 25.

FIG. 21 is a contour diagram of four gradations for the mesh of FIG. 19, and element numbers (T1 to T50: for drawing)
Is written. FIG. 22 shows a broken line for each element in FIG. 21 by a vector. The number in parentheses is the number of the cutout pattern (see FIG. 7), and the alphabet at the center of each element is classified by the outer boundary (FIG. 8).
The upper and lower rotation directions based on the node values indicate that the lowercase letter indicates leftward rotation and the uppercase letter indicates clockwise rotation. FIG. 23 is a counterclockwise closed curve obtained by connecting the broken lines in FIG. FIG. 24 is a drawing in which the termination processing is performed on FIG. 23, and each contour is a line drawn with one stroke.

That is, when the contour diagram of FIG. 21 is determined based on the cutout pattern classification diagram of FIG. 7 and the broken line pattern classification diagram of FIG. 8, the broken line is determined as shown in FIG. 22. FIG.
FIG. 23 shows a simple connection of the two folded lines, and FIG. 24 shows a series of line data after termination processing.

For the contours from the upper left to the lower right in FIG. 21, the symbols K1 to K22 are prepared in the broken line pattern in FIG. 22, and the connection data is shown in FIG. ○ Cut-out processing For example, for the element T3 not in contact with the external boundary,
As shown in FIG. 19, nodes P2, P9, and P8 are formed, and high, low, and medium contour values are assigned to the nodes, respectively, so that the element is a counterclockwise element a.

Since the contour passes near the low contour value,
It can be seen that the cut-out fold line K1 is a fold line corresponding to (1) in FIG. 7B.

The element T3 is converted into the elements T14, T2, T2 through the data for the element sides of the connection data table.
4 is known to be connected to the element T4, and the end point of the line K1 is connected to the element T14.

The element T6 in contact with the outer boundary is
As shown in FIG. 19, the node is composed of nodes P3, P4, and P10, and the high, middle, and low contour values are assigned to the nodes.

Since two contour lines pass over the contour value, the broken line K4 cut out is represented by (6) in FIG. 7B.
It can be seen that this is a broken line corresponding to.

Further, it is known that the element T6 is connected to the elements T7 and T5 and the external boundary (indicated by-in FIG. 20) via the data for the element side of the connection data table. Therefore, from d [1] of FIG. 8 (6), the fold line K4 is composed of five points, and is composed of two parts having T7, T5 and T5, an external boundary, and a connection destination of T7.

As a result of the cutout processing performed on the contour region of the upper left and lower right diagonal lines, the connection data from the broken line K1 to the broken line K22 is as shown in FIG. ○ Consolidation processing As pre-processing before performing the consolidation processing, the connection destination of the polygonal line is changed to the polygonal line number in the element belonging to the polygonal line. with this,
The connection of the broken lines is correlated, and it is immediately known which broken line is connected to each broken line. Next, the connecting process is performed from the folding line K1.

First, the coordinates of the starting point and the ending point of the folding line K1 are stored in the line data for storing the coordinate position. The broken line K1 is
Since this is one line segment, the folding line K1 is now used. Next, processing for adding broken line data is performed.

The end point of the line is a broken line K which is one line segment.
2 and add the coordinates of the end point of the line K2 (line K
2 becomes used).

The end point of the line is a broken line K having two line segments.
3 and the connection to the broken line K2 is the second half of the broken line K3 in FIG. 25, and the coordinates of the end point of the second half of the broken line K3 are added (the score of the broken line K3 is set to 2).

The end point of the line is a broken line K having a line segment and a broken line.
4 and connected to the broken line K3 is the latter half of the broken line, and two coordinates other than the start point of the latter broken line of the broken line K4 are added (the score of the broken line K4 is set to 2).

The end point of the line is a broken line K having two line segments.
6 and the connection to the broken line K4 is the first half of the line K6 in FIG. 25, and the coordinates of the end point of the first half of the broken line K6 are added. To make the score 2).

The end point of the line is a broken line K which is a four-point broken line.
8 and three coordinates other than the start point of the polygonal line K8 are added (the polygonal line K8 becomes used).

The end point of the line is connected to the broken line K7, which is a line segment, and the coordinates of the end point of the broken line K7 are added (the broken line K8 becomes used).

The end point of the line is connected to a broken line K6 having a line segment, and the coordinates of the end point of the broken line K6 are added (the broken line K6 becomes used).

The end point of the line is connected to the broken line K5 which is a line segment, and the coordinates of the end point of the broken line K5 are added (the broken line K5 becomes used).

The end point of the line is connected to the broken line K4, which is a line segment, and the coordinates of the end point of the broken line K4 are added (the broken line K4 becomes used).

The end point of the line is connected to a broken line K3 which is a line segment, and the coordinates of the end point of the broken line K3 are added (the broken line K3 becomes used).

The end point of the line is connected to the broken line K14 which is a line segment, and the coordinates of the end point of the broken line K14 are added (the broken line K1).
4 becomes used).

The end point of the line is connected to the broken line K13 which is a line segment, and the coordinates of the end point of the broken line K13 are added (the broken line K1).
3 becomes used).

The end point of the line is a broken line K having two line segments.
12 and the connection to the broken line K13 is the latter half line segment, and the coordinates of the end point of the latter half line segment of the broken line K12 are added (the score of the broken line K12 is set to 2).

The end point of the line is a broken line K having two line segments.
11 and the connection with the broken line K12 is the first half line segment, and the coordinates of the end point of the first half line of the broken line K11 are added (the data of the second half line of the broken line K11 is moved to the first half, and the score is 2). To).

The end point of the line is a broken line K having two line segments.
10 and connected to the broken line K11 is the first half line segment, and the coordinates of the end point of the first half line of the broken line K10 are added (the data of the second half line of the broken line K10 is moved to the first half, and the score is 2). To).

The end point of the second half line of the line is connected to a fold line K9 having a line segment and a fold line, and the first half line is connected to the fold line K10. Add (Move the data of the second half line of K9 to the first half,
Score 3).

The end point of the line is connected to K19 which is a line segment, and the coordinates of the end point of the broken line K19 are added (the broken line K19 becomes used).

The end point of the line is connected to the broken line K18, and two coordinates other than the start point of the broken line K18 are added (the broken line K18 becomes used).

The end point of the line is connected to the broken line K9, and two coordinates other than the start point of the broken line K9 are added (the broken line K9 becomes used).

The end point of the line is connected to the broken line K10 which is a line segment, and the coordinates of the end point of the broken line K10 are added (the broken line K1).
0 is used).

The end point of the line is connected to the broken line K11 which is a line segment, and the coordinates of the end point of the broken line K11 are added (the broken line K1).
1 is used).

The end point of the line is connected to the line K12, which is a line segment, and the coordinates of the end point of the line K12 are added (line K1).
2 becomes used).

The end point of the line is connected to the broken line K1,
Since the polygonal line K1 has already been used as the polygonal line at the time of departure, the additional processing is once completed, and a closed curve line whose start point coincides with the end point is created.

Fold lines K15 and K which are unused broken line data
16, K17, K20, K21 and K22 remain.

The process of adding the second piece of broken line data from the broken line K15 is continuously performed.

Since the broken line K15 has two line segments, the broken line K1
Add the coordinates of the start point and end point of the second half line of line 5 (fold line K1
5 is set to 2).

The end point of the line is a broken line K having two line segments.
16 and the connection to the broken line K15 is the latter half line segment, and the coordinates of the end point of the latter half line segment of the broken line K16 are added (the score of the broken line K16 is set to 2).

The end point of the line is a broken line K having two line segments.
17 and connected to the broken line K16 is the latter half line segment, and the coordinates of the end point of the latter half line segment of the broken line K17 are added (the score of the broken line K17 is set to 2).

The end point of the line is a broken line K having two line segments.
22 and the connection with the broken line K17 is the first half line segment, and the coordinates of the end point of the first half line of the broken line K22 are added (the data of the second half line of the broken line K22 is moved to the first half, and the score is 2). To).

The end point of the line is a broken line K having two line segments.
21 and the connection with the broken line K22 is the first half line segment, and the coordinates of the end point of the first half line of the broken line K21 are added (the data of the second half line of the broken line K21 is moved to the first half, and the score is 2). To).

The end point of the line is a broken line K having two line segments.
20 and the connection with the broken line K21 is the first half line segment, and the coordinates of the end point of the first half line of the broken line K20 are added (the data of the second half line of the broken line K20 is moved to the first half, and the score is 2). To).

The end point of the line is connected to the broken line K15, which is a line segment. Since the broken line K15 is the departure line of the second additional processing, the additional processing ends once. Considering the broken line K15 as the start, a closed curve line is created in which the second start point and end point coincide.

As the termination processing, the initial coordinates (the coordinates of the start point of the broken line K1) are added to the line data.

A broken line K1 which is not yet used broken line data
Since 5, K16, K17, K20, K21, and K22 remain, the process of adding the third piece of broken line data from the piece of broken line K15 is continuously performed.

Since the polygonal line K15 is one line segment, the coordinates of the start point and the end point of the polygonal line K15 are added (the polygonal line K15 becomes used).

The end point of the line is connected to the broken line K20 which is a line segment, and the coordinates of the end point of the broken line K20 are added (the broken line K2).
0 is used).

The end point of the line is connected to the line K21 which is a line segment, and the coordinates of the end point of the line K21 are added (line K2).
1 is used).

The end point of the line is connected to the broken line K22 which is a line segment, and the coordinates of the end point of the broken line K22 are added (the broken line K2).
2 becomes used).

The end point of the line is connected to the broken line K17 which is a line segment, and the coordinates of the end point of the broken line K17 are added (the broken line K1).
7 is used).

The end point of the line is connected to the broken line K16 which is a line segment, and the coordinates of the end point of the broken line K16 are added (the broken line K1).
6 becomes used).

The end point of the line is connected to the broken line K15 which is a line segment. Since the broken line K15 has already been used (and is the departure broken line of the third additional processing), the additional processing is once completed. .

If the broken line K15 is regarded as the beginning, a closed curve line having the third start point and the end point coincides with each other.

As the termination processing, the initial coordinates (the coordinates of the start point of the broken line K1) are added to the line data.

Since there is no unused polygonal line data, the process of linking the polygonal line data to the upper left / lower right diagonal contour area is completed, and a series of closed curves whose start point and end point coincide with each other are completed.

Next, these operations will be described with reference to flowcharts. (5) Description of line segment data cutout processing unit A3 FIG. 3 is a flowchart showing the operation of the line segment data cutout processing unit for obtaining contours.

First, the following processing is performed in the order of element numbers.

After selecting the element (C1) and selecting the element data (C2), the element processing unit C3 orders the node numbers by the values of the element nodes, and as shown in FIG. It is determined whether this element is ascending or descending. For three nodes of low, middle and high, the coordinate position, the node value, the node number,
The element number of the opposite element (on the side of the element) is stored. The boundary determination unit C4 looks at the element number opposite to the element to be examined, and determines which of the eight boundary patterns (rows in FIG. 8) will be based on whether the element to be examined includes a boundary. Make a judgment. If two of the element nodes match the contour value, the line segment formed by the nodes is a boundary line. If all three node values match the contour value, the three node values around the element are examined and "+"
"-" And "0" are evaluated. When all three are different, the middle line of the triangle element is set as a contour line (FIG. 7C). If the element includes a contour line, the process proceeds to the region selecting unit C6. If the element does not include a contour line, the process proceeds to the boundary determination unit C11. If the element includes a boundary line, the process proceeds to the boundary processing unit C12. If not, the process proceeds to the next element.

In the area selecting section C6, when this element is of the ascending type, it is selected from the low area to the high area, and when it is of the descending type, it is selected from the high area to the low area (FIG. 7A). In the present invention, since the contour is cut out by two line segments, if the processing is performed in this order, the data of the latter coordinate position among the line segment data can be used, and the counterclockwise line segment can be used. A pattern can be made. The pattern classification unit C7 determines which of the eleven patterns (FIG. 7 (B)) is to be obtained while cutting out the elements into three to pentagons by contour lines, and then proceeds to the data storage unit C8.

Further, the boundary processing section C12 determines the (0) (see FIG. 7) cutout pattern having no contour line, and goes to the data storage section C13. Data storage unit C8, C
At 13, the pattern is classified into the pattern shown in FIG. 8 according to the cutout and the boundary, and the element number which is the line segment data, the number of the cutout line segments, the coordinate position, and the connection destination to the side constituting the element are stored. (If the connection destination is an element number, it is set to a value obtained by subtracting the node number from -2 if it is a node number. With this, it is possible to distinguish the connection destination from an element or a node.)

FIG. 7 is a classification diagram of a contour cutting pattern according to the present invention. In the cutting pattern by contour lines of elements, eleven (1) to (6), (1 ′) to (5 ′),
There are a total of 12 patterns of (0) without contour lines. Among them, there are five triangles, six squares, and one pentagon. There are 12 patterns because the connection destinations are different.

FIG. 8 is a classification diagram of contour line segment data. There are eight patterns from a to h according to the boundary indicated by the thick line (the numbers in [] indicate the number of the line segment boundary). 12), there are twelve patterns (1) to (6), (1 ′) to (5 ′), and no contour line (0) in the cut-out type using contour lines of the element. The line segment data includes a vector and a closed polygon.
There are some of them, and those whose circled end points match the nodes. (6) Description of Line Segment Data Connection Processing Unit A4 FIG. 4 is a flowchart showing the operation of the line segment data connection processing unit.

Two arrays of the total number of elements are prepared, and the following processing is performed on line segment data of the same contour. Before starting the concatenation process, the auxiliary array creating unit D3 associates the element number with the line segment data number in the prepared array 1. If there is no correspondence, set to zero. Thus, if the element number of the connection destination is given, the line segment data of the connection destination can be obtained immediately. The prepared array 2 is associated with a line segment data number. This makes it possible to determine whether or not line segment data is used (if used, the value is changed to a negative value). Then, the total number of unused data, the start and end numbers of unused data, the current number, and seven numbers of a connection source, a connection destination, and a return destination can be stored. When all of this data is used for updating the line segment data status, the number of unused data is reduced by one, and the value of this number in array 2 is set to -1.
When the data number matches the unused start or end number, the value is changed.

First, the line data creating section D5 creates line data by using unused first data. If the line segment data is not separated, the data status updating unit is used. If the line segment data is separated into two, the latter part is used to reduce the number of vertices used. The return destination is stored from the connection destination at the start point of the used line segment data, and the connection source and the connection destination are stored from the value of the connection destination at the end point. Next, the data number of the connection destination is detected in D6, and if there is data, the process goes to the line segment data adding unit D10. In this way, the line segment data is connected in order, and when there is no line segment data, the process goes to the termination process D7.

If there is no unused line segment data, the value obtained by subtracting 1 from the number of line points becomes the effective number of line points.
The connection processing in this contour ends.

In the detection of the data number, if the value of the connection destination is positive, it is the element number. Therefore, the data number is detected by combining array 1 and array 2. If the value of the connection destination is negative, it is a node number. Therefore, the array 1 and the array 2 are made to correspond to the element including the node, and the data number whose starting point of the vertex data matches the node is detected. This detection value is
This is the current number of the line segment data.

If the detected value is positive, the adding unit D10 adds line segment data to the line data except for the starting point. If they are on the same straight line, line segment data is added excluding the end point of the line data as well as the start point of the line data. If the line segment data is not separated, the data status update unit is used. When the two are separated, it is determined which one to use by comparing the connection source and the connection destination of the starting point. In both cases, the number of vertices used is reduced, but when the first half is used, unused second half data is moved to the first half. Renumber the source and destination numbers with the destination value of the end point of the used line segment data. This makes it possible to prepare for use again.

In the termination process D7, when the detected value is negative or the connection destination and the return destination match, the first start point is added to the end point of the line data, and the process continues to the next connection process ( The created line data is a closed curve where the start point and the end point coincide.) (7) Description of Drawing Command Part A5 In the X window of the UNIX environment, the graphic attribute fill_rule that determines the inside of the polygon is set to EvenOddRule (default). For a polygon fill, the value of shape is Complex (a polygon whose sides intersect each other).
Since the coordinates of a given point are absolute coordinates, the value of mode is
Change to CoordModeOrigin.

In Windows, the connection mode IDM_RGN_XO
R (8) Drawing of Contour Lines A method of drawing contour lines will be specifically described with reference to FIGS. 9, 19, and 20 to 25.

FIG. 26 shows contour lines obtained by dividing the mesh of FIG. 19 into four parts, in which element numbers (T1 to T50: for drawing) are written. FIG. 27 shows a line segment for each element in FIG. 26 as a vector. The number in parentheses is the number of the cutout pattern (see FIG. 9). FIG. 28 is a line diagram in which the line segments of FIG. 27 are connected by adding an end point or a start point.

That is, when the contour line in FIG. 26 is determined as a line segment based on the cutout pattern classification diagram in FIG.
Becomes When the line segments in FIG. 27 are connected, the result becomes FIG. 28 and finally to FIG.

In contrast to the solid contour lines in FIG. 26, FIG.
The symbols L1 to L14 are prepared in the line segment pattern, and FIG.
Shows the connection data. ○ Cut-out processing For example, the element T3 is obtained from nodes P2, P9, P
8, which are assigned the high, low, and middle contour values, respectively, and are therefore counterclockwise elements.

Since the contour passes near the low contour value,
It can be seen that the cut line segment L1 is a line segment corresponding to (1) in FIG.

Further, the element T3 is converted into the elements T14, T2, T2 through the data for the element sides of the connection data table.
4 is known to be connected to the element T4, and the start point of the line segment L1 is connected to the element T4, and the end point of the line segment L1 is connected to the element T14. Similarly, element T4 is a clockwise element, and its line segment L2 corresponds to (4) in FIG. 9B, and is connected to elements T5 and T3.

As a result of cutting out the solid contour lines, the connection data of the line segments L1 to L14 is as shown in FIG. ○ Consolidation processing As a pre-processing before performing the coupling processing, the connection destination of the line segment is changed to the line segment number in the element belonging to the line segment.

Thus, the connections of the line segments are associated with each other, and it is immediately known which line segment each line segment is connected to.

The linking process is performed from the line segment L1. First, the coordinates of the start point and the end point of the line segment L1 are stored in the line data for storing the coordinate position. The line segment L1 has now been used. Next, an end point adding process is performed. Since the end point of the line is connected to the line segment L8, the coordinates of the end point of the line segment L8 are added. Since the end point of the line is connected to the line segment L7, the line segment L7
Add the coordinates of the end point of. Since the end point of the line is connected to the line segment L6, the coordinates of the end point of the line segment L6 are added. Since the end point of the line is connected to the line segment L5, the coordinates of the end point of the line segment L5 are added. Since the end point of the line is the outer boundary, the process of adding the end point ends here. Since the start point of the first line segment L1 has a connection destination with the line segment L2, it is necessary to perform a process of adding a start point. However, since it is desired to connect to a line created by adding an end point, the front and the back are reversed. Rearrange coordinate positions.

Since the end point of the line is connected to the line segment L2,
The coordinates of the start point of the line segment L2 are added. Since the end point of the line is connected to the line segment L3, the coordinates of the start point of the line segment L3 are added. Since the end point of the line is connected to the line segment L4, the line segment L4
Add the coordinates of the starting point of. Since the end point of the line is the outer boundary, the process of adding the start point ends here. Thus, a first line connected to the line segment L1 is created. Line segments L9 to L14, which are unused line segment data, remain.

The linking process is newly performed from the line segment L9. First, the coordinates of the start point and the end point of the line segment L9 are stored in the line data for storing the coordinate position (in an actual program, the next used for the line segments L1 to L8, that is, the next coordinate of the start point coordinate of the line segment L4 is The coordinates of the starting point of the line segment L9).

Next, an end point adding process is performed. Since the end point of the line is connected to the line segment L10, the coordinates of the end point of the line segment L10 are added. Since the end point of the line is connected to the line segment L11, the coordinates of the end point of the line segment L11 are added. Since the end point of the line is connected to the line segment L14, the coordinates of the end point of the line segment L14 are added. Since the end point of the line is connected to the line segment L13, the coordinates of the end point of the line segment L13 are added. Since the end point of the line is connected to the line segment L12, the coordinates of the end point of the line segment L12 are added. Although the end point of the line is connected to the line segment L9, since the line segment L9 has already been used, the process of adding the end point is completed, and the line becomes a closed curve in which the start point and the end point of the line data coincide.

As a result, a second line connected to the line segment L9 has been created. Since there is no unused line segment data, the process of linking the line segment data to the solid contour line ends.

Next, these will be described in detail with reference to flowcharts. (9) Description of contour line data cutout processing unit A3 FIG. 5 is a flowchart showing the operation of the contour line data cutout processing unit. The following processing is performed in the order of element numbers.
That is, the element processing unit E3 determines the node number in ascending order based on the value of the element node, and determines whether the system becomes a left-handed system or a right-handed system. The coordinate position, the contour value, the node number, and the opposing element number are stored for the three low, middle, and high nodes.
When all three node values match the contour values, the three node values around the element are examined, and the contour values are evaluated as “+”, “−”, and “0”. When all three are different, the middle line of the triangular element is taken as a contour line, and when only one is “−”, two line segments that are not “−” are taken as contour lines (FIG. 9).
(C)). If there is a contour line in the element, the pattern classification unit E7 determines which of the five patterns shown in FIG. 9 the contour line will be. The element number, the coordinate position, and the connection destination, which are minute data, are stored (when the connection destination is the element number, the value is obtained by subtracting the node number from -2 when the connection destination is the node number. Element or node).

FIG. 9 is a pattern classification diagram for contour lines, showing (A) for counterclockwise, (B) for clockwise, and (C) for midline. Because the connection destination is different, five vector patterns, (1), (1 '), (2), (2'),
(3), (4), (4 '), (5), (5'), (6)
There is. When the element side coincides with the contour line, the pattern for counterclockwise rotation (2) and the pattern for clockwise rotation (5) are used only for the minimum contour line value in order to prevent the contour lines from overlapping. End points that match the nodes are marked with circles.

When the node value of an element matches the contour value, if the node value around the element is different from the contour value, a contour line is drawn at the element (FIG. 10C).

The two figures on the left of (C) are different in the direction of the line segment which is the middle line.

In the right diagram of (C), the contour on the “−” side is not drawn, but is drawn on the remaining two sides. This is because it is decided to draw a contour line when the value becomes larger than the contour value. In this case, since the element has two line segments, a process of allocating one line segment to adjacent elements is performed. This can deal with the case of FIG. (10) Description of Contour Line Data Connection Processing Unit A4 FIG. 6 is a flowchart showing the operation of the contour line data connection processing unit A4.

Two arrays of the total number of elements are prepared, and the following processing is performed on the line data of the same contour.

Before starting the linking process, the auxiliary sequence creation unit F
In step 3, the number of the line segment data corresponds to the element number in the prepared array 1. If there is no correspondence, set to zero. Thus, if the element number of the connection destination is given, the line segment data can be obtained immediately. The prepared array 2 is associated with a line segment data number. This makes it possible to determine whether or not line segment data is used (if used, the value is changed to a negative value). Then, the start, end, and total number of unused data can be stored. When this data is used for updating the data status, the number of unused data is reduced by one, and the value of this number in array 2 is set to -1. When the data number matches the unused start or end number, the value is changed. First, the line data creation unit F5 creates line data by using unused first data. It also updates the data status. Next, the data number of the connection destination is detected in F6,
If there is data, the process is moved to the end point adding section F11 of the line segment data. Here, if there is no data, the process goes to the both ends determination unit F7. If both ends match, the line is stored, and the process proceeds to the next line. If the both ends do not match, the connection destination is a negative boundary, and the line data to be connected is connected to the start point of the line segment selected at the beginning of the contour line connection process after inverting the line data in the front-rear substitution unit F12. Are connected, and the starting point is added in this manner.

Thus, since one line row of contour lines has been created, the process proceeds to the next line row, and if there is no line segment data, the process proceeds to the next contour line.

In the detection of the data number, if the value of the connection destination is positive, it is the element number, so that the data number is detected by combining array 1 and array 2. If the destination value is negative,
Since it is a node number, array 1 and array 2 are made to correspond to the element including the node, and the starting point of the vertex data is
A data number corresponding to the node is detected. This detected value is the current number of the line segment data.

In the line data end point addition section F11, the end point of the line segment data is added to the line data if the detected value is positive, and the process returns if the detected value is negative. If they are on the same straight line, the end point of the line data is replaced with the end point of the line segment data. The data status is updated, and the destination connection destination is used as the next connection destination.

In the line data start point adding section F14, the start point of the line segment data is added to the line data if the detected value is positive, and the process returns if the detected value is negative. If they are on the same straight line, the start point of the line data is replaced with the end point of the line segment data. The data status is updated, and the connection destination at the start point is used as the next connection destination. (11) Description of the drawing command part A5 The coordinates of the given point are absolute coordinates, so the value of mode is Co.
Change to ordModeOrigin. (12) Specific Example of Drawing Contour (Color Tone Diagram) The potential was calculated by solving the Laplace equation by applying the triangular element finite element method to a rectangle of 5 cm × 10 cm. The boundary conditions provided a Dirichlet boundary of 0 V and 1 V on the short sides at both ends.

The environment used was an X window using a client-server system on a workstation with a SPECfp95 of 8. As an example of the drawing of the calculation result, FIG. 10 shows 100 meshes. (A) is the mesh, (B) is the initial value distribution diagram of the potential given by random numbers, (C) is the potential distribution diagram of the calculation result, (D) is the position differential of the potential, and interpolated to the value at the node. It is a current distribution diagram.
(B) to (D) are tiles of contours obtained by dividing the interval between the minimum value and the maximum value into five.

In this case, the drawing is the same as that of the present invention and the conventional example. The drawing of the random numbers in (B) is less advantageous to the present invention than the conventional example because the number of connected line segments is small.
The present invention is faster up to a practical mesh number of 5000. In the drawing of the current distribution in (D), since the gradient of the potential is constant, the values at all the nodes coincide within the calculation error. Since the slight difference is divided by the contour line, it is considered that the drawing becomes a typical general drawing. Next, a description will be given of the result of comparison between the present invention and Conventional Example 1 regarding the contour drawing time with respect to the number of meshes.

Here, Conventional Example 1 is slightly different from the description in the section of the prior art. Originally, in Conventional Example 1, drawing is performed by changing the color tone for each element, so that it takes time. For this reason, a storage capacity is required, but once the entire display area is stored, the display area is drawn for each designated color. Thus, although the amount of storage differs by the connection relationship, it is a comparison between drawing small polygons separately and drawing a large polygon connected to one.

Table 1 shows the contour drawing time with respect to the number of meshes. The contents are a random number, a potential, a current drawing time, and a pre-processing time. The pre-processing time increases substantially in proportion to the number of meshes, but is shorter than the current drawing time, so that there is no problem in terms of time.

For easy understanding, Table 2 and FIG.
The following shows the ratio of the drawing time of the present invention to Conventional Example 1.
If the number of meshes is less than 1000, drawing is performed in about 70% of the time. For 40000 with a large number of meshes, the random number is 4 times,
Drawing is performed in a quarter of the potential and 40% of the current. In general drawing drawings other than random numbers, drawing is realized faster as the number of meshes increases.

[0124]

[Table 1]

[0125]

[Table 2]

(13) Specific Example of Contour Drawing As an example of contour drawing, under the same conditions as in the above-described example,
FIG. 11 shows the number of meshes 2500. (A) is the mesh, (B) is a potential distribution diagram, and (C) is a conventional potential distribution diagram. (B) and (C) are contour lines obtained by dividing the range between the minimum value and the maximum value into six parts by solid lines and broken lines. The three broken lines are different between (B) and (C). If the contour line remains a line segment, the broken line will be distorted due to the difference between the period of the broken line and the length of the line segment. (B) is drawn as a series of polygonal lines by connecting the contour lines, whereas (C) is drawn as an irregular dashed line because the contour lines remain unchanged.

Next, Table 3 and Table 4 and FIG.
It is shown in (B). The ratio of the drawing time of the polygonal line to the line segment is 1.5 times at the maximum, and the drawing time is delayed. However, even if the number of meshes is 40000, there is no problem because the drawing time is 0.1 second except for the random numbers.

[0128]

[Table 3]

[0129]

[Table 4]

(14) Accurate Drawing of Contour Lines According to the present invention, when the value of a node coincides with the contour line value, the contour line can be accurately determined independently of the mesh structure by examining the node values around the element. Is drawn on. In particular, it is especially effective for contour drawing where symmetry is expected. Here, a case where the node is a saddle point and a case where the element line segment matches the contour line will be described with reference to FIGS. In the figure, "+" indicates a mountain, "-" indicates a valley, (A) indicates a contour by a hatched tile, and (B) indicates a contour by a thick broken line.

The point where the contour lines are cross-shaped along the elements and the peaks and valleys alternate are the saddle points. FIG. 13 is a schematic diagram of contour drawing when the node is a saddle point. The upper left figure is an expected drawing figure. When drawing only with node values of elements, the shape differs depending on the mesh structure,
The upper two are good, but the lower three do not have contour lines.

FIG. 14 is a schematic diagram showing contour line drawing when the element line segment coincides with the contour line. The left figure is an expected drawing figure. In the drawing using only the node values of the elements, the figures differ depending on the mesh structure, and the middle figure is good, but in the right figure, the contour lines are bent in a C-shape along the elements.

[0133]

Since the contour drawing method according to the present invention is constructed as described above, the following effects can be obtained.

The first effect is that the drawing speed is high. The reason is that the line data of the contour line and the boundary line, which are separated for each element, are connected, and the minimum necessary point data is drawn in a lump. The second effect is that the connection calculation of the line segment data is fast. The reason for this is that the line segment data has the number of the next line segment data to be connected due to the ordering of the line segment data in the element connection table, and there is no connection determination and sorting process based on position coordinates.

A third effect is that a table for element connection, which is pre-processing of a mesh, is created quickly. The reason is,
This is because numbering of element line segments and collection of element connection information are performed using a table of contained elements for each node.

A fourth effect is that the contour line drawing accuracy is high (especially when symmetry is expected). The reason is that when the contour line matches the side constituting the element, the node value around the element is examined to determine the presence or absence of the contour line. The fifth effect is that contour lines are drawn finely. In particular, it is effective for drawing contour lines by broken lines. The reason is that the image is drawn not as a set of line segments but as a set of a series of broken lines.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration for drawing contour lines according to the present invention.

FIG. 2 is a flowchart illustrating preprocessing of mesh data according to the present invention.

FIG. 3 is a flowchart illustrating a process of extracting line segment data from a contour.

FIG. 4 is a flowchart illustrating a process of connecting line segment data to contours.

FIG. 5 is a flowchart illustrating a process of extracting line segment data from a contour line.

FIG. 6 is a flowchart illustrating a process of connecting line segment data to contour lines.

FIG. 7 is a classification diagram of a cutout pattern of contours;
(A) is a diagram showing a calculation order, (B) is a classification diagram showing a cutout pattern, and (C) is a classification diagram used for a middle line.

FIG. 8 is a classification diagram of contour line data.

FIG. 9 is a pattern classification diagram for contour lines.

FIG. 10 shows an embodiment of drawing a contour (color tone diagram) diagram,
(A) is a mesh, (B) is an initial value which is a random number, (C)
Is a potential distribution diagram as a calculation result, and (D) is a current distribution diagram.

11A and 11B show an example of contour drawing, in which FIG. 11A is a mesh, FIG. 11B is a potential distribution diagram of the present invention, and FIG. 11C is a conventional potential distribution diagram.

12A and 12B show comparison graphs of drawing time with respect to the number of meshes, wherein FIG. 12A is a comparison graph of contours, and FIG. 12B is a comparison graph of contour lines. FIG.

FIG. 13 is a schematic diagram when a node is a saddle point;
(A) is a contour diagram, and (B) is a contour diagram.

14A and 14B are schematic diagrams when an element line segment matches a contour line. FIG. 14A is a contour diagram, and FIG. 14B is a contour diagram.

FIG. 15 is a diagram for describing contour drawing according to Conventional Example 1.

FIG. 16 is a flowchart for describing contour drawing according to Conventional Example 1.

FIG. 17 is a diagram for describing contour drawing according to Conventional Example 2.

FIG. 18 is a flowchart for describing contour drawing according to Conventional Example 2.

FIG. 19 is a diagram specifically showing mesh data.

FIG. 20 is a table schematically showing a connection data table generated in preprocessing.

FIG. 21 is a diagram illustrating an example of contour drawing.

22 is a diagram in which the contour diagram of FIG. 21 is determined based on the cutout pattern classification diagram of FIG. 7 and the broken line pattern classification diagram of FIG. 8;

FIG. 23 is a view obtained by connecting the folding lines of FIG. 22;

FIG. 24 is a diagram showing a state in which a termination process is performed to form a series of line data.

FIG. 25 is a diagram schematically showing a connection table for drawing contours.

FIG. 26 is a diagram illustrating an example of contour lines.

27 is a diagram in which line segments are determined from the contour lines in FIG. 26 based on the cutout pattern classification diagram in FIG.

FIG. 28 is a diagram obtained by connecting the line segments of FIG. 27;

FIG. 29 is a diagram showing final contour lines.

FIG. 30 is a chart schematically showing a connection table for drawing contour lines.

[Explanation of symbols]

 T1 to T50 elements S1 to L85 element sides P1 to P36 nodes K1 to K22 folded lines

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G06T 11/20 100 G06T 1/00 G09G 5/00 510

Claims (13)

(57) [Claims] A first step of generating a connection table for a triangular element for drawing; and a closed curve determining the contour using the connection table generated in the first step to determine a contour. Is classified as a line segment pattern of each element, and is cut out as polygonal line data, and the cut-out polygonal line data is stored in a memory allocated to the element, and a contour obtained in the second step is obtained. The third step of creating one closed curve by sequentially linking the polygonal line data that constitutes, and, in order to draw contour lines, from the closed curve that constitutes the contour, using the connection table, By cutting out a line segment in each element and storing it in a memory allocated to the element, and sequentially connecting the line segments obtained in the fourth step,
A fifth step of drawing contour lines, and a contour line drawing method. 2. A connection table generated in the first step includes a table of element numbers of elements including the node or an element made of the node for each node of the element, A table of line numbers of element sides constituting the element, and 2 which is an end point for each element side
The contour line according to claim 1, further comprising a table of a node number of one node, an element number of two elements facing each other through each of the element sides, and a node number of a node facing each other through each of the element sides. How to draw. 3. The method according to claim 2, wherein in the second step or the fourth step,
3. The contour line drawing method according to claim 1, wherein the connection destination data is detected based on the line segment number or the node number without performing the connection determination using the position coordinates. 4. In the second step, the broken line data for determining the contour is classified based on a pattern obtained in advance, and as a result, the obtained line segments are stored in a memory allocated to each element. 2. The contour drawing method according to claim 1, wherein: 5. The contour line drawing method according to claim 1, wherein the polygonal line data for determining contours obtained in the second step includes a boundary line which is an end of a drawing area. . 6. The pattern is determined from a state of whether or not each element side of the triangular element is the boundary line and a pattern of line segments that determine contours drawn in the triangular element. 6. The contour drawing method according to claim 1, wherein the contour drawing method comprises a plurality of folded line patterns. 7. The contour line drawing method according to claim 1, wherein the line segment determining the contour is a polygonal line having a predetermined direction of clockwise or counterclockwise. . 8. In the third step, after forming a large polygon in which a start point and an end point of a series of polygonal line data for determining the contour coincide with each other, the start point is increased by one to this large polygon, and then the next 8. The contour drawing method according to claim 1, wherein a plurality of large polygons are connected to one by performing a large polygon creation process. 9. The contour drawing method according to claim 1, wherein, in the fourth step, contours are selected and obtained from a line segment pattern obtained in advance. 10. The contour drawing method according to claim 1, wherein in the fourth step, the direction of the contour is determined based on the magnitude relation of the node values of the triangular elements. 11. When an element side constituting the element coincides with a contour line, a pair of node values is checked with respect to surrounding edges, a line segment different from the contour line value is regarded as a contour line, and a coincident line segment is excluded. 10. A structure as claimed in claim 1, wherein:
Or the contour line drawing method according to any one of 10 above. 12. A closed means for generating a connection table for a triangular element for drawing, and a closed curve for determining the contour using the connection table generated by the first means for determining a contour. Is classified as a line segment pattern of each element, and is cut out as polygonal line data, and the cut-out polygonal line data is stored in a memory allocated to the element, and the contour obtained by the second means is The third means for creating one closed curve by sequentially connecting the polygonal line data forming the, and, from the closed curve forming the contour, to draw a contour line, using the connection table, By cutting out as a line segment in each element and storing in a memory allocated to the element a fourth means, and sequentially connecting the line segments obtained by the fourth means,
A contour line drawing system, comprising: fifth means for drawing contour lines. 13. A first step of generating a connection table for a triangular element for drawing, and a closed curve determining the contour using the connection table generated in the first step to determine a contour. Is classified as a line segment pattern of each element, and cut out as polygonal line data, and the cut-out polygonal line data is stored in a memory allocated to the element; and a contour obtained in the second step is obtained. The third means for creating one closed curve by sequentially connecting the polygonal line data forming the, and, from the closed curve forming the contour, to draw contour lines, using the connection table, A fourth step of cutting out as a line segment of each element and storing it in a memory allocated to the element, and sequentially obtaining the line segment obtained in the fourth step. By connecting a fifth step of drawing the contours, for executing a series of processes consisting of city on a computer, a recording medium recording a method of drawing contours, characterized in that recording the program.