JP2003051020A - Method and device for approximating curve and curve approximation program to be used therefor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method, a device and a program for approximating curve which enable approximation of a form presented by a dot sequence composed of a plurality of dots as a curve passing the dot sequence by simple processing. SOLUTION: The method for approximating the form presented by the dot sequence composed of a plurality of dots as a curve passing the dot sequence, has a processing target dot selecting step for selecting any arbitrary dot included in the dot sequence as a processing target dot, a reference dot selecting step for selecting one or a plurality of dots included in the dot sequence as reference dots and an interpolation dot calculating step for calculating an interpolation dot for approximating the curve from the processing target dot and the reference dots.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve approximating method and a curve approximating apparatus for approximating a shape represented by a series of points as a curve passing through the series of points, and a curve approximating program used therefor. Regarding

[0002]

2. Description of the Related Art Natural spline curves, B-spline curves and NURBS (Non-Uniform Rational B-Splines) are used to represent figures in computer graphics.
A curve represented by a piecewise polynomial obtained from a plurality of coordinate points is used. Regarding these curves, for example, “Shape processing engineering by computer display” (written by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun) or “Comp.
uter Graphics Principles and Practice "(Foly, van
Details are described in Dam, Feiner, and Hughes, Addison Wesley).

Further, in Japanese Patent Laid-Open No. 3-129485, the connection state of the connection points of each straight short vector of the straight short vector sequence is obtained, and the curved portion and the straight line portion are formed based on the connection state of each connection point. There is disclosed a technique in which the curve is divided and divided into.

[0004]

By the way, in the case of expressing a general figure using a curve expressed by the above-described piecewise polynomial, the curve is combined or drawn from the step of drawing the figure. A curve is fitted to the drawn figure.

However, in the former method of drawing by combining curves at the stage of drawing a figure, the combination of curves may become inappropriate in the process of editing and deforming the figure after drawing.

For example, from the state of FIG.
Move 1001 and change point 1001 to a corner point.
It is assumed that the state of 9 (b) is changed.

Here, it is assumed that a cubic Bezier curve is used to represent a figure. The figure in Fig. 19 (a) is a single 3
It can be expressed by the following Bezier curve, but after transformation
The figure 9 (b) cannot be represented by one cubic Bezier curve. At this time, as shown in FIG. 20 (a), the curve is divided into two parts, a cubic Bezier curve defined by control points 1011-1014 and a cubic Bezier curve defined by control points 1014-1017. The transformation described above can be realized by converting the control points so that they are represented by Bezier curves, and then moving the respective control points to positions that represent the figure after the transformation as shown in FIG. . However, it is difficult to appropriately divide such a figure or automatically perform the process of moving the control points so as to match the figure after the transformation. Further, as a graphic is edited, it may be divided into many cubic Bezier curves, which causes a problem that the amount of data increases and the number of processes for drawing increases.

Further, the method described in Japanese Patent Laid-Open No. 3-129485 makes it possible to appropriately divide a figure in the above situation, but a curve is applied to a curved line portion (for a figure after transformation). It has not solved the difficulty of determining the control points so that they match.

The present invention has been made in order to solve the above problems, and its object is to make a shape represented by a point sequence consisting of a plurality of points simple as a curve passing through the point sequence. It is to provide a curve approximation method and a curve approximation device that are approximated by processing, and a curve approximation program used for the method.

[0010]

In order to solve the above-mentioned problems, a curve approximation method according to the present invention approximates a shape represented by a sequence of points consisting of a plurality of points as a curve passing through the sequence of points. In the method, a processing target point selecting step of selecting an arbitrary point included in the point sequence as a processing target point, and a reference point selecting step of selecting one or a plurality of points included in the point sequence as a reference point And an interpolation point calculation step of calculating an interpolation point for curve approximation from the processing target point and the reference point.

Here, the coordinates representing the points may be two-dimensional or three-dimensional. Further, the coordinates may be absolute coordinates or relative local coordinates.

With the above arrangement, the processing target point selecting step selects an arbitrary point included in the point sequence as a processing target point. Here, when the points included in the point sequence are ordered like a list structure, the points to be processed may be sequentially selected from the first point. Next, the reference point selection step selects one or a plurality of points as reference points from the point sequence. The reference point may be selected according to the processing target point. For example, when the points included in the point sequence are ordered like a list structure, points before and after the processing target point may be selected as reference points. Furthermore, several points before and after the processing target point,
If a plurality of points are selected as reference points, the interpolation points calculated in the subsequent interpolation point calculation step can be made more appropriate. Next, the interpolation point calculation step calculates an interpolation point from the processing target point and the reference point.

When approximating the shape as a curve, the processing target point selecting step sequentially selects all the points included in the point sequence as reference points, and the reference point selecting step is performed for each point. And the interpolation point calculation step. By connecting the interpolation points calculated in the interpolation point calculation step together with the point sequence by line segments, a line segment group approximating a curve passing through the point sequence can be obtained. As described above, a curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved, without changing the data structure. A figure represented by a sequence of points can be transformed.

A curve approximating method according to the present invention is a method for approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence, for solving the above-mentioned problems. A work point sequence preparation step of duplicating a sequence into a work point sequence, a processing target point selection step of selecting an arbitrary point included in the work point sequence as a processing target point, and a work point sequence A reference point selecting step of selecting one or a plurality of included points as a reference point; an interpolation point calculating step of calculating an interpolation point for curve approximation from the processing target point and the reference point; An interpolation point adding step of adding the interpolation points calculated in the step to the working point sequence, and the reference point selecting step, the interpolation point calculating step, and the interpolation point adding step satisfy predetermined conditions. It is characterized by repeated until.

With the above arrangement, the work point sequence preparing step duplicates the point sequence into a work point sequence. In the processing target point selecting step, an arbitrary point included in the work point sequence is selected as a processing target point. Similarly to the above, when the points included in the work point sequence are ordered like a list structure, it is sufficient to select the points to be processed in order from the first point. Next, the reference point selecting step selects one or a plurality of points as reference points from the working point sequence. Similar to the above, the reference point may be selected according to the processing target point. For example, when the points included in the work point sequence are ordered like a list structure, the processing is performed. Points before and after the target point may be selected as reference points. Next, the interpolation point calculation step calculates an interpolation point from the processing target point and the reference point. In the interpolation point adding step, the interpolation point calculated in the interpolation point calculating step is added to the working point sequence. When the points included in the working point sequence are ordered as in the list structure as described above, the ordering is modified so that the interpolation points are located between the interpolated points. It may be added to the point sequence for the work.

When approximating the shape as a curve, the process target point selecting step includes points other than the interpolation points added in the interpolation point adding step among the points included in the working point sequence. All points are sequentially selected as reference points, and the reference point selecting step, the interpolation point calculating step, and the interpolation point adding step are executed for each point. After that, when a predetermined condition is satisfied, the entire process is ended. The predetermined condition is, for example, when the time required for processing exceeds a predetermined time, or when the total number of points included in the work point sequence exceeds a predetermined number. . The prescribed conditions are not met, and
When the processing target point selecting step selects all points as reference points, and the execution of the reference point selecting step, the interpolation point calculating step, and the interpolation point adding step for each point is completed, the operation is performed. The above-described processing is repeated as the selection target in the processing target point selection step, including the interpolation point newly added to the use point sequence.

By connecting the points included in the work point sequence thus obtained with line segments, a line segment group approximating a curve passing through the point sequence can be obtained. As described above, a curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved, without changing the data structure. A figure represented by a sequence of points can be transformed. Furthermore,
Since this approximation processing is repeated until a predetermined condition is satisfied, the curve can be approximated as accurately as possible within the limits of the processing amount and the memory amount.

In order to solve the above-mentioned problems, the curve approximation method according to the present invention is, in addition to the above-mentioned configuration, a distance calculation step for calculating the distance between the processing target point and the reference point, and the distance calculation. An interpolation point necessity determination step for determining necessity / unnecessity of calculation of an interpolation point by referring to the distance calculated in the step, and the interpolation point calculation step calculates the interpolation point in the interpolation point necessity determination step. The feature is that an interpolation point is calculated when it is determined that

With the above arrangement, the interpolation point calculation step is performed only when the interpolation point necessity determination step determines that the interpolation point calculation is required according to the distance calculated in the distance calculation step. To calculate. For example, if the distance is smaller than a predetermined distance, it does not make much sense to generate an interpolation point between the processing target point and the reference point, so that calculation of the interpolation point is unnecessary. Good. In this way, unnecessary interpolation points can be prevented from being calculated, and the processing amount and memory amount required to approximate the curve can be reduced.

In order to solve the above problems, the curve approximating method according to the present invention is, in addition to the above configuration, an angle calculating step of calculating an angle formed by a vector composed of the processing target point and the reference point. And an interpolation point necessity judgment step for judging necessity / unnecessity of calculation of an interpolation point by referring to the angle calculated in the angle calculation step, wherein the interpolation point calculation step is the interpolation point necessity judgment step. The feature is that the interpolation point is calculated when it is determined that the calculation of the interpolation point is required.

With the above arrangement, the interpolation point calculation step is performed only when the interpolation point necessity determination step determines that the interpolation point calculation is required according to the angle calculated in the angle calculation step. To calculate. For example, when the difference between the angle formed by the three points of the processing target point and the reference points located before and after the processing target point and 180 degrees is smaller than a predetermined angle, the processing target point Since the reference point is located on a substantially straight line and it does not make much sense to generate an interpolation point, the calculation of the interpolation point may be unnecessary. In this way, unnecessary interpolation points can be prevented from being calculated, and the processing amount and memory amount required to approximate the curve can be reduced.

In order to solve the above-mentioned problems, the curve approximation method according to the present invention has, in addition to the above-mentioned configuration, the points included in the point sequence, each of which is a corner point connecting two line segments. Or a point on a curve is also included, and an angle for determining whether any one of the processing target point or the reference point is a corner point. A point determination step, wherein the interpolation point calculation step calculates an interpolation point when it is determined in the corner point determination step that either the processing target point or the reference point is not a corner point. Is characterized by.

With the above arrangement, in the interpolation point calculation step, in the interpolation point necessity judgment step, in the corner point judgment step, any one of the processing target point and the reference point is not a corner point. If the judgment is made, the interpolation point is calculated only when the judgment is made. In this way, even when a part of the shape includes a bending point, the above-mentioned interpolation point is not calculated for the corner point representing the bending point, so that the corner point and the points before and after it are not calculated. And have the same shape as the shape represented by the original point sequence, and a complicated figure can be approximated without performing the process of fitting a curve.

The curve approximating apparatus of the present invention is an apparatus for approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence in order to solve the above problems. A point sequence storage means for storing points included in the point sequence processing means, a processing target point selection means for selecting an arbitrary point among the points stored in the point sequence storage means as a processing target point, and the point sequence storage means. Reference point selecting means for selecting one or a plurality of points as reference points from the points stored in, and interpolation point calculating means for calculating an interpolation point for curve approximation from the processing target point and the reference point. It is characterized by having and.

With the above arrangement, the processing point selecting means selects an arbitrary point included in the point sequence as a processing point. Here, when the points included in the point sequence are ordered like a list structure, the points to be processed may be sequentially selected from the first point. Next, the reference point selection means selects one or a plurality of points as reference points from the point sequence. The reference point may be selected according to the processing target point. For example, when the points included in the point sequence are ordered like a list structure,
The points before and after the processing target point may be selected as reference points. Further, if a plurality of points before and after the processing target point are selected as reference points, the interpolation points calculated by the subsequent interpolation point calculating means can be made more appropriate. Next, the interpolation point calculation means calculates an interpolation point from the processing target point and the reference point.

When approximating the shape as a curve, the processing target point selecting means sequentially selects all the points included in the point sequence as reference points, and the reference point selecting means for each point is selected. And the interpolation point calculation means. By connecting the interpolated points calculated by the interpolated point calculation means together with the point sequence by a line segment, a line segment group approximating a curve passing through the point sequence can be obtained. As described above, a curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved, without changing the data structure. A figure represented by a sequence of points can be transformed.

In order to solve the above-mentioned problems, the curve approximating apparatus of the present invention is an apparatus for approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence. A point sequence storage means for storing the points contained in, a working point sequence preparation means for copying the point sequence stored in the point sequence storage means into a working point sequence, and a working point sequence. Processing target point selecting means for selecting any included point as a processing target point, reference point selecting means for selecting one or a plurality of points included in the working point sequence as reference points, and the processing target point And an interpolation point calculation means for calculating an interpolation point for curve approximation from the reference point and an interpolation point addition means for adding the interpolation point calculated by the interpolation point calculation means to the working point sequence. Then, the reference point selection means, the interpolation point calculation means, and the interpolation And additional means, is characterized by repeated until a predetermined condition is satisfied.

With the above arrangement, the work point sequence preparing means duplicates the point sequence into a work point sequence. The processing target point selecting means selects an arbitrary point included in the working point sequence as a processing target point. Similarly to the above, when the points included in the work point sequence are ordered like a list structure, it is sufficient to select the points to be processed in order from the first point. Next, the reference point selecting means selects one or a plurality of points as reference points from the working point sequence. Similar to the above, the reference point may be selected according to the processing target point. For example, when the points included in the work point sequence are ordered like a list structure, the processing is performed. Points before and after the target point may be selected as reference points. Next, the interpolation point calculation means calculates an interpolation point from the processing target point and the reference point. The interpolation point adding means adds the interpolation point calculated by the interpolation point calculating means to the working point sequence. When the points included in the working point sequence are ordered as in the list structure as described above, the ordering is modified so that the interpolation points are located between the interpolated points. It may be added to the point sequence for the work.

When approximating the shape as a curve, the processing target point selecting means selects points other than the interpolation points added by the interpolation point adding means from among the points included in the work point sequence. All points are sequentially selected as reference points, and the reference point selection, the interpolation point calculation, and the interpolation point addition are executed for each point. After that, when a predetermined condition is satisfied, the entire process is ended. The predetermined condition is, for example, when the time required for processing exceeds a predetermined time, or when the total number of points included in the work point sequence exceeds a predetermined number. . If a predetermined condition is not satisfied, and the processing point selection means selects all points as reference points, the reference point selection, the interpolation point calculation, and the interpolation point addition are performed for each point. When the execution of the above is finished, the above-mentioned processing is repeated as the selection target of the processing target point selecting means including the interpolation point newly added to the working point sequence.

By connecting the points included in the work point sequence thus obtained with line segments, a line segment group approximating a curve passing through the point sequence can be obtained. As described above, a curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved, without changing the data structure. A figure represented by a sequence of points can be transformed. Furthermore,
Since this approximation processing is repeated until a predetermined condition is satisfied, the curve can be approximated as accurately as possible within the limits of the processing amount and the memory amount.

A curve approximation program according to the present invention is a curve approximation program for causing a computer to execute the above-described curve approximation method.

It goes without saying that a computer-readable recording medium recording a curve approximation program for causing a computer to execute the above-described curve approximation method also belongs to the scope of the present invention.

[0033]

(First Embodiment) First Embodiment of the Present Invention
The embodiment will be described below with reference to FIGS. 1 to 5.

FIG. 1 is a flow chart for explaining the flow of processing of the first embodiment of the present invention. In the processing described here, it is assumed that the points included in the point sequence are managed by the array data structure and there is no space in the array.

First, the value of the counter variable i referred to in order to select the processing target point in the processing target point selection step is
The minimum value of the subscript of the array (here, 1) is substituted for initialization (step 101; hereinafter abbreviated as S101). The counter variable i is, for example, a register variable provided in a CPU (Central Processing Unit), a memory that is accessible from the CPU, or a memory that is accessible from the means that executes the process target point selection step. It may be stored by means.

Next, a point having the value of the counter variable i as a subscript is selected as a processing target point (processing target point selection step, S102).

Next, the reference point is selected with reference to the value of the counter variable i (reference point selection step, S103).

For example, when three points before and after the processing target point are selected as reference points, a point having a value of i-1 as a subscript (a point positioned before the processing target point) and i + 1 A point whose value is a subscript (a point next to the processing target point) and i
A point having a value of +2 as a subscript (a point located next to the point to be processed) is selected as a reference point. Detailed specific examples will be described later.

The number of reference points is not limited to this. The more reference points are selected, the higher the accuracy of approximation by the interpolation points calculated in the subsequent processing becomes, but the processing amount increases.

Next, the processing target point selected in S102 and S1
An interpolation point is calculated from the reference point selected in 03 (interpolation point calculation step, S104). A specific calculation method will be described later.

Next, the value of the counter variable i is incremented by 1 (S105).

Next, it is determined whether or not the value of the counter variable i is larger than the value obtained by subtracting 1 from the number of points included in the point sequence (= the maximum value of the subscript of the array-1). S106).
Here, 1 is subtracted because it is not necessary to calculate the interpolation point with the last point of the point sequence as the processing target point. When the value of the counter variable i is larger than the number of points included in the point sequence, the processing is ended. If the value of the counter variable i is less than or equal to the number of points included in the point sequence, S102
Return processing to.

Through the above processing, the interpolation points can be calculated with all the points included in the point sequence as the processing target points.

It is also possible to use a list structure instead of an array as a data structure for managing the points included in the point sequence. In this case, the counter variable i is a pointer variable for pointing the referenced element in the list, the processing of S101 is initialized by setting the value of the counter variable i to the pointer to the first element of the list, and the processing of S105 is performed by the counter. The pointer to the element next to the element pointed by the variable i is assigned to the counter variable i, and the processing of S106 determines whether the element pointed by the pointer variable i has reached the last element in the list. As described above, by replacing the respective processes, the interpolation points can be calculated with all the points included in the point sequence as the processing target points by the same algorithm.

FIG. 2 is a diagram showing a specific example of a point sequence managed by the array data structure. It is assumed that these point sequences represent one open curve. An x-coordinate value and a y-coordinate value are stored in association with each subscript value. Here, an example in which the point sequence is composed of 7 points is shown, but the number of points is not limited to this.

In this example, the coordinate values of the two-dimensional points are managed as an array, but in the case of the three-dimensional points, the z coordinate value may be stored in association with the subscript value. Further, when the point coordinate values are stored and stored in a separately defined structure or object instance, the pointer to the structure or instance is associated with the value of the subscript. It may be stored in memory.

An example of the sequence of points in FIG. 2 is shown in FIG. Points 201 to 207 have subscripts 1 to 7 in FIG. 2, respectively.
It corresponds to the point. Further, it is assumed that the solid line 200 is a curve that the points 201 to 207 are about to represent.

Hereinafter, with reference to the example of the point sequences in FIGS. 2 and 3, the flowchart shown in FIG.
An example of a specific process of to S104 will be described.

For example, when the value of the counter variable i is 2,
By the process of S102, the point 203 having the subscript 2 is selected as the processing target point. Further, by the processing of S103, points 201, 203, and 204 having subscripts 1, 3, and 4 are selected as reference points.

The coordinates of the processing target point are (X # i, Y # i), and the coordinates of the reference point are (X # (i-1), Y # (i-1)), (X # (i + 1), Y # (i +
1)), (X # (i + 2), Y # (i + 2)), the coordinates (X,
Y) is calculated, for example, by the following equation. X = (k1 x (X # i + X # (i + 1)) + k2 x (X # (i-1) + X # (i + 2))) /
k3 Y = (k1 x (Y # i + Y # (i + 1)) + k2 x (Y # (i-1) + Y # (i + 2))) /
k3 Here, k1, k2, and k3 are predetermined coefficients, for example, k1 = 9, k2 = -1, and k3 = 16. In the case of the above formula, k1 x 2 + k
It is desirable to satisfy the relationship of 2 × 2 = k3.

As described above, the interpolation point obtained by weighted averaging the coordinates of the processing target point and the reference point is the processing target point (in the above example, the point to be processed for curve approximation). 202) and the reference point (point 203 in the above example) located next to the processing target point.

If the above calculation method is applied to the entire point sequence as it is, reference points cannot be obtained near the ends of the point sequence such as the points 201 and 206 to be processed. In such a case, both ends of the point sequence may be virtually provided with a plurality of points having the same coordinates as the ends. That is, when the processing target point is the point 201, since there is no point located before the processing target point, the point 201 is used as a reference point,
Points 201, 202 and 203 are used as reference points. Similarly, when the processing target point is the point 206, there is no point located next to the processing target point, so that the points 205, 206, and 2 are used as the reference points.
Let 06 be the reference point (treat point 206 as two reference points).

An example of the coordinates of the interpolation point calculated as described above is shown in FIG. Further, the point sequence shown in FIG. 3 and the interpolation points 211 to 216 in FIG. 4 are also shown in FIG. A solid line 221 is a line segment sequence connecting the original point sequences 201 to 207, and a chain line 222 is an original dot sequence 201 to 207 and interpolation points 211 to 216.
It is a line segment connecting and. Comparing the solid line 221 and the one-dot chain line 222, the one-dot chain line 221 has a shape closer to the solid line 222 in FIG.

The above-mentioned processing, especially the processing near both ends of the point sequence, is the flow of processing when the point sequence represents an open curve. On the other hand, when the point sequence represents a closed curve, if the reference points cannot be obtained in S103 because they are near both ends of the point sequence, the other end point may be selected as the reference point. For example, assuming that the point sequence in the above example represents a closed curve, if the processing target point is the point 201, the points 207, 20
2, 203 are used as reference points, and similarly, when the processing target point is the point 206, the points 205, 206, 201 may be used as the reference points.

Furthermore, in the case of a closed curve, the value to be compared with the counter variable i in the processing of S106 is not the value obtained by subtracting 1 from the number of points included in the point sequence, but the point included in the point sequence. If the number is, it is possible to calculate an interpolation point located between the points at both ends of the point sequence. (Second Embodiment) Regarding the second embodiment of the present invention,
The following is a description with reference to FIGS. 6 to 10. In the first embodiment, the example in which the calculation of the interpolation point is performed once for each processing target point is shown, but the number of points included in the original point sequence is small for the shape to be expressed. In some cases, the approximation accuracy may not be sufficient. In the second embodiment, a method will be described in which the calculation of the interpolation point is repeated using the calculated interpolation point as a processing target point to further improve the approximation accuracy.

FIG. 6 is a flow chart for explaining the processing flow of the second embodiment of the present invention. In the process described here as well, as in the case described with reference to FIG. 1, it is assumed that the points included in the point sequence are managed by the array data structure and there is no vacancy in the array.

First, the data of the points included in the point sequence is copied to the work point sequence (work point sequence preparation step, S111). The working point sequence may be managed by, for example, an array data structure, and may be stored in a storage unit accessible from a unit that executes the process target point selection step, such as a memory accessible from the CPU.

The processing of S101 to S106 is the same as that of FIG. 1 except that the working point sequence is targeted, and therefore detailed description thereof is omitted.

When it is determined in S106 that the value of the counter variable i is larger than the number of points included in the point sequence, it is determined whether or not a predetermined ending condition is satisfied (S112). If the predetermined termination condition is satisfied, the processing is terminated. If the predetermined termination condition is not satisfied, the process proceeds to S113.

The end condition is, for example, when the time elapsed from the start of the process shown in this flowchart exceeds a predetermined time, the total number of points included in the work point sequence, and S104. For example, the total number of interpolation points calculated by the processing exceeds a predetermined number. According to the former condition, the processing shown in this flowchart can be guaranteed to be completed within a certain period of time, which is suitable for a dialogue system or a real-time system. According to the latter condition,
As a result of generating the interpolation points, if the amount of memory prepared as the work point sequence exceeds the amount of memory, the process is terminated, so it is suitable when the amount of available memory is limited.

If the predetermined processing condition is not satisfied in S112, the interpolation point calculated in S104 is added to the working point sequence (interpolation point adding step, S113).

At this time, each interpolation point is added to the position where the interpolation point should be located between the points included in the working point sequence. A specific example will be described later.

After the processing of S113, the processing is returned to S101.

Through the above processing, the generated interpolation points can be repeatedly calculated as the processing target points until the predetermined condition is satisfied.

If the same interpolation point calculation method as that described in the first embodiment is used for the example of the point sequence shown in FIG. 2, the work after the processing of S101 to S113 is performed once. The state of the point sequence is as shown in FIG. That is, this is a state in which the interpolation points shown in FIG. 4 are added to the point sequence shown in FIG. 2 at the position next to the processing target point, which is the position where each interpolation point should be located. Points with even subscripts in FIG. 7 are interpolation points added in S113.

Further, with respect to the work point sequence in FIG. 7, S101
The state of the work point sequence after the processes of to S113 are as shown in FIG. Similar to FIG. 7, points with even subscripts are interpolation points added in S113.

FIG. 9 shows a part of the interpolation points generated by repeating the above process. A solid line 221 is a line segment sequence that connects the original dot sequences, and a one-dot chain line 222 is a line segment sequence that connects the work point sequences after performing the processing of S101 to S113 once, and the two-dot chain line 22.
3 is a line segment sequence connecting the work point sequences after performing the processing of S101 to S113 twice, and dotted line 224 is a line segment sequence connecting the work point sequences after performing the processing of S101 to S113 three times. ,. In addition, FIG.
FIG. 10 is a diagram showing a part of the range shown in FIG. 9 in a further enlarged manner.

As described above, since an interpolation point is newly added each time the processing of S101 to S113 is repeated, it is possible to accurately approximate the shape represented by the original point sequence. (Third Embodiment) Regarding the third embodiment of the present invention,
The following is a description with reference to FIGS. 11 and 12. In the second embodiment, the method of increasing the approximation accuracy by repeatedly calculating the interpolation points has been described. However, in the case of a too fine shape or a shape close to a straight line, unnecessary interpolation points may be calculated. . In the third embodiment, a method of improving processing efficiency by omitting calculation of unnecessary interpolation points will be described.

FIG. 11 is a flow chart for explaining the flow of processing of the third embodiment of the present invention.

The processing of S101 to S106 and S111 to S113 is the same as that described with reference to FIGS.

After the processing of S103, it is determined whether or not the calculation of interpolation points is necessary (S121). If it is determined that the interpolation points need to be calculated, the process proceeds to S104. If it is determined that the calculation of the interpolation points is unnecessary, the process proceeds to S105.

In the processing of S121, for example, the distance between the processing target point selected in S102 and each of the reference points selected in S103 is calculated (distance calculation step), and the longest one of the distances is predetermined. If it is shorter than the distance, it is judged that the calculation of the interpolation point is unnecessary (interpolation point necessity judgment step).

In a display device used in a general computer or the like, a graphic is quantized and displayed in pixel units like a bit map display. Therefore, even if the shape is approximated to a precision finer than the pixel, it is not enough. has no meaning.
Therefore, when the distance between the processing target point and the reference point is small as described above, unnecessary processing can be omitted by not calculating the interpolation point.

Alternatively, in the processing of S121, for example, the vector connecting the processing target point selected in S102 and the reference point located immediately before the processing target point among the reference points selected in S103, and the processing target An angle formed by a vector connecting the point and the reference point located immediately after the processing target point among the reference points is calculated (angle calculation step), and the difference between the angle and 180 degrees is calculated from a predetermined angle. Is smaller, it is determined that the calculation of the interpolation point is unnecessary (interpolation point necessity determination step).

The angle calculated as described above is 180
If it is close to the degree, the processing target point and the reference point are on a substantially straight line, and therefore calculation of the interpolation point is meaningless, and unnecessary processing can be omitted.

It goes without saying that the above-described processing examples in S121 may be combined.

FIG. 12 is a diagram showing an example of a work point sequence after performing the processing of S101 to S113 three times. However, point 301
˜314 represent the interpolation points whose calculation is omitted by the processing of S121. Note that these points 301 to 314 are drawn at the positions where they are calculated without omission. As shown in this figure, calculation of a new interpolation point is omitted in a portion where the shape approximated by the interpolation point calculated in the process of repeating the original point sequence and S101 to S113 is close to a straight line. I understand. (Fourth Embodiment) Regarding the fourth embodiment of the present invention,
The following is a description with reference to FIGS. 13 to 15. In the first to third embodiments, the case where the shape represented by the original point sequence is a curve has been described, but in the case of a shape including a part of the bend, the above processing cannot approximate the shape. In the fourth embodiment, a method of approximating a shape including a bend by referring to information indicating whether the points included in the point sequence are corner points or curved points will be described.

FIG. 13 is a flow chart for explaining the flow of processing in the fourth embodiment of the present invention.

The processing of S101 to S106 and S111 to S113 is the same as that described with reference to FIGS.

After the processing of S103, it is determined whether any of the processing target point selected in S102 or the reference point selected in S103 is a corner point (S131).
If it is determined to be a corner point, the process proceeds to S104.
If it is determined that it is not a corner point, the process proceeds to S105.

FIG. 14 shows an example of the point sequence shown in FIG.
The example of the data which added the information showing whether it is a corner point is shown. Corresponding to the value of the subscript corresponding to each point, a value of 1 is stored if it is a corner point, and a value of 0 is stored if it is not a corner point.

The example of the point sequence shown in FIG. 14 is illustrated in FIG. The points 201 to 207 are the subscripts in FIG.
It corresponds to points 1 to 7. The solid line 230 indicates points 201 to 20.
Suppose 7 is the shape that we are trying to represent. It should be noted that the points 202 to 204 are connected by a straight line segment as compared with the example shown in FIG.

In the interpolation point calculation method described in the first embodiment, the position of the calculated interpolation point is a point located between the processing target point and the reference point located next to the processing target point.
Therefore, if either the processing target point or the reference point located next to the processing target point is a corner point, these points are connected by a straight line segment, so if the interpolation points are not calculated, Good.

That is, when the interpolation point calculation method described in the first embodiment is used, in the processing of S131, S1
It may be determined whether either the processing target point selected in 02 or the reference point located next to the processing target point among the reference points selected in S103 is a corner point.

FIG. 16 is a diagram showing an example of a work point sequence after performing the processing of S101 to S113 three times. Point 202 and point 203
The point to be processed is point 202 between points, and the point located next to the point to be processed is point 203, and the point to be processed is point 203 between point 203 and point 204. Not calculated. In this way, the interpolation points are not calculated before and after the corner point, and the original point sequence can be approximated by a shape connected by a straight line segment.

The curve approximating method described above is realized by a program for executing the curve approximating method. This program is stored in a computer-readable recording medium. In the present invention, a ROM (Read Only Memo) that is built in or connected to a general computer is used as the recording medium because the process is performed by a general computer.
A memory such as ry) may be a program medium, or a program reading device provided as an external storage device and readable by inserting a recording medium therein.

In any case, the stored program may be configured to be accessed and executed by a microprocessor, or in any case, the program is read and the read program is a general program. RAM (Random Access Memo) configured in the computer
The program may be downloaded to a program storage area such as ry) and the program is executed.
It is assumed that this download program is stored in the main body device in advance.

Here, the program medium is a recording medium which can be separated from the main body, and is a tape system such as a magnetic tape or a cassette tape, a magnetic disk such as a flexible disk or a hard disk, or a CD-ROM / MO / MD / Disc system of optical disc such as DVD, card system such as IC card (including memory card) / optical card, mask ROM, EP
It may be a medium that fixedly carries the program, including a semiconductor memory such as a ROM, an EEPROM, and a flash ROM.

Further, in the present invention, since the system configuration is such that it can be connected to a communication network including the Internet, it is possible to use a medium for carrying the program fluidly so as to download the program from the communication network. When the program is downloaded from the communication network in this way, the download program may be stored in the main body device in advance, or may be installed from another recording medium.

The content stored in the recording medium is not limited to the program and may be data.

The curve approximating method described in the first to fourth embodiments can be implemented by using a general computer as shown in FIG. In FIG. 17, reference numeral 201 denotes a CPU (Central Processing Unit) for performing calculation processing, 20
Reference numeral 2 is a memory in which data to be processed by the CPU 201 is stored, 203 is an external storage device such as a hard disk or CD-ROM that stores data, and 204 is a mouse for a user to input data by operating it. And an input device such as a keyboard, 205 is a display device that displays according to the data processed by the CPU 201, 206 is a clock generator that generates a clock for the CPU 201 and the memory 202 to take operation timing, and 207 is the CPU 201. , A memory 202, an external storage device 203, an input device 204, a display device 205, a clock generator 206, and the like.

FIG. 18 is a block diagram for explaining the structure of the curve approximating apparatus of the present invention. In FIG. 18, 301 is a point sequence storage unit that stores a point sequence representing a shape, and 302 is a processing target point that selects an arbitrary point among the points stored in the point sequence storage unit 301 as a processing target point. A selection unit, 303 is a reference point selection unit for selecting one or a plurality of points from the points stored in the point sequence storage unit 301 as a reference point, and 304 is a process selected by the processing target point selection unit 302. Interpolation point calculation means for calculating interpolation points for curve approximation from the target points and the reference points selected by the reference point selection means 303. The point sequence storage means 301 includes the memory 202 and the external storage device 2.
It may be configured to any one or both of 03. Further, the processing point selection means 302, the reference point selection means 303, and the interpolation point calculation means 304 may be configured as a CPU 201 that operates according to a program stored in the memory 202.

FIG. 18 mainly shows the configuration corresponding to the first embodiment, but in the second embodiment, the working point sequence preparing means for copying the point sequence into the working point sequence and the interpolating points for working are further provided. A means for adding to the point sequence is provided. In addition, the third embodiment
Then, it further comprises a distance calculation means for calculating a distance between the processing target point and the reference point, and an interpolation point necessity judgment means for judging whether the calculation of the interpolation point is necessary or unnecessary by referring to the distance. Further, it is provided with an angle calculation means for calculating an angle formed by a vector composed of the processing target point and the reference point. Further, the fourth embodiment further includes an corner point determination means for determining whether any one of the processing target point and the reference point is a corner point.

[0094]

As described above, the curve approximation method according to the present invention is a method of approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence, A processing target point selecting step of selecting any included point as a processing target point, a reference point selecting step of selecting one or more points included in the point sequence as a reference point, the processing target point and the reference And an interpolation point calculating step of calculating an interpolation point for curve approximation from the points.

Therefore, the curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved without changing the data structure. An effect that the figure represented by the dot sequence can be deformed is obtained.

As described above, the curve approximating method according to the present invention transforms a shape represented by a point sequence consisting of a plurality of points into
In a method of approximating as a curve passing through the point sequence, a working point sequence preparing step of duplicating the point sequence into a working point sequence, and selecting an arbitrary point included in the working point sequence as a processing target point A processing target point selecting step, a reference point selecting step of selecting one or a plurality of points included in the working point sequence as a reference point, and a curve approximation from the processing target point and the reference point An interpolation point calculation step of calculating an interpolation point, and an interpolation point addition step of adding the interpolation point calculated in the interpolation point calculation step to the working point sequence, the reference point selection step and the interpolation point calculation. It is characterized in that the step and the interpolation point adding step are repeated until a predetermined condition is satisfied.

Therefore, the curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved without changing the data structure. An effect that the figure represented by the dot sequence can be deformed is obtained. Further, since this approximation processing is repeated until a predetermined condition is satisfied, there is an effect that the curve can be approximated as accurately as possible within the limits of the processing amount and the memory amount.

As described above, in the curve approximation method according to the present invention, in addition to the above configuration, the distance calculation step for calculating the distance between the processing target point and the reference point and the distance calculation step are performed. And an interpolating point necessity determining step for determining whether or not the interpolating point should be calculated with reference to the calculated distance, and the interpolating point calculating step determines that the interpolating point needs to be calculated in the interpolating point necessity determining step. It is characterized in that an interpolation point is calculated when it is performed.

Therefore, it is possible to prevent unnecessary interpolation points from being calculated, and it is possible to reduce the processing amount and memory amount required to approximate the curve.

As described above, in the curve approximation method according to the present invention, in addition to the above configuration, an angle calculation step of calculating an angle formed by a vector composed of the processing target point and the reference point, and the angle An interpolation point necessity judgment step for judging necessity / unnecessity of calculation of an interpolation point with reference to the angle calculated in the calculation step, wherein the interpolation point calculation step is performed in the interpolation point necessity judgment step. The feature is that an interpolation point is calculated when it is determined that calculation is required.

Therefore, it is possible to prevent unnecessary interpolation points from being calculated, and it is possible to reduce the processing amount and memory amount required to approximate the curve.

As described above, in the curve approximation method according to the present invention, in addition to the above-mentioned configuration, whether the points included in the point sequence are corner points connecting two line segments,
An angle point determination step for determining whether or not any one of the processing target point or the reference point is an angle point, which also has information indicating whether it is a point on a curve The interpolating point calculating step is characterized in that the interpolating point calculating step calculates the interpolating point when it is judged in the corner point judging step that any one of the processing target point or the reference point is not a corner point. .

Therefore, even when a part of the shape includes a bending point, the above-mentioned interpolation point is not calculated for the corner point representing the bending point. The front and back points have the same shape as the shape represented by the original point sequence, and without the curve fitting process,
It is possible to approximate a complicated figure.

The curve approximating apparatus of the present invention, as described above,
In a device for approximating a shape represented by a point sequence composed of a plurality of points as a curve passing through the point sequence, a point sequence storage means for storing the points included in the point sequence, and the point sequence storage means. One or a plurality of points is selected as a reference point from the processing target point selecting means for selecting an arbitrary point as a processing target point from the points stored in and the points stored in the point sequence storage means. It is characterized in that it has a reference point selecting means and an interpolation point calculating means for calculating an interpolation point for curve approximation from the processing target point and the reference point.

Therefore, the curve passing through the point sequence can be approximated by a simple process, and only a part of the points included in the point sequence can be moved without changing the data structure. An effect that the figure represented by the dot sequence can be deformed is obtained.

A curve approximation program according to the present invention is a curve approximation program for causing a computer to execute the above-described curve approximation method.

Therefore, there is an effect that a general computer can realize the above-described curve approximation method.

[Brief description of drawings]

FIG. 1 is a flowchart for explaining a flow of processing according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a specific example of a point sequence managed by an array data structure.

FIG. 3 is a diagram illustrating an example of the point sequence in FIG.

FIG. 4 is an example of coordinates of interpolation points.

5 is a diagram showing the point sequence shown in FIG. 3 and the interpolation points shown in FIG. 4 together.

FIG. 6 is a flowchart illustrating a processing flow of the second embodiment of the present invention.

FIG. 7 is a diagram showing a state of a work point sequence after performing the processing of S101 to S113 once.

8 is a diagram showing a state of a work point sequence after performing the processing of S101 to S113 on the work point sequence of FIG.

FIG. 9 is a diagram illustrating a part of the interpolation points generated by repeating the interpolation point generation processing.

FIG. 10 is a diagram further enlarging a part of the range shown in FIG.

FIG. 11 is a flowchart for explaining a processing flow according to the third embodiment of the present invention.

FIG. 12 is a diagram showing an example of a work point sequence after performing the processing of S101 to S113 three times.

FIG. 13 is a flowchart illustrating a processing flow according to a fourth embodiment of the present invention.

FIG. 14 shows an example of data to which information indicating whether it is a corner point is added.

FIG. 15 is a diagram illustrating an example of the point sequence in FIG.

FIG. 16 is a diagram showing an example of a work point sequence after performing the processing of S101 to S113 three times.

FIG. 17 is a block diagram showing the configuration of a general computer used in the curve approximation method of the present invention.

FIG. 18 is a block diagram for explaining the configuration of a curve approximating apparatus of the present invention.

FIG. 19 is a diagram for explaining an example of a conventional curve approximation method.

FIG. 20 is a diagram for explaining an example of a conventional curve approximation method.

[Explanation of symbols]

S102 Process target point selection step S103 Reference point selection step S104 Interpolation point calculation step S111 Work point sequence preparation step S113 Interpolation point addition step S121 Distance calculation step S122 Interpolation point necessity determination step

Claims (8)

[Claims] 1. A method of approximating a shape represented by a point sequence composed of a plurality of points as a curve passing through the point sequence, wherein a processing target for selecting an arbitrary point included in the point sequence as a processing target point A point selecting step, a reference point selecting step for selecting one or a plurality of points included in the point sequence as reference points, and an interpolation for calculating an interpolation point for curve approximation from the processing target point and the reference point. A curve approximation method comprising: a point calculation step. 2. A method for approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence, a work point sequence preparing step of copying the point sequence into a work point sequence. A processing target point selecting step of selecting an arbitrary point included in the working point sequence as a processing target point, and a reference point selecting one or a plurality of points included in the working point sequence as a reference point A selection step, an interpolation point calculation step of calculating an interpolation point for curve approximation from the processing target point and the reference point, and an interpolation point calculated in the interpolation point calculation step is added to the working point sequence. And a step of adding the interpolation point, wherein the step of selecting the reference point, the step of calculating the interpolation point, and the step of adding the interpolation point are repeated until a predetermined condition is satisfied. 3. A distance calculation step for calculating a distance between the processing target point and the reference point, and an interpolation point for judging necessity / non-necessity of calculation of an interpolation point by referring to the distance calculated in the distance calculation step. 3. The method according to claim 1, further comprising: a necessity determination step, wherein the interpolation point calculation step calculates the interpolation point when it is determined in the interpolation point necessity determination step that the interpolation point needs to be calculated. The curve approximation method described in 2. 4. An angle calculation step of calculating an angle formed by a vector composed of the processing target point and the reference point, and necessity / non-necessity of calculation of an interpolation point by referring to the angle calculated in the angle calculation step. And a step of determining whether or not an interpolation point is required, wherein the interpolation point calculation step calculates an interpolation point when it is determined in the interpolation point necessity determination step that an interpolation point needs to be calculated. The curve approximation method according to claim 1 or 2. 5. The points included in the point sequence also have information indicating whether they are corner points connecting two line segments or points on a curve. A corner point determining step of determining whether any one of the processing target point or the reference point is a corner point, and the interpolation point calculation step is performed by the corner point determining step. Characterized in that an interpolation point is calculated when it is determined that one of the points or the reference points is not a corner point,
The curve approximation method according to claim 1. 6. An apparatus for approximating a shape represented by a point sequence composed of a plurality of points as a curve passing through the point sequence, and point sequence storage means for storing the points included in the point sequence, One or a plurality of points are selected from the processing target point selection means for selecting an arbitrary point as a processing target point from the points stored in the point sequence storage means, and the points stored in the point sequence storage means. A curve approximating device comprising: a reference point selecting means for selecting as a reference point; and an interpolation point calculating means for calculating an interpolation point for curve approximation from the processing target point and the reference point. . 7. An apparatus for approximating a shape represented by a point sequence consisting of a plurality of points as a curve passing through the point sequence, and a point sequence storage means for storing the points included in the point sequence, Work point sequence preparation means for copying the point sequence stored in the point sequence storage means to a work point sequence, and a processing target point for selecting any point included in the work point sequence as a processing target point Selecting means, reference point selecting means for selecting one or a plurality of points included in the working point sequence as reference points, and calculating interpolation points for curve approximation from the processing target points and the reference points Interpolation point calculating means and interpolation point adding means for adding the interpolation points calculated by the interpolation point calculating means to the working point sequence, and the reference point selecting means, the interpolation point calculating means, and the interpolation point. Repeat the additional means until the prescribed conditions are met. And a curve approximation device. 8. A curve approximation program for causing a computer to execute the curve approximation method according to any one of claims 1 to 5.