JP2980769B2 - Position data approximation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a position data approximation method for approximating position data of a point sequence using a function.

[0002]

2. Description of the Related Art In general, the shapes of characters, figures, etc. are read by an image scanner, and these are taken into a computer or the like as image data, reproduced by an output device such as a CRT or a printer, or recorded on a storage medium such as an FD. To do that is done actively.

In this case, an outline font is called,
2. Description of the Related Art Position data of only a contour portion of a character, a graphic, or the like is read, and a portion surrounded by the contour portion is reproduced as a character, a graphic, or the like.

In the graphic processing using such an outline font, the outline of a character, a graphic, or the like is regarded as a dot sequence and read or reproduced. However, today, the position data of the original graphic is used as it is. Not
Approximate position data obtained by approximating this using an arbitrary function is used. This is because the position data of the original figure generally requires a large capacity when stored in a memory because of a large change, and a long time is required for various data processing and a long time is required for reproduction. By approximating this using, for example, an arbitrary cubic function, the position data can be compressed, the storage capacity can be reduced, various data processing can be speeded up, and the reproduction time can be shortened. Can be reproduced.

In the conventional position data approximation method,
As shown in FIG. 6, the points of the contour of the original figure are equally divided for each desired number of points to form an approximate section, and the position of each of the divided sections is determined using an arbitrary function. The data was approximated.

[0006]

However, in the above-described conventional method of approximating position data, when determining a section to be approximated by using a function, the points of the contour of the original figure are determined for each desired number of points. Because it was performed by dividing equally, straight sections and curved sections are mixed in the section,
When the approximated position data is reproduced, there is an inconvenience that the joining condition at the connection point of the adjacent section is not theoretically smooth, and the reproduction quality of the position data is extremely inferior to the original figure.

[0007] The present invention has been made in view of these points, and overcomes the above-mentioned problems in the conventional art.
Smoothly joins approximate position data of adjacent sections and efficiently approximates the original figure position data.
And to provide an approximate method of location data that can be directed above.

[0008]

According to a first aspect of the present invention, there is provided a method for approximating position data, comprising dividing a position data of a point sequence into approximation sections and performing approximation using a function. in the approximate method of position data to be, after dividing the positional data of the point array shape as two approximation interval of the linear approximation interval and the curve approximation interval based on the value of the put that cosine in each point of the position data, the curve The approximation section is further divided into a straight approximation section and a curve approximation section based on the curvature value at each point in the curve approximation section, and is divided into two approximation sections of a straight approximation section and a curve approximation section as a whole. It is characterized by approximation. Further, the approximation method of the position data of the present invention according to claim 2, second position data linear approximation interval and the curve approximation interval of the point array shape on the basis of the value of cosine that put on each point of the position data one when classified as an approximation interval, among the points value of put that cosine in each point of the position data is less than or equal to a preset value, the column-shaped consecutive points less than the number of the first parameter value set in advance The position data as a straight line section, a curve section other than the straight line section is used, and the inside of the curve approximation section is further divided into a straight line approximation section and a curve approximation section based on the curvature value at each point in the curve approximation section. At the time of classification, among the points where the value of the curvature at each point of the position data is equal to or less than a preset value, the position data in the form of a point sequence continuous with the number of second parameter values set in advance is defined as a straight line section. And It is characterized in that the other than the straight section and a curved section.

[0009]

According to the position data approximation method of the present invention having the above-described configuration, when an approximate section is divided, a linear approximation section and a curve approximation section are formed using the cosine value of each point of the contour with respect to the position data. The curve approximation section is further divided into a linear approximation section and a curve approximation section based on the curvature value at each point in the curve approximation section. The approximate position data approximated based on the section and the curve approximate section are extremely smoothly joined, and the accuracy of the approximate position data reproduced with respect to the original figure position data can be efficiently set to the desired content. . Furthermore, when separating the sections, when dividing the positional data of the point array shape as two approximation interval of the linear approximation interval and the curve approximation interval based on the value of the put that cosine in each point of said position data, among the points which the value of put that cosine in each point of the position data is less than or equal to a preset value, the position data of the column-shaped consecutive points less than the number of the first parameter value set in advance with a straight section, When the section other than the straight section is defined as a curved section, and the inside of the curved approximate section is further divided into a linear approximate section and a curved approximate section based on the curvature value at each point in the curved approximate section, the position data Among the points where the value of the curvature at each point is equal to or less than a preset value, position data of a point sequence shape that is continuous to the number of the preset second parameter values or more is defined as a straight section, and a curve other than the straight section is defined as a curve. Since the approximate position data approximated based on this is more smoothly joined, the accuracy of the approximate position data reproduced with respect to the position data of the original figure is adjusted to the desired content. can do.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below with reference to FIGS.

FIGS. 1 and 2 show a continuous flow chart showing a method for approximating position data according to the present invention, and FIG. 3 shows a case where a contour point is divided by the method for approximating position data according to the present invention. FIG.

[0012] As shown in FIG. 1, the approximation of the position data is started, in step ST10, computes the value of the cosine that put on each point of the contour <br/>.

Next, in step ST11, the value of the cosine is equal to or less than a preset value, and in this embodiment, -0.9.
Look for points below 9. This point is the starting point of the straight line.

Next, in step ST12, it is determined whether or not the value of the cosine of the point following the start point of the straight line (end point of the straight line) is equal to or less than -0.99, and if the determination in step ST12 is YES, the process proceeds to step ST12. Proceeding to ST13, the end point of the straight line is extended (the next point after the start point of the straight line), and the process returns to step ST12. The end point of the straight line is sequentially extended and repeated until the determination in step ST12 becomes NO. The step ST
12 the determination is NO and proceeds to Step ST1 4.

[0015] The value of the cosine Te this step ST1 4 smell -
Among the points 0.99 or less, it is determined whether or not there is a continuous number of first parameter values or more, in this embodiment, 33 or more points. If the determination in step 14 is YES, the step The process proceeds to ST15a, and is extracted as the first straight line section, and then proceeds to the next step ST16. If the determination in step ST14 is NO (continuation of the cosine value of -0.99 or less is 32 points or less), step ST15b
To make a curved section, and then to the next step ST16.

Next, in step ST16, it is determined whether or not the determination has been completed for all points of the contour.
If the determination in step ST16 is NO, step ST16
Returning to step 11, the process is repeated until the determination in step ST16 becomes YES. If the determination of step ST16 is YES, and proceeds to the next step ST17, the beauty cosine value Oyo remaining section (the curved section except the first straight section is not -0.99 or less sections ) Are extracted as the first curved section, each point of the contour is divided into the first straight section and the first curved section, and the process proceeds to the next step ST18.

Next, in step ST18, it is determined whether or not it is the first straight section. If YES, the symbol A in FIG. 1 is connected to the portion indicated by the same symbol A in FIG. 2, and the process proceeds to step ST27. . If the determination in step ST18 is NO (first curve section), the symbol B in FIG. 1 is connected to the portion indicated by the same symbol B in FIG.
Proceed to.

Next, as shown in FIG.
At 19, the value of the curvature at each point of the first curve section is calculated.

Next, in step ST20, the value of the curvature is equal to or less than a preset value, and in this embodiment, ± 0.0
Find points within 5 This point is the starting point of the straight line to be extracted included in the first curved section.

Next, in step ST21, it is determined whether or not the value of the curvature at the point next to the start point of the straight line (end point of the straight line) is within ± 0.05. If the determination in step ST21 is YES, the process proceeds to step ST21. Proceeding to ST22, the end point of the straight line is extended (the next point next to the start point of the straight line), the process returns to step ST21, and the end point of the straight line is sequentially extended and repeated until the determination in step ST21 becomes NO. The step ST
If the determination at 21 is NO, the process proceeds to step 23.

Next, at step 23, the value of the curvature is ±
Of the points within 0.05 , set the second parameter
Data values, more than 33 points in this embodiment
Or organic Rukado determines Te, If the determination in step 23 is YES, it proceeds to step ST24a extracted as a second straight section, and then proceeds to next step ST25. Also,
If the determination in step ST23 is NO (continuation of the curvature value within ± 0.05 is 32 points or less), step ST23 is executed.
The process proceeds to 24b to form a curved section, and proceeds to the next step ST25.

Next, in step ST25, it is determined whether or not the determination has been completed for all points in the first curve section. If the determination in step ST25 is NO,
Returning to step ST20, the determination in step ST25 is YES
Repeat until. If the determination in step ST25 is YES, the process proceeds to next step ST26,
All the sections other than the second straight section (the curved section and the section whose curvature exceeds ± 0.05) are extracted as the second curved section, and all the points in the first curved section are extracted as the second curved section. It divides into a straight section and a second curved section, and proceeds to the next step ST27.

Next, in step ST27, the attribute of the start point of each of the straight section defined by the first straight section and the second straight section and the curved section defined by the second curved section is determined and terminated.

[0024] That is, in this embodiment, the value of the cosine of the points of the contour is the starting point of the straight line the points -0.99 or less in the step ST11, the value of the starting point or et cosine of the straight line -
When 33 or less points of 0.99 or less are continuous (first parameter value), it is extracted as a first straight section, and the remaining section is extracted as a first curve section. And step ST
At 20, the points in the first curved section are defined as having a curvature value of ±
A point within 0.05 is defined as a start point of the second straight line, and when a point having a curvature value of ± 0.05 or more from the start point of this straight line continues for 33 or more points (second parameter value), the second straight line section is defined. Then, the remaining section is extracted as the second curve section.

In this embodiment, the case where the cosine value of -0.99 or less continues for 33 points or more, and the case where the value of. ± .0.05
The case where the value of the curvature within the range of 33 or more is continuous is defined as a straight section, but the value of the cosine, the value of the curvature, and the number of the continuous points may be determined by the design concept, and in particular, the present invention is limited to the present embodiment. Not something.

As described above, after the contour points are divided into a straight section defined by the first straight section and the second straight section and a curved section defined by the second curved section, predetermined points are defined for each section in the same manner as in the prior art. Approximate position data is obtained by approximation using the following function.

Next, shown in detail the method for calculating the cosine values that put on each point of the contour.

In general, the shape of the binary data can be held by a closed loop of one or a plurality of aligned point sequences. The sequence of points P1, P2,..., Pn on the contour are coordinates (X1, Y1), (X2, Y2), (Xn, Yn), respectively.
, A certain point Pi (Xi, Yi)
(N = 1,2, ..., n ) value of the cosine that put the point of the two points determined by any number k for example a positive integer such Pi-k (Xi-k, Y
ik), Pi + k (Xi + k, Yi + k) to seek, these three points Pi, Pi-k, 2 two vectors formed by Pi + k <br/> preparative Le Pi Pi-k, It can be obtained from the following equation 1 using Pi Pi + k.

[0029] The value of the arbitrary number k may be determined according to the design concept, and is not particularly limited to the present embodiment.

Further, a method of calculating the value of the curvature in the first curve section will be described in detail.

In general, the curvature R at a point (x, y) on a curve represented by y = f (x) can be obtained from the following equation (2).

[0032] However, since the point sequence takes a discrete direction at every 45 degrees, a good result cannot be obtained by approximating the differential value of Equation 2 using only the left and right adjacent points. Therefore, using the concept of averaging, it is decided to consider the average of k neighboring point sequences. Now, a differential value is calculated as follows when considering the average of k pieces adjacent to the left and right of the point (xi, yi) for which the curvature is to be obtained.

[0033] As a result of various studies, the present inventor has found that it is desirable to use at least three parameters of a curvature value , a cosine value, and a Hessian distance in section division using curvature. For example, as shown in FIG. 3, the curvature at each point of the curved section is shifted 16 points to the left and right from the target point for which the curvature is determined.
The curvature is calculated from the dot (point) and three ranges of 16 dots across the target point, and the value of the curvature is ± 0.0 as described above.
Detect a point indicating within 5 and if it is 512 mesh,
The section length is 32 dots or more, and the cosine value of each point is -0.9
When the Hessian distance is smaller than 9 and the Hessian distance does not exceed 1.4142, it is extracted as the second straight line (diagonal line) section. By using the Hessian distance in determining the second straight section, the swelling of the section at the target point from the center line of the section can be regulated, and the accuracy of the linearity of the second straight section is maintained at a desired value. Can be done easily.

The number of dots, the value of the curvature, the value of the cosine, the value of the Hessian distance, and the like from the target point for which the curvature is to be determined may be determined according to the design concept. In particular, the present invention is not limited to this embodiment. Absent.

As described above, according to the present embodiment , the
Calculates the value of cosine, delimiting the first first straight section with a point less than the predetermined value of the cosine of this value and the first curved section, the said first inner curved section by then using the curvature It is divided into two straight sections and a second curved section, and is divided into a straight section composed of the first straight section and the second straight section and a curved section composed of the second curved section as a whole. Since the approximation section obtained in this manner is used for approximation, the reproduced approximation figure has a very smooth connection between the straight line and the curve, and the approximation accuracy in each approximation section is reduced. It can be improved efficiently. This is because when relatively compared with the division of the section by section and the curvature of the section by the cosine, in terms of extraction of the straight section has excellent technique by curvature, methods by cosine in terms of calculating speed Are better. That can not segment alone is strict division of the section by the cosine, the only segment of the section by the curvature, it takes a great deal of processing time. So first
Since configuration for extracting the straight section by curvature; then performed only may extract straight section, then only a curved section of the subject by division of the section by the cosine, the connection state of the adjacent approximation interval is extremely smooth As a result, the approximation accuracy in each approximation section can be efficiently improved. In the first section by the cosine, that the value of the cosine is continuous small, details of the point equal to or less than the value that the value of the cosine is preset to the number more than the first parameter value set in advance A continuous point, that is, a continuous portion having high linearity is regarded as a straight section, and in the second section based on the curvature, of the curve section obtained in the first section, a continuous point having a small curvature value, In detail, among the points where the value of the curvature is equal to or less than a preset value, a point that is continuous to the number of the second parameter values or more that is set in advance, that is, a continuous portion having high linearity is regarded as a straight section. By obtaining a certain straight section, there is an extremely excellent effect that the joining between adjacent approximate sections can be made smoother.

FIG. 5 shows a concrete example according to the method of the present invention. The figure of FIG. B obtained by approximating the original figure of FIG. A based on the method of the present invention is approximate reproduced by the conventional method. It can be seen that the reproduction accuracy is extremely excellent as compared with the figure shown in FIG.

In the embodiment described above, the first music piece
When the line section is divided into the second straight section and the second curved section, the division is performed using the curvature value of each point. After the curvature value of each point is obtained, By taking the difference between the absolute values of the adjacent point curvatures and dividing the second straight section and the second curve section using this difference value, the curvature can be prevented from fluctuating ± as shown in FIG. And the approximation accuracy can be further improved.

That is, after the step ST19 in FIG. 2, a step of "calculating the absolute value of the curvature of all points in the curved section from the adjacent points" is added, and then the values of the curvature in steps ST20 and ST21 are added. May be replaced with this difference value to perform the processing. Then, this step ST20 and step ST20
For example, a value of ± 0.000002 may be used as a difference value serving as a criterion for determination in 21, and processing may be performed so as to search for a point within this value.

As described above, after the value of the curvature is obtained, the difference between the absolute values of the curvatures of the adjacent points is further obtained, and by using the value of the difference, it is possible to reduce the fluctuation of the curvature to ±. And the approximation accuracy can be further improved.

It should be noted that the present invention is not limited to the above-described embodiment, and can be modified as needed.

[0041]

As described above, according to the position data approximation method of the present invention, the reconstructed approximate figure has an extremely smooth connection state between adjacent approximate sections and the approximate figure within each approximate section. It exhibits an extremely excellent effect that is above efficiently direction accurately.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a position data approximation method according to the present invention.

FIG. 2 is a flowchart showing a position data approximation method according to the present invention;

FIG. 3 is an explanatory diagram illustrating a range in which a curvature is obtained.

FIG. 4 is an explanatory diagram for explaining ± fluctuation of curvature.

5A is an original graphic to be approximate-reproduced, b is an approximate reproduced graphic according to the method of the present invention, and c is an approximate reproduced graphic according to the conventional method.

FIG. 6 is a diagram showing a case where a contour point is divided by a conventional method.

Claims (2)

(57) [Claims] Together delimit a 1. A point sequence approximation interval of the position data of the shape, the approximate method of position data to be approximated using a function, the point sequence shape based on the cosine value that put on each point of the position data After dividing the position data into two approximation sections, a straight approximation section and a curve approximation section, the curve approximation section is further divided into a straight approximation section and a curve approximation section based on a curvature value at each point in the curve approximation section. A position approximation method characterized by dividing into two approximation sections of a straight line approximation section and a curve approximation section as a whole, and performing approximation. Wherein when classified as two approximation interval of the linear approximation interval and the curve approximation interval of the position data of the point array shape on the basis of the value of cosine that put on each point of the position data, the position data among the points which the value of put that cosine at each point is equal to or less than a preset value of the position data of the column-shaped consecutive points less than the number of the first parameter value set in advance with a straight section, said straight section Other than the curve section, when further dividing the curve approximation section into a linear approximation section and a curve approximation section based on the curvature value at each point in the curve approximation section, Among the points where the value of the curvature is equal to or less than the preset value, the position data in the form of a series of points continuous to the number of preset second parameter values or more is defined as a straight section, and the other sections are defined as curved sections. thing Approximation of the position data according to claim 1, wherein.