JP2717013B2 - Position data approximation method - Google Patents

Description

Description: 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.

[Conventional technology]

2. Description of the Related Art In general, reading shapes of characters, figures, and the like with an image reader and reproducing them on a CRT, paper, or the like has been actively performed.

In this case, an outline font is used to read only the position data of outlines of characters, figures, and the like, and reproduce the portion surrounded by the outlines as characters, figures, and the like.

The graphic processing using such an outline font captures the outline of a character, a graphic, or the like as a point sequence and reads or reproduces it.Today, without using the position data of the original graphic as it is, 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 large changes, and the time required for various data processing is also long, and the time required for reproduction is long. This is approximated by using, for example, an arbitrary cubic function, thereby compressing the position data, reducing the storage capacity, speeding up various data processing, shortening the reproduction time, and almost equivalent to the original figure. Can be reproduced.

The conventional approximation method will be described with reference to FIG. 5. Extremal points P ₀ , P ₁ , P ₂ , P ₃ whose tangents are parallel to the X direction and the Y direction are obtained from the point sequence of solid lines representing the contour of the original figure. , P ₄ ..., And approximation sections delimited by these extreme points are approximated using arbitrary functions.

[Problems to be solved by the invention]

However, in the related art, the approximation section approximated by using a function is a section in which both ends are separated by extreme points, and when the approximate position data is reproduced, as shown in FIG. There has been an inconvenience that the degree of joining at the value point is not theoretically smooth, but sharp when sharp.

SUMMARY OF THE INVENTION The present invention has been made in view of these points, and makes it possible to smoothly join approximate position data of adjacent approximate sections, and to reproduce the original figure while maintaining the approximate accuracy with respect to the position data of the original figure at a predetermined value. It is an object of the present invention to provide a method of approximating position data that can be performed.

[Means for solving the problem]

In the position data approximation method of the present invention, the position data of the point sequence shape is divided into a plurality of approximation sections of the point sequence shape, and the position data is approximated using a function within each approximation section to obtain approximate position data. In the approximation method, when the point sequence shape has an extremum point and an inflection point, the approximation separated by an extremum point that sets the approximation accuracy of the approximate position data to the inflection point and the position data to a predetermined value It is characterized by approximation with intervals.

(Operation)

According to the present invention, since both ends of the approximated section are separated by the inflection point, the approximate position data approximated by the function to the adjacent approximated section has the tangent slope equal at the inflection point to be joined. , Resulting in extremely smooth joining.

Furthermore, according to the present invention, an approximation section is set by approximating a point sequence shape including not only an inflection point but also an extreme point, and approximation is performed. The data is smoothly joined, and the approximation accuracy of the approximate position data with respect to the position data of the original figure can be set to a desired content by adding an approximate section delimited by the extreme point.

〔Example〕

An embodiment of the present invention will be described below with reference to FIGS.

The method of the present invention will be described with reference to FIG.

The point sequence shape shown in FIG. 1 has inflection points t ₀ , t consisting of points at which the convexity changes between the extreme points P ₁ and P ₂ and between the extreme points P ₃ and P _4. Have _one .

In the present invention, the point sequence in FIG. 1 is changed to inflection points t ₀ and t _1.
… And the inflection point from the base point 0 as an approximate section
section up to t _0, the inflection point t interval from ₀ to t _1, section are separated at the inflection point at both ends so that the section from the inflection point t ₁ until the next inflection point 0~T ₀ , T ₀ -T ₁ , T _1-, and approximates each of these approximate intervals using a predetermined function to obtain approximate position data.

The approximate position data obtained in this manner is extremely smoothly joined because the tangents at the inflection points at the ends of the approximate sections are equal.

As described above, when the approximation accuracy of the approximate position data approximated using the approximate section delimited by only the inflection point with respect to the position data of the point sequence shape does not fall within a predetermined value, the approximation processing is further performed as follows. Perform

That is, by selecting an extremum point that can bring the approximation accuracy within a predetermined value by increasing the approximation interval, the approximation interval is set by dividing the point sequence shape by the extremum point and the inflection point, and The function is approximated by a function in the approximate section. For example, the extreme point to join, if you select the P _1, P ₃ is the approximation interval _{0~P 1, P 1 ~t 0,} t 0 ~P 3, P 3 ~t
₁ , t ₁ .

As a result, although the joining of the approximate position data at each extreme point P ₁ , P ₃ is slightly angular, the approximate accuracy of the position data of the point sequence as a whole is within a predetermined value, and a good reproduction shape is obtained.

Next, the method of the present invention will be described with reference to the flowchart shown in FIG.

First, look for extreme point on the object points of all the position data of the column-shaped points to be approximated in a step ST _1.

Next, at step ST _2, as the first inflection point search section to search the inflection point, three extreme points P _i consecutive, P _{i + 1,} P
Set the section including _{i + 2} . In this case, when the point sequence shape is closed endlessly, any extremal point is set as the first inflection point search interval, and when the point sequence shape is open, the first inflection point search interval from the base point is set Good to do.

Next, in step ST _3, performs exploration inflection point of inflection point search in interval set in step ST _2.

In the search for the inflection point, for example, a point sequence in the inflection point search section is regarded as one function, and a point at which the convexity of the function changes is obtained as an inflection point. Specifically, as shown in FIG. 3, three points B ₁ , B ₂ , and B ₃ on the point sequence are determined, and the point B ₂ is obtained by moving the point B ₂ from the point B ₁ to the point B ₃ . relationship between the slope m ₂ between the slope m ₁ and point B ₂ B ₃ between ₁ B ₂ is, m ₁ <m ₂ (or m _1> m ₂₎ determined as full of missing inflection point points.

Next, performs determination of whether the inflection point is present in step ST4, if YES, proceeds to step ST _5,
If NO proceeds to step ST _6.

In one step ST _5, the inflection point of all determined and stored (memory), extreme values of the following variables songs point search section preceding the inflection point search section P _i ~P _{i + 2} endpoints and from the point P _{i + 2} from the two extreme points P _{i + 3,} section P _{i + 2,} which advances the P _{i + 4} to P _{i + 4,}
To proceed to the next step ST _7.

In the other step ST _6, P the next inflection point search section than the inflection point of the previous search period P _i to P _{i + 2,} from P _{i + 1} that move forward across only one extreme point _i include ₊₂ and section up P _{i + 3,} proceeds to the next step ST _7.

In step ST _7, it is determined whether or not subjected to inflection point search with respect to all of the extreme points. If NO, the flow returns to step ST _3.

In the embodiment shown in FIG. 1, from the base point 0 to the extreme point P ₁
Since there is no inflection point in the inflection point search section up to, steps ST ₁ , ST ₂ , ST ₃ , ST ₄ , and ST ₆ in FIG. the interval from the point P ₀ to P _2.
Since there is an inflection point t _{0 in} this inflection point search section, the process proceeds to steps ST ₇ , ST ₃ , ST ₄ , and ST _5, and saves the inflection point t ₀ and searches for the next inflection point and the section from the extreme point P ₂ to P _4, progresses to step ST _7.

When such inflection point search is performed for the entire column-shaped point, including all of the extreme points, proceeds from step ST ₇ to step ST _8.

In this step ST _8, the approximation process using a function for all approximation interval, separated by inflection point only is performed, the approximate location data are determined.

Next, in step 9, the approximation accuracy for positional data of the point sequence shape of the approximate position data obtained in step ST ₈ is determined whether within a predetermined value.

If the determination in step ST ₉ is YES, proceed to the next step ST _11, the approximate location data is stored, to be used for the next reproduction and the like.

On the other hand, if the determination in step ST ₉ is NO, proceeds to step ST _10, using a function for all the approximation interval delimited by the extreme points elected in order to increase the approximation accuracy as the inflection point The approximation process is performed.

Thereafter, the process returns to step ST ₉ again, whether the approximation accuracy or within the predetermined value is determined, the process of step ST ₉ → ST ₁₀ → ST ₉ until the determination in step ST ₉ becomes YES is repeated, YE
Proceeds to step ST ₁₁ becomes the S, approximate location data in the same manner as described above is stored, the approximate positional data of the point array shape is completed.

FIGS. 4 (a), (b), (c) and (d) show examples in which the present invention is applied to an actual point sequence shape.

FIG. 4 (a) shows a point sequence shape to be approximated,
FIG. 2B is an approximation using an approximation section delimited only by extreme points (marked by x in the figure), and FIG. 2C is delimited only by inflection points (marked by △ in the figure). FIG. 4D shows an approximation using an approximation section divided by using an inflection point and a necessary extremum point.

In the present embodiment, the point sequence shown in FIG. 4A is complicated, and as shown in FIG. 4D, the point sequence is divided by only the inflection points as shown in FIG. The approximation in the approximate section divided by the inflection point and the extremal point enables the reproduction of the approximate position data that is accurately approximated to the point sequence shown in FIG. In addition, when approximation is performed in an approximation section delimited only by extreme points as shown in FIG.
Each joint is square and the approximation accuracy is inferior to that of FIG.

Note that the present invention is not limited to the above embodiment, and can be modified as needed.

〔The invention's effect〕

Since the position data approximation method of the present invention is constructed and operated in this way, it is possible to smoothly join the approximate position data of adjacent approximation sections, and to set the approximation accuracy for the position data of the original figure to a predetermined value. Thus, it is possible to obtain the effect of being able to hold and reproduce the image.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram showing a case of approximation by the position data approximation method of the present invention, FIG. 2 is a flowchart showing the present invention method, FIG. 3 is an explanatory diagram showing convexity of a function, and FIG. ) Is a diagram showing the shape of a point sequence to be approximated, and FIG. 2B is a reproduction diagram obtained by approximating the shape using an approximation section delimited by only extreme points (marked by x in the diagram), and FIG. Is the inflection point (△
(D), a reproduction diagram approximated using an approximation section demarcated only by an asterisk), and FIG. 5 (d) is a reproduction diagram approximated using an approximation section demarcated using an inflection point and a necessary extremum point. FIG. 6 is an explanatory diagram similar to FIG. 1, and FIG. 6 is a reproduction diagram of data approximated by a conventional method.

Claims (1)

(57) [Claims] 1. The position data approximation method, wherein the position data of the point sequence shape is divided into a plurality of approximate intervals, and the approximate position data is approximated using a function within each approximate interval. When the point sequence shape has an extremum point and an inflection point, approximation is performed using an approximation section divided by an extremum point that sets the approximation accuracy of the approximation position data to the inflection point and the position data to a predetermined value. A method for approximating position data, characterized by the following.