JPH04170684A - Method for approximating positional data - Google Patents

Abstract

PURPOSE:To smooth a connection state between a straight line and a curve by adopting only a boundary point candidate for setting up the approximation accuracy of approximate position data to a certain positional data to a prescribed value as a boundary point when a dot shape has a boundary point on which a straight line is connected to a curve. CONSTITUTION:All of connection points between a straight line and a curve are adopted as boundary point candidates, and whether the value of a narrow angle be tween the curve and the straight line on the boundary point candidates is a prescribed value or not is decided and an element P2 more than the prescribed value is removed from the boundary point candidates. Whether the ratio of length of segments between the curve and straight line on the boundary point candidates is a prescribed value or not is decided and an element P4 more than the prescribed value is removed from the boundary point candidates. Furthermore, whether the whole shape formed by the straight line and the curve through the boundary candidate is a projected shape or not is decided, and a point P7 having no projected shape is removed from the boundary point candidates. Consequently, approximate position data in adjacent approxi mate sections can be smoothly joined, and while holding the approximate accuracy of an original graphic to the position data at a prescribed value, the original graphic can be reproduced.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a position data approximation method for approximating position data in the form of a point sequence using a function.

[Conventional technology]

In general, it is common practice to read the shapes of characters, figures, etc. with an image reader and reproduce them on CRTs, paper, and the like.

In this case, the font is called an outline font, and the position data of only the outline of a character, figure, etc. is read and the part surrounded by this outline is reproduced as a character, figure, etc.

Graphic processing using such outline fonts captures the contours of characters, graphics, etc. as a series of dots and reads and reproduces them. Approximate position data obtained by approximating this using an arbitrary function is used.

This is because the position data of the original figure generally changes significantly, so it requires a large capacity to be stored in a memory, requires a long time for various data processing, and takes time to reproduce. For example, by approximating this using an arbitrary cubic function, etc., the position data can be compressed, reducing storage capacity, speeding up various data processing, and shortening playback time. Almost equivalent reproduction figures can be reproduced.

In the conventional approximation method, all connection points between straight lines and curves are found, and each approximation section divided by these connection points is approximated using an arbitrary function.

[Problem to be solved by the invention]

However, in the past, when determining the approximate interval to be approximated using a function, all connection points were used as points to define the interval, so when the approximate position data is played back, the connection points of adjacent approximate intervals are The problem is that the joint is not theoretically smooth, and in extreme cases it becomes sharply rounded.

The present invention has been made in view of these points, and it is possible to smoothly join the approximate position data of adjacent approximate sections, and also maintain the approximation accuracy with respect to the position data of the original figure at a predetermined value for reproduction. The purpose of this invention is to provide a method for approximating position data that can be used to approximate position data.

[Means to solve the problem]

The position data approximation method of the present invention divides the point sequence shape into a plurality of approximation intervals, and approximates the position data using a function within each approximation interval to obtain approximate position data. In the approximation method, when the point sequence shape has a boundary point where a straight line and a curved line are connected, an approximation interval separated by the boundary point that makes the approximation accuracy of the approximate position data to the position data a predetermined value. It is characterized by approximating by .

[For production]

According to the present invention, when an approximate interval is divided by a boundary point, it is divided by a boundary point that makes the approximation accuracy of the approximate position data to a predetermined value to the position data, so the approximate position approximated based on this is The data will be joined very smoothly at the boundary points.

〔Example〕

Embodiments of the present invention will be described below with reference to FIGS. 1 to 4.

FIG. 1 is a flowchart showing a method for selecting boundary points according to an embodiment of the present invention, which will be explained in order below.

First, when the selection of boundary points starts, step ST,
Smell hand and boundary point candidates are extracted. These boundary point candidates include all connecting points between straight lines and curved lines.

Next, it is determined whether it is a boundary point according to steps ST2 to ST4.

That is, in step ST2, it is determined whether the included angle between the straight line and the curved line in the boundary point candidate is greater than or equal to a predetermined value, and if it is greater than or equal to the predetermined value, the process proceeds to step ST3. proceed.

In this step ST2, the smoothness of the transition from a straight line to a curved line is checked, and if the transition is not smooth, the process proceeds to step 6 and is removed from the boundary point candidates. To further explain with reference to FIG. 2, between the boundary point candidate P1 in FIG. 2(a) and the boundary point candidate P2 in FIG. are removed from the boundary point candidates. In this case, this can be easily determined by finding the inner product (COS) of the angle between the straight line and the curve and comparing that value with a predetermined value.

In step ST3, it is determined whether the ratio of line segment lengths between straight lines and curved lines that sandwich the boundary point candidate is greater than or equal to a predetermined value, and if the ratio is greater than or equal to the predetermined value, the process proceeds to the next step ST4. However, if the value is not equal to or greater than the predetermined value, the process proceeds to step 6 and is removed from the boundary point candidates. In this step ST3, if the length of each line segment between a straight line and a curved line sandwiching the boundary point candidate is very short on one side compared to the other, even if that point is obtained as a boundary point and an approximate interval point, This is because good joint processing effects cannot be obtained. To further explain with reference to FIG. 3, the boundary point candidate P3 between FIG. 3(a) and FIG. 3(b). When determining P4, LL/L2 and L3/L4, which are the length ratios of short line segments to long line segments, are determined, and it is calculated whether they are larger than a predetermined value. In FIG. 3, one point P3 continues to be a boundary point candidate, and the other point P4 is removed from the boundary point candidates.

In step 4, it is determined whether the overall shape of the straight line and curved line sandwiching the boundary point candidate has convexity, and if it has convexity, the process proceeds to the next step 5. Those that do not have a boundary point proceed to step 6 and are removed from the boundary point candidates.

This is because, in step ST5, when the overall shape of the straight line and curved line sandwiching the boundary point candidate has a convexity, the connection state becomes smoother than when the overall shape has no convexity. To further explain with reference to FIG. 4, boundary point candidate P5. When determining P7, line segment 1 extending from the straight line in the curve direction, boundary point candidates P5 to P6 or curve 2 from P7 to P8, and both boundary point candidates P
If the relationship with line segment 3 connecting line segment 5 to P6 or P7 to P8 is such that line segment 2 is located between line segments 1 and 3, it is determined that there is convexity. In Figure 4, one point P
5 continues to be a boundary point candidate, and the other point P7 is removed from the boundary point candidates.

Thereafter, the process proceeds to step ST-, and the points determined as boundary point candidates in step 4 are stored as boundary points.

Thereafter, the process proceeds to chip ST7, where it is determined whether or not determinations for all boundary point candidates have been completed.

If it has not been completed, the determination from step 2 is repeated, and if it has been completed, the boundary point extraction is ended.

According to this embodiment, when the point sequence shape has a boundary point where a straight line and a curved line are connected, only the boundary point candidates that make the approximation accuracy of the approximate position data to the position data a predetermined value are selected. Since these are adopted as boundary points and approximated using approximate sections separated by these boundary points, the reproduced approximate figure has an extremely smooth connection state between straight lines and curves.

Furthermore, if an approximate interval is set by adding to the boundary points obtained by the present invention, inflection points and extreme points obtained from the position data that improve the approximation accuracy, and the approximate position data is obtained and reproduced, the As shown in Figure 5, the approximation accuracy is much better than that shown in Figure 6, which is obtained by the conventional method using approximation sections separated only by connecting points between straight lines and curves. Recognize.

Note that the present invention is not limited to the above embodiments,
It can be changed as necessary.

〔Effect of the invention〕

Since the position data approximation method of the present invention is configured and operates as described above, it is possible to smoothly join the approximate position data of adjacent approximation sections, and also to maintain the approximation accuracy with respect to the position data of the original figure to a predetermined value. It has the advantage that it can be held and played back.

[BRIEF DESCRIPTION OF THE DRAWINGS] FIG. 1 is a flowchart showing the case of approximation by the position data approximation method of the present invention, FIGS. Figures 3 (a) and (b) are diagrams for explaining the determination of the size of line segment ratios, Figures 4 (a) and (b) are diagrams for explaining the determination of convexity, and Figure 5 is an illustration of the method approximated by the method of the present invention. FIG. 6 is a reproduction diagram of data approximated by the conventional method. Applicant's agent Shunsuke Nakao Figure 1 Figure 2 (a) (b) Figure 3 (a) (b) Figure 4 Figure 5 Figure 6

Claims (1)

[Claims] In a method for approximating position data in which the point sequence shape is divided into a plurality of approximation intervals and approximated using a function within each approximation interval to obtain approximate position data, the point sequence shape is a straight line. and a curve, the position data is characterized in that when the position data has a boundary point where the approximate position data is connected to the position data, the position data is approximated using an approximation interval separated by the boundary point that makes the approximation accuracy of the approximate position data to a predetermined value. approximation method.