JP2735974B2 - Curve linear 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 linear approximation method for obtaining an integer coordinate value from a real number coordinate value of a curve and performing linear approximation.

[0002] Output devices such as displays and printers are required to have high quality output. In particular, with regard to a method of outputting characters, a method of expressing contours such as a curved outline font by a curved expression is used to output high-quality characters.

However, the curved outline font has a drawback that the method of expressing the curved line is complicated and the processing speed is slow, and there is a high demand for a linear outline font whose outline is represented by a straight line. Therefore, a straight-line approximation method for expressing the outline of a character with a straight line closer to a curve is desired.

[0004]

2. Description of the Related Art FIG. 6 shows a configuration of a conventional linear approximation method for approximating a curve with a straight line. According to the configuration of FIG. 6, the real coordinate values of the curve are converted to integer coordinate values by rounding or the like,
The integer coordinate values of the approximate straight line are obtained by extracting the integer coordinate values at regular intervals from the converted integer coordinate values. Hereinafter, the configuration and operation of FIG. 6 will be briefly described.

FIG. 6 shows an explanatory diagram of the prior art. In FIG. 6, a curve coordinate calculator 21 calculates real coordinate values of a curve of a contour of a character or the like, and stores the calculated values in a real coordinate memory 24 of the curve.

The integer coordinate calculation unit 22 converts (eg, rounds) the real coordinate values extracted from the real coordinate memory 24 of the curve into integer coordinate values, and stores the converted integer coordinate values in the integer coordinate memory 25 of the curve. Things.

[0007] The equal interval extracting section 23 extracts equidistant values from the integer coordinate values extracted from the integer coordinate memory 25 of the curve and stores them in the linear coordinate memory 26.
Next, the operation will be described.

(1) The curve coordinate calculation unit 21 calculates the real coordinate values of a curve of a contour line such as a character and stores it in the real coordinate memory 24 of the curve (for example, the vector of the curve coordinates in FIG. Is calculated and stored in the curve's real number coordinate memory 24).

(2) The integer coordinate calculator 22 calculates the real coordinate values extracted from the real coordinate memory 24 of the curve as follows.
It is converted into an integer coordinate value (for example, rounded off) and stored in an integer coordinate memory 25 for the curve.

(3) The equal-interval extracting unit 23 extracts the integer coordinate values extracted from the integer coordinate memory 25 of the curve at equal intervals and stores them in the linear coordinate memory 26. When the stored integer coordinate values extracted at regular intervals are connected by a straight line and are schematically displayed, a straight line connecting the line segments of FIG. 7B is obtained.

[0011]

When the vector of the curve coordinates in FIG. 7A is converted into an integer coordinate value by the configuration of FIG. 6 described above, extracted at equal intervals and connected by a line segment, the vector shown in FIG. As shown in FIG. 2B, there is a problem that, unlike the original curve shape, unnecessary jaggedness occurs. This unnecessary jaggedness is caused by an error when the real coordinate value of the curve is converted into an integer coordinate value, and is extracted at equal intervals, so that the error between the curve and the obtained line segment is obtained. Does not always extract small integer coordinate values,
It was jagged. For this reason, it is demanded to eliminate the jaggedness and obtain an integer coordinate value of a smooth straight line close to the original curve.

The present invention has been developed to solve these problems.
After converting the real coordinate values of the curve into integer coordinate values, find the error between the real coordinate value of the original curve and this integer coordinate value, take out only the integer coordinate values with small errors, and connect them to obtain an approximate straight line It is an object of the present invention to generate a high-quality approximate straight line close to a curve that prevents quality deterioration during enlargement.

[0013]

Means for solving the problem will be described with reference to FIG. In FIG. 1, an integer coordinate calculator 2 calculates an integer coordinate value from a real number coordinate value of a curve.

The coordinate selector 3 calculates an error between the real coordinate value of the original curve and the calculated integer coordinate value, and selects an integer coordinate value equal to or less than a predetermined threshold value.

[0015]

According to the present invention, as shown in FIG. 1, an integer coordinate calculator 2 calculates integer coordinate values from the real coordinate values of a curve, and a coordinate selector 3 calculates the real coordinate values of the original curve and the calculated integers. An error from the coordinate value is obtained, integer coordinate values equal to or less than a predetermined threshold value are selected, and the selected integer coordinate values are connected by a straight line to approximate a straight line.

The integer coordinate calculation unit 2 calculates an integer coordinate value from the real coordinate value of the curve, and the coordinate selection unit 3 calculates an error between the real coordinate value of the curve and the calculated integer coordinate value. Of the integer coordinate values, and connects the selected integer coordinate values with a straight line, calculates an error between the straight line and the real coordinate value of the curve, and obtains the straight line when the maximum value of the error is equal to or less than a predetermined threshold. A straight line, while narrowing the interval between the real coordinate values of the curve when the maximum value of the error is equal to or greater than a predetermined threshold,
The process is repeated from the beginning.

Further, the integer coordinate calculator 2 calculates an integer coordinate value from the real coordinate value of the curve, and the coordinate selector 3 calculates an error between the real coordinate value of the curve and the calculated integer coordinate value. Is selected, and the selected integer coordinate values are connected by a straight line, and the maximum value of the error between the straight line and the real coordinate value of the curve is calculated. When the maximum value of the error is equal to or less than a predetermined threshold, the straight line is calculated. , And when the error is equal to or greater than a predetermined threshold, the interval between the real coordinate values of the preceding and following curves is made smaller, and the process is repeated from the beginning on this smaller portion.

Therefore, after converting the real coordinate value of the curve into an integer coordinate value, an error between the real coordinate value of the original curve and the integer coordinate is obtained, and only the integer coordinate value with a small error is extracted and connected. Calculate the approximate straight line or further calculate the maximum value of the error between the straight line connecting the integer coordinate values and the real coordinate value of the curve. Accordingly, it is possible to generate a high-quality approximate straight line close to a curve in which quality deterioration is prevented.

[0019]

Next, the structure and operation of an embodiment of the present invention will be sequentially described in detail with reference to FIGS.

FIG. 1 is a block diagram showing one embodiment of the present invention.
In FIG. 1, a curve coordinate calculation unit 1 calculates a real coordinate value of a curve from an expression formula expressing a contour of a character or the like by a curve vector. For example, as shown in FIG. 3A, real coordinate values of the Y coordinate are 3.00, 3.03,.
・ It is calculated as follows. The calculated real number coordinate values are stored in the real number coordinate value memory 4 for the curve.

The integer coordinate calculator 2 calculates integer coordinate values from the real coordinate values of the curve read from the real coordinate memory 4 for the curve. The calculation of the integer coordinate value is performed by, for example, rounding off the real number coordinate value of the curve. The calculated integer coordinate value is stored in the curve integer coordinate memory 5.

The coordinate selecting section 3 has a real coordinate memory 4 for curves.
And the integer coordinate memory 5 of the curve read from the
An error between the coordinate value and the integer coordinate value read from is calculated, and only the integer coordinate value whose error is equal to or less than a predetermined threshold value is selected. An integer coordinate value of which the selected error is equal to or less than a predetermined threshold is
It is stored in the linear coordinate memory 6. In addition, an integer whose error is equal to or less than a predetermined threshold value is connected by a straight line, and when the maximum value of the error between the straight line and the real coordinate value of the curve is equal to or more than the predetermined threshold, the real coordinate value of the curve by the curve coordinate calculation unit 1 is calculated. All the intervals to be calculated are made finer (to be described later with reference to FIG. 4), or the intervals near the real number coordinate values having the maximum error in the real number coordinate values of the curve by the curve coordinate calculation unit 1 are made finer. , The maximum value of the error does not exceed a predetermined threshold.

The real coordinate memory 4 of the curve is a memory for storing the real coordinate values of the curve. For example, as shown in FIG. This is a memory for storing a column of coordinate values.

The curve integer coordinate memory 5 is a memory for storing integer coordinate values read from the curve real number coordinate memory 4 and converted into integers (see FIG. 3B). The linear coordinate memory 6 stores, among the integer coordinate values read from the integer coordinate memory 5 of the curve, those whose error (absolute value) from the real coordinate value read from the real coordinate memory 4 of the curve is equal to or smaller than a predetermined threshold value. (See FIG. 3D).

Next, the operation of the configuration of FIG. 1 will be described in detail according to the order shown in the flowchart of FIG. In FIG. 2, S1 calculates a real coordinate value of a curve. For example, for the vector of the curve coordinates in FIG. 3E, the real coordinate value of the Y coordinate is calculated at a predetermined interval, here, X = 1.00, as shown in FIG. 3A. .

In step S2, an integer coordinate value of the curve is calculated. In this case, for example, the integer coordinate values in FIG. 3B are calculated by rounding off the real number coordinate values of the curve in FIG. S3 is the absolute value of the difference between the real coordinate value and the integer coordinate value (=
Error). For example, the absolute value of the difference between the real coordinate value of the curve shown in FIG. 3A and the integer coordinate value shown in FIG. 3B is calculated as an error.

In step S4, it is determined whether the error is equal to or smaller than a threshold. YE
In the case of S, the integer coordinate value is output in S5 (the integer coordinate value is stored in the linear coordinate memory 6), and the process proceeds to S6. In the case of NO, the process proceeds to S6. For example, it is determined whether the error of FIG. 3C (here, the error of the Y coordinate) is a predetermined threshold value (here, 0.15 or less), and the result of YES is output as shown in FIG. 3D.

A step S6 decides whether or not the coordinate data is completed. This is because the real coordinate value of the curve calculated in S1 is
It is determined whether all of the processes from S5 to S5 have been completed. If YES, the process ends (END). In the case of NO, the next coordinate data (the actual coordinate value of the curve) is changed from S2 to S5.
Is repeatedly executed.

As described above, for example, with respect to the vector of the curve coordinates in FIG. 3E, the real coordinate values of the curve are calculated at predetermined intervals (S1, see FIG. 3A), and the real coordinate values of the curve are calculated. Is rounded to calculate an integer coordinate value (S
2, (b) of FIG. 3), an error which is an absolute value of a difference between a real coordinate value and an integer coordinate value of the curve is obtained (S3, FIG. 3).
(C)), those whose errors are equal to or smaller than a predetermined threshold are selected and output (YES in S4, S5, see (d) in FIG. 3). Thereby, it is possible to select and output only integer coordinate values whose error is equal to or less than a predetermined threshold value from the real coordinate values of the curve, and to obtain a smooth approximate straight line along the curve as shown in FIG. Becomes

FIG. 3 shows a specific example of the present invention. FIG. 3A shows an example of the real coordinate values of the curve. This is shown in FIG.
(E) of the curve coordinate vector, the X coordinate of 1..
The real coordinate value of the Y coordinate at that time is calculated as shown in FIG.

FIG. 3B shows an example of the integer coordinate values of the curve. This is obtained by calculating the integer coordinate value by rounding off the Y coordinate value of the real number coordinate value of the curve in FIG.

FIG. 3C shows an example of the error between FIGS. 3A and 3B. The error is calculated by the following equation (1). Error = | real number coordinate value of curve−integer coordinate value | ... (1) Here, the real number coordinate value of the curve is, for example, 3 of the Y coordinate in FIG. .03, and the integer coordinate value is 3.00 of the Y coordinate in FIG. 3 (b). Therefore, these two values are substituted into the equation (1), and the error = | 3.03−3.00 | = 0 .03.

FIG. 3D shows the case where the integer coordinate values whose error in FIG. 3C is 0.15 or less are selected. Here, an integer coordinate value selected by using a dotted arrow is shown.
FIG. 3E shows an example of a curve coordinate vector. This is an example of a curve coordinate vector of the contour line of the curved portion of the character. From the vector of the curve coordinates, the real coordinate value of the Y coordinate is calculated at intervals of 1.00 with respect to the X coordinate.
(A) is obtained.

FIG. 3 (f) shows an approximate straight line connecting the integer coordinate values of FIG. 3 (d) with a straight line. As can be seen from this approximate straight line, the present invention selects only integer coordinate values whose error is equal to or less than a threshold value (here, 0.15 or less) of the real number coordinate value of the curve and connects them to form an approximate straight line. 7, only the integer coordinate value having a small error when the actual coordinate value of the curve is rounded off to the integer coordinate value is eliminated, and the jaggedness that occurs in the conventional approximate line of FIG. 7B is eliminated, and the smooth approximate line along the curve is eliminated. Can be calculated.

FIG. 4 is a flowchart (part 1) for explaining another operation of the present invention. According to the flowchart of FIG. 2, when the maximum value of the error between the integer coordinate value output in S5 and the straight line connecting the integer coordinate value and the real coordinate value of the curve exceeds a predetermined threshold, the curve The interval at which the real coordinate values are calculated is made smaller so that the maximum value of the error is equal to or less than a predetermined threshold value. This will be described below.

In FIG. 4, S1 to S6 correspond to S1 in FIG.
1 to S6, the description is omitted. S7
Connects integer coordinate values with a straight line.

In step S8, the absolute value (= error) of the difference between the real coordinate value and the straight line is calculated. In step S9, it is determined whether or not the maximum error is equal to or smaller than a threshold. In the case of YES, it is determined that the error between the straight line connecting the obtained integer coordinate values and the real coordinate value of the curve is equal to or smaller than the threshold value, and thus a series of processing ends. On the other hand, in the case of NO, since the maximum value of the error between the straight line connecting the obtained integer coordinate values and the real coordinate value of the curve is found to be equal to or larger than the threshold value, the coordinate calculation interval is reduced in S10, and S1 is set. Execute the following. As a result, the interval for obtaining the real coordinate values of the curve is made smaller, the interval for linearly approximating the curve is made shorter, and an approximate straight line along the curve is obtained.

As described above, when the maximum error between the straight line connecting the integer coordinate values calculated according to the flowchart of FIG. 2 and the real coordinate value of the curve is equal to or greater than the threshold value, the interval for obtaining the real coordinate value of the curve is dynamically adjusted. It is possible to automatically obtain a high-quality approximate straight line along the curve.

FIG. 5 is a flowchart (part 2) for explaining another operation of the present invention. According to the flowchart of FIG. 2, when the maximum value of the error between the integer coordinate value output in S5 and the straight line connecting the integer coordinate value and the real coordinate value of the curve exceeds a predetermined threshold value, The interval for calculating the real coordinate values of the curves before and after exceeding the predetermined threshold value is made finer, and the maximum value of the error is set to be equal to or less than the predetermined threshold value. This will be described below.

In FIG. 5, S1 to S6 correspond to the S in FIG.
1 to S6, the description is omitted. S17
Connects integer coordinate values with a straight line.

In step S18, the absolute value (= error) of the difference between the real coordinate value and the straight line is calculated. A step S19 decides whether or not the maximum error is equal to or smaller than a threshold. In the case of YES, it is determined that the maximum value of the error between the straight line connecting the obtained integer coordinate values and the real coordinate value of the curve is equal to or smaller than the threshold value, and thus a series of processing is ended. On the other hand, in the case of NO, the maximum value of the error between the straight line connecting the obtained integer coordinate values and the real coordinate value of the curve is found to be equal to or larger than the threshold value. Between the coordinate intervals, and recalculate the curve coordinates.
Execute the second and subsequent steps. Thereby, for the part where the error between the real coordinate value of the straight line and the curve is the largest, the interval for obtaining the real coordinate value of the curve is made finer, the interval when the curve is approximated by a straight line is shortened, and an approximate straight line along the curve is obtained To do.

As described above, when the maximum value of the error between the straight line connecting the integer coordinate values calculated according to the flowchart of FIG. 2 and the real coordinate value of the curve is equal to or greater than the threshold value, the real coordinate value of the curve having a large error is calculated. Dynamically refine the required interval,
It is possible to automatically obtain a high-quality approximate straight line along the curve.

[0043]

As described above, according to the present invention,
After converting the real coordinate values of the curve into integer coordinate values, find the error between the real coordinate value of the original curve and this integer coordinate, take out only the integer coordinate values with small errors, and connect them to obtain an approximate straight line. Furthermore, the maximum value of the error between the straight line connecting the integer coordinate values and the real coordinate value of the curve is obtained, and when the difference is equal to or larger than a predetermined threshold value, the whole of the real coordinate value or before and after the fine value is refined, and the processing is repeated. Therefore, it is possible to generate a high-quality approximate straight line close to a curve. Thereby, an integer coordinate value with a small error is selected from the real number coordinate value of the original curve, and the selected integer coordinate value is used as an approximate straight line coordinate, to prevent the quality degradation at the time of enlargement seen in the conventional linear approximation, It is possible to obtain an integer coordinate value of a high-quality approximate straight line that is close to a curve even when enlarged.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of one embodiment of the present invention.

FIG. 2 is a flowchart illustrating the operation of the present invention.

FIG. 3 is a specific example of the present invention.

FIG. 4 is a flowchart (part 1) for explaining another operation of the present invention.

FIG. 5 is a flowchart (part 2) for explaining another operation of the present invention.

FIG. 6 is an explanatory diagram of a conventional technique.

FIG. 7 is a specific example of the related art.

[Explanation of symbols]

 1: Curve coordinate calculation unit 2: Integer coordinate calculation unit 3: Coordinate selection unit 4: Real number coordinate memory of curve 5: Integer coordinate memory of curve 6: Linear coordinate memory

Claims (3)

(57) [Claims] A linear approximation method for obtaining an integer coordinate value from a real coordinate value of a curve and linearly approximating the same, comprising: an integer coordinate calculator (2) for calculating an integer coordinate value from the real coordinate value of the curve; An error between the real number coordinate value and the calculated integer coordinate value is obtained, and a coordinate selection unit (3) for selecting an integer coordinate value whose error is equal to or less than a predetermined threshold value is provided. A straight-line approximation method of a curve characterized by being configured to approximate. 2. A linear approximation method for obtaining an integer coordinate value from a real coordinate value of a curve and performing linear approximation, wherein: an integer coordinate calculation unit (2) for calculating an integer coordinate value from the real coordinate value of the curve; An error between the real coordinate value and the calculated integer coordinate value is obtained, and a coordinate selector (3) is provided for selecting the integer coordinate value whose error is equal to or less than a predetermined threshold value. An error between the straight line and the real coordinate value of the curve is calculated, and when the maximum value of the error is equal to or less than a predetermined threshold, the approximate straight line is determined. A straight-line approximation method for a curve, characterized in that processing is repeated from the beginning by narrowing value intervals. 3. A linear approximation method for obtaining an integer coordinate value from a real coordinate value of a curve and performing linear approximation, wherein: an integer coordinate calculation unit (2) for calculating an integer coordinate value from the real coordinate value of the curve; An error between the real coordinate value and the calculated integer coordinate value is obtained, and a coordinate selector (3) is provided for selecting the integer coordinate value whose error is equal to or less than a predetermined threshold value. An error between the straight line and the real coordinate value of the curve is calculated, and when the maximum value of the error is equal to or less than a predetermined threshold value, the approximate line is determined as an approximate straight line. A straight line approximation method for a curve, characterized in that the interval between the real number coordinate values of the curve before and after the value is made fine, and the processing is repeated from the beginning for this fine part.