JPH09212666A - Bejer curve approximation device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To extremely increase the Bejer curve division processing speed by deciding the end of the division processing according to a fact whether a reference point is included in an area of the prescribed width that is defined by a straight line set parallel to a straight line that connects together the start and end points of a Bejer curve. SOLUTION: When an area decision means decides that a reference point P9 is included in a prescribed area, a y-intercept calculation means calculates a y-intercept (b) of the straight line that is set parallel to a straight line P0 P3 and also passes through the point P9 . Then the area decision means decides whether the y-interception (b) is included in an area C formed between the y-intercepts b1 and b2 . If the y-intercept (b) is not included in the area C, a division end decision means decides that the division operation of a Bejer curve division means is further necessary. If the y-intercept (b) is included in the area C, the division end decision means decides that the point P9 is included in an area having the division decision reference value H0 based on the line P0 P3 and discontinues the subsequent division processing of the Bejer curve division means.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a Bezier curve creating method, and more particularly to a Bezier curve approximating apparatus for approximating a Bezier curve with a straight line.

[0002]

2. Description of the Related Art As a conventional method of creating an approximate straight line from a Bezier curve, as shown in FIG. 13, a starting point P ₀ , two control points P ₁ , P ₂ and an end point P ₃ are specified. There is a method of drawing the Bezier curve S. The Bezier curve S is a pseudo-curve drawn by connecting short straight lines. In particular, the reference point P ₉ when the Bezier curve S is divided is obtained by repeating the following midpoint division. That is, the midpoints P ₄ , P ₅ , P ₆ dividing the line segments P ₀ P ₁ , P ₁ P ₂ , P ₂ P _{3 in} the middle are obtained, and then the line segments P ₄ P ₅ , P ₅ P ₆
Obtains each of the middle point P _7, P ₈ of, and finally the line segment P ₇ P ₈
The reference point P ₉ can be obtained as the midpoint of.

After this, the distance h between the reference point P ₉ and the line segment P ₀ P ₃
When it is determined that the distance h is larger than the division determination reference value, division is performed with the reference point P ₉ as a boundary (reference), and instead of the four points P ₀ , P ₁ , P ₂ , P ₃ , New 4 points P ₀ , P ₄ , P ₇ , P ₉ and another set of 4 points P ₉ , P ₈ ,
It is divided into two sets of P ₆ and P ₃ , and the same processing as described above is performed for each of the 4 points. When it is determined that the reference points P ₁₀ and P ₁₁ on the curve S obtained as a result are distances to the line segments P ₀ P ₉ and P ₉ P ₃ are smaller than the division determination reference value, a short straight line is drawn. A method in which it is determined that the connected pseudo curve S has approached a curve that can be regarded as a real curve and it does not matter, and the creation of the Bezier curve is terminated without performing the above-described division processing on the curve S any further. As a conventional method, there is a method of creating a Bezier curve.

[0004]

However, in order to calculate the distance h between the reference point P ₉ and the line segment P ₀ P ₃ , the coordinates of P ₉ are (x ₉ , y ₉ ), the coordinates of P ₀ . Where (x ₀ , y ₀ ) and the coordinates of P ₃ are (x ₃ , y ₃ ), it must be calculated by the following equation (1).

H = {(x ₉ −x ₀ ) × (y ₃ −y ₀ ) + (x ₃ −x ₀ ) × (y ₉ −y ₀ )} / √ {(x ₃ −x ₀ ) ² + ^{_{(y 3 -y 0) 2}}} ...... (1)

The calculation formula (1) requires four multiplications, one division, and one calculation of the square root (√), which requires a considerable amount of time. If such a calculation is repeated many times, there is a problem that it takes a huge amount of time to create a Bezier curve.

In order to solve such a problem, conventionally, there is a method of speeding up the distance calculation of h by using an approximate calculation. In this method, the distance is made larger than the true distance by the approximate calculation of the distance so that the roughness of the curve is not noticeable. There is a problem in that the load of the processing of filling or drawing a line using the vector group calculated dynamically becomes large, which affects the processing speed of the graphics system as a whole. Other than this, various attempts have been made to solve the problem of the processing speed, but none of them are drastic, and none of them can dramatically increase the processing speed.

Therefore, an object of the present invention is to provide a Bezier curve approximating apparatus capable of dramatically increasing the Bezier curve division processing speed.

[0009]

In order to solve the above problems, the Bezier curve approximating apparatus according to the present invention has the following configuration.

(1) A positional relationship between a Bezier curve dividing means for linearly approximating a Bezier curve from a start point, an end point and two control points of the Bezier curve, and a reference point when dividing the Bezier curve by the Bezier curve dividing means. A division end determining means for deciding whether to end the division processing, and when the division end determining means determines the division end, line drawing or a region based on a straight line approximated to a Bezier curve by the Bezier curve dividing means A graphic processing means for processing such as filling, and a straight line inclination calculating means for forming a straight line connecting the start point and the end point of the Bezier curve, and calculating the slope of the straight line when the start point or the end point is the origin of the coordinate axis. An area determination unit that determines whether the reference point is within a predetermined area, and the reference point is parallel to a straight line connecting a start point and an end point of the Bezier curve. Whether to end the division processing is determined depending on whether or not the area is within a predetermined width area defined by a line.

(2) The positional relationship between the Bezier curve dividing means for linearly approximating the Bezier curve from the start point and the end point of the Bezier curve and the two control points, and the reference point when dividing the Bezier curve by the Bezier curve dividing means. A division end determining means for deciding whether to end the division processing, and when the division end determining means determines the division end, line drawing or a region based on a straight line approximated to a Bezier curve by the Bezier curve dividing means A graphic processing means for processing such as filling, and a straight line inclination calculating means for forming a straight line connecting the start point and the end point of the Bezier curve, and calculating the slope of the straight line when the start point or the end point is the origin of the coordinate axis. An area determining means for determining whether the reference point is within a predetermined area, and an area having a predetermined width provided by a plurality of representative straight lines in parallel with each other. A storage means for storing both in a determination table, within a region of a predetermined width provided along a representative straight line having a slope closest to the slope of the straight line connecting the start point and the end point of the Bezier curve of the determination table It is determined whether or not the division processing is ended depending on whether or not there is the reference point.

According to the Bezier curve approximating apparatus having the constitution (1) of the means for solving the above problems, the reference point when the Bezier curve dividing means divides the Bezier curve is the start point and the end point of the Bezier curve. Since it is determined whether to end the division processing depending on whether it is within the area of a predetermined width provided by the straight line parallel to the connecting straight line, the division processing can be performed easily without the need for complicated calculations as in the past. Since it is possible to determine whether to end, the Bezier curve division processing speed can be dramatically increased.

Means (2) for solving the above problems
According to the Bezier curve approximating apparatus of the configuration, by storing a plurality of representative straight lines of the determination table together with the area of a predetermined width provided by straight lines parallel to each, the start point and the end point of the Bezier curve A representative straight line having a slope closest to the slope of the connecting straight line is called, and it is determined whether to end the division process depending on whether the reference point is within a region of a predetermined width provided by a straight line parallel to the straight line. Since this is done, it is not necessary to perform complicated calculations one by one as in the conventional method, and like the means (1) for solving the above-mentioned problem, a straight line parallel to the straight line connecting the start point and the end point of the Bezier curve is used. It is not necessary to perform the arithmetic processing from the beginning to provide the area of the predetermined width, and it is sufficient to call the area of the predetermined width provided by the representative line and the straight line parallel to the representative table from the determination table. Because, it can be more easily determined whether to end the division process can be further dramatically faster Bezier curve dividing processing speed.

[0014]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. 1 to 11 are views for explaining a first embodiment of a Bezier curve approximating apparatus according to the present invention.

FIG. 1 is a block diagram showing the configuration of the Bezier curve approximating apparatus, and FIG. 2 is a flowchart showing the operation of the Bezier curve approximating apparatus. The Bezier curve approximating device is actually mounted on an image processing device such as a personal computer and implemented.

For example, when drawing on the screen of a personal computer, selecting the Bezier curve creation mode, selecting the cursor position on the screen with the mouse or the like and designating the start point, the end point and two control points, Based on this, the Bezier curve dividing means 3 as the operation of the Bezier curve creation program operates to automatically draw a pseudo curve of a continuous set of short straight lines constituting the Bezier curve on the screen.

At this time, when the drawn pseudo curve is in a state in which a jagged feeling is noticeable and cannot be used as a curve, the division end judging means 1 judges to continue the division processing. As a result, as described in the related art, the eight points obtained by making the four points more fine are divided into two sets of four with the reference point as a boundary, and the same process is repeated to obtain a new reference point. Thus, the Bezier curve dividing means 3 operates.

The division end determination means 1 determines the division end by the straight line inclination calculation means 5 which forms a straight line connecting the start point and the end point of the Bezier curve and calculates the inclination of the straight line when the start point is the origin of the coordinates. Of the area determination means 7 for determining whether the reference point for dividing the Bezier curve by the Bezier curve dividing means 3 is within a predetermined area formed by a straight line parallel to the straight line connecting the start point and the end point of the Bezier curve Is performed using motion.

When the division end judging means 1 judges that the division is completed, the graphic processing means 8 is based on the set of continuous straight lines approximated to the curve by the Bezier curve dividing means 3.
Performs registration such as line drawing and area filling, and the image thus registered is displayed on the screen of a CRT or the like, or is printed by an output unit such as a printer if necessary.

Next, the operation of such a Bezier curve approximating apparatus will be described with reference to FIGS. First, the Bezier curve dividing means 3 starts the operation of calculating the Bezier curve, and after the Bezier curve S is created by the four points P ₀ , P ₁ , P ₂ and P ₃ , the reference point P obtained in the final process is created. The distance h to the line connecting the start point P ₀ and the end point P _{3 of the} Bezier curve of ₉ is obtained. When the distance h is larger than the division determination reference value according to the determination result of the division end determination means 1, the Bezier curve division means 3 changes the Bezier curve S to the curve B1 (P ₀ ,
P _4, P _7, created by four points P ₉₎ and curve B2 (P _9, P
Two Bezier curves of ₈ points, P ₆ points, and P ₃ points) are divided at the reference point P ₉ (step S in FIG. 2).
1).

After this, one of the divided Bezier curves B1
If the distance h ′ (not shown) between the reference point P ₁₀ in FIG. 13 and the straight line connecting the start point P ₀ and the end point P ₉ is smaller than the division determination reference value, it is determined that the division processing is completed (see FIG. 2). If YES in step S2) and the distance h'is larger than the division determination reference value, it is determined that the division continues (NO in step S2). The same processing is performed on the other divided Bezier curve B2.

If YES is determined in step S2 of FIG. 2, registration is performed after the graphic processing means 8 performs the above-described processing (step S3), and then the processing is ended (END). NO in step S2
If it is determined that the two Bezier curves B1 and B2 are further divided (step S4).
Then, returning to step S2 again, the division end determination means 1
It is determined whether or not to end the division by, and the process proceeds to step S3 or step S4.

Next, a method of judging the division end from the start point, the end point and the reference point in step S2 will be described with reference to FIGS. 3 and 4. In the present embodiment, the start point P ₀ , the end point P ₃ , and the reference point P ₉ will be used for description. First, the inclination calculating means 5 calculates the inclination a of the straight line connecting the starting point P ₀ and the ending point P ₃ of the Bezier curve S as shown in FIG. 13 when the starting point P ₀ is the origin (step S1 in FIG. 3). , Graph y = ax is obtained (broken line shown in FIG. 4). Next, two straight lines (y = ax + b, y = ax−) extending in parallel with the width of the division determination reference value H ₀ on both the + side and the − side of the straight line.
b) is formed, and the determination area K is provided between the two straight lines (step S2 in FIG. 3).

Next, the area determination means 7 determines whether the reference point P ₉ of the Bezier curve in FIG. 13 is within the determination area K at the above coordinates (step S3 in FIG. 3), and the division is performed based on this determination. The end determination means 1 is YES in the area determination means 7.
If it is determined that the division is completed, the area determination means 7
If NO is determined, it is determined that further division is necessary.

As described above, according to the Bezier curve approximating apparatus of the first embodiment, it is only necessary to determine whether or not the reference point P ₉ on the coordinates is within the predetermined area K, which is different from the conventional case. Since it is possible to easily determine whether or not to end the division processing without performing complicated calculations, the Bezier curve division processing speed can be dramatically increased.

Next, a second embodiment of the Bezier curve approximating apparatus according to the present invention will be described. As can be seen from the block diagram showing the configuration of the Bezier curve approximating apparatus according to the second embodiment shown in FIG. 5, in the configuration of the Bezier curve approximating apparatus according to the first embodiment shown in FIG. The difference is that a storage unit 10 for storing a table, a coordinate conversion unit 12, a y-intercept calculation unit 14, and a determination table change unit 16 are added.

The storage means 10 stores a determination table for each of a plurality of representative straight lines prepared in advance, and the plurality of representative straight lines are divided so as to have slightly different inclinations as shown in FIG. There is.

As shown in FIG. 6, the inclinations of the plurality of representative straight lines have the inclinations a which are slightly different between the x-axis and the straight line of y = x. That is, the maximum of their inclination a is 1.
And then the slope a is 1/2, 1/4, 1/8, 1
It is basically divided in the order of / 16.

When the inclination a is between 1 and 1/2, (1/2) × (1/16), (1/2) × (2/1)
6), ... It is divided into 16 by adding a gradient of (1/2) × (15/16). Further, when the slope a is between ½ and ¼, (1/4) × (1/8), (1
/ 4) × (2/8), ... (1/4) × (7/8) is added to divide it into eight. And the slope a
Between 1/4 and 1/8 is (1/8) × (1 /
4), (1/8) x (2/4), ... (1/8) x (3
It can be divided into four by adding a slope of / 4).

The plurality of representative straight lines in the determination table of the storage means 10 as described above have slightly different inclinations a as described above.
At the same time, a region between two straight lines extending along the representative straight line apart from the respective representative straight lines by +/- both sides by the distance of the division determination reference value H ₀ is stored as a set in the determination table.

The coordinate conversion means 12 is a starting point P of the Bezier curve.
_{When 0} is arranged at the origin (0, 0) of the coordinate axis, the end point P ₃ is in the first quadrant of the coordinate, that is, in the + side coordinate area for both the x axis and the y axis, the straight line of the x axis and y = x (inclination 45 ° The coordinate conversion of the Bezier curve is performed so that the Bezier curve is arranged in a 45 ° area (area F in FIG. 8) sandwiched between the origin and the straight line passing through the origin (0, 0).

For example, as shown in FIG. 8, when the starting point P _{0 of the} Bezier curve is located at the origin (0,0) of the coordinate axis, the ending point P ₃
Is in the third quadrant (both the x-axis and the y-axis are −side coordinate regions), the coordinate conversion means 12 first performs the primary conversion on the y-axis to set the end point P ₃ to the fourth quadrant (the x-axis is the + side). , Y-axis is moved to the coordinate area on the minus side) to be P _31, and then P ₃₁ is moved to the first quadrant by performing a linear transformation on the x-axis to P ₃₁ .
_Then, P ₃₂ can be moved to the opposite side of the straight line of y = x by performing a linear transformation on the straight line of y = x, and P ₃₃ can be obtained. By moving the end point P ₃ to the area F in this way, it is sufficient to prepare only the inclinations in the area F for each representative straight line of the determination table as shown in FIG.

The y-intercept calculating means 14 is a straight line P ₀ when the starting point P _{0 of the} Bezier curve is located at the origin (0, 0) of the coordinate axis.
The value of the y-intercept is defined by two straight lines that extend parallel to each other and are separated from each other by a distance equal to the division determination reference value H ₀ from P ₃ . The determination table changing unit 16 is the storage unit 1.
The number of a plurality of representative straight lines in the determination table of 0 and the interval of inclination are changed, or the distance (division determination reference value H ₀ ) between each of the representative straight lines and two parallel straight lines is changed. It is a thing.

Next, the operation of the Bezier curve approximating apparatus according to the second embodiment having such a configuration will be described. The basic operation shown in FIG. 2 is the same as that of the first embodiment, but as shown in FIG. 7, the determination method of whether the Bezier curve dividing means 3 finishes dividing the Bezier curve is shown in FIG. This is different from the first embodiment shown.

First, when the start point P _{0 of the} Bezier curve is placed at the origin of the coordinate axis and the end point P ₃ is not in the F region of the first quadrant, the coordinate conversion means 12 performs the coordinate conversion as described above and the end point. moving the P ₃ to the F region (step S1 in FIG. 7). At this time, the reference point P ₉ obtained by the dividing operation of the Bezier curve dividing means 3 is also moved along with the coordinate conversion of P ₃ while maintaining the relative positional relationship with the end point P _{3 on the} Bezier curve.

Next, as shown in FIG. 9, a straight line L ₁ extending in parallel to the negative side of the y-axis by a division determination reference value H ₀ from the x-axis.
If, to set the region A is sandwiched between the straight line L ₂ extending in parallel away from the straight line y = x only end point P ₃ with division determination reference value H ₀ on the opposite side, the reference point P ₉ is this The area determination means 7 determines whether the area is within the area A. Then, as shown in FIG. 9, when it is determined that the reference point P ₉ is not within the area A, the area determining means 7 determines NO (N in step S2 in FIG. 7).
O), the division end determination means 1 determines that the division operation by the Bezier curve division means 3 is further required.

When the area determining means 7 determines that the reference point P ₉ is within the area A (YE in step S2 in FIG. 7).
S), then the inclination calculating means 5 calculates the inclination a of the straight line of P ₀ P ₃ (step S3 in FIG. 7), and y is obtained as shown in FIG.
A straight line P ₀ P ₃ of = ax is created. Then, the representative straight line y = a ₁ x, y = having the slopes a ₁ and a ₂ that are the closest to the slope a calculated by the slope calculating means 5 from the determination table of the storage means 10.
a ₂ x is selected (step S4 in FIG. 7), the two representative straight lines are called, and the straight line P as shown by the broken line in FIG.
A straight line y = a ₁ x which is created so as to sandwich ₀ P ₃ and is separated from the two representative straight lines by the division determination reference value H _0.
Create + b ₁ and y = a ₂ x + b ₂ . In this way, the area B is provided, and then the area judging means 7 judges whether the reference point P ₉ is within this area B or not.

That is, in FIG. 10, a point Q _{0 at} which a vertical line passing through the reference point P ₉ and parallel to the y axis intersects the upper limit of the region B,
It is judged by the area judging means 7 whether the y coordinate of the reference point P _{9 is} between the lower limit of the area B and the point Q ₁ intersecting with the lower limit, and FIG.
As shown in 0, when the y coordinate of P ₉ is not between the points Q ₀ and Q ₁ , the area determination means 7 determines NO (NO in step S5 of FIG. 7), and the division end determination means 1 It is determined that the division operation by the Bezier curve dividing means 3 is further required.

If the area determining means 7 determines YES in step S5 of FIG. 7, then the y-intercept calculating means 14
Calculates a y-intercept b of a straight line parallel to the straight line P ₀ P ₃ and passing through the reference point P ₉ as shown in FIG. 11 (step S6 in FIG. 7). The area determination means 7 determines whether the y-intercept b calculated by the y-intercept calculation means 14 is within the area C between the y-intercepts b ₁ and b ₂ (step S7 in FIG. 7).
Then, as shown in FIG. 11, when the determining unit 7 determines that the y-intercept b is not within the area C (N in step S7).
O), the division end determination means 1 determines that the division operation by the Bezier curve division means 3 is further required.

In step S7, the area determination means 7 returns Y.
When it is determined as ES, the division end determination means 1 determines the reference point P.
_It is determined that ₉ is within the area of the division determination reference value H ₀ from the straight line P ₀ P ₃ , and the subsequent division processing by the Bezier curve dividing means 3 is stopped (YES in FIG. 2), and FIG. Then, the process shifts to step S3 to finish the creation of the Bezier curve.

In the above embodiment, the case where the division end is judged without calculating the distance h between the reference point P ₉ and the straight line P ₀ P ₃ obtained by the method shown in FIG. 13 has been described. In addition to the method shown in FIG. 13, a method for calculating the distances h ₁ and h ₂ between the two control points P ₁ and P ₂ and the straight line P ₀ P ₃ as well as the method shown in FIG. Yes,
Even in such a case, by using the present invention,
It is also possible to determine the division end without calculating the distances h ₁ and h ₂ between the two control points P ₁ and P ₂ and the straight line P ₀ P _3, and the same effect as the present invention can be obtained.

[0042]

As described above, according to the Bezier curve approximating apparatus of the present invention, it is possible to easily determine whether or not to end the division processing without performing a complicated calculation as in the conventional case. , The Bezier curve division processing speed can be dramatically increased.

Further, according to the second embodiment, it is not necessary to perform a complicated calculation as in the conventional case, and a straight line connecting the start point and the end point of the Bezier curve is required as in the first embodiment. Since it is not necessary to perform arithmetic processing from the beginning to provide a region having a predetermined width by a straight line parallel to the line, it is sufficient to call a region of a predetermined width provided by a straight line parallel to the representative line from the determination table. It is possible to more easily determine whether to end the division processing, and the Bezier curve division processing speed can be dramatically increased.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a Bezier curve approximating apparatus according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing an operation procedure of the Bezier curve approximating apparatus of FIG.

FIG. 3 is a flowchart showing an operation procedure of determination of division end of the Bezier curve approximating apparatus of FIG.

FIG. 4 is a coordinate diagram for explaining the operation of a region determination means 7 of the Bezier curve approximating apparatus of FIG.

FIG. 5 is a block diagram showing a configuration of a Bezier curve approximating apparatus according to a second embodiment of the present invention.

6 is a coordinate diagram showing sections of inclination of a plurality of representative straight lines in the determination table of the storage means 10 of the Bezier curve approximating apparatus in FIG.

7 is a flowchart showing an operation procedure of division end determination of the Bezier curve approximating apparatus of FIG.

8 is a coordinate conversion means 12 of the Bezier curve approximating apparatus of FIG.
FIG. 8 is a coordinate diagram for explaining the operation of FIG.

9 is a coordinate diagram for explaining the operation of the area determination means 7 of the Bezier curve approximating apparatus in FIG.

10 is a region determination means 7 of the Bezier curve approximating apparatus of FIG.
FIG. 8 is a coordinate diagram for explaining the operation of FIG.

11 is a region determination means 7 of the Bezier curve approximating apparatus of FIG.
FIG. 8 is a coordinate diagram for explaining the operation of FIG.

FIG. 12 is a diagram for explaining a conventional Bezier curve division end determination method.

FIG. 13 is a diagram for explaining a conventional Bezier curve division method and division end determination method.

[Explanation of symbols]

1 division end determination means 3 Bezier curve division means 5 straight line inclination calculation means 7 area determination means 8 graphic processing means 10 storage means 12 coordinate conversion means 14 y intercept calculation means 16 determination table changing means P ₀ start point P ₃ end point P ₉ reference point K, F, A, B, C area

Claims (7)

[Claims] 1. A Bezier curve dividing means for linearly approximating a Bezier curve from a start point and an end point of a Bezier curve and two control points, and a positional relationship between a reference point when dividing the Bezier curve by the Bezier curve dividing means. When the division end determination unit that determines whether to end the division process and the division end determination unit determines that the division is completed, line drawing or a region is drawn based on a straight line approximated to the Bezier curve by the Bezier curve dividing unit. Graphic processing means for processing such as filling, forming a straight line connecting the start point and the end point of the Bezier curve, and a straight line slope calculating means for calculating the slope of the straight line when the start point or the end point is the origin of the coordinate axis, An area determining means for determining whether the reference point is within a predetermined area, and the reference point is a straight line parallel to a straight line connecting a start point and an end point of the Bezier curve Thus it by whether in the region of a predetermined width provided to determine whether to end the division processing Bezier curve approximation apparatus according to claim. 2. A Bezier curve dividing means for linearly approximating a Bezier curve from a start point and an end point of a Bezier curve and two control points, and a positional relationship between reference points when dividing the Bezier curve by the Bezier curve dividing means. When the division end determination unit that determines whether to end the division process and the division end determination unit determines that the division is completed, line drawing or a region is drawn based on a straight line approximated to the Bezier curve by the Bezier curve dividing unit. Graphic processing means for processing such as filling, forming a straight line connecting the start point and the end point of the Bezier curve, and a straight line slope calculating means for calculating the slope of the straight line when the start point or the end point is the origin of the coordinate axis, A region determination means for determining whether the reference point is within a predetermined region and a region of a predetermined width provided by a plurality of representative straight lines are provided. A storage means for storing in a determination table, within a region of a predetermined width provided by a straight line parallel to a representative straight line having a slope closest to the slope of the straight line connecting the start point and the end point of the Bezier curve of the determination table A Bezier curve approximating apparatus, characterized in that it is determined whether or not to end the division processing depending on whether or not there is the reference point. 3. The horizontal axis is the x-axis, the vertical axis is the y-axis, and when the starting point of the Bezier curve is located at the origin of the coordinate axis, the end point is between the x-axis of the first quadrant of the coordinates and the straight line of y = x. Providing coordinate conversion means for performing coordinate conversion of the Bezier curve so that the reference point is within a predetermined region after the Bezier curve is subjected to the coordinate conversion so that the Bezier curve is coordinated so as to be arranged in a sandwiched 45 ° region. The Bezier curve approximating apparatus according to claim 2, wherein it is determined whether to continue the division processing by. 4. The reference is within an area formed by two straight lines parallel to the two representative straight lines of the determination table having a slope closest to the straight line connecting the start point and the end point of the Bezier curve. The Bezier curve approximating apparatus according to claim 3, wherein it is determined whether to continue the division processing by determining whether there is a point. 5. A y-intercept calculating means for calculating a y-intercept of a straight line which is parallel to a straight line connecting a start point and an end point of the Bezier curve and which passes through the reference point is provided, and the y-intercept is one of the two representative straight lines. The Bezier curve approximating apparatus according to claim 4, wherein it is determined whether or not the division processing is ended by determining whether or not the division processing is completed by determining whether or not the division processing is within a region between two y-intercepts of parallel lines that are apart from each other by a predetermined distance. . 6. The method according to claim 2, wherein the slopes of a plurality of representative straight lines in the determination table stored in the storage unit are divided based on a value obtained by multiplying (1/2) to the nth power. 5. The Bezier curve approximation device according to any one of 5 above. 7. The determination table changing means for changing a value of a predetermined width of an area formed by a straight line parallel to each of a plurality of representative straight lines of the determination table is provided. Item 7. The Bezier curve approximation device according to any one of Items 6.