JPH0785293A - Information processing equipment - Google Patents

Abstract

(57) [Summary] [Purpose] Draw smooth parallel curves at high speed using Bezier curves. A parallel Bezier is obtained from the control point P and the line width W input from the input unit 1 by the control point determining unit 2 or from the control point P and the line width W of the reference Bezier curve L divided by the dividing unit. A new control point Q for drawing the curve M is determined. The parallelism between the parallel Bezier curve M and the reference Bezier curve L by the control point Q determined here, for example, t = M and L
The parallelism evaluation means 3 evaluates whether or not the distance d between the points of 0.5 satisfies a predetermined reference value, and if it satisfies the reference value, the parallel Bezier curve drawing means 5 draws a parallel curve. . On the other hand, if not satisfied, the reference Bezier curve dividing unit 4 sets the reference Bezier curve L to, for example, t = 0.
Divide by 5 points. Similarly, the determination of a new control point Q, the parallelism evaluation, and the division are repeated for both Bezier curves L after the division until the parallelism satisfies a predetermined criterion.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an information processing apparatus, and more particularly to an information processing apparatus having a parallel curve drawing function using Bezier curves.

[0002]

2. Description of the Related Art Personal computers, office computers, workstations, electronic publishing systems, word processors and other various information processing devices are used in offices,
Widely used in factories, design offices, homes, etc. In such an information processing apparatus, when creating various drawings such as a road map and architectural drawings, it is necessary to draw a curve. As a method for realizing the drawing of a curve, a Bezier curve may be used as a curve interpolation method for drawing an approximate straight line using coordinate information of four control points.

FIG. 4 shows a curve drawing state by a Bezier curve. As shown in FIG. 4, among the four control points P0, P1, P2, and P3 (hereinafter represented by reference symbol P), a point P0 is set as a start point, a point P3 is set as an end point, and a start point P0, an end point P3 are set. Yes, two control points P1 and P
The Bezier curve L0 determined by the direction and distance of 2 is drawn. This Bezier curve L0 is calculated by the following cubic Bezier function B (t). B (t) = (1- t) 3 · P0 +3 (1-t) 2 · t · P1 +3 (1-t) · t 2 · P2 + t 3 · P3 where a 0 ≦ t ≦ 1, P0 , P1, P2, and P3 indicate control points. By the way, when drawing such a curve using an information processing apparatus, curves having equal intervals (referred to as parallel curves in this specification) may be drawn.

11 and 12 show four control points P0 and P.
The drawing shows a state in which a parallel curve having a width W is drawn on the Bezier curve L0 designated by 1, P2, and P3. As shown in FIG. 11, when drawing a parallel curve, the control points P0, P
Control points P0 ', P1', which are obtained by simply translating 1, P2, P3 in a predetermined direction (for example, the direction of arrow A) by a width W.
Even if the Bezier curve L0 'is drawn from P2' and P3 ',
Generally, it does not become a parallel curve. Therefore, in the conventional information processing device, when drawing a parallel curve by a Bezier curve,
A straight line 31 having a width W is drawn in the normal direction at a plurality of points on the basic Bezier curve L0. Or these straight lines 3
Parallel curves are drawn by connecting the points at both ends of 1 with straight lines.

[0005]

However, when drawing a parallel curve with the straight line 31 in the normal direction, it is necessary to take an extremely large number of coordinates at both ends of the straight line 31 in the normal direction, and it takes time for the drawing process. There was a problem of this. On the other hand, it is possible to speed up the drawing process by reducing the number of straight lines 31 in the normal direction, but in this case, there is a problem that a smooth parallel curve cannot be drawn. Further, if the distance between the straight lines 31 is short, the normal direction may differ from the actual line width direction, and it may not be possible to draw a clean parallel curve.

Therefore, an object of the present invention is to provide an information processing apparatus capable of drawing a smooth parallel curve by a Bezier curve at high speed.

[0007]

According to the present invention, as shown in principle in FIG. 1, in an information processing apparatus for drawing a Bezier curve from four control points, a control point P and a line width of a reference Bezier curve L are drawn. From the input means 1 for inputting W, the control point P of the reference Bezier curve L and the line width W, the control point determination means 2 for determining a new control point Q for drawing the parallel Bezier curve M.
And parallelism evaluation means 3 for evaluating whether or not the parallelism between the parallel Bezier curve M and the reference Bezier curve L by the new control point Q determined by the control point determination means satisfies a predetermined reference value. If the parallelism evaluation unit determines that the reference value is not satisfied, the reference Bezier curve dividing unit 4 that divides the centerline Bezier curve L and the parallelism evaluation unit determine that the reference value is satisfied. The above-mentioned object is achieved by equipping the information processing apparatus with the parallel Bezier curve drawing means 5 that draws the parallel Bezier curve M that has been created.

According to a second aspect of the present invention, in the information processing apparatus according to the first aspect, the center line Bezier curve L to the line width W.
/ 2 parallel Bezier curves M are drawn on both sides of the centerline Bezier curve L. According to a third aspect of the invention, in the information processing apparatus according to the second aspect, the control point determining means is configured to control each control point P.
Is P0, P1, P2, P3, the straight line [P0P
1] on a straight line orthogonal to the control point P0, a point having a distance W / 2 from the start point P0 is set as a start point Q0, and a straight line orthogonal to the straight line [P2P3] and the control point P3 is separated from the end point P3 by a distance W / 2. A point is set as an end point Q3, an intersection of a parallel line having a distance W / 2 from the straight line [P1P2] and a straight line passing through the start point Q0 and parallel to the straight line [P0P1] is set as a control point Q1, and the parallel line and the end point Q3 are set. An intersection with a straight line passing through and parallel to the straight line [P2P3] is defined as a control point Q2. According to a fourth aspect of the present invention, in the information processing apparatus according to the first or second aspect, the parallelism evaluation means has a point of t = 0.5 of the reference Bezier curve L and t = 0 of the parallel Bezier curve M. The parallelism is determined from the distance d and the width W from the point of 0.5. According to the invention of claim 5, in the information processing apparatus of claim 1 or 2, the reference Bezier curve dividing means divides the reference Bezier curve L at a point of t = 0.5.

[0009]

In the present invention, the control point determining means 2 is used to control the control points P and the line width W input from the input means 1, or the control points P and the line width W of the reference Bezier curve L divided by the dividing means. From this, a new control point Q for drawing the parallel Bezier curve M is determined. The parallelism between the parallel Bezier curve M and the reference Bezier curve L by the control point Q determined here, for example, M
The parallelism evaluating means 3 evaluates whether or not the distance d between the points t and 0.5 of L and t satisfies a predetermined reference value. If the distance d satisfies the predetermined reference value, the parallel Bezier curve drawing means 5 evaluates. Draw parallel curves. On the other hand, if not satisfied, the reference Bezier curve dividing means 4 divides the reference Bezier curve L at, for example, a point of t = 0.5. Similarly, the determination of a new control point Q, the parallelism evaluation, and the division are repeated for both Bezier curves L after the division until the parallelism satisfies a predetermined criterion.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the information processing apparatus of the present invention will be described in detail below with reference to FIGS. Figure 2
Represents the hardware configuration of the information processing apparatus. As shown in FIG. 1, the information processing apparatus includes a CPU (central processing unit) 11 that performs various processing operations such as parallel curve drawing processing according to this embodiment. The CPU 15 is provided with a ROM 15 and an R via a bus line 13 such as a data bus.
AM17, image memory 19, input device 21, scanner 2
3, printer 25, display 27, communication control unit 29
Are connected to each other.

The ROM 15 is a read only memory in which various programs for controlling the entire apparatus by the CPU 11 and various data are stored. The ROM 13 stores a graphic processing program such as a parallel curve drawing processing program by a Bezier curve according to the present embodiment, a Bezier function, data in the parallel curve drawing processing, and the like. R
The AM 17 is a random access memory used as a working memory used in various processing operations performed by the CPU 11 and used for storing various data. The RAM 17 stores graphic drawing data for specifying coordinate values of various graphics such as straight lines and parallel curves and graphic types drawn by graphic processing.

The image memory 19 stores image data, stores graphics drawn by the graphic drawing data stored in the RAM 17, and the data stored in the image memory 19 is stored in the printer 23 or the display. 25
It is designed to be output to. The input device 21 includes various input devices such as a mouse 211 as a pointing device and a keyboard 213. In addition, various input devices such as a tablet and a digitizer (not shown) can be connected to the input device 21. The scanner 23
The input device for reading image data stores the read image data in the image memory 19. The printer 25 and the display 27 are devices that output the graphic data expanded in the image memory 19 according to the graphic drawing data. As the printer 25, various devices such as a dot printer, a laser printer, and an XY plotter are used. Also, as the display 27, CR
Various displays such as T displays and liquid crystal displays are used.

The communication control unit 29 includes a LAN (local area network), a facsimile communication network, and an ISDN.
Personal computers, office computers, etc. via various communication networks such as (service integrated digital network)
It is connected to work stations, electronic publishing systems, word processors and other various information processing devices, and devices of different models. Communication of various data such as graphic drawing data is performed between other information processing devices via the communication control unit 29.

Next, the parallel curve drawing processing in the information processing apparatus thus configured will be described. 1. Principle of parallel curve drawing processing A cubic Bezier curve can be divided into two cubic Bezier curves without changing the shape. In particular, the cubic Bezier curve P
The method of dividing into two cubic Bezier curves at the point t = 0.5 when expressed by a parametric curve of (t) (0 ≦ t ≦ 1) is often used because it is easy.

For example, four points P0, P1 and P shown in FIG.
The cubic Bezier curve L0 defined by 2 and P3 can be divided into two cubic Bezier curves without changing the shape. That is, the Bezier curve L0 has four points P0, P4, P
7th, P3 cubic Bezier curve L1 and 4 points P
Cubic Bezier curve L2 defined by 9, P8, P6 and P3
Can be divided into Here, P4 = (P0 + P1) / 2 P5 = (P1 + P2) / 2 P6 = (P2 + P3) / 2 P7 = (P4 + P5) / 2 = (P0 + 2P1 + P2) /
4 P8 = (P5 + P6) / 2 = (P1 + 2P2 + P3) /
4 P9 = (P7 + P8) / 2 = [P0 + 3 (P1 + P2)
+ P3] / 4. As described above, the cubic Bezier curve has a property that it can be subdivided endlessly by repeatedly applying the division recursively.

When drawing a parallel curve of Bezier curves (referred to as parallel Bezier curves in this specification), four control points P0, P1,
From P2, P3 and the line width W of the parallel curve, four new control points Q0, Q1, Q2, Q3 (hereinafter represented by the symbol Q) are calculated. Then, at the Bezier curve L0, t = 0.
Point 5 (point P9) and new control points Q0, Q1, Q2,
If the distance d from the parallel Bezier curve M drawn from Q3 to the point of t = 0.5 is not more than a predetermined reference value, the parallel Bezier curve M is drawn. On the other hand, if the distance d is not less than or equal to the predetermined reference value, the property of the Bezier curve described above is used to divide the original reference Bezier curve L0 into L1 and L2, and the distance d between points at t = 0.5 is calculated. calculate. The division is repeated until the distance d becomes equal to or less than the predetermined reference value.

Next, the parallel curve drawing operation will be described in detail with reference to FIGS. FIG. 4 shows a reference Bezier curve which is a reference when drawing a parallel curve. As shown in FIG. 4, the start point, two control points, and the end point are P0, P1, P2, and P3, respectively, and the reference Bezier curve drawn by these four control points is L0.
And The width of the parallel curve to be drawn is W. In the parallel curve drawing process, a control point determination process for automatically determining a new control point Q for setting the line width W, a parallel Bezier curve M drawn by the determined new control point Q,
There are parallelism evaluation processing for evaluating the interval with the reference Bezier curve L and reference Bezier curve division processing for repeating the processing of dividing the reference Bezier curve, and each of them will be described.

Control Point Determination Processing FIG. 5 is a diagram for explaining determination of the control points Q of the parallel Bezier curve M and evaluation of parallelism. In FIG. 5, four control points P0, P1, P2, P3 and a line width W are input, and new control points Q0, Q1, Q2, Q3 for drawing a parallel curve are drawn from these figure drawing information. Shall seek. The line width W input from the input device
To draw the Bezier curve of, four control points P0, P
A smoother parallel curve is drawn by uniformly thickening the lines on both sides with the Bezier curve L0 by 1, P2, and P3 as the center line. Therefore, the Bezier curve having the width w = W / 2 described below is drawn twice on both sides of the Bezier curve L0.

First, an intersection of a parallel line 81 located at a distance w from the straight line [P0P1] and a parallel line 82 located at a distance w from the straight line [P1P2] is set as a new control point Q1. Parallel line 82
And a point of intersection with the parallel line 83 at a distance w from the straight line [P2P3] is set as a new control point Q2. And a straight line [P0P
1] and a straight line orthogonal to the starting point P0 and the parallel line 81 are set as a new starting point Q0. In addition, a straight line [P2P
[3] and a straight line orthogonal to the end point P3 and the parallel line 83 are set as a new end point Q3. As described above, four new control points Q0, Q1, Q2, Q3 are determined.

Parallelism evaluation processing Four new control points Q0 and Q calculated in the control point determination processing
When the Bezier curves for 1, Q2, and Q3 are parallel Bezier curves M0, the points at t = 0.5 of the parallel Bezier curve M0 and the original Bezier curve L0 are obtained, and Q9,
P9. Then, the distance d0 between the point Q9 and the point P9 is calculated and compared with the line width w. If the difference between the distance d and the width w (referred to as parallelism in this specification) is equal to or smaller than a predetermined reference value, for example, if | d−w | ≦ (w / 256), it has already been obtained. A parallel curve by a Bezier curve is drawn using each control point Q that exists.

Reference Bezier curve division processing New control points Q0, Q1, Q calculated in the control point determination processing
When a Bezier curve is drawn from 2 and Q3, when the line width d with the original Bezier curve L0 is obtained, the line width near the midpoint may differ from the line width near the end points. Therefore, in order to realize a uniform line width, the reference Bezier curve is divided as follows. That is, if the difference (parallelism) between the distance d and the width w is not less than or equal to a predetermined value, the original reference Bezier curve L0 serving as the center line is t = 0.
At the point 5, the reference Bezier curve L1 formed by the control points P0, P4, P7, and P9 and the reference Bezier curve L2 formed by the control points P9, P8, P6, and P3 are divided.

After the above-described reference Bezier curve division processing, the control point determination processing, until the parallelism becomes below the reference value again,
The parallelism evaluation processing and the reference Bezier curve division processing are repeated. FIG. 6 shows the reference Bezier curves L1 and L2 after division.
For determining a new control point Q for As shown in FIG. 6, the reference Bezier curve L
After the division processing of 0, four control points P0, P4, P7, P9 for the divided reference Bezier curve L1 and four control points P9, P8, P6, P3 for the reference Bezier curve L2.
On the other hand, a control point determination process and a parallelism evaluation process are performed. That is, after the division processing of the reference Bezier curve L0, as shown in FIG. 7, from the four control points P0, P4, P7, and P9 for the divided reference Bezier curve L1, four new control points are obtained by the control point determination processing. Points Q0, Q4, Q7,
Determine Q9. Also, four new control points Q9, Q8, Q6, Q3 are similarly determined from the four control points P9, P8, P6, P3 for the Bezier curve L2.

FIG. 7 is for explaining the parallelism evaluation processing of the parallel Bezier curve with respect to the divided reference Bezier curve. As shown in FIG. 7, control points Q0, Q4, Q
7 and Q9, the point Q10 of the parallel Bezier curve M1 ′ at t = 0.5, and the divided Bezier curve L1 at t = 0.5.
From the distance d1 between the point P10 and the width w (= W / 2), the parallelism evaluation process for the parallel Bezier curve M1 ′ is performed. Similarly, parallelism evaluation processing of the parallel Bezier curve M2 'is performed from the distance d2 and the width w between the parallel Bezier curve M2' and the reference Bezier curve L2.

FIG. 8 is a diagram for explaining the parallelism of the Bezier curves M0 and M0 'with respect to the reference Bezier curve before and after the division, and shows both the parallel Bezier curves of FIGS. 4 and 7. As shown in FIG. 8, the parallel Bezier curve M0 before division has a line width near the midpoint smaller than w. On the other hand, the parallel Bezier curve M0 ′ after the division is divided from the point P9 at t = 0.5 of the reference Bezier curve L1 to the point Q9 having the width w,
Since the end point of the parallel Bezier curve M1 'and the start point of the parallel Bezier curve M2' are used, the parallelism is closer to the reference value.

FIG. 9 is a flowchart showing the operation of the parallel curve drawing process described above. The CPU 11 monitors whether or not the parallel curve drawing mode is specified, for example, from the keyboard 213 (step 11). When the parallel curve drawing mode is specified (step 11; Y), CP
The U11 displays on the display 27 via the bus line the input of the control points P0, P1, P2, P3 and the line width W of the parallel curve with respect to the reference Bezier curve L0 which is the center of the parallel curve (step 12). ). Mouse 211
When these values P and W are input from the or keyboard 213, the CPU 11 causes the reference Bezier curve Ln (n is 0, 1,
A new control point Q is calculated from the four control points P and the line width w for (2, ...) (Step 13), and parallelism evaluation processing for the parallel Bezier curve M is performed (Step 1).
4).

When the parallelism is not less than the predetermined reference value (step 14; N), the reference Bezier curve Ln is divided (step 15) and the process proceeds to step 13.
On the other hand, when the parallelism is less than the reference value (step 14;
Y), after drawing the parallel Bezier curve M for the control point Q (step 16), if the drawing of the parallel Bezier curve M for the divided reference Bezier curve Ln is not completed (step 17; N), (step 17). The process moves to 13. When the drawing of the parallel Bezier curve M whose parallelism is equal to or less than the reference value is completed for all the divided reference Bezier curves Ln (step 17; Y), the process is ended. , A parallel curve on one side with respect to the original reference Bezier curve L0 is drawn, and similarly for the other side, the control point determination process, the parallelism evaluation process, and the reference Bezier curve division process are repeated. A parallel curve having a line width W (2w) is drawn.

FIG. 10 is for explaining another control point determination process. In this control point determination processing, the determination is made from the centers of curvature C0 and C3 at both ends of the reference Bezier curve L0. That is, the control points P0 and P1 of the reference Bezier curve L0
From the straight line [P0P1] connecting the
1 and 92. Then, the intersection of the straight line 93 passing through the center of curvature C0 and the control point P0 and the parallel lines 91 and 92 is set as the starting point Q0 of the outer and inner parallel Bezier curves M. Also,
A straight line 94 passing through the center of curvature C0 and the control point P1 and a parallel line 9
Both intersections with 1 and 92 are control points Q1 of the outer and inner parallel Bezier curves M. Similarly, the other center of curvature C3
Then, the control point Q2 and the end point Q3 are determined from the control points P2 and P3.

In the embodiment described above, the total line width is set to W by drawing two parallel Bezier curves on both sides having a distance w (= W / 2) with respect to the center line Bezier curve L0. A parallel Bezier curve M may be drawn only on one side having a distance W with respect to the Bezier curve L0, and a parallel curve may be drawn by the parallel Bezier curve M and the reference Bezier curve L0. The parallel curve drawing by this method is effective when the line width W is narrow, and since only one parallel Bezier curve M is required, the processing time is further shortened.

Although the parallel Bezier curves are drawn in the embodiments described above, it is also possible to draw thick lines from the parallel curves according to the present embodiment by the parallel Bezier curves. That is, by performing the filling process between the Bezier curves drawn according to the embodiment, it becomes possible to draw the Bezier curves of arbitrary thickness at high speed.

[0030]

According to the information processing apparatus of the present invention, it is possible to draw a smooth parallel curve with a Bezier curve at high speed.

[Brief description of drawings]

FIG. 1 is a principle diagram showing a principle of an information processing apparatus of the present invention.

FIG. 2 illustrates a hardware configuration of an embodiment of an information processing device of the present invention.

FIG. 3 is an explanatory diagram of division of a Bezier curve in the same as above.

FIG. 4 is an explanatory diagram showing a reference Bezier curve that serves as a reference when drawing a parallel curve.

FIG. 5 is an explanatory diagram of determination of a control point Q of the parallel Bezier curve M and evaluation of parallelism.

FIG. 6 is an explanatory diagram for determining a new control point Q for the reference Bezier curves L1 and L2 after division.

FIG. 8 is an explanatory diagram of parallelism evaluation processing of a parallel Bezier curve with respect to the divided reference Bezier curve.

FIG. 9 is a flowchart showing the operation of parallel curve drawing processing.

FIG. 10 is an explanatory diagram for another determination of the control point Q in the information processing apparatus of the present invention.

FIG. 11 is an explanatory diagram of conventional parallel curve drawing.

FIG. 12 is an explanatory diagram showing a conventional parallel curve drawing method.

[Explanation of symbols]

 1 Input Means 2 Control Point Determining Means 3 Parallelism Evaluating Means 4 Parallel Bezier Curve Drawing Means 5 Reference Bezier Curve Dividing Means 11 CPU 13 Bus Lines 15 ROM 17 RAM 19 Image Memory 21 Input Device 211 Mouse 213 Keyboard 23 Scanner 25 Printer 27 Display 29 Communication control unit

─────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission date] March 16, 1994

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Brief description of the drawing

[Correction method] Change

[Correction content]

[Brief description of drawings]

FIG. 1 is a principle diagram showing a principle of an information processing apparatus of the present invention.

FIG. 2 illustrates a hardware configuration of an embodiment of an information processing device of the present invention.

FIG. 3 is an explanatory diagram of division of a Bezier curve in the same as above.

FIG. 4 is an explanatory diagram showing a reference Bezier curve that serves as a reference when drawing a parallel curve.

FIG. 5 is an explanatory diagram of determination of a control point Q of the parallel Bezier curve M and evaluation of parallelism.

FIG. 6 is an explanatory diagram for determining a new control point Q for the reference Bezier curves L1 and L2 after division.

FIG. 7 is an explanatory diagram of parallelism evaluation processing of a parallel Bezier curve with respect to the divided reference Bezier curve.

FIG. 8 is an explanatory diagram of parallelism between Bezier curves M0 and M0 ′ with respect to a reference Bezier curve before and after division.

FIG. 9 is a flowchart showing the operation of parallel curve drawing processing.

FIG. 10 is an explanatory diagram for another determination of the control point Q in the information processing apparatus of the present invention.

FIG. 11 is an explanatory diagram of conventional parallel curve drawing.

FIG. 12 is an explanatory diagram showing a conventional parallel curve drawing method.

[Explanation of Codes] 1 Input Means 2 Control Point Determining Means 3 Parallelism Evaluating Means 4 Parallel Bezier Curve Drawing Means 5 Reference Bezier Curve Dividing Means 11 CPU 13 Bus Lines 15 ROM 17 RAM 19 Image Memory 21 Input Device 211 Mouse 213 Keyboard 23 Scanner 25 Printer 27 Display 29 Communication control unit

Claims (5)

[Claims] 1. An information processing apparatus for drawing a Bezier curve from four control points, an input means for inputting a control point P and a line width W of a reference Bezier curve L, and a control point P and a line width of the reference Bezier curve L. Control point determining means for determining a new control point Q for drawing the parallel Bezier curve M from W, and the parallel Bezier curve M and the reference Bezier curve L by the new control point Q determined by this control point determining means. Parallelism evaluation means for evaluating whether or not the parallelism with and satisfies a predetermined reference value, and if the parallelism evaluation means determines that the reference value is not satisfied, the centerline Bezier curve L is divided. An information processing apparatus, comprising: a parallel Bezier curve dividing unit that draws a parallel Bezier curve M that is determined to satisfy a reference value by the parallelism evaluation unit. 2. The information processing apparatus according to claim 1, wherein parallel Bezier curves M having a line width W / 2 from the centerline Bezier curve L are drawn on both sides of the centerline Bezier curve L. 3. The control point determining means sets each control point P to P0,
When P1, P2, and P3 are set, a straight line [P0P1] and a control point P0 are orthogonal to each other, and a point at a distance W / 2 from the start point P0 is set to a start point Q0, and a straight line [P2P3] is orthogonal to the control point P3. On the straight line, the point at the distance W / 2 from the end point P3 is set as the end point Q3, and the intersection point between the parallel line of the distance W / 2 from the straight line [P1P2] and the straight line passing through the start point Q0 and parallel to the straight line [P0P1] is controlled. 3. The information processing apparatus according to claim 2, wherein a point Q1 is set, and an intersection of the parallel line and a straight line passing through the end point Q3 and parallel to a straight line [P2P3] is set as a control point Q2. 4. The parallelism evaluation means judges the parallelism from the distance d and the width W between the point of t = 0.5 of the reference Bezier curve L and the point of t = 0.5 of the parallel Bezier curve M. The information processing apparatus according to claim 1, wherein the information processing apparatus comprises: 5. The information processing apparatus according to claim 1 or 2, wherein the reference Bezier curve dividing means divides the reference Bezier curve L at a point of t = 0.5.