JP2002063587A - Apparatus and method for image processing and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make easily detectable a point on a curve, which is the closest from a point located in the vicinity of the curve. SOLUTION: In a step S1, the curve B is divided into n pieces of segments. In a step S2, the point Q on each segment, which is the closest from the point P located in the vicinity of the curve B, is detected. In a step S3, the point M that is the closest from the point P among detected points Q is detected.

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 method, and a recording medium, and more particularly to information capable of detecting a part of a corresponding object on an image from a designated point. The present invention relates to a processing device and method, and a recording medium.

[0002]

2. Description of the Related Art A curve B as shown in FIG. 1 processed by a so-called computer and displayed as an image.
When editing the display of (t), for example, by dividing it into two, the user operates a pointing device such as a mouse to move the pointer to a place to be edited (a place to be divided), Specify the point you want to edit.

[0003] Since the curve B (t) on the display is constituted in pixel units, the curve B (t) is usually used in the above-described operation.
A point on (t) is not specified. For example, a point near the curve B (t) is specified as a point P in FIG.

Thus, instead of a point on the curve B (t),
When a point in the vicinity of the point is designated, in the computer, a point on the curve B (t) closest to the designated point (point P in the example of FIG. 1) (point M in the example of FIG. 1). ) Is performed.

[0005] Generally, a curve handled by a computer is as follows.
Using the media variable t (0 ≦ t ≦ 1), (X (t), Y (t)) for two dimensions and (X (t), Y for three dimensions)
(T), Z (t)). Where X
(T), Y (t), and Z (t) are each of class C1 (the first-order differential value is continuous). Specifically, Bezier (Be
zier) curves are famous. Here, for simplicity, designation of a point in a curve (X (t), Y (t)) in two dimensions will be considered.

First, the parameter t is set to a value (0, 1/2 ²⁰ , 2) that is an integral multiple of a predetermined value (1/2 ^{20 in} this example).
/ 2 ²⁰ ,..., (2 ²⁰ -1) / 2 ²⁰ , 1) (hereinafter, when it is not necessary to distinguish them individually, these are collectively referred to as a parameter ta). ) Is calculated. That is, a point on the curve B (t) (= (X (ta), Y (t
a)) and a point P specified by the user (= (Xu, Yu))
Is calculated for each value of the parameter ta. Distance = (X (ta) −Xu) ² + (Y (ta) −Yu) ² (1)

Then, ta (= tout) when the minimum distance is obtained from the calculated distances is detected, and a point indicated by the detected value is a point M (= (X (tout)) closest to the point P. , Y
(tout))).

[0008] In this manner, the point M is detected.

The equation (1) is differentiated to obtain a parameter t (solution) when the differential value becomes 0, and a point specified by the parameter t is determined on a curve closest to the point designated by the user. However, as described above, in the cubic Bezier curve, X (t) and Y (t)
Is a function of a cubic expression of the parameter t, so that even if the expression (1) is differentiated, it is a quintic expression, and a solution cannot be obtained. Therefore, as described above, using the parameter t of a predetermined value, tout is detected as an approximate value of the parameter t when the differential value of the equation (1) becomes zero. That is, (in this case, the value of 1/2 ²⁰ Interval) value of the parameter t is based on the accuracy of approximation is required,
For example, by using denser values, approximation with higher accuracy can be performed.

In the above, the curve B (t), which is a quadratic curve, has been described as an example, but basically the same processing is performed in the case of a three-dimensional curve.

[0011]

However, as described above,
Method, the calculation of the distance (calculation of equation (1)) is
It is necessary to perform the operations in proportion to the accuracy, and the point M (= (X
(tout), It takes time to detect Y (tout)))
was there. In the above example, the calculation of equation (1) is 2 ²⁰=
(= 1/2²⁰) Times.

The present invention has been made in view of such a situation, and a point M on a curve B (t) closest to a point P specified by a user can be easily detected. It is to be.

[0013]

According to the present invention, there is provided an information processing apparatus comprising: first acquisition means for acquiring graphic data of a first curve; and second acquisition means for acquiring position data of a first point. First detecting means for detecting, based on the graphic data, a second point on the first curve where the inclination of the tangent is at a predetermined angle; and a second point detected by the first detecting means. Generating means for generating a divided curve having the first point as an end point by dividing the first curve, and a third point closest to the first point on the divided curve generated by the generating means. A second detecting means for detecting based on the graphic data and the position data;
And a third detecting means for detecting a point closest to the first point among the third points detected by the detecting means based on the graphic data and the position data.

The second point is that any angle less than 90 degrees,
The angle can be detected based on a tangent of an angle that is an integral multiple of the angle and ranges from 0 to 360 degrees.

According to the information processing method of the present invention, a first obtaining step of obtaining graphic data of a first curve, a second obtaining step of obtaining position data of a first point, A first point at which the inclination of the tangent becomes a predetermined angle based on the graphic data, and a second point detected in the processing of the first step.
Generating a divided curve having the second point as an end point, and generating a third point closest to the first point on the divided curve generated in the processing of the generating step by using a graphic A second detection step for detecting based on the data and the position data, and, among the third points detected in the processing of the second detection step, a point closest to the first point is defined as graphic data and position data. And a third detection step of performing detection on the basis of the information.

The program of the recording medium according to the present invention comprises a first obtaining step of obtaining graphic data of a first curve, a second obtaining step of obtaining position data of a first point,
A first detection step of detecting, based on the graphic data, a second point on the first curve where the inclination of the tangent becomes a predetermined angle, and a second point detected in the processing of the first detection step Generating a division curve having the second point as an end point by dividing the first curve at a point; and generating a third curve closest to the first point on the division curve generated in the processing of the generation step. A point closest to the first point among the third points detected in the processing of the second detection step, based on the graphic data and the position data. And a third detection step of detecting based on the data and the position data.

According to the information processing apparatus and method of the present invention, and a program for a recording medium, graphic data of a first curve is obtained, position data of a first point is obtained, and a tangent line on the first curve is obtained. Is detected based on the graphic data, the first curve is divided at the detected second point, and a divided curve having the second point as an end point is obtained. A third point closest to the first point on the generated and generated division curve is detected based on the graphic data and the position data, and from among the detected third points, The closest point is detected based on the graphic data and the position data.

[0018]

FIG. 2 shows a configuration example of an image processing apparatus 1 to which the invention is applied.

The operation unit 11 executes a program stored in the program memory 12. For example, the graphic data stored in the data memory 13 is converted into image data and stored in the frame memory 14. Display unit 15
Displays an image corresponding to the image data stored in the frame memory 14.

In this example, since the graphic data of the curve B (t) shown in FIG. 1 is stored in the data memory 13, the arithmetic unit 11 converts the graphic data into image data, It is stored in the frame memory 14. That is, the display unit 15 displays the curve B (t).

The arithmetic unit 11 operates the input unit 16 including a mouse, a keyboard, and the like while the curve B (t) is displayed on the display unit 15 by the user, and edits a point (for example, a curve) to be edited. B (t) into two points), a point near the curve B (t), for example, as shown in FIG.
Is specified, a curve B closest to the point P
(t) A process (detection process) of detecting the point M on the touch panel is executed.

The input / output terminal 17 inputs graphic data before editing (for example, graphic data of the curve B (t)) supplied from an external device, and graphic data after editing (for example, from the point M to the point M). The figure data of the curve B (t) divided into two is output to an external device. The bus 18 is connected to each unit to transmit programs and data.

Next, the arithmetic unit 1 for executing the detection processing
The first processing procedure will be described with reference to the flowchart of FIG. Here, in the state where the image of the curve B (t) shown in FIG. 1 is displayed on the display unit 15, the point P
Is specified.

In step S1, the curve B (t) is divided into n regions (hereinafter, referred to as segment B) in which the angle between the tangents at any two points in the range is less than 90 degrees.
Described as i (t). (n + 1) division points for division into i = 0, 1, 2,... n-1) are detected. That is, (n
The (n + 1) parameter t (hereinafter, parameter t specifying the division point) for specifying (particularly, specifying the coordinates) the +1) division points is referred to as a parameter tj. j
= 0, 1, 2,... N-1, n) are detected.

The parameter tj is t0 = 0 <t1 <t2 <
... <Tn-1 <tn = 1 holds, and the segment Bi (t) starts from the point (X (tj), Y (tj)) on the curve B (t), and X (tj + 1), Y (tj + 1)) is the same curve as the curve B (t) in a range ending at the point.

The details of this process are shown in the flowchart of FIG. That is, in step S11, the arithmetic unit 11 determines from the graphic data of the curve B (t) stored in the data memory 13 that the inclination of the tangent is an integral multiple of 45 degrees (0, 45, 90 degrees). 135 degrees, 18
(0 degree, 225 degrees, 270 degrees, or 315 degrees), and detects the number of the points and the value of the parameter t specifying the points.

Specifically, (dX (t) / dt, dY (t) / d
A point at which t) is a scalar multiple of (sin (s), cos (s)) when s = 0, 45, 90, and 135 degrees is detected.

When the angle of the inclination of the tangent is 0 degree, (dX (t) / dt, dY (t) / dt) at that point is (sin (s), cos when s = 0 degree). (s)) is a positive scalar multiple, and when the inclination of the tangent is 180 degrees, (dX (t) / d
t, dY (t) / dt) is (sin (s), cos when s = 0 degree)
(s)) is a negative scalar multiple of (s)).

When the inclination of the tangent is 45 degrees, (dX (t) / dt, dY (t) / dt) at that point is (sin (s), cos (s) when s = 45 degrees. )) Is a positive scalar multiple, and when the inclination of the tangent is 225 degrees, (dX (t) / d
t, dY (t) / dt) is (sin (s), co when s = 45 degrees)
s (s)) is a negative scalar multiple.

When the inclination of the tangent is 90 degrees, (dX (t) / dt, dY (t) / dt) at that point is (sin (s), cos (s) when s = 90 degrees. )) Is a positive scalar multiple, and when the inclination of the tangent is 270 degrees, (dX (t) / d
t, dY (t) / dt) is (sin (s), co when S = 90 degrees)
s (s)) is a negative scalar multiple.

When the inclination of the tangent is 135 degrees, (dX (t) / dt, dY (t) / dt) at that point is s = 1.
When (sin (s), cos (s)) at 35 degrees is a positive scalar multiple, and when the slope of the tangent is 315 degrees, (dX / dt, dY / dt) at that point is s = At 135 degrees (si
n (s), cos (s)).

According to such a principle, (dX (t) / dt, d
Y (t) / dt) is a tangent line by detecting a point that is a scalar multiple of (sin (s), cos (s)) when S = 0, 45, 90, and 135 degrees. Is 0 degree, 45 degrees, 90 degrees
Degrees, 135 degrees, 180 degrees, 225 degrees, 270 degrees, or 3
A point that is 15 degrees can be detected, and thereby the number of the point and the value of the parameter t specifying the point are detected.

Since X (t) and Y (t) of the cubic Bezier curve are cubic expressions of the parameter t, dX (t)
/ Dt and dY (t) / dt are quadratic. That is, in this processing, s = 0, 45, 90, 135
In each case, the solution of the quadratic equation yields at most two solutions. As a result, a maximum of eight solutions are obtained as a whole.

In this example, a point at which the inclination of the tangent is an integral multiple of 45 degrees is detected. However, if the inclination is less than 90 degrees, the angle may be an integral multiple of another angle.

Next, in step S12, the arithmetic unit 1
1 is the number of points detected in step S11 (the number of solutions)
, And 1 to determine the number (n) of segments. That is, when the curve B (t) is a cubic Bezier curve as in the case of this example, 1 ≦ n ≦ 9.

In step S13, the calculation unit 11
In step S11, the detected parametric variables t (n-1 parametric variables t when expressed by n, which is the number of segments) are arranged in ascending order, and these are set as t1,... Tn-1. , Value 0 as t0 and value 1 as tn, the sum (n
Determine +1) parameters tj.

As described above, when (n + 1) tj have been detected, the process ends. Thereby, the curve B
(t) is specified by the parameter tj (X (tj), Y (t
j)) and the point (X (tj + 1), Y (tj + 1)) can be divided into n segments Bi (t) starting and ending, respectively.

Next, the reason why the angle between the tangents at any two points on the segment Bi (t) thus divided is less than 90 degrees will be described (step S).
In 1, the parameter tj is detected so that the segment Bi (t) has such properties.)

The segment Bi (t) is represented by a curve B (t)
Starting from the point of (X (tj), Y (tj)), (X (tj + 1), Y (tj)
j + 1)) is the same curve as the curve B (t) in the range defined as the end point, but the parameter tj specifying the start point and the end point is, as described above, on the curve B (t). Of the tangents are 0, 45, 90, 135, 180 and 22
The parameter t specifying the point at which the angle is 5 degrees, 270 degrees, or 315 degrees is arranged in ascending order.

That is, since the maximum angle between the tangents at any two points in the segment Bi (t) is 45 degrees between the tangents of the start point and the end point, the segment Bi (t)
The angle between the tangents at any two points in
It is less than 0 degrees (less than 45 degrees).

Since the curve B (t) is of class C1,
In a predetermined range, the same segment Bi (t) is also C
First grade. That is, in the segment Bi (t), the inclination of the tangent is 0 degree, 45 degrees, 90 degrees, 135 degrees, 180 degrees,
Although there always exist points at 225 degrees, 270 degrees, or 315 degrees, in this example, these points are set as the start point or end point of the segment Bi (t) in the processing of step S1, And the angle between the tangents is 45 degrees 2
The existence of the two points contradicts the result of the above-described processing.

From this, it can be said that the angle between the tangents at any two points in the segment Bi (t) is less than 90 degrees (less than 45 degrees).

Next, returning to FIG. 3, in step S2, a point Qi on each segment Bi (t) closest to the point P (= (Xu, Yu)) is detected. Before describing the details of this processing, the properties of the segment Bi (t) will be further described.

A segment having a point (X (tj), Y (tj)) on the curve B (t) as a start point and a point at (X (tj + 1), Y (tj + 1)) as an end point Since the angle between the tangents at any two points present in Bi (t) is less than 90 degrees, the point on segment Bi (t) must pass through start point s, as shown in FIG. There is a straight line L1 perpendicular to the straight line L0 connecting the start point s and the end point e, and a straight line L2 passing through the end point e and perpendicular to the straight line L0.

That is, the point P is changed to the point Pa (= (Xua, Yu)
As in a)), when located on the side opposite to the end point e with respect to the straight line L1, the point Qi on the segment Bi (t) closest to the point Pa can be set as the start point s (to be approximated). Can be).

The point P is changed to the point Pc (= (Xuc, Yu).
When the line is located on the opposite side of the start point s with respect to the straight line L2 as in c)), the point Qi on the segment Bi (t) closest to the point Pc can be the end point e (approximately). be able to).

The point P is changed to the point Pb (= (Xub, Yu)
b)), when located between the straight line L1 and the straight line L2, a straight line L3 passing through the point Pb and perpendicular to the straight line L0;
The point of intersection X with the segment Bi (t) is defined as
It can be (or can be approximated) a point Qi on segment Bi (t). The segment Bi (t) intersects the straight line L3 with the segment Bi (t) at one intersection X.

The above-described approximation can be realized by regarding the segment Bi (t) of the start point s and the end point e as a straight line connecting the start point s and the end point e because its length is short. That is, if the segment Bi (t) is finely divided (the distance between the start point s and the end point e is shortened), the point Qi can be more accurately approximated, and finally, the point M can be more accurately approximated. .

For example, in step S1, if a point where the tangent is at an angle smaller than 45 degrees, for example, 30 degrees, is detected, the number of segments Bi (t) increases.
It can be divided into smaller segments Bi (t), and the accuracy of approximation can be increased.

The processing in step S2 will be described with reference to the flowchart in FIG.

In step S21, the calculation unit 11
The value of a counter i for counting the value of i is initialized to 0. In step S22, the arithmetic unit 11 determines whether or not the value of the counter i is equal to or less than the value (n-1). When it is determined that the value is equal to or less than the value, the process proceeds to step S23.

In step S23, the calculation unit 11
A segment Bi (t) indicated by the value of the counter i (for example,
If the value of the counter i is 0 (initial value), the segment B
0 (t), and if the value is n-1, the segment Bn-1
(t)), it is determined whether or not the point P is located on the opposite side to the end point e with respect to the straight line L1 with respect to the segment Bi (t) as at the point Pa in FIG. However, if it is determined that it is located on the opposite side, the process proceeds to step S24.

In step S24, the calculation unit 11
The point Qi on the segment Bi (t) closest to the point P is defined as a start point s (= (X (ti), Y (ti))).

In step S23, the point P is
If it is determined that it is not located on the opposite side of the end point e with respect to 1, the process proceeds to step S25.

In step S25, the calculation unit 11
It is determined whether the point P is located on the opposite side to the start point s with respect to the straight line L2, like the point Pc in FIG. 5, and if it is determined that the point P is located on the opposite side, the process proceeds to step S26.

In step S26, the arithmetic section 11
The point Qi on the segment Bi (t) closest to the point P is defined as an end point e.

In step S25, the point P is
If it is determined that the position is not located on the opposite side of the start point s, the process proceeds to step S27. That is, when the point P is located between the straight line L1 and the straight line L2, like the point Pb in FIG. 5, the process proceeds to step S27.

In step S27, the arithmetic section 11
The point Qi on the segment Bi (t) closest to the point P is defined as the intersection X of the straight line L3 passing through the point P and perpendicular to the straight line L0 and the segment Bi (t).

Here, how to find the intersection X will be described.

A vector having the start point s and the end point e of the segment Bi (t) as a start point and an end point (hereinafter, referred to as a vector A), and a vector having the start point s and the point P (point Pb) as a start point and an end point, respectively. (Hereinafter referred to as vector B) inner product (IP1)
, A vector A, a vector having a start point s and an arbitrary point on the segment Bi (t) as a start point and an end point (hereinafter referred to as a vector C
) Is calculated.

Then, IP1 (the inner product of the vector A and the vector B) and IP2 (the inner product of the vector A and the vector C) are compared, and when they are equal, the vector C
A point on the segment Bi (t), which is the end point of, is defined as a point Qi (a parameter t specifying the coordinates of the point Qi (hereinafter, referred to as a parameter tqi) is detected).

IP2 is 0 when the start point s is the end point of the vector C, and is IP2 when the end point e is the end point of the vector C. Therefore, ti ≦ t
When ≤ti + 1, IP2 monotonically increases. Accordingly, the parameter t (tqi) when IP1 = IP2 can be calculated by, for example, a bisection method (Bisection method) or a Newton-Raphson method. According to the bisection method or the Newton-Raphson method, if the precision of the parameter t is 2 ²⁰ , the predetermined calculation is 2
By repeating about 0 times, the parameter tqi can be calculated.

When a point Qi (parameter tqi) on the segment Bi closest to the point P is detected in step S24, step S26, or step S27, the process proceeds to step S28, and the arithmetic unit 11 sets the counter i to After incrementing the value by 1, the process returns to step S22, and the subsequent processes are executed.

In step S22, the value of the counter i becomes n
When it is determined that the difference is not smaller than −1 (when it is determined that the difference is larger than n−1), the process ends. That is, from all the segments B0 (t) to Bn-1 (t), the points Q0 to Qn-1 closest to the point P (parameters tq0 to tqn-1)
Until is detected, steps S22 to S28
Is repeatedly executed.

Thereafter, the processing ends.

Next, returning to FIG. 3 again, the process proceeds to step S3, where the calculating section 11 detects a point Qi closest to the point P from the points Q0 to Qn-1 detected in step S2. Let the point Qi be the point M on the curve B (t) closest to the point P.

Specifically, the equation (2) is calculated by substituting the (n + 1) parameters tqi detected in step S2. Distance = (X (tqi) −Xu) ² + (Y (tqi) −Yu) ² (2)

Then, the parameter tqi at the time when the minimum distance is obtained from the calculated distances is detected, and the detected parameter is used as the parameter tout, and the point M (= (X (tout), Y (tout)) )
Is determined.

As described above, when the point M on the segment Bi (t) closest to the point P is detected, the processing ends.

As described above, the point Qi on the segment Bi (t) closest to the point P is calculated for each segment Bi (t) as follows:
It is obtained by about 20 calculations (step S2). In this example, since the number (n) of the segments Bi (t) is nine at the maximum, the point Qi can be detected by a maximum of 180 calculations. The point M is determined by calculating the distance between the point P and up to nine points Qi. That is, the point M can be detected with a smaller number of calculations as compared with the number of calculations ( ²²⁰ times) in the conventional case.

The series of processes described above can be realized by hardware, but can also be realized by software. When a series of processing is realized by software, a program constituting the software is installed in a computer, and the program is executed by the computer, so that the above-described image processing apparatus 1 is functionally realized. .

FIG. 7 is a block diagram showing an embodiment of a computer 101 functioning as the image processing apparatus 1 described above. CPU (Central Processing Uni
t) 111 is connected to an input / output interface 116 via a bus 115, and the CPU 111 allows the user to input a keyboard,
When a command is input from an input unit 118 composed of a mouse or the like, for example, a magnetic disk 131, an optical disk 132, or a magneto-optical disk 1 mounted on a ROM (Read Only Memory) 112, a hard disk 114 or a drive 120.
33 or a program stored in a recording medium such as the semiconductor memory 134 is stored in a random access memory (RAM).
y) Load into 113 and execute. Thus, the various processes described above (for example, the processes shown by the flowcharts in FIGS. 3, 4, and 6) are performed. Further, the CPU 111
Sends the processing result to, for example, the input / output interface 1
Via a display 16, the data is output to a display unit 117 such as an LCD (Liquid Crystal Display) as necessary. The program is stored in the hard disk 114 or the ROM 112 in advance and provided to the user integrally with the computer 101, or the magnetic disk 131, the optical disk 132,
It can be provided as a package medium such as the magneto-optical disk 133 and the semiconductor memory 134, or can be provided to the hard disk 114 via a communication unit 119 from a satellite or a network.

In the present specification, the step of describing a program provided by a recording medium may be performed not only in chronological order according to the described order but also in chronological order. This also includes processing executed in parallel or individually.

[0074]

According to the information processing apparatus and method of the present invention, and the program of the recording medium, the second point on the first curve at which the inclination of the tangent is a predetermined angle is detected, and the detected second point is detected. The first curve is divided at the second point, a divided curve having the second point as an end point is generated, and a third point closest to the first point on the generated divided curve is detected and detected. Since the point closest to the first point is detected from the third points, the point on the curve closest to the first point can be quickly detected.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a curve B (t).

FIG. 2 is a block diagram illustrating a configuration example of an image processing apparatus 1 to which the present invention has been applied.

FIG. 3 is a flowchart illustrating a detection process.

FIG. 4 is a flowchart illustrating details of a process in step S1 of FIG. 3;

FIG. 5 is a flowchart illustrating details of a process in step S2 of FIG. 3;

FIG. 6 is a diagram illustrating a segment Bi (t).

FIG. 7 is a block diagram illustrating a configuration example of a personal computer 101.

[Explanation of symbols]

11 arithmetic unit, 12 program memory, 13 data memory, 14 frame memory, 15 display unit,
16 input sections, 17 input / output terminals, 18 buses

Claims (4)

[Claims] 1. A first method for acquiring graphic data of a first curve.
Acquiring means for acquiring position data of a first point; and acquiring a second point on the first curve at which a tangent slope is a predetermined angle based on the graphic data. A first detecting means for detecting by the first detecting means, and the second point detected by the first detecting means,
Generating means for generating a divided curve having the first point as an end point by dividing the first curve; and a third closest to the first point on the divided curve generated by the generating means. A second detecting means for detecting a point based on the graphic data and the position data; and a point closest to the first point among the third points detected by the second detecting means. An information processing apparatus comprising: a third detection unit configured to detect based on the graphic data and the position data. 2. The second point is an arbitrary angle less than 90 degrees and an integer multiple thereof, and is detected based on a tangent of an angle in a range of 0 to 360 degrees. The information processing apparatus according to claim 1, wherein: 3. A first method for acquiring graphic data of a first curve.
And a second acquisition step of acquiring position data of a first point. A second point on the first curve, at which a tangent is inclined at a predetermined angle, is determined based on the graphic data. The first curve is divided by the second point detected in the processing of the first detection step, and a divided curve having the second point as an end point is obtained by dividing the first curve. A generating step of generating; and a second step of detecting a third point closest to the first point on the divided curve generated in the processing of the generating step based on the graphic data and the position data. A third step of detecting, based on the graphic data and the position data, a point closest to the first point among the third points detected in the processing of the second detecting step. And a detecting step. Processing method. 4. A first method for acquiring graphic data of a first curve.
And a second acquisition step of acquiring position data of a first point. A second point on the first curve, at which a tangent is inclined at a predetermined angle, is determined based on the graphic data. The first curve is divided by the second point detected in the processing of the first detection step, and a divided curve having the second point as an end point is obtained by dividing the first curve. A generating step of generating; and a second step of detecting a third point closest to the first point on the divided curve generated in the processing of the generating step based on the graphic data and the position data. A third step of detecting, based on the graphic data and the position data, a point closest to the first point among the third points detected in the processing of the second detecting step. A detecting step. Recording medium which is recorded a program causing a computer to execute the.