JP3137050B2 - Area determination apparatus, method, and storage medium - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an area determining apparatus and method for determining whether an arbitrary point on a rectangular coordinate system is included in a closed area represented by a polygon, and a method for realizing the method. And a storage medium storing the program.

[0002]

2. Description of the Related Art LSI (Large Scall Integrated Circuit)
it) and other wiring connection information using CAD (Computer Aided Des
ign), it is necessary to determine whether any point on the rectangular coordinate system is included in a closed area represented by a polygon (hereinafter referred to as a polygon area) There are cases.

[0003] As a general method for determining whether or not an arbitrary point on the rectangular coordinate system is within a polygonal area, the number of times that an infinite half-line drawn from a point to be determined intersects a side of the polygon is determined. The method of examining is known. in this way,
If the number of intersections between the infinite half line and the sides of the polygon is odd, it is determined that the point to be determined is within the polygon area, and if it is even, it is outside the polygon area.

[0004]

However, in this method, it is necessary to devise how to handle the case where the infinite half line overlaps the vertex of the polygon, and the calculation becomes complicated. In order to solve this problem, Japanese Patent Publication No. 1-49992 discloses a method of determining whether the number whose vector cross product is negative is an even number or an odd number.

However, since the operation of the cross product of the vectors used in this method requires a matrix operation,
Computation becomes relatively complicated. On the other hand, each side of the polygon is represented by a linear equation, and the sign of the calculation result obtained by substituting the coordinates of the point to be determined into these linear equations is determined. A method for determining whether or not the area is within the area is disclosed in JP-A-6-4678 (paragraph "0021").
-"0024").

In order to realize this method, each side is expressed by the following equation.
It is represented by the polynomial shown in

## EQU1 ## f (x, y) = a.times.x + b.times.y + c The signs of the coefficients a, b, and c of the respective terms in Equation 1 are obtained by substituting the coordinate values of the points to be determined at points inside the polygon. It is necessary to determine in advance that the calculated result is negative for any side. That is, the straight line represented by multiplying the right side of Equation 1 by -1 does not change, but the sign of the result calculated by substituting the coordinate value of the point to be determined is reversed. For this reason, in order to determine whether any point on the rectangular coordinate system is included in the polygonal area by this method, at least one point included in the polygonal area must be known.
Obtaining the points included in such a polygonal area is
It is not easy when the shape of the polygon is complicated.

This method can be applied to all determinations as to whether or not a point to be determined is included in a region inside a convex polygon. However,
Regarding a concave polygon, the result of substituting coordinate values into Equation 1 may be positive or negative depending on the position of the point even within the polygon area. It cannot be applied to the determination of inclusion.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems of the prior art, and can determine whether or not an arbitrary point is included in a closed region without requiring complicated calculations. An object of the present invention is to provide an area determination device and method, and a storage medium storing a program for implementing the method.

Further, the present invention stores an area determining apparatus and method capable of determining whether or not an arbitrary point is included in a closed area regardless of the shape, and a program for realizing the method. It is intended to provide a storage medium.

[0010]

In order to achieve the above-mentioned object, a region judging device according to a first aspect of the present invention is arranged such that an arbitrary point on a rectangular coordinate system is a polygon which exists on the rectangular coordinate system. An input means for inputting the coordinates of a point to be determined, and a reference point acquisition for acquiring coordinates of a point outside the closed area. Means, an expression obtaining means for obtaining an expression of a straight line indicating a side of the polygon having a predetermined relationship with the point to be determined inputted from the input means, and the straight line obtained by the expression obtaining means In each of the expressions, reference information obtaining means for obtaining information on the sign of a product obtained by multiplying the result obtained by substituting the coordinates of the points obtained by the reference point obtaining means, and the straight line obtained by the expression obtaining means Expression of it A determination information obtaining unit that obtains information about a sign of a product obtained by multiplying the result of substituting the coordinates of the point to be determined input from the input unit, and the information obtained by the reference information obtaining unit. And a match judging unit for judging whether or not the information acquired by the judging information acquiring unit coincides. If the judgment result of the coincidence judging unit is a match, the point to be judged is outside the closed region. A first output unit that outputs a determination result indicating that the point to be determined is within the closed region when the determination result of the match determination unit does not match. Comprising.

In this area determining apparatus, if an expression indicating a side having a predetermined relationship with the point to be determined is obtained, the subsequent calculation will be performed with the coordinates of the point to be determined and the coordinates of the reference point. It is only necessary to calculate by substituting into the obtained expression. Here, it is possible to obtain an expression indicating a side having a predetermined relationship with the point to be determined, for example, by a simple condition such that the point to be determined is within the coordinate range of the vertices at both ends of the side. It is. For this reason, this region determination device can determine whether or not an arbitrary point is included in a closed region represented by a polygon, without requiring a complicated calculation such as a matrix operation.

Further, the reference point acquiring means acquires a point outside the closed area, so that it is relatively easy to acquire the coordinates of the point. Note that this region determination device is applicable not only to a case where a polygon is convex but also to a case where an arbitrary point is included in a closed region represented by a polygon when the polygon is concave. can do.

[0013] The above-mentioned area determination device further comprises vertex storage means for storing coordinates of each vertex of the polygon, and a straight line indicating each side of the polygon from the coordinates of each vertex stored in the vertex storage means. And an equation calculating means for calculating the equation.

In the above-mentioned area determination apparatus, for example, the expression obtaining means obtains an expression indicating an edge having a predetermined relationship between the coordinates of the vertices at both ends and the coordinates of the point input from the input means. Can be.

[0015]

In the above-mentioned area determination apparatus, the information obtained by the determination information obtaining means may further substitute the coordinates of a point input from the input means into each of the straight line expressions obtained by the expression obtaining means. When the result of multiplying the results by one is 0, the second output unit may output a determination result that the point to be determined is on a side of the polygon.

The point to be determined may exist on the side of the polygon. The second output unit is configured so that the information obtained by the determination information obtaining unit is obtained by substituting the coordinates of a point input from the input unit into each of the straight line expressions obtained by the expression obtaining unit. With a simple condition that the product is 0, it is possible to output a determination result that the point to be determined exists on the side of the polygon.

In order to achieve the above object, a region determining method according to a second aspect of the present invention is directed to a closed region in which an arbitrary point on a rectangular coordinate system is represented by a polygon existing on the rectangular coordinate system. An area determining method for determining whether or not the area is included in the input step, an input step of inputting coordinates of a point to be determined, a reference point obtaining step of obtaining coordinates of a point outside the closed area, and the input step In the equation acquisition step of acquiring a straight line equation indicating the side of the polygon having a predetermined relationship with the point to be determined input in the equation, and in each of the straight line equations acquired in the equation acquisition step, A reference information acquisition step of acquiring information on the sign of a product obtained by multiplying the result obtained by substituting the coordinates of the points acquired in the reference point acquisition step, and a formula for the straight line acquired in the equation acquisition step, A determining information acquisition step of acquiring code information on the product obtained by multiplying together the results obtained by substituting the coordinates of the judgment subject to point inputted by the input step,
A match determining step of determining whether the information obtained in the reference information obtaining step matches the information obtained in the determination information obtaining step, and when the determination result in the match determining step is a match, A first output step of outputting a determination result that the point to be determined is outside the closed region; and, if the determination result in the match determination step does not match, the point to be determined is closed. And a second output step of outputting a determination result that the area is within the area.

In this area judging method, the information obtained in the judging information obtaining step further substitutes the coordinates of the point input in the input step into each of the straight line equations obtained in the equation obtaining step. The method may include a third output step of outputting a determination result that the point to be determined is on a side of the polygon when the product of the results is 0.

In order to achieve the above object, a storage medium according to a third aspect of the present invention has an arbitrary point on a rectangular coordinate system,
A storage medium storing a program for determining whether or not a closed area represented by a polygon present on the orthogonal coordinate system is included, wherein an input step of inputting coordinates of a point to be determined; A reference point acquisition step of acquiring coordinates of a point outside the area, and an equation acquisition of acquiring a straight line equation indicating a side of the polygon having a predetermined relationship with the point to be determined input in the input step Step and, for each of the straight line equations acquired in the equation acquisition step,
The reference information obtaining step of obtaining information on the sign of a product obtained by multiplying the result obtained by substituting the coordinates of the points obtained in the reference point obtaining step, and the input of the input to each of the straight line equations obtained in the equation obtaining step A determination information obtaining step of obtaining information relating to a sign of a product obtained by multiplying the result of substituting the coordinates of the determination target point input in the step, and the information and the determination information obtaining step obtained in the reference information obtaining step A match determining step of determining whether or not the information obtained in step 1 matches; and a determination result that the point to be determined is outside the closed region when the determination result in the match determining step is a match. And the point to be determined is closed when the results of the determination in the first output step and the match determination step do not match. Storing a program for implementing a second output step of outputting a determination result that in the region, characterized in that.

In the above-mentioned storage medium, the information obtained in the determination information obtaining step may further include a result obtained by substituting the coordinates of the point input in the input step into each of the linear expressions obtained in the expression obtaining step. Is a result of multiplying each other by 0, a third determination result that the determination target point is on a side of the polygon is output
May be stored.

[0022]

Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a block diagram showing a configuration of an area determination device according to this embodiment. As shown in the figure, the area determination device includes an input device 1, a polygon data storage device 2, a data processing device 3, and an output device 4.

The input device 1 is constituted by a keyboard, a mouse, a digitizer, or the like, and it is checked whether the input device 1 is included in a closed area represented by a polygon on the XY plane (hereinafter, referred to as a polygon area). (Hereinafter referred to as a survey point). The input device 1 has a buffer for storing the input coordinate data of the survey point.

The polygon data storage device 2 is composed of a semiconductor memory or a magnetic memory or the like, and stores coordinate data of each vertex of a polygon for determining whether or not a survey point is included in a format shown in FIG. Store as a polygon data file. In the polygon data file of FIG. 2, the coordinates (x-coordinate and y-coordinate) between adjacent vertices are continuously stored. The vertices indicated by the coordinates stored last and the coordinates stored first are also adjacent to each other.

The data processing device 3 is mainly composed of a CPU (central processing unit), a main storage device and an auxiliary storage device. The CPU reads out from the auxiliary storage device and executes a program stored in the main storage device. Implements the function described later, and determines whether the survey point is included in the polygonal area. The output device 4 is configured by a display device, a printer, or the like, and outputs a processing result of the data processing device 3.

FIG. 3 is a functional block diagram showing functions of the data processing device 3 of FIG. As illustrated, the data processing device 3 includes a polygon data reading unit 31, an edge data generation unit 32, a survey point data reading unit 33, an edge selection unit 34, a reference point selection unit 35, a reference value calculation unit It comprises a unit 36, a polynomial value calculation unit 37, an area determination unit 38, an edge data file 3a, and a polynomial storage buffer 3b.

The polygon data reading section 31 reads a polygon data file from the polygon data storage device 2.
The edge data generation unit 32 generates edge data from a polygon data file as described later, and stores the edge data in the edge data file 3a. Survey point data reading unit 33
Reads the coordinate data of the survey point stored in the buffer of the input device 1. The edge selection unit 34 selects an edge required for generating a determination polynomial as described later, and stores the edge in the polynomial storage buffer 3b. The reference point selection unit 35 selects a reference point necessary for determining whether or not the survey point is included in the polygon area, as described later. The reference value calculation unit 36
As will be described later, a reference value is obtained by substituting the coordinate data of the reference point into the generated polynomial. The polynomial value calculator 37 obtains a polynomial value in which the coordinate data of the survey point is substituted, as described later. The area determination unit 38 determines whether the survey point is included in the polygonal area based on the calculation result of the polynomial value calculation unit 37.

The operation of the area determining apparatus according to this embodiment will be described below. Here, it is assumed that the coordinates of each vertex of the polygon to be determined are stored in the polygon data storage device 2 as a polygon data file.
In this state, when the operator inputs the coordinates of the survey point from the input device 1, the processing in the data processing device 3 is started.

In the data processing device 3, first, the polygon data reading unit 31 reads a polygon data file stored in the polygon data storage device 2, and passes the read polygon data file to the edge data generating unit 32. .
Then, the process proceeds to the processing of the edge data generation unit 32.

The edge data generation unit 32 calculates the equation (3) based on the coordinates of adjacent vertices in the polygon data file.
The coefficients a, b, and c of the equation representing each side of the polygon represented by Equation 2 are obtained by performing the calculation shown in Equation 2.

## EQU2 ## aX + bY + c = 0

## EQU3 ## a = Y_m-1-Y_m b = -X_m-1+ X_m c = (Y_m-1-Y_m) × X_m-1− (X_m-1 −
X_m) × Y_m-1 (M is an integer from 2 to n)

Then, the edge data generation unit 32
The coordinates of the vertices at both ends of the side used in the calculation as shown in
And the calculated coefficient in association with the edge data file 3
Stored in a.

When the edge data file 3a is generated, the processing shifts to the processing of the survey point data reading unit 33, and the coordinate data of the survey point stored in the buffer of the input device 1 is read. Upon completion of the reading of the coordinate data, the processing of the survey point data reading unit 33 ends.

Next, the processing shifts to the processing of the edge selection unit 34 and the reference point selection unit 35, where the processing of generating a judgment polynomial and selecting the reference point is performed. This processing will be described with reference to the flowchart in FIG. Here, it is assumed that the x coordinate of the survey point is stored in the variable x and the y coordinate is stored in the variable y.

When the process of the flowchart of FIG. 6 starts, first, edge data is read one by one from the edge data file 3a (step S11). Then, the x coordinate of the inspection point is larger than the x coordinate X _m-1 of the first vertex in the read edge data and smaller than the x coordinate X _{m of} the second vertex, or x determines whether less than the x-coordinate X _m-1 of the first vertex greater than the coordinate X _m (step S12).

The x coordinate of the survey point in step S12, the read greater than the x-coordinate X _m-1 of the first vertex in the edge data of the second vertex x smaller than the coordinate X _m, or second the larger than the x-coordinate X _m of the vertex 1 of the vertices of x
When it is determined that the coordinate is smaller than the coordinate _Xm-1, the coefficients a, b, and c of the straight line of the equation representing the corresponding side in the edge data are sequentially stored in the polynomial storage buffer 3b as shown in FIG. It goes (step S13). Polynomial storage buffer 3b
Is multiplied by the polynomial having the coefficients a, b, and c stored in. Then, the processing of step S14
Proceed to reason.

[0036]

[0037]

In step S14, it is determined whether or not unprocessed edge data is stored in the edge data file 3a. If it is determined in step S14 that unprocessed edge data is still stored, the process returns to step S11, and the same processing is performed on the next edge data. If it is determined in step S14 that unprocessed edge data is not stored, the search point and x
Select coordinate points outside the polygon area is the same as the base reference point (step S25), and ends the processing of this flowchart.

Next, the processing shifts to the processing of the reference value calculation unit 36, and the processing of the reference value calculation is performed. This processing will be described with reference to the flowchart in FIG. When the process of the flowchart in FIG. 7 starts, first, 1 is substituted for a variable flag (step S31).

Next, the coefficients a, b, and c of the equation of the straight line representing the side stored in the polynomial storage buffer 3b are read (step S32). Then, the read coefficient and the x and y coordinates of the reference point selected in the processing of FIG.
The calculation is performed by substituting into aX + bY + c shown in, and it is determined whether the calculation result is not 0 (step S3).
3).

If it is determined in step S33 that the calculation result is 0, the determination result that the reference point is a point on the side of the polygon is output to the output device 4 (step S37).
However, since the reference point is selected by the above method, such a determination result does not occur. If it is determined in step S33 that the calculation result is not 0, it is further determined whether the calculation result is smaller than 0, that is, whether the calculation result is negative (step S34).

If it is determined in step S34 that the calculation result is smaller than 0, that is, if it is determined that the result of substituting the coordinates of the reference point into the expression representing the side is negative, the variable fl
The result obtained by multiplying ag by -1 is again substituted for the variable flag (step S35), and the process proceeds to step S36. If it is determined in step S34 that the calculation result is not smaller than 0, the process directly proceeds to step S36. By repeating such processing, the sign of the result of substituting the x-coordinate and y-coordinate values of the survey point into the decision polynomial in which the coefficients are stored in the polynomial storage buffer 3b is obtained.

In step S36, it is determined whether or not unprocessed coefficients a, b, and c are stored in the polynomial storage buffer 3b. If it is determined in step S36 that unprocessed coefficients a, b, and c are stored, the process returns to step S32, and the same processing is performed for the next coefficients a, b, and c. In step S36, the unprocessed coefficient a,
If it is determined that b and c are not stored, the value of the flag at that time is set as a reference value (step S38), and the process proceeds to the polynomial value calculation unit 37. When there are two or more survey points for the same polygon area, the calculation of the reference value can be omitted for the second and subsequent points.

The processing in the polynomial value calculating section 37 is not a reference point in step S33 or step S34.
The processing is the same as the processing in the reference value calculation unit 36, except that the determination is performed by substituting the x coordinate and the y coordinate of the survey point into X and Y.

When the polynomial value is calculated by the polynomial value calculation unit 37, the process proceeds to the area judgment unit 38. The processing in the area determination unit 38 will be described with reference to the flowchart in FIG. When the process of the flowchart of FIG. 8 starts, first, the reference value calculated by the reference value calculation unit 36 is substituted for the variable V0 (step S41). Next, the polynomial value calculated by the polynomial value calculator 37 is substituted for the variable V1 (step S42). And the product of V0 and V1 is -1
That is, it is determined whether the sign of the calculation result obtained by substituting the coordinates of the reference point into the judgment polynomial and the sign of the calculation result obtained by substituting the coordinates of the investigation point into the judgment polynomial are determined (step S43).

In step S43, the product of V0 and V1 is-
1, that is, when it is determined that the sign of the calculation result obtained by substituting the coordinates of the reference point into the decision polynomial and the sign of the calculation result obtained by substituting the coordinates of the survey point into the decision polynomial are different, the survey point is in the polygonal region. Is output to the output device 4 (step S44), and the process ends.

In step S43, the product of V0 and V1 is -1.
In other words, if it is determined that the sign of the calculation result obtained by substituting the coordinates of the reference point into the judgment polynomial and the sign of the calculation result obtained by substituting the coordinates of the investigation point into the judgment polynomial are the same, the investigation point is outside the polygonal area. Is output to the output device 4 (step S45), and the process ends.

The determination result output in step S37, S44 or S45 is output from the output device 4 to the outside and shown to the operator.

Hereinafter, the determination of whether or not the survey point is included in the polygonal area by the area determining apparatus of this embodiment will be described with reference to a specific example. First, as a first example, the coordinates (4
(0, 90) and a point at coordinates (50, 60) are determined. Here, a point at coordinates (60, -20) is selected as the reference point.

The decision polynomial in this example is as shown in Equation 4 regardless of whether the survey point is the point of (40, 90) or the point of (50, 60).

## EQU4 ## (Y-160) × (Y-140) × (Y-10
0) x (Y-80) x (Y-40) x (Y-20)

In this equation, the coordinates of the reference point, X = 60, Y
= -20,

[Equation 5] (−20−160) × (−20−140) ×
(-20-100) x (-20-80) x (-20-4)
0) × (−20−20)> 0. That is, the reference value is positive.

In this equation, X = 4 which is the coordinate of the first survey point
Substituting 0, Y = 90 gives

(90−160) × (90−140) × (90
-100) x (90-80) x (90-40) x (90
-20) <0. In this case, since the polynomial value is negative and the sign is different from the reference value, it can be seen that the point at the coordinates (40, 90) is within the area represented by the polygon.

In this equation, X = 5 which is the coordinate of the second inspection point
Substituting 0, Y = 60 gives

(7) (60-160) × (60-140) × (60
-100) x (60-80) x (60-40) x (60
-20)> 0. Since the polynomial value in this case is positive and has the same sign as the reference value, it can be seen that the point at the coordinates (50, 60) is outside the area represented by the polygon.

Next, as a second example, a point having coordinates (100, 60) and a point having coordinates (100, 100) are respectively included in the polygonal area of the character "A" shown in FIG. Here is a case where it is determined whether or not to be performed. Here, a point having coordinates (90, 130) is selected as the reference point.

The decision polynomial in this example is as shown in Expression 8 regardless of whether the survey point is the point of (100, 60) or the point of (100, 100).

## EQU8 ## (2X + Y-280) × (Y-20)

In this equation, the coordinates of the reference point, X = 90, Y
= 130

(2 × 90 + 130−280) × (130−20)> 0. That is, the reference value is positive.

In this equation, X = 1, which is the coordinate of the first survey point,
00, Y = 60,

(10) (2 × 100 + 60−280) × (60−20) <0. Since the polynomial value in this case is negative and has a different sign from the reference value, it can be seen that the point at the coordinates (100, 60) is within the area represented by the polygon.

In this equation, X = 1, which is the coordinate of the first survey point,
Substituting 00, Y = 100,

## EQU11 ## (2 × 100 + 100-280) × (100
-20)> 0. Since the polynomial value in this case is positive and has the same sign as the reference value, it can be seen that the point at the coordinates (100, 100) is outside the area represented by the polygon.

As described above, the region determining apparatus of this embodiment can determine whether or not a survey point is included in a polygonal region without performing a complicated operation such as a matrix operation. Further, since the reference point in this area determination device is a point outside the polygonal area, it can be obtained relatively easily. Further, this area determination device can be applied to determination as to whether or not any point is included in any polygon including a concave shape as shown in the above specific example.

In the above-described embodiment, the area determining apparatus for determining whether an arbitrary point in the XY plane is included in a closed area represented by a polygon has been described. However, the present invention is not limited to the above. Hereinafter, modified embodiments of the present invention will be described.

In the above embodiment, the data on the polygon to be determined as to whether or not to include the survey point is given by the coordinates of the vertices, but may be given by the equation of a straight line representing each side. . In this case, the coordinates of the vertices may be calculated by determining the intersection of the straight lines, and then it may be determined whether or not the survey point is included in the area within the polygon by the above method.

In the above embodiment, the data processing device 3
The program executed by the CPU is stored in an auxiliary storage device in the data processing device 3 in advance. However,
This program may be provided in a form stored in a storage medium such as a CD-ROM or a floppy disk, and may be installed in an auxiliary storage device in the data processing device 3. Also,
The program stored in such a storage medium may be directly read into the main storage device and executed by the CPU.

[0063]

As described above, according to the present invention,
It is possible to determine whether an arbitrary point is included in a closed region represented by a polygon without performing a complicated operation such as a matrix operation. Further, since a point outside the closed region is used as a reference, it is relatively easy to obtain a reference point. Furthermore, in the present invention, there is no restriction due to the shape of the polygon, such as determining whether an arbitrary point is included in the concave polygon.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of an area determination device according to an embodiment of the present invention.

FIG. 2 is a format of a polygon data file stored in the polygon data storage device of FIG. 1;

FIG. 3 is a functional block diagram illustrating functions of the data processing device of FIG. 1;

FIG. 4 is a format of an edge data file stored in the edge data file of FIG. 2;

FIG. 5 shows a format of polynomial data stored in a polynomial generation buffer of FIG. 2;

FIG. 6 is a flowchart showing a process of generating a determination polynomial and selecting a reference point in an edge selection unit and a reference point selection unit in FIG. 3;

FIG. 7 is a flowchart showing a process of calculating a reference value in a reference value calculating unit of FIG. 3 or a process of calculating a polynomial value in a polynomial value calculating unit;

FIG. 8 is a flowchart illustrating a region determination process performed by a region determination unit in FIG. 3;

FIG. 9 is a diagram illustrating a first example of a polygon to be subjected to area determination and whether or not a survey point is inside the polygon.

FIG. 10 shows a second example of a polygon to be subjected to area determination,
It is a figure explaining whether a survey point is inside this polygon.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Input device 2 Polygon data storage device 3 Data processing device 4 Output device 31 Polygon data read part 32 Edge data generation part 33 Survey point data read part 34 Edge selection part 35 Reference point selection part 36 Reference value calculation part 37 Polynomial value Calculation unit 38 Area determination unit 3a Edge data file 3b Polynomial storage buffer

Claims (8)

(57) [Claims] An area determination device for determining whether an arbitrary point on a rectangular coordinate system is included in a closed region represented by a polygon existing on the rectangular coordinate system, and is a determination target. Input means for inputting the coordinates of a point, reference point obtaining means for obtaining the coordinates of a point outside the closed area, and the polygon having a predetermined relationship with the point to be determined input from the input means An expression obtaining unit that obtains an expression of a straight line indicating the side of, and a result obtained by substituting the coordinates of the point obtained by the reference point obtaining unit into each of the expressions of the straight line obtained by the expression obtaining unit. Reference information acquiring means for acquiring information on the sign of the product, and the result of substituting the coordinates of the point to be determined inputted from the input means into each of the straight line equations acquired by the equation acquiring means. Each other Determination information obtaining means for obtaining information about a sign of a product multiplied by a number; match determining means for determining whether the information obtained by the reference information obtaining means matches the information obtained by the determination information obtaining means And, when the determination result of the coincidence determination unit is a match, outputs a determination result that the point to be determined is outside the closed region, and when the determination result of the match determination unit does not match, A first output unit that outputs a determination result that the point to be determined is within the closed region. 2. A vertex storage means for storing coordinates of each vertex of the polygon, and an equation calculation for calculating an equation of a straight line indicating each side of the polygon from the coordinates of each vertex stored in the vertex storage means. The area determination device according to claim 1, comprising: 3. The formula obtaining means according to claim 1, wherein the formula obtaining means obtains a formula indicating a side having a predetermined relationship between the coordinates of the vertices at both ends and the coordinates of the point input from the input means. 3. The area determination device according to 2. 4. The information obtained by the determination information obtaining means is multiplied by a result obtained by substituting the coordinates of a point input from the input means into each of the straight line expressions obtained by the expression obtaining means. 4. The apparatus according to claim 1, further comprising a second output unit configured to output a determination result that the point to be determined is on a side of the polygon when the product indicates 0. 5. The area determination device according to any one of the above. 5. An area determining method for determining whether an arbitrary point on a rectangular coordinate system is included in a closed area represented by a polygon existing on the rectangular coordinate system, and is a determination target. An input step of inputting coordinates of a point; a reference point obtaining step of obtaining coordinates of a point outside the closed region; and the polygon having a predetermined relationship with the point to be determined input in the input step An equation obtaining step of obtaining a straight-line equation indicating the side of, and a product obtained by multiplying each of the straight-line equations obtained in the equation obtaining step by a result obtained by substituting the coordinates of the point obtained in the reference point obtaining step. A reference information obtaining step of obtaining information relating to the sign of, and a result obtained by substituting the coordinates of the determination target point input in the input step into each of the straight line equations obtained in the equation obtaining step. A determination information obtaining step of obtaining information on a sign of a product obtained by multiplying the information by a code; and a match determination of determining whether the information obtained in the reference information obtaining step matches the information obtained in the determination information obtaining step. And a first output step of outputting a determination result that the point to be determined is outside the closed region when the determination result in the match determination step is a match, And a second output step of outputting a determination result that the point to be determined is within the closed region when the determination results do not match with each other. 6. The product obtained by multiplying the information obtained in the determination information obtaining step by a result obtained by substituting the coordinates of the point input in the input step into each of the linear expressions obtained in the expression obtaining step. 6. A third output step of outputting a determination result indicating that the point to be determined is on a side of the polygon when 0 indicates 0. 6. The method according to claim 5 , wherein Area determination method. 7. A storage medium storing a program for determining whether or not an arbitrary point on a rectangular coordinate system is included in a closed area represented by a polygon existing on the rectangular coordinate system. An input step of inputting coordinates of a target point; a reference point obtaining step of obtaining coordinates of a point outside the closed region; and a predetermined relationship with the point to be determined input in the input step. An expression obtaining step of obtaining an equation of a straight line indicating the side of the polygon, and a result obtained by substituting the coordinates of the point obtained in the reference point obtaining step into each of the equations of the straight line obtained in the expression obtaining step. A reference information acquisition step of acquiring information on the sign of the multiplied product; and a formula for the straight line acquired in the equation acquisition step. A determination information obtaining step of obtaining information on a sign of a product obtained by multiplying the results obtained by substituting a target, and whether the information obtained in the reference information obtaining step matches the information obtained in the determination information obtaining step. A first output step of outputting a determination result that the point to be determined is outside the closed region when the determination result in the match determination step is a match; And a second output step of outputting a determination result that the point to be determined is within the closed area when the determination result in the match determination step does not match, is stored. Storage medium. 8. The product obtained by multiplying the information obtained in the determination information obtaining step by multiplying each of the straight line equations obtained in the equation obtaining step by the results of substituting the coordinates of the point input in the input step into each of the straight line equations. Indicates that the point to be determined is on the side of the polygon when the value is 0. A program for realizing a third output step of outputting a result of the determination that the point to be determined is on a side of the polygon is stored. Item 8. The storage medium according to Item 7 .