JPH03103992A - Calculating device for regular polygon vertex - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

DETAILED DESCRIPTION OF THE INVENTION (Summary) A device for calculating vertices of a regular polygon, which outputs the coordinate values of the vertices of a regular polygon to be obtained from the radius and number of angles of a circumscribed circle input. Regarding the calculation device, the purpose of the regular polygon vertex calculation device is to obtain the coordinate values of the vertices as accurately as possible even for regular polygons with a large number of angles, and to determine whether the specified number of strokes is an even number or an odd number. If the number of angles of the specified regular polygon is odd, the even/odd judgment unit calculates the coordinates of the vertices belonging to two adjacent quadrants of a plane orthogonal coordinate system whose origin is the center of the circumcircle of the specified regular polygon. , and a vertex coordinate calculation unit that calculates the coordinates of vertices belonging to one quadrant divided by both coordinate axes of a rectangular coordinate system having the origin at the center of the circumscribed circle when the specified regular polygon has an even number of angles; and a sign conversion section that converts the sign of the coordinates of the vertices calculated by the vertex coordinate calculation means to calculate the coordinates of the vertices belonging to other quadrants.

[Industrial application field]

The present invention relates to a regular polygon vertex calculation device, and more particularly to a regular polygon vertex calculation device that outputs coordinate values of the vertices of a regular polygon determined from the input radius and number of angles of a circumscribed circle.

(Prior Art) In recent years, computer-aided design, or CAD (Comp
(UterAided Design) has become popular, and is especially frequently used in the manufacturing industry of electrical equipment, machinery, etc. In such CAD, intersection points are calculated when creating design and assembly drawings of parts, etc., until the design is completed. In such a case, if the data regarding the coordinates of the part contains an error greater than the allowable amount, correct processing cannot be performed. For this reason, it is necessary to input data regarding a regular polygon on a plane, which is the basis of each data, with as few errors as possible.

Conventionally, such regular polygons are calculated by calculating the coordinates of each vertex based on the coordinates of the center of the circumscribed circle of the regular polygon, the diameter of the circumscribed circle, and the number of angles. A device for calculating vertices of regular polygons outputs the values on the system.

When this vertex calculation device outputs a regular n-gon whose circumscribed circle has a diameter r, it calculates the vertices on the X-axis on the x-y plane (i.e., coordinates (r + 0)) as shown in As the first vertex (indicated by ■), the i-th vertex is Xi = COS (θ 511 + Δ θ)
*r-(1)y,=sin(θ1-1+Δθ)*r・・
・(2) (However, Δθ=2π/n r θi−1=Δ
θ*i−2) , i=2, . . . , n) The coordinates of the next vertex are calculated in order from the coordinates of the first vertex. In FIG. 6, (a) shows an example of a hexagon, and (b) shows an example of a pentagon.

? [Problems to be Solved by the Invention] By the way, in the conventional regular polygon vertex calculation device described above, the coordinate value of the vertex is calculated based on the value representing the previous vertex (in the above example, the angle θi−■). Since the values are calculated sequentially, errors accumulate, and the later the vertex is calculated, the larger the error in the coordinate values becomes.

Such errors become larger and become more problematic when the number of angles is larger, such as a regular 100-gon used as an approximation of a circle.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide an apparatus for calculating the vertices of a regular polygon, which can obtain the coordinate values of the vertices as accurately as possible even for a closed polygon with a large number of angles.

(Means for solving the problems) In the present invention, the means for solving the above problems are as follows:
As shown in Figure 1, in a regular polygon vertex calculation device that outputs the coordinate values of the vertices of a regular polygon determined from the radius of the input circumscribed circle and the number of angles, it is possible to determine whether the specified number of strokes is even or odd. An even-odd determining unit 1 that determines, and when the number of angles of a specified regular polygon is an odd number, vertices belonging to two adjacent quadrants of a plane orthogonal coordinate system whose origin is the center of the circumcircle of the specified regular polygon. Vertex coordinate calculation that calculates the coordinates of the vertices that belong to the first quadrant divided by both coordinate axes of the orthogonal coordinate system whose origin is the center of the circumscribed circle when the number of angles of the specified regular polygon is even. 2 and a sign conversion section 3 that converts the sign of the coordinates of the vertices calculated by the vertex coordinate calculation means to calculate the coordinates of the vertices belonging to other quadrants.

[Operation] According to the present invention, the even/odd determining unit 1 determines whether the specified regular polygon has an even number of polygons or an overodd number of polygons, and based on this determination, the vertex coordinate calculation unit 2 determines whether the specified regular polygon has an even number of polygons or an overodd number of polygons. When the number of angles of a polygon is odd, the coordinates of vertices belonging to two adjacent quadrants of a plane orthogonal coordinate system whose origin is the center of the circumcircle of the specified regular polygon, and the angles of the specified regular polygon. If the number is even, the coordinates of the vertices belonging to one quadrant divided by both coordinate axes of a rectangular coordinate system with the origin at the center of the circumscribed circle are calculated. Then, the code conversion unit 3 converts the sign of the coordinates of the vertices calculated in the vertex coordinate calculation group and calculates the coordinates of the vertices belonging to other quadrants, so the degree of error accumulation is 1/2 or 1/4 It is possible to obtain the coordinates of the vertices of a regular polygon with high accuracy.

〔Example〕

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a regular polygon vertex calculation device according to the present invention will be described below with reference to the drawings.

2 to 5 show a first embodiment of a regular polygon vertex calculation device according to the present invention. In this embodiment, the even-odd determination section and the vertex coordinate calculation section are combined to form the coordinate calculation section 11.

In this embodiment, any point on the xy plane (x
, y) as the center of the circumscribed circle.

In Figure 2, 11 is the diameter r and center of the circumscribed circle? The input part 12 inputs the coordinate values (x, y) and the number of corners N, and the input part 12 inputs the coordinate values of the first quadrant or the adjacent quadrant according to the input values by formulas (1) and (2) in the same way as before. 13 is the coordinate value X or y of the vertex calculated by this coordinate value calculation unit.
Or, 14 is a sign inversion function that inverts the sign of the X and y coordinate values and outputs the value of the coordinate in the quadrant that was not calculated by the above coordinate value calculation unit. Data output that outputs the coordinates (X1, y) to (xN, yN) of each vertex of the regular polygon to be sought, in addition to the input center coordinates (x, y) to the coordinates of all vertices of the polygon. It shows Iku.

Next, the operation of the regular polygon vertex calculation device according to this embodiment will be explained. FIG. 3 is a flowchart showing the operation of the regular polygon vertex calculation device according to this embodiment. In this embodiment, as shown in FIG. 4(a), when the number of angles input to the input section is an even number, the coordinate value calculation section 12 performs (STI, ST2).
As one quadrant, calculate the coordinate values of vertices existing in the first quadrant (r0α≧X≧O and r10α≧y≧O, where r and α are arbitrary positive constants) (ST3), Also, Fig. 4(b)
As shown in , when the input angle number is odd, (ST
2), the first and fourth quadrants (r
10α≧X≧−(r1α) r1α≧y≧O (where r and α are any positive constants) Calculate the coordinate values of vertices (S
T5).

Then, as shown in FIG. 5, the sign inverting unit l3 inverts the sign of the coordinate values X or y or the coordinate values of When the input number of angles is an even number, the coordinates of the vertices existing in the second, third, and fourth quadrants are obtained (ST4), and when the input number of angles is odd, the coordinates of the vertices existing in the second and third quadrants are obtained. The coordinate value (ST6) of is calculated. Then, by adding the coordinates (x, y) of the stop of the input circumscribed circle to the value of each vertex found, it moves to a predetermined position and outputs this value (S
T7).

For example, if the number of angles entered is an even number, 6, the radius of the circumscribed circle is r
Then, in this embodiment, the coordinate value (rl O) of the vertex ■ of the first quadrant indicated by diagonal lines in FIG. Calculate the coordinate values (rcosg/6, rsinπ/6) of the vertex ■, and
As shown in the figure, by changing the sign of the X coordinate in the table of these vertices, the coordinate value of the vertex ■ (-r cos
π/6, rsinπ/6) and the coordinate value of the vertex (1 r,
O), and by changing the sign of the y coordinate of vertex ■, the coordinate value of vertex ■ (rcosπ/6, -rsinπ/6)
Also, by reversing the signs of the X and y coordinates of vertex ■, the coordinate value of vertex ■ (-rcosπ/6, 1rs
ing/6).

Also, if the number of angles entered is an odd number, 5, the radius of the circumscribed circle is r
Then, similarly, the coordinate values of the apex ■ (r, O) of the first and fourth quadrants indicated by diagonal lines in FIG. By calculating the coordinate values of the vertex ■ (r cos2π/5, rsin2π/5) and changing the signs of the y coordinates of these vertices, the coordinate values of the vertex ■ (− r co sπ/5, rsin
π/5) and the coordinate value of the vertex ■ (rcos2π/5, rs
in2π/5).

Therefore, according to this embodiment, the accumulation of errors can be reduced to one-fourth for even-numbered polygons, and one-half for odd-numbered polygons, compared to the conventional method, resulting in accurate regular polygonal painting. You can get the coordinates of the vertices.

In the above embodiment, the calculation is performed in the first quadrant for an even number, or the first and fourth quadrants for an odd number, and the sign is inverted, but the calculation may be performed in other quadrants.

〔Effect of the invention〕

As explained above, according to the present invention, the coordinate calculation device of the vertices of a regular polygon includes an even/odd determination unit that determines whether the specified number of strokes is an even number or an odd number, and the number of angles of the specified regular polygon is an odd number. Sometimes the coordinates of vertices belonging to two adjacent quadrants of a plane orthogonal coordinate system whose origin is the center of the circumscribed circle of the specified regular polygon, or the circumscribed circle if the specified regular polygon has an even number of angles. a vertex coordinate calculation method that calculates the coordinates of vertices belonging to one quadrant divided by both coordinate axes of a rectangular coordinate system with the origin at the center of the vertex coordinate system; Since the code conversion unit calculates the coordinates of vertices belonging to the quadrant of It has the effect of being able to

[Brief explanation of drawings]

FIG. 1 is a diagram of the principle of the present invention, FIG. 2 is a block diagram showing an embodiment of the regular polygon vertex calculation device according to the present invention, and FIG. 3 is a block diagram of the regular polygon vertex calculation device shown in FIG. A flowchart showing the operation, FIG. 4 is a diagram showing the coordinate calculation range of the regular polygon vertex calculation device shown in FIG. 2, and FIG. 5 is a diagram showing the coordinate calculation range of the regular polygon vertices shown in FIG. FIG. 6 is a diagram illustrating an example of the sign inversion operation of the calculation device, and FIG. 6 is a diagram showing a vertex calculation method of a conventional regular polygon vertex calculation device. 11 1... Even-odd judgment unit 2... Vertex coordinate calculation unit 3... Code conversion unit 1 2 r people) 1- + Z - 2 × x Y (a) (b) No-smartness calculation 1go p's 10, 龜, 3 Kyouide ILff
iFigure 4 Y Y (0) (b)

Claims (1)

[Scope of Claim] A regular polygon vertex calculation device that outputs the coordinate values of the vertices of a regular polygon determined from the input radius and number of angles of a circumscribed circle, which determines whether the specified number of strokes is an even number or an odd number. Even-odd judgment part (1) When the number of angles of a specified regular polygon is odd, vertices belonging to two adjacent quadrants of a plane orthogonal coordinate system whose origin is the center of the circumcircle of the specified regular polygon. Vertex coordinate calculation that calculates the coordinates of the vertices that belong to the first quadrant divided by both coordinate axes of the orthogonal coordinate system whose origin is the center of the circumscribed circle when the number of angles of the specified regular polygon is even. (2), and a code conversion unit (3) that converts the sign of the coordinate of the vertex calculated by the vertex coordinate calculation unit (2) to calculate the coordinate of the vertex belonging to another quadrant. A device for calculating the vertices of a regular polygon.