JPH0452776A - Plotting system for circle - Google Patents

Abstract

PURPOSE:To easily calculate plotting dots on a periphery and to plot a circle at high speed only by means of the generation of dots on a 1/8 periphery by obtaining the dots on the periphery by the operation of an axial direction distance minimum method and obtaining the symmetrical dots on the 1/8 periphery. CONSTITUTION:A plotting data generation means by the operation of the axial direction distance minimum method, a Y=X axis symmetrical coordinate generation means 8 generating coordinate data symmetrical to a (Y=X) axis, a second storage means 5e, an X-axis symmetrical coordinate generation means 9 generating coordinate data symmetrical to the X-axis, a fourth storage means 5g, a Y-axis symmetrical coordinate generation means 10, and a sixth storage means 5i are used. The dots on the 1/8 periphery are sequentially generated, and the dots symmetrical to the (Y=X)-axis, the X-axis and the Y-axis are simultaneously or sequentially generated. Thus, the circle can be plotted by the operation of the 1/8 periphery and the arbitrary circle can be plotted at high speed with simple constitution.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention is particularly applicable to the minimum axial distance method (Reference 2 EPNEWS magazine basic technology of DTP) in graphics output devices such as personal computers, such as displays and printing devices. Regarding the high-speed circle drawing method used.

BACKGROUND ART When drawing a circle in the graphics output of a personal computer or the like, accurate drawing data can be obtained by performing calculations such as SIN and CO8. However, performing calculations such as SIN and CO8 takes too much time, so attempts are made to speed up the calculations by using a dedicated processor for calculations. In addition, if an approximate circle is allowed when drawing a circle, the approximate circle is drawn using an inscribed regular polygon with an appropriate angle, the 1/4 circumference dot is calculated and the remaining circle is symmetrical with the X axis, and the remaining circle is symmetrical with the Y axis. Find points that are axially symmetrical and symmetrical to the origin,
Find the leftmost point and oldest point of the circle and use DDA (Digital D
The drawing speed is improved by a method (Japanese Patent Publication No. 1-20471) in which points on the circumference are simultaneously generated upward and downward from the leftmost point and the rightmost point by calculation (iferential analyzer).

Problems to be Solved by the Invention However, the method using the processor dedicated to calculations has a drawback that the processing speed is fast, but the contour is too bulky. It is necessary to generate points, and the drawing speed is slow.

The present invention has been made to solve the above problems, and it is possible to easily calculate the drawn dots on the circumference using the minimum axial distance method, and to generate a circle by generating only points on the circumference of 178 circles. The purpose of this invention is to provide a circle drawing method that can be completed and drawn at high speed.

Means for Solving the Problems In order to achieve the above object, the circle drawing method of the present invention includes a drawing data generation means based on the calculation of the minimum axial distance method, and (
means for generating coordinate data symmetrical about the Y-axis (Y=X), and means for storing the same; means for generating coordinate data symmetrical about the data of a circle by sequentially generating points on the 1/8th circumference and then simultaneously or sequentially generating points symmetrical to the (Y=X) axis, the X axis, and the Y axis. It has a configuration that generates.

Operation With the above configuration, it is possible to generate points on the circumference by calculating the 91st equation by using the minimum axial distance method, and also to generate points on the 178th circumference that are symmetrical about the Y=X axis, By finding points that are symmetrical about the X-axis and points that are symmetrical about the Y-axis, a circle can be drawn at high speed with a simple configuration.

Embodiment Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The present invention utilizes a circular arc generation method called the minimum axial distance method, and first, an outline of the minimum axial distance method will be explained. In FIG. 3, a circle C having a radius R and centered on the origin 0 on the xY plane is expressed by the following equation.

x+y=R Point P (Xp, Yp) inside circle C has the length of op as Rp,
If the angle with the X axis is θ, then P (Xp, Yp) = P (Rpcosθ, Rpsi
nθ), so Xp2+ Yp2== (Rpcosθ)2+ (Rp
sinθ′)2==Rp2(cos2θ+5in2θ)
:Rp2(R2 holds true. Then, if we set '(!, 7)=R2-(x2+y2), the point where f(x, y)<o is a point inside the circle, and i(x , y)>o is a point outside the circle.Now, let us consider a method of generating a circle on a memory containing an array of dots.On the memory, we draw the xY plane so that the lattice points overlap with the centers of the dots. This is a method of drawing a circle by approximating the circle using grid points.However, the radius is expressed by the number of dots and takes an integer value.

Set the starting point of drawing to the oldest point P, (X
l, Y, )=P, (R, o) To L, select grid points that approximate a circle counterclockwise op. Now, p, 1(xi
-1,y,1) is determined and P.

(xi, y,) Want me. From the property of 178 circles from Pl(R,o) to 45 degrees counterclockwise, Pi-1(x knee,.

Yi-1) The selectable points for K and Pi(Xi, Yi) are shown in Figure 6.
There are only two points: + 1), T, and (X, -1-1, Yi-1+1). Then, these midpoints Zi(X,,
,,Yi-1+1) If it is located inside the circle ('), then P
, as S, , if it is located outside or on the circumference, then P
Select Ti as i.

Using the above f(x, y), f (Z,) = f (Xi-1-,, Y,, +1
)〉.

Then, Pi(Xi, y,)=si(xi, , Yi
-1-4-1) f (Zi) = f (Xi, , 1
− , , Y, −, +1)≦0, then Pi(Xi,
Yi)=T, (Xi-1-1, Yi-1+1). At this time, each f (Zi+1): f(xi
-i, Y, +1) is useful.

When f (Zi) >0(7), p, = siyo p, t
(Z, +1) = f(X,, -H, Y, -4-1-1-)
-1)=f(Z,)-(2Y,-1+1)f(Z,)≦
O(When D, pi='r, twist, f(z,+1)=f(
4-1-1-5, Yl, , 1+1+1)=f (Z
i) -(2Yi-1+1) + (2X,-1+1
) Teal. ΔYi-1=2Y, -, +1, ΔX1
-1=2Xi-1+1 If f (Zi) )o, then P, = (X,-1,Y,1+1)f(zi+1
) = f(zi) -ΔY1-1ΔY, =ΔYi-1+
2 ΔX, = Δxi-1 f If (Z,) ≦ 0, then P, = (x, -1-1, Yi + 1 decade f (Z, 1) = f (Z) - ΔY, -1 + 1 Xi-
1Δ7. = ΔYi-4+2 Δ](, = ΔX, -1-2 It has been conventionally confirmed that approximate grid points on the circumference can be obtained sequentially. The initial value at circle C in Fig. 3 is P1=(R,o) f (Z2) =R2-((R) 2+ (0+ 1
)2)=R-giant ΔY1=1 ΔX1=2R+1. Since the term f(Zi) includes a fraction, in actual calculations, all expressions regarding f(x, y) are executed by multiplying by four.

The present invention is to draw a circle at high speed with a simple configuration using the above-described minimum axial distance method, and a specific embodiment thereof will be described below with reference to FIG.

In Figure 1, 1 is the center coordinate of the circle to be drawn (:r:, y
) and an input device for inputting the radius R, 2 is a circle generator using the circle drawing method of the present invention, 3 is a CPU that controls the circle generator 2, and 4 stores a program for the CPU 3. Program ROM, 6a is f (Zi)
[Storing f (Z,) il! storage means, 6b is l
ΔYi value storage means for storing Yi values; 5C is lxi value storage means for storing Δxi values; 5d is pi (xi, yi)
6. is a first storage means for storing the coordinate value of the coordinate value stored in the first storage means 6d; 6f is a second storage means for storing the coordinate value symmetrical to the Y=X axis of the coordinate value stored in the first storage means 6d; and 6f is the first storage means 5d. 5q is a fourth storage means for storing the X-axis symmetric coordinate values of the coordinate values stored in the second storage means 6e. , 6h is a sixth storage means for storing Y-axis symmetrical coordinate values of the coordinate values stored in the first storage means 6d, and 51 is a second storage means 6.
A sixth storage means stores a Y-axis symmetrical coordinate value of the coordinate value stored in e, and a seventh storage means 6j stores a Y-axis symmetrical coordinate value of the coordinate value stored in the third storage means 6f. The means 6 stores the Y coordinate value stored in the fourth storage means 6q.
8th storage means for storing axially symmetrical coordinate values, 6 is f (Z
, +1), 7a is f(Z,)f(Zi))o(Zl)≦o
7b is a second determining means for determining whether the relationship between the X and Y coordinates stored in the first storage means 6d satisfies Y)X; 8 is a second determining means for determining whether (Y=X ) axis-symmetrical coordinate generation means for generating axis-symmetrical coordinate values (Y=x), 9
is an X-axis symmetric coordinate generation means for generating X-axis symmetric coordinate values,
1o is a Y-axis symmetrical coordinate generation means for generating Y-axis symmetrical coordinate values; 11 is a center coordinate storage means for storing the center coordinates (+, y) of a circle given from the input device 1; and 12 is the first Based on the coordinates stored in the storage means 6d to the eighth storage means 6k, the center coordinates (x, y) of the circle stored in the center coordinate storage means 11 are added to draw a dot on the memory. A dot drawing means, 13 is a memory arranged so that one pit corresponds to one dot, and 14 is an output device for outputting the circular figure drawn on the memory 13 onto a display or recording paper.

The operation of the circle generating apparatus using the circle drawing method of the present invention constructed as described above will be explained with reference to the flowchart shown in FIG. Center coordinates regarding the circle to be drawn (
” * 'l), the radius R is input multiple times from the input device 1 (of the step). The center coordinates of the input circle (!, 7)
is defined in the memory 13 as shown in FIG. It is expressed as yX coordinates and is arranged to coincide with the center of the dot. Next, by storing the center coordinates (x, y) in the center coordinate storage means 11, the influence of the center coordinates on subsequent calculations is removed (step @). Determine f (Z2) = 4 R5 from the input yen data, store it in f (Z,) value storage means 6a, and convert ΔY1-4 to ΔY
Store in the i value storage means 5b, calculate ΔX1=8R+4, and calculate Δx
Stored in the th value storage means 5c, the drawing start point p1=(R
, o) in the first storage means 6d (step f3)
. The coordinate values (R, O) in the first storage means 5d are (Y=X)
Transfer to the axially symmetrical coordinate generating means 8 (y=x) to obtain the axially symmetrical coordinate value (step O). As shown in FIG. 6, the determined coordinate values (0, R) symmetrical to the (Y=X) axis are stored in the second storage means 6e (in step). Next, the first storage means 6
The coordinate values (R, O) in d are transferred to the X-axis symmetric coordinate generating means 9 to obtain the X-axis symmetric coordinate values (Step G). The determined X-axis symmetrical coordinates M(R, O) are stored in the third storage means 6f (step 2). Coordinate values (o,
R) is transferred to the X-axis symmetrical coordinate generating means 9 to obtain the X-axis symmetrical coordinate value (step). As shown in FIG. 7, the determined coordinate values (o, -R) symmetrical to the X axis are stored in the fourth storage means 6q (step 2). Next, the coordinate values (R, o) in the first storage means Sd are transferred to the X-axis symmetrical coordinate generating means 10 to obtain Y-axis symmetrical coordinates (step 2).

As shown in Figure 8, the coordinate values symmetrical to the Y axis (-R
, O) in the sixth storage means 6h (step ■).

The coordinate values (o, R) in the second storage means 5e are transferred to the Y-axis symmetrical coordinate generating means 1o to obtain Y-axis symmetrical coordinates (step 2). The determined coordinate values (o, R) symmetrical to the Y axis are stored in the sixth storage means 51 (step ◎). Third storage means 5
The coordinate values (R, o) in f are transferred to the X-axis symmetrical coordinate generation means 10 to obtain the Y-axis symmetrical coordinate values (step [shares]). The determined Y-axis symmetrical coordinate value (-R2O) is stored in the seventh storage means 5j (step 0). The coordinates (o, -R) in the fourth storage means 6q are transferred to the Y-axis symmetrical coordinate generating means 1o to obtain the Y-axis symmetrical coordinate value (step @). The determined Y-axis symmetrical coordinate values (o, -R) are stored in the eighth storage means 6 (step 2).

Y=X-axis, X-axis, Y-axis symmetrical coordinate values have been generated and stored, so dot the dots corresponding to each coordinate value stored from the first storage means 6d to the eighth storage means 6k. Drawing is performed on the memory 13 via the drawing means 12. At this time, the dot drawing means 12 uses the center coordinates (X) of the circle stored in the center coordinate means 11.

The address of each dot to be drawn is generated while referring to y) (step (21). Next, in order to find the point P2 to be drawn using the minimum axial distance method, the value of f (Z2) is determined by the first determining means 7a. If f(Z2) > O, the point directly above P is selected as P2, so proceed to step ■ (
Step ■). The determined coordinate value (R, -1) of P2 is stored in the first storage means 6d (step 2). For the next drawing point, f(Z3) is calculated by the f (Zi+1) calculation device 6. (of steps). Found f (Z3)=
4R-9woi (z,) g.

Store it in the storage means 5a (step). For the next calculation, ΔY2 is obtained and stored in the ΔYi value storage means 6b (step 0). Similarly, find Δx2 for the next calculation and use dx
The i value is stored in the i value storage means 6c (step ■). In step 2, if f (Z 2 )
, 1) are stored in the first storage means 5d (step ■)
. Next drawing point number f (23) 'e f (Zi
+1) Calculate by the calculation device 6 (step ■). The obtained f (Z3): 12R-s is stored in the f (Zi) value storage means 6a (step @). For the next calculation, ΔY2 is calculated and ΔY is stored in the value storage means 6b (step ■), and at the same time, Δx2 is calculated and Δxi value storage means 6c.
(Step O). In step ■, 1/8th drawing is completed (R, 1), so Y2 x X2 V step G
Return to (step of). The coordinate values of point P2 shown in Fig. 9 (
R, 1) from step @ to step ■, the coordinate values (1, R) symmetrical to the Y=X axis of P2 and the coordinate values symmetrical to the X axis (R ，−
1), (1, -R), their coordinate values symmetrical to the Y axis (-
R,1), (-1,R).

(R, -1), (-1, -R) are found and the next step ■
Then, these eight points are drawn in the memory 13 as dots.

In order to determine the next point P3 to be drawn, steps 2 to 2 are executed. As described above, steps @ to step (2) are sequentially executed until the drawing of 1/8 circle is completed. The relationship between the X and Y coordinates of the point Pi at which the 1/8th circle has been drawn is Yi)X.

When this occurs, the drawing of the circle is terminated in step (2) by a signal from the second determining means 7'b. At this time, a circle shown in FIG. 11 is drawn in the memory 13.

The circle drawn in the memory 13 is visualized on the output device 14.

In addition, in the above embodiment, after generating coordinate values that are symmetrical about the Y=X axis, coordinates are generated in the order of X axis symmetry and then Y axis symmetry.
After generating coordinate values that are symmetrical about the Y=X axis,
The same method can be implemented even if the coordinates are generated in an axially symmetrical order.

Effects of the Invention According to the circle drawing method of the present invention, a circle can be drawn with calculations for 1/8th of the circumference, and since the minimum axial distance method is used as the calculation method, only linear equation calculations are required. Therefore, it is excellent in practical use because it can draw arbitrary circles at high speed with a simple configuration.

[Brief explanation of drawings]

Fig. 1 is a block diagram of an embodiment of the circle drawing method of the present invention, Fig. 2 is an operation flowchart of the above embodiment, and Fig.
Figures 4 and 5 are explanatory diagrams for explaining the circle generation means based on the minimum axial distance method, Figures 6, 7, and 8.
FIGS. 9, 10, and 11 are explanatory diagrams showing the state of drawing a circle, and FIG. 12 is an explanatory diagram of the circle to be drawn and the coordinate system arranged in the memory. 1...Input device, 2...Yen generator,
3...CPU, 4...Program RO
M, 5a...f(Z,) value storage means, 6b...
...ΔY, value storage means, 6c...ΔX, X
Integer value means, 6d...First storage means, 6e...
...Second storage means, 6f...Third storage means,
6q...Fourth storage means, 6h...Sixth
Storage means, 61...Sixth storage means, 5j...
...Seventh storage means, 6k...Eighth storage means,
6...f (Z, +1) arithmetic device, 7a.
...First judgment means, 7b...Second judgment means, 8...Y=x axis symmetrical coordinate generation means, 9...
. . . X-axis symmetrical coordinate generation means, 10 . . . Y-axis symmetrical coordinate generation means, 11 . . . Center coordinate storage means, 12 . . . Dot drawing means, 13.・・・・・・
Memory, 14... Output device. Name of agent: Patent attorney Shigetaka Awano and 1 other person 2nd
Figure diagram circle diagram? . ↑ Koji-7-1 ↑ ×(-1 Figure Figure Figure Figure Figure 11 Figure A Figure 10 Figure 12 Figure No [5

Claims (1)

[Claims] center coordinate storage means for storing center coordinate data of a circle to be drawn; means for determining and storing coordinate data of a drawing start point from the center coordinate data and radius data of the circle; and coordinates symmetrical to the (Y=X) axis. A means for generating data and a storage means for the same; a means for generating coordinate data symmetrical about the X-axis and a storage means thereof; a means for generating coordinate data symmetrical about the Y-axis and a storage means thereof; and an axial direction for determining a circle. It has means for sequentially generating drawing data up to 1/8th of the circumference by calculating the minimum distance method, first generating coordinate data symmetrical to the (Y=X) axis from the initial drawing data, and then generating these coordinate data. A circle drawing method that generates coordinate data symmetrical about the X-axis and Y-axis from the data simultaneously or sequentially, and generates circle drawing data by performing this for 1/8th of the circumference.