JPS59211165A - Circular arc generating system - Google Patents

Abstract

PURPOSE:To display quickly a circle having a small error to a regular circle by storing the value of (n) of a regular n-polygon corresponding to the radius value of a circle to a table, reading out the (n) value by the value of a designated radius and then displaying a circle in the form of the regular n-polygon. CONSTITUTION:A division table 1 stores a regular n-polygon which can approximate to a circle within the maximum allowance error range in response to the radius (r) of a circle or a circular arc. A host computer 3 gives the center (Xc, Yc) and the radius (r) of a circle to a parameter control part 2. The part 2 retrieves the table 1 based on the value of the radius (r) and sends back the corresponding (n) to the part 2 itself. At the same time, the center value of the circle is given to a vector generator 7 to perform positioning. Then the coordinate code of each quadrant is read out of a quadrant table 4. The part 2 transfers the value of said code to a coordinate arithmetic part 5, and the part 5 calculates the coordinates by means of an Sin stable 6 and sets the generator 7 to display a circle or circular arc to a CRT8.

Description

DETAILED DESCRIPTION OF THE INVENTION (A) Technical Field of the Invention The present invention relates to an arc generation method in a graphic display device, and more particularly to an arc generation method that can display a nearly perfect circle on a graphic display device.

(B) Background of the Technology Generally, when circles and arcs are displayed on a display device, a perfect circle is approximated by a regular n polygon and displayed. That is, the coordinates indicating the vertices of the regular n-polygon are determined, and each coordinate is connected with a straight line and approximately displayed as a circle.

(C) Problems with the Prior Art In the conventional arc generation method, the value of n of a regular n polygon that is always approximated is constant regardless of the radius of the circle or the arc. Since the value of n is constant, the speed of calculating the coordinates to be determined is also constant, so the speed of displaying circles and arcs is almost constant regardless of the size of the radius.

The fact that the value of n of a regular n-polygon is constant regardless of the radius causes the following problem. FIG. 1 is a diagram for explaining the case where the value of n is constant regardless of the radius. This figure shows the case where the first quadrant arc is displayed in orthogonal coordinates. A circular arc AB (solid line) with radius r is displayed as a straight line AB (broken line). At this time, the maximum value of the error between the circular arc AB and the straight line AB is expressed as a straight line C (M is the midpoint of the straight line AB, C is the middle point of the straight line AB, and C is 7---N\ in the circular arc AB. At this time, the circular arc A' The maximum error between B' and straight line A'B' is the distance a' of straight line M'C'(M' is the midpoint of straight line A'B', C' is the midpoint of arc A'B'). As can be seen from Fig. 1, a'> a. In other words, the error a increases in proportion to the radius r. However, in the conventional circle and arc generation method, the correct value for approximating the circle is independent of the radius r. Since the value of n in the n-polygon is constant, when a circle or arc with a large radius r is displayed, the error a becomes large, so that it looks like an angular circle or arc.

Furthermore, although many of the circles and arcs that are actually displayed have a relatively small radius r, the display speed is almost the same as that of a circle with a large radius r, resulting in a slow overall display speed.

(D) Purpose of the Invention In view of the above conventional drawbacks, the present invention changes the value of n of a regular n polygon that approximates a perfect circle depending on the size of the radius r,
The object of the present invention is to provide a high-speed arc generation method with a small error from a perfect circle.

(B) Structure of the Invention The object of the present invention is to provide a method for generating circular arcs in a graphic display device that approximates and displays circles and circular arcs using regular n-polygons. A predetermined value of n is read from the partition table based on the radius values of the circles and arcs to be displayed, and the correct value determined by the predetermined value of n is calculated. This is achieved by providing an arc generation method characterized in that the displayed circles and arcs are approximated by n-polygons.

(F) Embodiment of the Invention Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. The maximum error between the arc AB and the straight line AB shown in Figure 1 is:
The approximated regular polygon is expressed as a regular n-polygon. r is the radius of the circular arc AB. Here, the radius r is expressed by the number of dots on the display screen. The case where this maximum error is misjudged by one dot (on a display screen, an error of one dot can be considered as a misjudgment range if resolution etc. are considered) holds true. If r and n are determined using equation (1), the result will be as shown in Table 1.

Table 1 Also, in this example, 3inθ and cosθ are sin and co
It shall be obtained from the s table. The sin table is 1 up to sinθo-3inθ129 as shown in Figure 2.
It stores 29 pieces of data.

Here θ0. θ and -θ/29 are angles that increase in steps of 360° and 1512, and θo=0°θng=90°. Also, since it can be expressed as cos θ-5in (90°-θ), by storing the values of sin θ for θ from 0° to 90°, that is, the values of the first quadrant in Cartesian coordinates, the sin θ of all quadrants, The value of cos θ can be obtained. Specifically, sin θ in the first quadrant
To obtain the value of , search sequentially from θ0 in the sin table,
CO8θ can be searched sequentially starting from θ+'251. Second
To obtain the values of sin θ and CO3θ in the quadrant, conversely, sin θ is sequentially searched from the sin table θ129, and c.

Sθ can be searched sequentially starting from θ0 and multiplied by -1. Similarly, sin θ in the third and fourth quadrants.

The value of cos θ can be obtained.

FIG. 3 is a block diagram for explaining the arc generation method according to the present invention. In the figure, 1 is a partitioned table that stores the values of n for r shown in Table 1, 2 is a parameter control unit, 3 is a host computer, and 4 is a partition table that stores the values of n for r shown in Table 1. A quadrant table, 5 a coordinate calculation unit that performs coordinate calculations for generating a circle, and 6 a sin table.

7 is a hector generator, and 8 is a CRT.

Below, we will first describe the arc generation method when displaying a circle.

Center of the circle to be displayed from the host computer (XC+, yc)
and radius r are given to the parameter control section 2. The parameter control unit 2 searches the division table 1 and determines n of the regular n polygon corresponding to the radius r.

Then, the starting point (x5゜yS) which is the starting point for generating a circle
is given to the hector generator for positioning.

Here, Xs””rcO3θO+XC, y5. =rS
inθo +y, (r+xc, yc). FIG. 4 is a diagram for explaining the case where a circle is generated in the first quadrant, and the orthogonal coordinates have the center (XC, yc) of the circle as the origin, and the first... Second. The 3rd degree is the 4th quadrant. Next, the parameter control unit 2 reads out the code of the coordinate in each quadrant from the quadrant table 4. This sign is the same as normal orthogonal coordinates with the origin (0,0), so in the first quadrant (
x, y), i.e. (r co sθ, rs
inθ) are both positive. The parameter control section 2 obtains the above values and sets them in the coordinate calculation section 5. The coordinate calculation unit 51 reads data from the sin table 6 based on the value of n read from the division table 1. In this embodiment, since the value of θ is taken in 1512 increments of 360°, v and w are calculated using the following equation.

v-l·512/n w=128-6·512/n Here, β is the number of times the sin table 6 is searched, and l is incremented by 1 for each search. and V≦12
In the case of 8, it is assumed that arc generation in the first quadrant has ended, and the parameter control unit 2 is driven again, and the process moves to arc generation in the second quadrant. Further, if V>422, the values corresponding to v and w in the sin table 6 shown in FIG. 2 are read out.

Assuming that the read values of sin θ and cor θ are Av and AW, the coordinates are calculated using the following formula.

X = r - Aw + Xc Y = r - Aw + Yc Multiply the values of (X, Y) from Beta 1 to Generator 7 and find the vector connecting the two points with the starting point (Xc, Yc) set earlier. generated and displayed on the CRT8. ■≦128
If it is determined that the arc is generated in the second quadrant, l is reset and counted up again from O. We also know from quadrant table 4 that the arc is generated in the second quadrant (x,
Read that the sign of y) is (minus, plus).

To know which quadrant you are in, first. 2nd゜3rd.
The value corresponding to the fourth quadrant is 00. Of, 02°03,
All you have to do is count up each time you perform a comparison operation. This is always number one. Second. Third. This is because fourth, arc generation is performed. This oo, oi.

Set 02.03 as θ, and do the same for 3rd. Circle generation in the fourth quadrant is performed in order.

Next, a method of generating an arc when displaying an arc will be described. FIG. 5 is a diagram for explaining the arc generation method according to this embodiment. When generating an arc, first host computer 3
center point <Xc, Yc), arc generation start angle θl1 arc generation end angle θ2. A radius r is given to the parameter control section 2. Then, the parameter control unit 2 reads the n value of the regular n polygon from the division table 1 corresponding to the radius r. First, in order to find out which quadrant θl is located in, θl and 128 are compared. If θl ≧128, θl−12
8 and set this value as θl, then θl and 12
Compare 8 again. In this way, the above calculation comparison is performed until θl<128, and the quadrant in which θl exists is examined. If θl≦128, the quadrant at that time is detected from the quadrant table 4, and sin θ, co corresponding to that quadrant is calculated.
Read the sign of sθ. In the case of arc generation, as in the case of circle generation, the first . Second. Third. Since arc generation is performed in order with the fourth quadrant, it is possible to know in which quadrant θl exists, as in the case of circle generation. Next, the coordinates of the starting point (Xs, Ys) shown in FIG. 5 are determined using the following equation.

Xs-Xc+rcosθ5 Ys=Yc+rsinθS 0 Set this value to the vector generator file.

The following is the same as the case of the circle generation method, but in the case of circle generation, the starting angle θI is O, so it is omitted, but in the case of circular arc generation, v
, the values of w are different. That is, v−j2・512/n+θ
5 W-128-12+512. /n+O3. Also V
The following equation is used to determine whether and W has reached the end angle.

θs≦V10·128 Here, θ is a value corresponding to a quadrant. If the above formula holds, the coordinates of (X', Y) are not calculated, and θλ is substituted for θE using the same procedure as checking which quadrant θl exists, and θε and 128 are compared. and do it. And sin
Read out the values of sin θε and cos θE from Table 6. Then, the end point (XE, YF:,) is determined by the following formula.

XE=-rcoSθE+Xc '1'5=rsinθε10Y The value is given to the vector generator 7 and displayed on the CRT 8.

1 (G) Effects of the Invention As explained in detail above, according to the present invention, a positive
Since the value of n of the polygon is made variable, the maximum error is within one dot on the screen, and can be kept within the allowable error range.

Furthermore, since the value of n is small for circles and arcs with small radii that are generally frequently displayed, the number of times the sin table is searched is reduced, and circles and arcs can be generated at high speed overall.

[Brief explanation of the drawing]

FIG. 1 is a diagram for explaining a conventional circle generation method. Fig. 2 is a diagram showing the configuration of a sin table, Fig. 3 is a block diagram showing an embodiment of the circle and arc generation method according to the present invention, and Fig. 4 is a diagram showing the case where a circle is generated in the first quadrant. , FIG. 5 is a diagram for explaining the generation of circular arcs. In the figure, ■ is a partition table, 2 is a parameter control unit, 3 is a host computer, 4 is a quadrant table, 5 is a coordinate calculation unit, 6 is a sin table, 7 is a 2 vector generator, and 8 is a CRT. 3 foil 1 figure

Claims (1)

[Scope of Claims] An arc generation method in a graph ink display device that approximates and displays circles and circular arcs using regular n polygons, comprising: a plurality of positive n polygons corresponding to the radius values of the circles and arcs
It is equipped with a division table that stores the values of n of polygons, reads a predetermined value of n from the division table based on the radius values of circles and arcs to be displayed, and generates a regular n polygon determined by the predetermined value of n. An arc generation method characterized by approximating the displayed circle and arc.