JPS6370387A - Circular arc drawing system - Google Patents

Abstract

PURPOSE:To rapidly and accurately draw a circular arc by setting up a function (s) indicating the degree of reduction of an X coordinate in accordance with the increase of a Y coordinate and outputting the output of an (s) inspection device through an X coordinate device or a 45 deg. inspection device in accordance with a condition. CONSTITUTION:A mode is set up by a mode setting means 1 in accordance with a required approximate mode and the initial value of the function (s) indicating the degree of reduction of the X coordinate in accordance with the center coordinates (x0, y0) of a circle, its radius (r) and the increase of the Y coordinate is set up. An (s) calculating device 3 increases the Y coordinate and calculates the change of the function (s) based on the shown and equality. When the calculated (s) is s>=0, the output is informed to an X coordinate changing device 5, and at the time of s<0, the output is informed to the 45 deg. inspection device 6. The device 5 reduces the X coordinate by one unit to calculate the value of (s) and returns the calculated result to the device 4. On the other hand, the device 6 receives the information from the device 4 and compares the X and Y coordinates with each other. When the Y coordinate is smaller or equal than/to the X coordinate, the coordinate is returned to the device 3, and in case of larger than the X coordinate, the processing is completed. The X and Y coordinates are replaced and transferred to 45-90 deg., their codes are replaced to transfer the images to other quadrants and the circular arc is formed by a digital differential analyzer.

Description

[Detailed Description of the Invention] [Summary] This is a method for drawing circular arcs on graphic displays, etc., and there is no need to store a coordinate value table of a reference circle as in the past, and it is possible to draw arcs using any specified approximation accuracy. It occurs sequentially and nonparametrically.

[Industrial Field of Application] The present invention relates to a method for drawing circular arcs in graphic displays and the like.

Drawing an arc on a display is used not only for graphic displays but also for character displays, such as pie chart display, etc. It is an arc that requires less storage capacity and whose precision can be varied depending on the purpose of use. There is a demand for a drawing method.

[Prior Art] Conventionally, the following method has been generally used to draw an arc in a graphic display or the like.

That is, a circle is approximated as a polygon, the accuracy of the approximate polygon is stored as a coordinate table of the reference circle of the bone, or a table of sin and cos, and this is read out to find the points on the circle, and the distance between these points is calculated. Straight lines are sequentially generated and connected using a digital differential analyzer.

[Problems to be Solved by the Invention] According to the conventional arc drawing method described above, a coordinate value table (or sin , Cos table), which requires a considerable amount of storage capacity.

The present invention aims to solve these conventional problems and provide a novel arc drawing method that requires a table (and can arbitrarily set approximation accuracy).

[Means for Solving the Problems] FIG. 1 shows a block diagram of the principle of the arc drawing method of the present invention.

In the figure, reference numeral 1 denotes a mode setting means, which sets the mode according to desired approximation accuracy.

2 is an initial condition setting means, which increments the X coordinate (inc= 2″′ pixel unit), and calculate the X coordinate, the X coordinate, and the initial value of the function S (x=r,
y=o, 5=-r).

3 is an S calculation means, which increases the X coordinate by the increment calculated by the initial condition setting means 2, and calculates the accompanying change in the function S using the following equation.

s=s+y*2ys+im (ys=md+1, im=inc*2
”) 4 is an S testing means, which tests whether S calculated by the S calculation means 3 is positive or negative, and if S is positive or 0, it notifies the means 5, and if S is negative, it notifies the means 6. do.

5 is an X coordinate changing means, and when notified from the S inspection means 4, it decreases the X coordinate by 1 unit (X=x-1) and changes S accordingly (s=s-2*X). is calculated and returned to the S inspection means 4.

6 is a 45 degree inspection means, and when it receives a notification from the S inspection means 4, it judges whether the X coordinate at that time is larger than the X coordinate, and if it is smaller or equal, outputs the X coordinate and the X coordinate. Then, the process returns to the S calculation means 3, and if it is larger, the process ends.

By swapping the X coordinates of these sequentially output points, they are mapped to 45 to 90 degrees, and by changing the signs, they are mapped to other quadrants, and the points between these points are sequentially mapped using a digital differential analyzer. Draw an arc by generating straight lines and connecting them.

[Operation] With the above configuration, a circular arc can be drawn by arbitrarily setting the circle approximation accuracy as the mode.

The mode is an integer 0, 1, 2, 3. -, and the increment (inc) of the X coordinate at that time is 2° = 1 dot, 2' = 2 dots, 22 = 4 dots), 2' = 8
Dot becomes -.

That is, it specifies how many dots apart a circle should be approximated, and when mode O is specified, the circle is drawn dot by dot.

The principle of arc drawing according to the present invention is based on an extension of Ilorn's algorithm.

The calculations for drawing an arc according to the present invention can be performed only by addition, subtraction and shift calculations, and the number of calculations required to calculate one point is as follows.

However, the calculated points are not necessarily the targets of output. That is, as a result of the test by the S test means 4, points where S is positive or zero are invalid points that are not output, and are simply points obtained during calculation.

Type of operation Maximum Minimum Addition/Subtraction 4 times 3 times Shift 2 times 1 time Increment 1 time 0 times Test 1 time 1 time Here, the maximum and minimum are the differences in whether or not processing by the X coordinate changing means 5 is required.

FIG. 2 is a diagram showing an example of arc drawing according to the present invention, and shows an example of drawing with three types of accuracy (mode).

In the figure, the C mark indicates an output point, the Δ mark indicates a point that is calculated until finding the point (○) on the circle and is not output, and the X mark indicates a point filled in by the line generator.

The innermost arc is drawn with a radius of 5 dots and mode O (1 dot per increment in the X coordinate), which is exactly the Horn algorithm.

The middle arc is drawn with a radius of 10 dots and mode 1 (2 dots per increment in the X coordinate).

The outermost circular arc has a radius of 20 dots and is drawn in mode 2 (4 dots per increment in the X coordinate).

As described above, the arc drawing method according to the present invention has the following features.

(1) Approximation accuracy is variable, and high speed or accuracy can be selected as necessary.

(2) The approximation accuracy is specified by the mode, that is, "how many dots to approximate", so as the radius of the circle increases, the number of angles of the approximate polygon increases accordingly, and therefore the drawing accuracy becomes relatively The target will rise.

(3) Operations necessary for drawing can be performed only by addition, subtraction, and shift operations. Therefore, it is possible to perform high-speed drawing by using hardware.

[Example] The present invention will be explained in more detail with reference to an example shown in FIGS. 3 and 4.

FIG. 3 is a flowchart showing processing in one embodiment of the present invention. In the figure, step ■ is initial condition setting, which calculates the increment in the y direction (inc), sets the center coordinates (xo, yo) and radius (r) of the circle, and defines auxiliary variables YS and im. , the X coordinate, the X coordinate and the initial value of the function S are set.

Step (2) increments the X coordinate by an increment (inc) and calculates the change in S associated with the increment.

Step (2) checks whether S is positive or negative, and if S is positive or zero, the process jumps to step (2), and if it is negative, the process proceeds to step (2).

Step (2) decrements the X coordinate by L units, calculates the accompanying change in S, and returns to step (2).

Step ■ checks whether y is larger than X. If it is, proceed to step ■; otherwise, step ■
Proceed to.

Step ■ is the coordinates of the point determined by the previously output x and y (
xo +x+ yo +y) and the newly output xr.

Draw a straight line between the coordinates (xo + xr, yo + yr) of the point determined by yr, and return to step (2).

Step ■ calculates a −2* (xr−yr),
Point (xo +xr+yo +yr) and point (xO+x
Draw a straight line between r a +yO+yr-a).

As a result, 1/8 circle is drawn.

FIG. 4 is a processing flow of one embodiment of the present invention.

The processing flow is written in C language, and the symbols used have the following meanings.

s+=: , s=s+ <<: Shift m-: Decrement Items 11) to 118 are declarations of names and data types (integers).

Section 120 is the definition of auxiliary variables, and Section 121 is the setting of initial conditions.

Items 122 to 124 indicate that y is incremented, S is calculated accordingly, and X is set to XrSY as yr.

Item 125 indicates to check S, and if S is positive or zero, decrement X and compute S.

Item 126 checks whether y is greater than
) means execute item 6.

Items 127 to 136 calculate a = 21 (xr-yr) and calculate the point (xo' + xr + yo + yr) and the point (X
Request the digital differential analyzer (dda) to connect the line between This means to do the same thing and end the process.

138-1) Item 6 is the coordinates of the point determined by the previously output x and y (xo + 1 (, yo + y) and the newly output xr.

The coordinates of the point determined by yr (xo + Xr+ Yo +yr
), ask the digital differential analyzer to connect the lines between This means that you should return to processing.

This draws a complete 360 degree arc.

[Effects of the Invention] As explained above, according to the present invention, by arbitrarily specifying the approximation accuracy, it becomes possible to draw an arc by selecting high speed or accuracy depending on the purpose. The practical effects are extremely large.

[Brief explanation of the drawing]

Fig. 1 is a block diagram of the principle of the present invention, Fig. 2 is a diagram showing an example of arc drawing according to the invention, Fig. 3 is a flowchart showing processing in an embodiment of the invention, and Fig. 4 is an embodiment of the invention. It is a processing flow of an example. In the drawings, 1 is a need setting means, 2 is an initial condition setting means, 3 is an S calculation means, 4 is an S inspection means, 5 is an X coordinate changing means, and 6 is a 45 degree inspection means. , Example of 11:l arc crystal picture a change/failure diagram 82 by Toritsukiha Yontanuki Pro\II Riri Yuu l Enfusei%r

Claims (1)

[Claims] A method for drawing circular arcs on a graphic display, etc., comprising: mode setting means (1) for setting a mode according to desired approximation accuracy; center coordinates, radius, and According to the mode set by the mode setting means (1), the increase in the y-coordinate is calculated, and the initial value of the x-coordinate, the y-coordinate, and the function s indicating the degree to which the x-coordinate decreases as the y-coordinate increases is set. an initial condition setting means (2) for increasing the y-coordinate by the increment calculated by the initial condition setting means (2), and an s calculation means (3) for calculating a change in the function s associated with the increase, and an s calculation means ( s testing means (4) for testing whether the function s calculated by 3) is positive or negative; and when the function s is positive or zero as a result of the testing by the s testing means (4), the x coordinate is decreased by one unit; When the function s is negative as a result of the inspection by the x-coordinate changing means (5) that calculates the change in the function s associated with this, and the s-checking means (4), it is determined whether the y-coordinate is larger than the x-coordinate. , if they are smaller or equal, output the x and y coordinates and return to the processing by the s calculation means (3), and if larger, terminate the processing, the output x coordinate, An arc drawing method characterized in that an arc is drawn by sequentially connecting y coordinates with straight lines.