JPS60200371A - Graphic generator - Google Patents

Abstract

PURPOSE:To produce at a high speed a curve of second degree such as a parabola, an oval, a hyperbola, etc. in addition to a straight line and a circle with an algorithm containing no multiplication, by using adders, error registers, selectors and a positive signal detecting circuit, etc. CONSTITUTION:When a curve of second degree is given in the form of f(x, y)=0, the value of f(X, Y) obtained from the coordinate value (X, Y) on a display part is defined as an error ERR. While DX, DY, DDX and DDY are used as parameters which count up the values of X and Y and approximate them to ''0'' while the ERR is always set at the value close to ''0''. The initial values of these parameters are set at registers 12 and 14 as well as 11 and 13, and the comparison between positive and negative errors ERR and various types of additions to the coordinate value in a single direction of X and Y respectively are carried out via adders 15, 16, etc., selectors 19 and 21, a positive signal detecting circuit 22, etc. Thus it is possible to produce at a high speed a curve of second degree by means of an algorithm using additions and no multiplication.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a figure generation device that generates figures to be displayed on a graphic display or the like.

[Technical background of the invention and its problems]

Conventionally, in order to display quadratic curves such as circles and parabolas on graphic displays, it has been necessary to draw them using software that includes multiplication due to the characteristics of quadratic curve equations. If this was done using ordinary hardware, there would be a drawback that the processing would take a long time because it would involve multiplication calculations.

Additionally, hardware that can perform multiplication calculations at high speed is commercially available, but these are extremely expensive.

As a method for eliminating these drawbacks, a ``high-speed yen generation algorithm'' written by Mikio Takagi et al. at the 27th National Convention of the Information Processing Society of Japan is known.

In this method, grid points are selected as if tracing the edge of a circle, and the value of the circular function fcx, y) is incremented instead of subtracted each time. For this reason, the algorithm included only addition, which had the advantage of shortening the processing time.However, this algorithm only draws 1/8 circle, and can draw parabolas, hyperbolas, ellipses, etc. Since it was not possible to draw quadratic curves, it could not be applied to cases where one wanted to draw various quadratic curves, which was very inconvenient.

[Purpose of the invention]

An object of the present invention is to provide an apparatus that can generate not only a straight circle but also quadratic curves such as an ellipse, a parabola, and a hyperbola at high speed using an algorithm that does not involve multiplication.

[Summary of the invention]

The present invention provides coordinate values in the X direction and Y direction of a figure to be displayed on the display section, an increment value that increases or decreases the coordinate values in the X direction and Y direction, the true value of the figure, and the coordinate value on the display section. Initializes the error with the value of the figure, the first increase/decrease value in the X and Y directions that increases or decreases the error, and the second increase/decrease value in the X and Y directions that increases or decreases the first increase/decrease value. a setting means for comparing whether the error is positive, negative, or "0"; and a comparing means for comparing whether the error is positive, negative, or "0"; , add a preset step value to the coordinate value, add a second increase/decrease value to the first increase/decrease value, add the added first increase/decrease value to the error, and add it by the comparison means. If the error set in the setting means is determined to be positive or "0", or if the error set in the setting means is determined to be positive or "0", the coordinate value is changed in the other direction of X or Y. A preset nine-step value is added, a second increase/decrease value is added to the first increase/decrease value, and the added first increase/decrease value is determined to be positive or 0'' by the comparison means. an addition means for adding to the error, the error output from the addition means, the X direction and the Y direction;
The coordinate values in the direction, the step value, the first increase/decrease value, and the increase/decrease value of M2 are initialized again in the setting means, and the coordinate values in the X direction and the Y direction are output.

〔Effect of the invention〕

According to the present invention, it is possible to generate a quadratic curve at high speed by an algorithm using addition, which makes it highly practical and improves efficiency.

[Embodiments of the invention]

Hereinafter, one embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a flow diagram of an algorithm according to one embodiment of the invention. In the present invention, taking into account that the digital quadratic curve displayed as a dot pattern on the display contains errors in any case, high speed is achieved by allowing errors within a range that does not cause any practical problems.

In other words, when a quadratic curve is given in the form f(xty)=O, the value of f(X, Y) due to the coordinate values (XtY) on the display is defined as the error (ERR), and if ERR<O If so, dot (X
IY) exists inside the curve f(x,y)=00 and ERR
)Q, then the point (xty) is the curve f (”t y)=
It can be seen that it exists outside of 00. Therefore, the curve f (”
By selecting grid points so as to follow e y ) = o, a digital curve that approximates this curve can be obtained. In this case, in the algorithm of the present invention, ERR(Q
It includes two judgment steps: and ERR≧0.
Based on this judgment result, in order to advance the coordinate value in the X direction or Y direction, the coordinate (x
, y) are drawn continuously. In addition, in this algorithm, ERR is always close to 00, so in order to increase the values of X and Y by steps, DX, DY, DDX,
I am using DDY. DX and DY are values to be added to ERR when the values in the X direction and Y direction are incremented, respectively.
In the algorithm shown in Fig. 1, when ERR (0), the X coordinate is incremented by DLX, but at this time, DX is added to ERR, and the value of ERR approaches O (DX>0).
When R≧0, the X coordinate is incremented by DLY, but in this case, DY is added to ERR and the ERRO value becomes 0.
approaches (DY (0). The values of DX and DY are not constant, and DDX and DDY are added to each in parallel with the above calculation. In other words, the increment and decrement values of ERR are always increasing and decreasing. Therefore, the ERRO value always takes a value near O at an accelerating rate, and the X coordinate value.

The X coordinate value can be incremented. For this reason, by setting the values of DX, DY, DDX, and DDY to match the equation of the quadratic curve that you want to draw on the display, as described later, you can obtain a digital curve that closely approximates this quadratic curve. Therefore, there is.

Next, each step in the flow diagram of FIG. 1 will be explained.

First, start point (xo, yo), end point (xe ye)
and ERR, DXo, DY6, DDX.

As the initial values of DDY, DLX, and DLY, desired values are given as will be described later. DX,,DY, are values to be added when ERR is negative or positive, and are DX, +DY of ERR.

Set the initial value to approximately □. In step 1, it is determined whether the ERR is positive or negative, and if it is negative, the calculation in step 2 is performed, and if it is positive or 0, the calculation in step 4 is performed. Here, if ERR is negative, the initial value (
Xo + Yo ) exists inside the true curve,
The X coordinate is incremented as shown in step 2 (X =
Xo + D L
RR1DX) o As a result, the value of ERR becomes closer to 0 than the initial value, but if this ERR is positive or 0, or if it is determined to be positive or O in step 1, (xeyo) exists outside the true curve, the X coordinate is incremented (Y=Y, +DLY) as shown in step 4, and the addition/subtraction value DY to be added to ERR
, is added to (DY=DY, +DDY), and the addition result DY is added to ERR (ERR=ERR+
DY). If it is determined in step 3 that ERR is negative, the calculation in step 4 is not performed. The seat 1 (XIY) thus advanced is plotted on a display (not shown) as shown in step 5.

In order to draw an h circle as shown in FIG. 2(b), which will be described later, this is possible by repeating Step 5.

In order to draw a complete circle, it is necessary to invert the signs of several parameters at the y-axis or four poles parallel to the y-axis (P*qyr*' in FIG. 2(C)). In other words, Fig. 2(c)
As shown in , the % circle connected in the 1st and 2nd quadrants is 1#, so that DX and DY are It is necessary to take symmetrical values. Also, it is necessary to reverse the advancing direction of the
must be positive and DY must be negative, but as mentioned above, 2
DDY is added to DXKDDX, DY because it is a parameter of the next curve. For this reason, a point where DX≦0°DY≧0 occurs. In Figure 2 (C), DY is p, l', D
X is q+''. That is, Figure 2 (a) I (b)
When it is stepped to the coordinates of the arrow as shown in
Since the sign of Y becomes positive, DLX, DDX,
Invert the sign of DDY to return DY to negative, and DX
, it is necessary to reduce DY. For this reason, steps 8 and 9 are provided in the flow shown in FIG. In other words, if DY is determined to be positive or O in step 8, DDX and DDY will have different signs, so they will be increased at the same rate when drawing the % circles in Figures 2 (a) and (b), for example. When drawing a percentage circle (not shown) after the arrow dot, DX and DY decrease at the same rate. Also, since DLX also has a different sign, the X coordinate moves in the negative direction, but the Y coordinate moves in the positive direction, so it is connected to the circle shown in Fig. 2 (b), An X circle congruent with this can be drawn. Step 9 of the flow diagram is performed at p+r 2 in Figure 2 (C).
At this point, the sign of DY becomes positive, and the process of step 9 is required to keep it negative. Regarding DX, the first point. DX of IV quadrant and 11th. DX in the I quadrant must take a symmetrical value with points q and 8 as the boundary.The sign of DX is negative at the two points q and S in Figure 2 (c), but if this DX is Step 6.7 is provided in order to restore the value and take a symmetrical value. If it is determined in step 6 that DX is negative or O, then in step 7 DX and DY have different signs, and DLY also has different signs, so the advancing direction of Y is reversed, and D
Since X is also returned to positive, drawing can be continued. In this way, in step 10, the preset end point (xe・~e) and the stepped coordinates (x s y ) are compared, and if they match, the flow process ends, and if they do not match, the process is repeated from step 1. .

Now, change the initialized parameters to coordinate values (xo = yo
), for convenience, ERR=0, first increase/decrease value DX6, D
Y6, second increase/decrease values DDX, DDY, and the parameters after being stepped an appropriate number of times are coordinate values (X, Y),
ERR (kio), first increase/decrease value DX, DY, then DX=DXo+(X-Xo)*DDX ・・・・・・(
A) DY-DYo + (Y Y6 ) * DD Y
...(B) holds true. Here, in equation (C), (
Substituting and expanding formulas A) and (B), we get Skewaku E RR= (X-Xo)*DXo+ Chestnut*(X
o) * (X X6 + 1) + (Y Yo) *
D Yo ten ri* (Y-Yo) * (Y Yo +
1) DDX DDX = −(x−x, )t + (DXO+ ]) (X
-xo) + Sato (y-yo) 2 + (Dy0 + Kumi X) (
y-yo)2...(D) Here, since ERR is always considered to be close to O, if ERR=0, then equation (D) corresponds to an equation representing an arbitrary quadratic curve. In other words, the equation of the quadratic curve to be drawn is modified so that it can be matched with equation (D), and the parameter DXo is
, DYo, DDX, and DDY.

For example, if DDX=DDY=0, equation (D) becomes DXo
(X-Xo) 10DYo(Y-Yo) = 0,
Represents a straight line passing through the point (XO, YO).

DDX=DDY=2, DXo=-1, DYo=-2
01, equation (4) is (X-Xo)" + (Y-Y, -100)" =
(100)” and the center (x, , Yo+100)
, represents a circle with radius 100.

DDX=2. DDY=0. DX,=-1, DYO=-1
00, formula (D) is (X Xo)'' too(y-yo)=.

It represents a parabola with a vertex (xotyo).

D D X=2 e D D Y-2* D Xo”
1, D Yo ” 199, equation (D) is −(X−Xo)” + (Y Yo 100 )” =
100” and the vertex (Xo, Ya +100)
represents the hyperbola of

DDX=5000, DDY=20000, DX
0=-2500.

If DY0=-1010000, equation (D) becomes,
Center (X, , y, +50), major axis 100. It represents an ellipse with a minor axis 50.

Figures 2(a) and (b) show the circle X2+ (
This is a table of coordinate values calculated using this algorithm when drawing ``Y-10)'' = 10', and a digital curve shown by the corresponding dots.As an initial value, (X,
Y)=(0,0).

DDX=2. DDY=2. DXo=1, DY6=
21° Set DLX=1, DLY=1 and ERR-NT(DX0+DY0)=-11.

This is because ERR changes while always taking a value near 0 by adding DX and DY.
The initial values are DX and DY.

This is because the intermediate value of Yen is obtained.

Note that it is not always necessary to start the step from (0, 0) as in this example; for example, if you want to draw the step in the opposite direction from the arrow dot in FIG. 2(b), set DLX=-1, DL
Assuming Y=-1, DX, DY at the coordinates of the arrow dot,
The ERR can be calculated and initialized. Also, Figure 2 (a
), (b) shows an example of drawing a circle, but a parabola, hyperbola, and ellipse can also be drawn using the flow shown in Figure 1. In this case, step 5 draws a parabola, a hyperbola draws a % part bordering the vertex, and an ellipse draws a % circle, and steps 6 to
9, all desired parts can be drawn.

3 and 4 are configuration diagrams of hardware for processing the algorithm flow according to the present invention. The hardware shown in FIG. 3 is built into an image data output device connected to a display, and 11 is a register that holds DDX, 13 is a register that holds DDY, J2 is a register that holds DXo, and 14 is a register that holds DYo. 15.16 are 1 no and 12 respectively
This is an adder that adds the contents of 13 and 14.

17 is a register that holds the ERRO value;
II is output to the adder 18 and selector 19, which will be described later, and when the code pit in the register is 1, that is, when gun<0, the signal (1, # is sent to the signal line 23).
Output to. 18 is an adder that adds the output contents of adder 15 and the contents of error register 17; 19 is register 1;
Register 17 depending on whether ERR held in 7 is positive or negative.
02o is a selector that switches and outputs the content of the adder 16 and the output content of the adder 18. 02o is an adder that adds the output content of the adder 16 and the output content of the selector 19. 21 is the selector 1
a selector that switches and outputs the output content of the selector 19 and the output content of the adder 20 depending on whether the output content of the selector 9 is positive or negative;
22 is a positive signal detection circuit that outputs a signal Lr I I+ when a positive signal is input; 23, 24°; 25 is a signal line;
26.27 is an AND circuit, 28.29 is set in advance to be incremented by +1, (DLX=1.DLY=1
) An X counter and a Y counter which are incremented each time the output from the AND circuits 26 and 27 is input.

Next, the operation in this configuration diagram will be explained. C not shown
PU is stored in registers 11, 12, 13 and 14.
) Set X, DX, DDY, and DY) Set the initial value of ERR in L and error register 17, and set x and X counter 2.
8.29 (sets the initial value of (x, y). (Assume that the ERR set in the error register 17 is negative).

The circuit shown in FIG. 3 performs the operations up to step 5 in the flowchart of FIG. 1, and when drawing a circle, it can be drawn with two % circles. That is, the X coordinate stored in the X counter 28 and Y counter 29 when the clock signal is input.

The Y coordinate is incremented, but when drawing a complete circle,
DX stored in register 12.14.

The CPU (not shown) selects register 11 according to the sign of DY.
．． The signs of DDX and DDY stored in 13, the step number (DLX) set in the X counter 28, and the id Y
This is possible by inverting the sign of the step number (DLY) set in the counter 29. Now, in FIG. 3, the clock signal is sent to the X counter 28. Y
This is input to increment the coordinates (x, y) in the counter 29, store the error in the error register 17, and store DX and DY in the DX register 12 and DY register 14. The following operations are performed during the input interval. The adder 15 adds the DDX output from the register 1 and the DX output from the register 12, and outputs the addition result (DX) to the adder 18. From the error register 17, ERR (signal "
1” passes through the signal line 23 to the selector 19.AND circuit 2
6. The adder 18 adds the DX output from the adder 15 and the ERR output from the error register 17 and outputs the result. However, since the selector 19 inputs the signal "1", the adder 18 outputs the resultant DX. It takes in the ERR and outputs it.

Here, if the sign bit in the error register 17 is 0, that is, the ERR output from the error register 17
is positive or 0, the signal “1” is output from this register.
” is not output, the selector 19 is set to the error register 17.
Input the ERR output as is. Next, the ERR output from the selector 19 is output to the adder 20 and selector 2) through the signal line 24, but this ERR≧
0, the positive signal detection circuit 22 outputs a signal “1” to the selector 2 and the AND circuit 27 through the signal line 25. In the adder 16, the DDY output from the register 13 and the DY output from the register 14 are combined.
are added, this addition result (DY) is output to the adder 20, and the adder 20 outputs it from the selector 19.
R and DX outputted from the adder 16 are added together and outputted, but if the selector 19 inputs the signal "1#", the ERR outputted from the adder 20 is taken in and outputted,
If the signal "1" is not input, the ERR output from the selector 19 is input as is.In this way, before the clock signal is input, the AND circuits 26 and 27 receive the signal "1'' according to the sign of ERR. 1'' is input, the selector 21 outputs ERR, and the adder 5.16 outputs the addition results DX and DY. A new ERR is stored in the error register 17 by inputting a clock signal thereto. Also, signal “1”
Since a signal is output from the AND circuit to which `` is input, for example, in the AND circuit 26, the
is incremented by 1 and a new DX is stored in the register 12. X counter 28. Coordinate 1 from Y counter 29
Although direct X and Y are output, an image data processing device (not shown) displays the corresponding dot on a display etc. using the coordinates (x, y). This is a block diagram of the 71-ware, which is different from the circuit shown in FIG. This hardware outputs a set of coordinate values (x, y) by inputting about 8 clock signals. 30 is an octal counter, and the counted numbers 0 to 7 correspond to the addition of the 8 formula in step 4 of FIG. 1 (replaced with ERR=ERR 10 in step 1.3). This counter also outputs an output enable signal to a register to be described later. 031 is an address ROM.
, and stores the addresses where each of the parameters stored in the register file 32, which will be described later, is stored.○
It also outputs clock signals individually to flip-flops and X and Y registers, which will be described later. 32 is a register file that holds each of the parameters necessary for addition.

33 is an adder, which adds the two parameters (addend, summand) output from the register file 32, and if the result of this addition is negative (1 is set in the sign bit in the adder). 7) Lip-flop 3
Output to 4. 34 is a T flip-flop, which turns on the write enable signal connected to the register file 32 by inputting the signal "P1" and the clock signal.
It is something to do. 35 and 36 are for taking in the X and Y coordinates of the addition result output from the adder 33 using the clock signal output from the address ROMJ7. Next, the operation in this configuration diagram will be explained. First, when the first clock is input to the counter 30, the counter 3
0 outputs a total of K (1) to the address ROM 3. In other words, it instructs to perform the first addition (ERI (=ERR+0)).
Sends the address where "R""O" is stored.The register file 32 sends "'E R" based on this address.
R”ri Ou is sent to the adder 33 through data buses A and B.
Output to. The Kaga device 33 performs addition, but if the addition result (ERR) is negative, a signal r is sent to the flip-flop 34.
r, output IT. The address ROM 31 outputs a clock signal to the flip-flop 34 between the first and second clock inputs. Now, the addition result (E
Assuming that RR) is negative, the flip-flop 34 turns on the write enable signal to the register file 32 using this signal P1'' and the clock signal.

(The clock output from the address ROM is the first
is outputted between the second, fifth and sixth clocks. ) The ERR output from the adder 33 is returned to D of the register file/1732 through the data bus, but O
When the second clock enters the counter 30 after 0, which is written into the original address by write enable No. 9 which is N, it outputs "1 number 2". In response to this, address R
OM outputs the address of "X""DLX"',
The register file 32 is based on this address.
I"D L In the 0 register file sent to the Y register 36, X is written to the original address by the write enable signal that is turned ON.Also, a clock signal is output from the address ROM only to the X register 35, and the addition result X is It is stored in the register 35.

Thereafter, in synchronization with the third and fourth clocks, the third addition (DX=DX+DDK) and the fourth addition g (ER
R, = ERR + DX), the fifth addition (ERR = ER
After the fifth clock, a clock signal is output from the address ROM 31 to the flip-flop 34. At this time, the fifth addition result ERR (=ER
If R+O) is positive or 0, adder 33 does not output signal 1111+ to flip-flop 34. Therefore, even if the clock signal is input to the flip-flop 34, the write enable signal remains ON. At this time, the following 6th addition result (Y = Y + DLY), 7th addition result (DY = DY + DDY), 8th addition result (ERR = ERR + DY), 9th addition result (1 The addition result (ERR=ERR+0) of register file 3
It is written to the corresponding address of 2. Furthermore, if the fifth addition result ERR is negative, the signal LL III is input to the flip-flop 34, thereby turning off the write enable signal. Therefore, the 6.7th and 8.9th addition results are not written, and since the 9th (1st) addition result ERR is naturally negative, the signal "1" and the clock signal are input to the flip-flop 34 again. As a result, the write enable signal is turned ON.

By the way, after the 6th clock, the address ROMJ
7 to the Y register 36, the addition result Y (=Y+DLY) is stored in the register 36. Then, after the 8th clock (that is, the counter 30 changes from "111" to "000") ” counter 30)
From X register 35. Output enable signals are simultaneously output to the Y register 36 and a set of coordinates (x, y) is output.
is output. In this way, if the hardware shown in Figure 4 is used, one set of (x, y) can be output in about 8 clocks, and only one adder is required, and the number of nodes is small. As shown above, by using the algorithm of the present invention, it is possible to generate two curves only by determining whether the error is positive or negative and adding steps, so even a cheap microcomputer without an instruction for multiplication can generate a quadratic curve at high speed. This is very convenient in practice.

[Brief explanation of drawings]

Fig. 1 is a flow diagram of the algorithm of the present invention, Fig. 2 is a diagram of coordinate values and graphs of a quadratic curve using the algorithm of the present invention, and Figs. 3 and 4 show the operation of the algorithm of the present invention. FIG. 2 is a hardware configuration diagram. II, 12, 13. 14...Register, 15° 16.
18.20... Adder, Noah... Error register, 1
9.21...Selector, 22...Positive signal detection circuit,
23, 24.25 signal line, 26.27...AND circuit, 28.29...up/down counter. Agent Patent Attorney Sosuke Chika (and 1 other person) 1st I
2iI Figure 2) ↓ (/:12 1c1 Figure 1 f

Claims (1)

[Claims] Coordinate values in the X and Y directions of the figure to be displayed on the display, step values that increase or decrease the coordinates in the X and Y directions, and the true value of the figure and the coordinate values on the display. Setting means for initializing an error with the value, a first increase/decrease value in the X direction and Y direction that increases or decreases the error, and a second increase/decrease value in the X direction and Y direction that increases or decreases the first increase/decrease value. and a comparison means for comparing whether the error is positive or negative or 110I+, and if the error is determined to be negative by this comparison means, a coordinate value is preset in one direction of X or Y. Add the second increase/decrease value to the first increase/decrease value, add the added first increase/decrease value to the error, and determine whether the error added by the comparison means is positive or If it is determined that the error set in the setting means is positive or 0'', the step value set in advance for the coordinate value in the other direction of X or Y. is added, the second increase/decrease value is added to the first increase/decrease value, and the added first increase/decrease value is determined to be positive or 0 by the comparing means.
'', and the error output from the addition means, the coordinate value 9 step value in the X direction and the Y direction, the first increase/decrease value, and the second increase/decrease value are A graphic generation device characterized in that initial settings are made in the setting means anew and coordinate values in the X direction and the Y direction are output.