JPS60252951A - Generation of digital graphic signal - Google Patents

Abstract

PURPOSE:To obtain an equation of an oval accompanied by the revolution of a coordinate axis at a high speed just with a simple addition/subtraction function, by applying a replacement comparison method to a digital oval signal accompanied by the revolution of the coordinate axis. CONSTITUTION:For an equation (6) of an oval accompanied by the revolution of a coordinate axis, parameters A-C and G are set to a command register 11. Then an oval generating command is given to an input control part 1, and a microprogram control part 4 obtains a dot most close to an oval on an axis (x) or (y). Then a parabola is newly defined and a replacement comparison method is applied to produce an optimum dot at a start point. Thus the (x) coordinates and a displacement are obtained at that time point. These obtained coordinates and displacement are used as the initial displacement of the start point to produce optimum dots successively with use of the displacement comparison method.

Description

TECHNICAL FIELD OF THE INVENTION The present invention relates to a method for generating digital graphic signals used in graphic display devices and numerical machine tools.

(Prior art) It is necessary to generate line figures such as circles at high speed and with high precision. For this reason, various graphic generation algorithms have been studied, and line graphic generators that incorporate these algorithms into hardware have been proposed.

As a conventional line figure generation method, a displacement comparison method is often used.

The displacement comparison method is, for example, ■Kamae, Kosugi, Hoshino: Dot display of one figure IEICE Theory Vol. 1.56-A, No. 7. P
, 40j (July.

1973) ■B, W, Jordan, Jr.
W, J, Lannon, B, D, Ho1m
:”An improved a1gorijin hIII
for the generation of no
nparametric curves” IEICE
Trans, C-22, No, +2. P, +052
(Dec,, +973) When the equation of the line figure written on the cape and to be generated is % formula % (1), the dot to be selected next to the already selected dot including the starting point is 1f mtnl f( pgl = l f(pj)l
then take pj (2) (1,jCll l
=1,2909.8) This is a method of sequentially selecting one dot based on K and generating it from among the candidate dots of each degree shown in FIG. 6 (see FIG. 6 for l).

Equation (1) is expressed as %3D object* = as shown in Figure 7.
It can be considered as the intersection line between f(x+y) (3) and the 17 plane (z=0),
f(Pl) indicates the displacement in )PIK from the X7 plane. Then, compare the absolute value of the displacement using equation (2),
The candidate dot with the smallest displacement is selected as the optimal dot.

When K f (X17) is a quadratic curve and the starting point is on a line figure, the value of 2 in equation (5) can be calculated simply by addition and subtraction.

However, when using this method to generate an ellipse with rotation of the coordinate axes as a line figure, the starting point is not necessarily on the line figure, so by substituting the coordinates of the starting point into equation (5), first calculate the displacement 2. It is necessary to set the initial value. In this case, a multiplication function is required, which complicates the hardware, which is undesirable. In other words, the equation of an ellipse with rotation of the coordinate axes is f(X, y) = Ax2+By2+ Cxy+ G
== 0 (4), and the coordinates of the starting point are P, (!, l y
, ), then the initial value 2 of displacement 2 is z, = f(P,) = Ax, +By, + Cx
, y, + G (5).

(Object of the present invention) The present invention was made in view of the problems in the prior art, and its purpose is to solve the equation t (x, y) = A
x2+By2+Cxy+G= 0 (G is an integer)
Using the displacement comparison method, a digital ellipse signal with rotation of the coordinate axes described in
The purpose of this invention is to provide a graphic generation method that is highly accurate and can be generated with as simple a configuration as possible.

(Configuration of the present invention) The configuration of the present invention to achieve such an object is as follows: The first equation z, == f, (: ly) = Ax2+ By
The present invention is characterized in that a digital graphic signal accompanied by rotation of the coordinate axes described by 2+Cxy+c=:0 is generated by including the following steps (a) to (e).

(1) A step of comparing the absolute values of coefficient A and coefficient B.

(b) In the step (a), if IAI≧IB+, the second equation with X and u as variables and A and G as coefficients is expressed as y and Ma as variables and B and G as coefficients. The fifth equation “5
='3(y+su= By2+Q-y == 0 is defined, and from these, +2 (x, u) == At the neighboring points of Q, the truest value on the X axis that satisfies u==o Nearest digital value 3C
r ” ); satisfies o + 6 points Q, 2 (0, c ),
In the case of the fifth equation 3, is (y, v):
A process in which each point that satisfies 9.5 (0, Q) is given as a starting point, and optimal dots are sequentially generated using a displacement comparison method.

(6) In the first equation, P, 1 (x, + O)
The starting point is t or p, 2(o, y,), and the known f2 (xlo
) or f3(0+3'a) is given as the initial displacement of the starting point in each case, and based on this, the optimal dots are sequentially generated using the one-displacement comparison method.

(Embodiment) FIG. 1 is a block diagram of the configuration of an apparatus for implementing the method of the present invention. This apparatus includes an input control section 1. Output section 2
, a register operation section 3, and a microprogram control section 4.

The input control section 1, the output section 2, and the register operation section 3 are interconnected by an internal bus ABK.

The input control section 1 is a section that controls initial values, commands, etc. given from a host computer (not shown) via the system bus 8B.

The output unit 2 is an external display device (not shown) such as an image memory.
K % X This is the part that outputs the Y coordinate values, and the X register 21. It has a Y register 22, and respective values are set to the x and y registers via an internal bus AB.

The register calculation unit 5 is a part that performs numerical calculations, and R
It is formed by an ALU (register & logical unit) sl and a status register 32.

RALU 3 + has a plurality of internal registers S5, and logical arithmetic operations (eg, addition/subtraction, AND, OR, shift operations, etc.) can be executed between the registers. The status register 32 stores each status (overflow, carry, sign,
(zero flag, etc.) is temporarily held and input to the microprogram control section 4, which will be described later.

The microprogram control section 4 is a section that executes the overall control and graphic generation algorithm, and switches signals from the pipeline register 41, the microprogram memory 42, the address sequencer 43, and the status register 52 of the register operation section 5. Enter i Lunaplexer 4
It is composed of 4.

The pipeline register 41 holds the output from the microprogram memory 42 and sends it to each of the above-mentioned input control section 1, output section 2, and register calculation section 5! It supplies macro instructions. A conditional branch in a microprogram is performed by selecting one of the various statuses from the status register 32 in the multiplexer 44, inputting it to the address sequencer 45, and making a decision.

The operation of this sK configured device will now be described.

Here, as shown in Figure 2 0) and (b), centering on the origin, the equation f(x, y) = AX2+B72-G
: We will deal with the case where an ellipse described by O (where G is an integer) is rotated around the coordinate axes X and 7, centering on the origin.

The equation of an ellipse with coordinate axis rotation is given by equation (6).

*1=fl(xry)=Ax2+By2+cxy
+c=O(6) Next, the operation of the figure generator shown in FIG. 1 will be explained using the flowchart shown in FIG.

■ From a host computer, etc., send each parameter A, B, C, and G shown in equation (6) to the command register 11 via the system bus 8B, and issue an ellipse generation command to the input control unit 1. multiply.

When the ellipse generation command is applied, the microprogram control unit 4 stores the parameters A, B, C, and G set in the command register 11 into an internal register in the register calculation unit 3 via the internal bus AB. do.

■ Next, we compare the absolute values of the parameter person and B, and
If AI≧IB+, as shown in Figure 3 (b),
The dot closest to the ellipse at the point on the axis P, 1(x, O
), IAI < IBI-1i lever, Figure 3 (a) K
The closest point to the ellipse at the point on the y-axis, as shown, is
Add P, 2(0, y ”).IAI≧IB1゜IAI
<IBI Since the procedure is the same for both cases, the case where IAI≧IB+ will be explained here.

■ Parabola z2=f2 (x, u) = kx' +
G −u = 0 is newly defined and the starting point is Qs2(O2
0), displacement t of the starting point, 2. = f2(0,G) =
Using the displacement comparison method with 0 as the initial value, Figure 4←)K
As shown, optimal dots are generated one dot at a time from the starting point Qa2 until u=O.

(2) Stop the generation of the parabola when u=0, and set the x1 displacement of the X coordinate at that time to ``2e = f2 (x, O).

■ “m” “2a, start point Pa, (z, 0),
Displacement of starting point '1g = '1 ("s") = "2m
Then, using the displacement comparison method, the starting point P, , sequentially 1 do,
The optimum dot is generated for each point, and the XrY coordinate values of the optimum dot are set in the X and Y registers of the output section each time, and the optimum dot is printed.

O ■ Repeat step ■ with the tile that has reached the final point.

Based on the above operations, an ellipse with rotation of the coordinate axes can be generated at high speed and with high accuracy using only simple addition and subtraction functions.

(Effects of the present invention) As explained above, the method of the present invention has 2. =f1(z,
y) =Ax2+By2+Cxy+G= o For the elliptic equation described by
x, u ) = 2 Ax2+ G −u = 0 or 13 = f5 ()'
l'I) = n, 2'' Define G-ma = 0, apply the displacement comparison method to this parabola, and calculate the starting point of the ellipse and the displacement of the starting point using only simple addition and subtraction functions without using a multiplication function. Since the value can be easily calculated, according to the method of the present invention, an ellipse with rotation of the coordinate axes can be generated at high speed using only simple addition and subtraction functions.

Also, by comparing the absolute values of coefficients A and B, IAI
When ≧IB+, K on the X-axis, and when IAI < IB+, K B on the y-axis.Since the starting point is switched to be selected on the y-axis, compared to fixing it on either axis, the starting point and starting point are The time required to calculate the displacement can be further shortened.

[Brief explanation of the drawing]

FIG. 1 is a diagram showing the configuration of the apparatus for realizing the method of the present invention, and FIGS. 2 to 4 are diagrams for explaining the operation.
Figure g5 is a flowchart showing an example of the algorithm of the method of the present invention, and Figures 6 and 7 are explanatory diagrams for explaining the conventional method. DESCRIPTION OF SYMBOLS 1... Input control part, 2... Output part, 3... Register calculation part, 4... Microprogram control part, 8B.
...Si;, -Has, AB...Internal bus. Figure 3 Figure 4 Figure 5

Claims (1)

[Claims] (1) A digital figure signal with rotation of the coordinate axes described by the formula % formula of 1Ii1 with x, y as variables and real numbers A, B, C, and integer G as known coefficients is expressed as follows ( A method of generating a digital graphic signal including the steps of a) to (,). (&) Step (b) of comparing the magnitudes of the absolute values of coefficient A and coefficient fiB. In the step (,), if IAI≧IB1, a second Equation z2 = f2 (x + u) ==Ax2+ G -u
=O+ l A l (In the case of IB+, the fifth equation uses y and Ma as variables, and B and G as coefficients ycs = f3
(y+v)=B, 2 +G-v=o, and from these, at points near f2(x, u)=0, the digital value x closest to the true value on the X axis that satisfies u=0. ,,or,
f5c! At points near pma) = 0, the digital value y on the y-axis that satisfies ma = 0 is closest to the true value, and in the case of the second equation, f2(x, u) == 0. (c) In the first equation, Psl ("@*O
) i or P, □(' + ys) as the starting point, x above
, t or y, the known t2(xs,')i9 is given '3(0pys) as the initial displacement of the starting point in each case, and based on this, 1
A process of sequentially generating optimal dots using the displacement comparison method.