JPH0223884B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a nonparametric graphic generation device that can generate quadratic curves at high speed.
In this non-parametric figure generator, the present invention allows the next point to proceed from the current coordinate point to one of eight directions that differ by 45 degrees from each other, including the X-axis direction and the Y-axis direction. An 8-pixel concatenation method that occurs by advancing one predetermined step in the direction,
This method is also used as a four-pixel concatenation method in which pixels are generated by advancing one predetermined step in one of the four directions of the X-axis direction and the Y-axis direction.

[Conventional technology]

Conventionally, as a device that generates quadratic curves at high speed,
Those that use the JORDAN method (“IEEE
TRAN−SACTION ON COMPUTERS DEC,
1973.P.1052～1060 “An Improved Algorithm
for the Generation of Nonparametric
Curves"BERNARD W.JORDAN et al." ) and (Japanese Patent Application No. 56-65795, Japanese Patent Application Laid-Open No. 57-182232) by the same applicant as the present application ("Quadratic Curve Signal Generating Method and Apparatus") are known. In the first step, 3 or 2 points are selected as the next candidate points on the XY coordinates from the points in 8 directions, and in the second step, one point with the minimum absolute value is selected from these candidate points. Select this point and make this point the next point.

Here, the principle of figure generation will be explained.

A quadratic curve is expressed as f(X, Y)=0. In _addition ^{, the} first- _order ^differential coefficient of _this curve ^is expressed _{as f} = δ ² f/δyx,

Now, when z = f (X, Y), if we select the point where the absolute value of z is the smallest from several candidate points on the quadratic curve, we can make f (X, Y) = 0. Approximate figures can be displayed.

Then, the displacement amounts in the X-axis and Y-axis directions are Δx and Δy
(At this time, Δx and Δy take either 0, +1, or -1) and the current coordinate position is P ₀ (x ₀ , y ₀ ), then the position can be determined by the following three equations. can.

(1) When Δx≠0, Δy=0, f(x ₀ +Δx, Δy ₀ )=f(x ₀ , y ₀ +f _x0・Δx+1/2f _xx0・(Δx) ² (2) Δx=0, Δy When ≠0, f(x ₀ , y ₀ +Δy)=f(x ₀ , y ₀ ) +f _y0・Δy+1/2f _yy0・(Δy) ² (3) When Δx≠0, Δy≠0, f( x ₀ + Δx, y ₀ + Δy) = f (x ₀ , y ₀ ) + f _x0・Δx＋f _y0・Δy +1/2 (f _xx0・(Δx) ² +2f _xy0・Δx・Δy +f _yy0・(Δy) ² ) here Since the second-order differential coefficient is a constant, each displacement can be calculated only by addition and subtraction operations, and the above (1)
A quadratic curve can be drawn by calculating equation (3), comparing these absolute values, selecting the coordinate position of the minimum position and using it as the next coordinate position, and updating it sequentially. .

Next, FIGS. 1 and 2 show the configuration of a conventional example. FIG. 2 shows a block diagram of the essential parts of the graphic generator disclosed in Japanese Patent Application No. 56-65795, and FIG. 1 shows the configuration of the output circuit 16 shown in FIG. That is, the output of the program memory 10 in which the microprogram is stored is sent to the control circuit 11.
guided by. The control output of this control circuit 11 is led to registers 12, 13 and an arithmetic circuit 14, respectively. The signal is led to the output register 15 of the arithmetic circuit 14, and its most significant digit (MSB) is led to the sign register of the control circuit 11. The output of this register 15 is led to the registers 12 and 13, respectively.

From the output circuit 16 of this control circuit 11, an up/down counter 18 that holds the X coordinate value and a Y
The ΔX signal and ΔY signal are respectively guided to the input terminals of the up-down counter 19 that holds the coordinate values.
A sign [X] signal and a sign [Y] signal are respectively led to the adjustment terminal. Then, the values of the up-down counters 18 and 19 are taken out to a display device such as a CRT or a plotter, and a quadratic curve is drawn.

This quadratic function curve display device displays the quadratic function f(X,
When displaying the point (X,
The first-order differential coefficients in the _X and Y directions in
When f _Y , the following three steps of calculation and judgment process are performed.

First, by determining whether the signs of the first-order differential coefficients f _X and f _Y are positive or negative, the number of candidate points to proceed to next is limited from eight to three. That is, in the case of a quadratic function, its tangential direction is determined by the first-order differential coefficient. Therefore, by determining whether the sign of the first-order differential coefficient is positive or negative, it is determined to which of the four quadrants the next point belongs.

Next, the candidate points to be selected next are limited to two points by comparing the absolute values of the first-order differential coefficients f _X and f _Y . In other words, by comparing the absolute values of _the first-order differential coefficients _f Alternatively, limit it to two points: a point in the Y direction and a point with a direction of 45 degrees in the positive or negative direction.

Then, for these two restricted points, put their first-order differential coefficients f _X and f _Y into the coordinates
calculate the value of this new f(X, Y) value G ₀ ,
The absolute values of G ₁ are compared, and the coordinates X and Y for which G ₀ and G ₁ give smaller values are selected as the next point to proceed to.

Then, by using this point as the initial value for the next calculation process and repeating the calculation in sequence, f(X, Y)
A quadratic function graphic signal of =0 is generated.

The output circuit shown in FIG. 1 has the configuration of the output circuit 16 shown in FIG. 2 described above, and operates as follows. When the next point is determined, the graphic signal sending output is inputted to input terminal 1 as a logic "1" signal, and AND circuits 2 and 3 are opened. If this determined next point is a point in the 45 degree direction, input terminal 4
Logic "1" is given to the circuits 5 and 6, and the AND circuits 2 and 3 are applied to the up-down counter 7 for the X-axis coordinate and the up-down counter 8 for the Y-axis coordinate.
give input to . As a result, the up-down counters 7 and 8 add or subtract, respectively, in accordance with the sign [X] signal and the sign [Y] signal to generate graphic signals in the 45-degree direction.

Furthermore, if this determined next point is a point in the X direction, logic "1" is given to the input terminal 9, and the up-down counter 7 is added or subtracted through the OR circuit 5 and the AND circuit 2. Generates a graphic signal in the X direction.

Furthermore, if this determined next point is a point in the Y direction, logic "0" is given to the input terminal 9, logic "1" is inverted by the inverter, and the logic is passed through the OR circuit 6 and the AND circuit 3. The up-down counter 8 is added or subtracted to generate a graphic signal in the Y direction.

[Problem to be solved by the invention]

However, in such conventional devices, the control method is fixed to the 8-pixel connection method, and cannot be used in the 4-pixel connection method, which cannot directly step in diagonal directions. As a solution to this problem, a graphic generation device that also uses a reprocessing method is also known. However, it is necessary to change internal arithmetic expressions and control programs each time, making the device complex and expensive.

The present invention solves these problems and has 8
It is an object of the present invention to provide a graphic generation device that can perform display using either a pixel connection method or a four-pixel connection method, does not require complicated additional circuits, and can be constructed at low cost. .

[Means to solve the problem]

The present invention includes at least two registers that store each coefficient and each parameter, an arithmetic circuit that adds and subtracts signals from these registers and stores the arithmetic results in the register, and an arithmetic result from this arithmetic circuit. With a predetermined sequence of operations,
It is equipped with a control circuit that provides an operation instruction signal to the above-mentioned arithmetic circuit, and two up-down counters that hold coordinate position signals of X and Y coordinates and to which an increase/decrease signal of the coordinate position is given from the control circuit. By taking a predetermined step in one of eight directions that differ by 45 degrees from each other on the XY plane, including the It is a device that generates an increment/decrement or an increment/decrement in the Y-axis direction, and the arithmetic means constituted by the control circuit and the arithmetic circuit calculates the first-order differential coefficient f _X of the given quadratic function and the first-order Y By determining the sign of the differential coefficient _f The first calculation means to be selected and the absolute value of the first-order differential coefficient of the above X | f _X
| and the absolute value of the first-order differential coefficient of Y above |f _Y 2 which are 45 degrees different directions
A second calculation means for selecting a point, and the coordinate values of the two points obtained by this second calculation means are substituted into the quadratic function to obtain the function value, and the absolute value of the function value is compared. By selecting the smaller one, the next point to proceed to is in the X-axis direction or 45
and a third calculation means for determining whether the direction is different by 45 degrees, the Y-axis direction, or a direction different from this by 45 degrees, and the control circuit determines which direction to proceed next based on the calculation results of the first to third calculation means. X coordinate,
In a graphic generator equipped with an output circuit that sends out Y-coordinate increase/decrease signals, the output circuit is provided with selection means for selecting between 8-pixel connection and 4-pixel connection, and the selection means selects 4-pixel connection. In this case, means for outputting an increase/decrease signal in the X-axis direction or Y-axis direction common to the two points when the calculation by the second calculation means is completed;
When a point in a direction 45 degrees different from the X-axis direction or Y-axis direction is determined at the stage where the calculation of the third calculation means is completed, in addition to the increase/decrease signal in the X-axis direction or Y-axis direction outputted above, It is characterized by comprising means for outputting an increase/decrease signal in the Y-axis direction or the X-axis direction of the point determined by the third calculation means.

〔Example〕

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 3 is a circuit diagram of an output circuit according to an embodiment of the present invention. This is the configuration of the output circuit 16 shown in FIG. 2, and shows a characteristic configuration of the present invention.

This output circuit connects the input terminals 20 and 21 into which the step signal of the microprogram is input to the switching terminals a ₁ and a ₂ of the selection circuit 22, respectively, and connects the common contact of the selection circuit 22 to the AND circuits 23 and 2.
Connect to one input terminal of 4. The other input terminal of this AND circuit 23 is connected to an input terminal 25 into which a direction indicating signal indicating the X or Y direction is input. Further, the input terminal 25 is connected to another input terminal of the AND circuit 24 via an inverter 26 .

Input terminal 2 into which the 45 degree component direction signal is input
7 to one input terminal of the AND circuit 28,
The input terminal 21 is connected to the other input terminal of the AND circuit 28. The output of AND circuit 28 is led to one input terminal of AND circuits 29 and 30, respectively. The output of the inverter 26 is led to the other input terminal of the AND circuit 29, and the input terminal 25 is connected to the other input terminal of the AND circuit 30. The outputs of the AND circuits 29 and 30 are respectively guided to switching terminals b ₁ and b ₃ of a selection circuit 31 which is interlocked with the selection circuit 22, and the output of the AND circuit 28 is guided to switching terminals b ₂ and b ₄ , respectively.

The two sets of common contacts of the selection circuit 31 are led to one input terminal of the OR circuits 32 and 33, and the output of the AND circuit 23 is led to the other input terminal of the OR circuit 32. The output of the AND circuit 24 is led to the terminal. The output of this OR circuit 32 is led to the input terminal of the up-down counter 18, and the output of the OR circuit 33 is led to the input terminal of the up-down counter 19.

FIG. 4 is a flowchart when drawing a circle using the apparatus of this embodiment shown in FIG.

With such a circuit configuration, first, it is selected whether the present device is used for 8-pixel display or 4-pixel display. Now, the case where it is used in a 4-pixel display will be explained.
A 4-pixel display selection signal is applied to selection circuits 22 and 31. As a result, the selection circuit 22 selects the switching terminal a ₁
The selection circuit 31 is connected to the switching terminal b ₁ side, b ₃ side
Each side is selected. This selection may be made by operation from the console or by a signal from another device.

In this state, first registers 12 and 13
Various data regarding the quadratic curve f (X, Y) = 0 to be drawn (specifically, the first-order differential coefficients f _X , f _Y and the second-order differential coefficients f _XX , f _YY , f _XY , where f _X = δf/δx, f _Y = δf/δy, f _XX = δ ² f/δx ² , f _XY = δ ² f/δyδx, f _YY = δ ² f/
δy ² is given. The calculation sequence is stored in the program memory 10 as a microprogram. The control circuit 11 uses a combination of the operation command of this microprogram and the contents of the code register.
instructs the arithmetic circuit 14 to add or subtract the contents of any address in the register 12 and the contents of any address in the register 13, and to store the result of the operation in the register 15.

That is, as shown in Figure 4, the sign of the first-order differential coefficient is determined, and if f _Y is negative, the sign [X] signal is added; if f _Y is positive, the sign [X] signal is subtracted, and _f If is negative, the sign [Y] signal is subtracted, and if f _X is positive,
The sign [Y] signal is a signal indicating addition,
The signals are applied to up-down counters 18 and 19, respectively. This operation is performed in steps.

Next, the magnitude of the absolute value of f _X |f _X | and the absolute value of f _Y |f _Y | is compared, and this result is compared with the
Based on the results with the step, there are 8 candidate points for the next point to draw.
Restricted to points in two directions from the direction.

In other words, if _{| f}
Candidate points are limited to two points. Also, |f _X |>|
If f _Y |, the candidate points are limited to two points: one point in the Y direction (Y) and the other point in the 45 degree direction (XY). This judgment is made in steps.

In this step, the operation that is a feature of the present invention is performed. In other words, in the case of 4-pixel connected display, 2
When a direction indicating signal in the X direction (when the candidate point is X, XY) or the Y direction (when the candidate point is Y, XY), which is the direction common to these two points at a candidate point limited to Sent to a display device.

Direction signal X or Y indicating the point in this X direction
A direction indicating signal Y indicating a point in the direction is applied to an input terminal 25 in FIG. That is, if the direction indication signal is X, it is applied to the input terminal 25 as a logic "1" signal, and if it is the direction instruction signal Y, it is applied to the input terminal 25 as a logic "0" of its complement signal. At this time, input terminal 2
0 is given a T5 signal of logic ``1'' indicating that the step is being executed. Therefore, when the AND circuits 23 and 24 are opened and the direction indicating signal It is added or subtracted according to the sign [X] signal. Moreover, if the direction indication signal Y is sent out, its complement signal is sent to the inverter 2.
6, the signal is inverted at step 6, passed through an AND circuit 24, and inputted to an up-down counter 19 indicating the Y-axis coordinate via an OR circuit 33, where it is added or subtracted in accordance with the sign [Y] signal in synchronization with the clock signal. be done. The output of this up-down counter 18 or 19 is sent to an external display device as a graphic signal.

Next, the absolute values of the functions for the two candidate points determined in the above steps are calculated, and the magnitudes of these are compared and the smaller candidate point is determined to be the next point. That is, in the step, the absolute value |G ₀ | of the candidate point in the X direction or Y direction is calculated,
Absolute value of candidate point in 45 degree direction |G ₁ |
is calculated. Absolute value of these two candidate points |G ₀ |
The magnitude of and |G ₁ | is compared in steps.

As a result, if it is determined that |G ₀ |≧|G ₁ |, 2
The next point among the candidate points is determined to be a point in the 45 degree direction, and the G of this selected point is used as the value for the next calculation (step). Then, in a step, Δx or Δy that was not determined in the above step is determined and outputted as an addition or subtraction signal, and outputted to an external display device. Also, from this determined value, the differential coefficients f _x , f _{y ,} etc. to be used in the next step are determined and stored in a register.

This will be explained using the operation of the output circuit shown in FIG.

That is, the direction instruction signal XY is sent to the input terminal 27 in FIG. 3 as a logic "1" signal. At this time, a T10 signal of logic "1" indicating that the step is being executed is applied to the input terminal 21.
Therefore, the AND circuit 28 is opened and a direction indication signal is generated.
XY is output from the AND circuit 28. here,
The direction indication signal X or the direction indication signal Y is
Since it is held up to this step, if the direction instruction signal
An input is given to the up-down counter 19 via the up-down counter 19. As a result, the up-down counter 19 adds or subtracts in accordance with the sign [Y] signal in synchronization with the clock signal, and equivalently, a graphic signal in the 45-degree direction is sent to the display device.

Conversely, if the direction instruction signal Y is sent out in the step, the up-down counter 18 is added or subtracted via the AND circuit 29 and the OR circuit 32, and equivalently, a graphic signal in the 45-degree direction is sent to the display device. Sent out.

Also, if it is _determined that |G ₀ |
If there are two points in the X and Y directions, the next point is determined to be a point in the X direction. This judgment is made in steps. At this time, since the step has already sent the direction instruction signal in the X direction or the Y direction to the display device, the step does not send out the graphic signal.

Next, the operation of the output circuit shown in FIG. 3 in the case of 8-pixel connected display will be explained.

In this case, an 8-pixel display selection signal is applied to selection circuits 22 and 31. As a result, selection circuit 2
2 is connected to the switching terminal a ₂ side, and the selection circuit 31 is connected to the switching terminals b ₂ side and b ₄ side, respectively. In this state, the T5 signal is blocked by the selection circuit 22 in the step, so even if the direction instruction signal is not sent. Step input terminal 21
When the T10 signal is given to the AND circuit 23, 2
4.28 will be held. When the next point is determined in the 45-degree direction in this state, the direction instruction signal Given the input,
Addition or subtraction is performed in the same manner as in the case described above.

In addition, if the point in the 45 degree direction is not determined as the next point in the step, the input terminal 25 is selected in the step.
The direction instruction signal X or the direction instruction signal Y given to the AND circuit 23 or 24 and the OR circuit 32
or 33 to the up-down counter 18 or 19, and addition or subtraction is performed in the same manner as in the case described above.

In this step, the point selected based on the above judgment is updated as the current point, and calculations are performed in advance for the operation after the step of determining the next point.

〔Effect of the invention〕

As explained above, according to the present invention, a selection circuit is provided in the output circuit, and a point in a 45 degree direction in an 8-pixel connected display is temporally shifted in two steps by switching the selection circuit in a 4-pixel connected display. I decided to display it.

Therefore, the figure generator can be used as an 8-pixel connected display or a 4-pixel connected display, and is also applicable to 8-pixel connected graphics displays, NC work, or 4-pixel connected XY plotters. The versatility of the device can be significantly improved. Further, the additional circuit for this purpose has a simple structure, and the device can be constructed at low cost.

[Brief explanation of drawings]

FIG. 1 is a block diagram of a main part of a conventional output circuit. FIG. 2 is a block diagram of the main parts of a conventional device.
FIG. 3 is a block diagram of an output circuit according to an embodiment of the present invention.
FIG. 4 is a flowchart for drawing a circle in this embodiment. 1, 4, 9, 20, 25, 27...input terminals,
2, 3, 23, 24, 28, 29, 30...AND circuit, 5, 6, 32, 33...OR circuit, 7,
8, 18, 19...Up-down counter, 10
...Program memory, 11...Control circuit, 1
2, 13, 15...Register, 14...Arithmetic circuit, 16...Output circuit, 22, 31...Selection circuit.

Claims (1)

[Scope of Claims] 1. At least two registers that store each coefficient and each parameter, an arithmetic circuit that adds and subtracts signals from these registers and stores the results of the arithmetic operations in the registers; a control circuit that provides an operation instruction signal to the arithmetic circuit according to a predetermined arithmetic sequence based on the arithmetic results; and two control circuits that hold coordinate position signals of the X and Y coordinates and to which the control circuit provides an increase/decrease signal for the coordinate position. A given quadratic It is a device that generates a graphical signal of a function as an increment/decrement in the X-axis direction or an increment/decrement in the Y-axis direction, and the arithmetic means constituted by the control circuit and the arithmetic circuit is configured to generate a graphical signal of the given quadratic function X. By determining the positive and negative signs of _the first-order differential coefficient _f A first calculation means that selects three points from the eight directions above, and compares the magnitude of the absolute value of the first-order differential coefficient of the above-mentioned X |f _X | and the absolute value of the first-order differential coefficient of the above-mentioned Y |f _Y | a second calculation means for selecting two points from among the eight directions to proceed next, which are the X-axis direction and a direction 45 degrees different from this, or the Y-axis direction and a direction 45 degrees different from this; By substituting the coordinate values of the two points obtained by the second calculation means into the above-mentioned quadratic function to obtain the function value, comparing the absolute values of the function values and selecting the smaller one, next a third calculation means for determining whether the point to proceed is in the X-axis direction or in a direction 45 degrees different from this, or in the Y-axis direction or in a direction 45 degrees different from this; Based on the calculation result of the calculation means, the X coordinate and Y coordinate to proceed next
In a figure generator equipped with an output circuit that sends out coordinate increase/decrease signals, the output circuit is provided with selection means for selecting between 8-pixel connection and 4-pixel connection, and when 4-pixel connection is selected by the selection means. means for outputting an increase/decrease signal in the X-axis direction or Y-axis direction common to the two points at the stage when the calculation by the second calculation means is completed, and at the stage when the calculation by the third calculation means is completed. X-axis direction or Y-axis direction and 45
When points in different directions are determined, in addition to the output increase/decrease signal in the X-axis direction or Y-axis direction,
A figure generator comprising means for outputting an increase/decrease signal in the Y-axis direction or the X-axis direction of the point determined by the third calculation means.