JPS60252950A - Generation of digital segment signal - Google Patents

Abstract

PURPOSE:To produce a digital segment connecting the start and end points at a high speed and high accuracy by changing a dynamically the larger coordinate in both differences in absolute value at the start and end points, every 1 or 2 according to the condition. CONSTITUTION:Both X and Y coordinates of the start and end points of a digital segment are set to a command register 11 and started. Thus a control part 4 reads out successively the parameters set at the register 11 and stores them to a register of a register arithmetic part 3. Then various parameter values needed for generation of segments are calculated. The larger coordinates of both absolute values of differences DELTAX and DELTAY of the start and end points are changed dynamically by 1 and 2 according to the conditions. In the case of a change by 2, an optimum dot preceding by two steps is decided by the decision of conditions. At the same time, an optimum dot preceding by one step is decided clearly regardless of the decision of conditions.

Description

DETAILED DESCRIPTION OF THE INVENTION (Technical Field) The present invention relates to a method for generating digital line segment signals used in graphic display devices and numerically controlled machine tool rings.

(Prior Art) In fields such as graphic display devices and numerically controlled machine tools, it is necessary to generate line figures such as digital line segments and digital arcs at high speed and with high precision. For this reason, various graphic generation algorithms have been developed.

As a conventional digital line segment generation method, Bramenha
The method of m is often used.

Bresanham's method is used, for example, by Fujio Yamaro:
Graphic processing engineering using computer displays 1 Nikkan Kogyo Shimbun Publishing Co., Ltd. Described in 1982, this is a method that can generate digital line segments (hereinafter simply referred to as line segments) with high speed, high precision, and simple hardware. known as.

Bresenham's method μ, of the absolute values of the differences between the X and Y coordinates of the starting point and ending point of the line segment, the larger coordinate is changed by 1, and the other coordinates are set to the digital value closest to the true value. It's a way of choosing.

In Figure 9, the starting point of the line segment is PO (XD, YO), the ending point is Pl (Xi, Yl), and Δx=x+-xo, ΔY
An example of the generation of a line segment according to Bremenham's method in the case of 0<ΔY×ΔX from == yt −YO will be shown.

In this case, the first X value IX (i) F′i, IXI
)=IX(+-1)+1. Also, IX(1-
1), the error between the true value of Y and IY(1-1) is expressed as E
(1-1), E(1) in IX(i) is
E(+)=E(1-1)+ΔVΔX, and E(+
) < o, s, then IY(1) = IY(i-1) E(
+)≧0.5 then IY(1)=IY(1-1)
IYO) is determined as +1.

If the Y value is incremented by +1, E(1) needs to be decreased by 1.

FIG. 10 shows a diagram of the principle of K Breaenham's algorithm. FIG. 11 is a modification of FIG. 10, simplified so that all variables are integers and no division is necessary. Generally, the Brasanham method refers to the type shown in FIG.

However, this method has the problem that the line segment generation speed cannot be increased any further because it is necessary to perform sign determination using the error IEIC and update the IE every time the line advances one step.

(Objective of the present invention) The present invention was made in view of the problems in the prior art, and its purpose is to create a digital line segment connecting a starting point and an ending point at high speed, with high precision, and in the simplest possible way. The purpose of this invention is to provide a method for generating digital line segments that can be generated with a configuration.

(Configuration of the present invention) The configuration of the present invention that achieves the above object is as follows (a)
The steps (e) are included to generate a digital line segment signal connecting the starting point and the ending point. That is, (a) Difference Δ between the X and Y coordinates of the starting point and the ending point, respectively.
A process of comparing the absolute values of X and ΔY.

(b) In the step (a), if 1ΔX1≧1ΔYI, a step of comparing 217Yl and 1ΔX1.

(c) In the step (b), 2IΔY1<1ΔX1
When , the Y of the previous selected dot and the current dot
If the coordinate difference Dx is 1, the X coordinate of the current dot is changed by two, and if the absolute value Kx of the change in the Y coordinate is 0.5 or more, the X coordinate is changed as the next two consecutive dots. 1
The only change is 9 do, g and the x coordinate is 2. Select the dot whose Y coordinate has changed by 1, then change the X coordinate by 2, and if Kx is less than 0.5, select the dot whose X coordinate has changed by 1 and the X coordinate as the next two consecutive dots. Select the dot whose value has changed by 2, change the next KX coordinate by 1,
On the other hand, if Dx is 0, the X coordinate of the current dot is set to 1, and if KX is greater than or equal to O,S, the next dot is
The coordinates are 1. If the Y coordinate changes by 1, select 9 Do, G, then change the KX coordinate by 2, and if the odor is less than 0.5,
The process of selecting a dot whose X coordinate has changed by 1 as the next dot, and changing the next KX coordinate by 1.

(d) In the step (b), 21ΔY1≧1ΔX1
If Dx is 0, set the current dot's X coordinate to 2.
If Kx is less than 1.5, the next consecutive 2
As two dots, the X coordinate is 1. The Y coordinate changes by 1, and the X coordinate changes by 2. The Y coordinate changes by 1 and 6 dots are selected, the next KX coordinate is changed by 2, and if Kx is 1.5 or more, the next two consecutive dots are selected and the X coordinate is 1. A dot whose Y coordinate changes by 1 and whose X coordinate changes by 2.
．． Select the dot whose Y coordinate has changed by 2, then change the X coordinate by 1, and if DX is 1, the current dot's
If the coordinates are changed by 1 and Kx is less than 0.5, select the dot whose X coordinate has changed by 1 as the next dot,
Step of changing the next KX coordinate by 2, and if Kx is 0.5 or more, select a dot whose X coordinate has changed by j and Y coordinate by 1 as the next dot, and changing the next KX coordinate by 1. .

(e) In the step (a), 1ΔX1 × 1Δyl
In this case, further compare 21ΔX1 and 1ΔY1,
Divide into two cases: 21ΔX1<1ΔY1 and 21ΔX1≧1ΔY1, swap the relationship between the X and Y coordinates, change the KY coordinate by 1 or 2 instead of the X coordinate, and repeat the above process thereafter) (in the case of 1ΔX1≧1ΔY1) A process that performs the same process as.

(Embodiment) FIG. 1 is a block diagram showing the configuration of an apparatus for implementing the method of the present invention. This device L1 manual control section 1. Output section 2
．． It is composed of the main parts of a register operation section 3 and a microprogram control section 4.

Input control section 1. Output section 2. Each part of the register operation section 3 is interconnected by an internal bus ABK. The input control unit 1 is a part that controls initial value settings from a higher-level computer or the like (not shown) provided via the system bus SB. The output unit 2 is a part that outputs XY coordinate values to an external display device (not shown) such as an image memory, and has an X register 21.
．． It has a Y register 22, and respective values are set in the X and Y registers via an internal A bus AB. The register calculation unit 3 is a place where numerical calculations are performed, and the RALU
(Register & Arismetituta Logical Uni.

g) It is formed by the month and the status register 32.

The RALU 51 has a plurality of internal registers 53, and performs logical arithmetic operations (eg, addition/subtraction, AND, OR, shift operations, etc.) between the registers. Various statuses (overflow, carry) in the operation results in the status register 32tri and RALU 31.

(sign/zero flags, etc.) are temporarily held and input to the microprogram control unit 4, which will be described later. The microprogram control unit 4 executes the overall control and line segment generation algorithm, and switches signals from the pipeline register 41, the microprogram memory 42, the address sequencer 45, and the status register 52 of the register calculation unit 5. It is configured to include a multiplexer 44 for input. A pipeline register 41 holds the output from the microprogram memory 42 and supplies microinstructions to each of the above-mentioned input control section 1, output section 2, and register operation section 3. A conditional branch in the microprogram is executed by the status register 3 in the multiplexer 44.
This is done by selecting one of the various statuses from 2 and inputting it to the address sequencer 45.

The operation of the apparatus configured in this way will be described next.

First, the principle of the algorithm of the digital line segment generation method according to the present invention will be explained.

The method of the present invention is an improvement on the above-mentioned Br@sanham algorithm. In Bresanham's algorithm, among the absolute values of the differences ΔX and ΔY between the starting point and the ending point, the larger coordinate is changed by 1, and the other coordinates are selected as digital values that are close to the true value. While the dots to be selected next to the already selected dots (including the starting point) (optimal dots) are generated one dot at a time, in the method of the present invention, the larger coordinates are generated in increments of 1 or 2 depending on the conditions. , when dynamically changing and changing by 2, the optimum dot two places ahead is determined by the condition judgment, and at the same time, the optimum dot one place ahead is determined uniquely, regardless of the condition judgment. . That is, if the larger coordinate is changed by 2, two consecutive dots can be generated at once as the next optimal dot after the already selected dot.

FIG. 2 shows the principle diagram of the algorithm of the method of the present invention.
The case of ΔY≦ΔX will be shown. From the slope m=J'Vj +) If E(t)≧0.5, the optimal dot 1r
x(+)=rx(t-1)+1. IY(1)=xY(
1-1)+1z 2 IX(++1)=IX(1)+1
．． IY(1+1)=IY(1)IY Error K(++z)=E(1)-1+2-Fj-(1-
2) If E(i)〈o, s, then optimal dot IIX(
1)=IX(1-1)+1. IY(μ)=IY(i-1
)IY Error E(!+1)=E(1)+π (2) If o, s≦m≦1 (2-1”) If DI)≧0.5, optimal dot 11
X(1)=IX(1-1)+1. IY(1)=IY(
1-1) +1ΔY error B(++1)=K(1)-1+7 (2-2)
If E(1)<0.5, then optimal dot 1rx(s)=x
x(+-1)+1. ry(+)=Iy(+-1)2
xx(++1)=xx(+)++, IY(1+1)=
The X and Y coordinates of the optimal dot are determined so as to satisfy IY(+)+1ΔY error E(1+2)=E(1)-1+2T5j-.

In Figure 2, instead of E, 2ΔX・(go, s
) By using the multiplied quantity rE, all variables are integers and no division is necessary, and instead of comparing the magnitude of IK and 0.5, it is enough to check the sign of Ic and IE, which simplifies the algorithm. This makes it easy to implement in hardware.

This algorithm is shown in FIG.

Next, using the flowchart in Figure 3, O≦ΔY≦Δ
Regarding the method of the present invention in the case of X, the operation of the line segment generator shown in FIG. 1 will be explained. A host computer (not shown) sets the X and Y coordinates of the start point (xo, yo) and end point (X+, yl) of the digital line segment in the command register 11 via the system bus SB, and performs input control. A start activation is applied to s12. When a start is activated, the microprogram control unit 4 sets the key command register 1.
Parameters set to 1: XO, YO, Xl, Yl
are read out sequentially, and the registers in the register calculation unit 3 are read out via the internal bus AB, RXO, RYO, RXj, R.
Each is stored in Yj. Register operation unit 3ij, registers RXO, RYO, RXl.

Using the value of RYl, the values of various parameters necessary for line segment generation are calculated. And registers RXO and RYO.

From the values of RXl and R1, IX = Xl -XO, ΔY=
Calculate Yl - YO and register R (IX) IR (IY
)K respectively.

Also, the values of registers R(Δx) and R(IY) are 2Δ
X.

Calculate 2ΔY, 4ΔY, register R(2ΔX), R(
2ΔY)lR(4ΔY). Also, register R(IX).

The values of R(2ΔX), R(2ΔY), and R(4ΔY) are 4ΔY−IX.

Calculate 2ΔY-2ΔX, 4ΔY-2ΔX, and register R
(4ΔY-IX)ll(27Y-2ΔX), R(4Δ
Y-2ΔX)K are stored respectively. Subsequently, the register calculation unit 3 and the microprogram control 4 perform the following steps.
Generate a line segment. Note that the code in 0 before the explanatory text corresponds to the code indicating the procedure in the flowchart of FIG.

(d-1) First, the contents of register R (4ΔY-IX) are stored in register RIE.

(d-2) The contents of registers RXO and RYO are stored in register RIX.

Store in RIY.

(d-5) Compare the contents of register RIE and register R (IX) and find (RIE) ≧ (R (ΔX)) (
[ ] means the contents of the register), the procedure (
Execute d-+a) and subsequent steps, (RIK)〈[R(ΔX)
), the KFi procedure (d-4) and subsequent steps are executed.

(d-4) Perform output operation. Specifically, each register is set and writing is performed at the dot position in the image memory specified by the X and Y registers.

(d-5) Check the contents of register RIX and register RX1. Here, if they are equal, the line segment generation operation is ended. If they are not equal, the procedure (d
-6) Execute the following steps.

(d-6) Increment the contents of V register RIX by +1.

(d-7) Perform the same output operation as (d-4).

(d-a) Similar to (d-5), the contents of register RIX and register RXI are checked against each other, and if they are equal, the line segment generation operation is terminated, and if they are not equal, the procedure (
Execute d-9) and subsequent steps.

(d-9) Increment the contents of register RIE by +1.

(d-+O) Check the sign of the contents of register RIE.

If (RIE)≧00, execute step (d-11) and subsequent steps (RIE) (if 0, move 1K (d-1s)).

(d-+1) Increment the contents of Custar RIY by +1.

(d-12) Add the contents of register R (4ΔY-2ΔX) to the contents of register RIIH. Thereafter, steps (a-a) and subsequent steps are repeated until the contents of register RIX and register RX1 become equal.

(d-1s) Register (2Δ
Add the contents of Y). He then repeats steps 1K (d-7) and subsequent steps until the contents of register RIX and register RX1 become equal.

When 0.5≦mE (ΔY/ΔX)≦1 (d-U) The contents of register R (2ΔX) are subtracted from the contents of register RIE.

(a-1s) Performs the same output operation as hand 11 (d-4).

(d-+6) Similarly to hand 1K (d-5), register RI
A check is performed between X and the contents of the register RX1, and if they are equal, the line segment generation operation is ended, and if they are not equal, steps 11R (a-17) and subsequent steps are executed.

(d-17) Increment the contents of register RIY by +1 (d-+p) Perform the same output operation as step 11 (d-4).

(d-2o) Similar to (d-5), the contents of register RIX and register RX1 are checked against each other, and if they are equal, the line segment generation operation ends at K. If they are not equal, proceed to step (d-21). ) and the rest.

(d-2+) Increment the contents of register RIX by +1.

(d-22) Similar to procedure (d-to), register RI
The sign of the contents of K is determined. If (RIE)≧0, execute move It Cd-25>; if (RIE) (0, execute move @ (a-2S)).

(d-2S) Increment the contents of register RIY by +1.

(d-24) Add register R(2) to the contents of register RrE.
ΔY−2ΔX) is added. After that, step (d-
U) Repeat the following steps until the contents of register RIX and register RX1 become equal.

(d-2s) Add register R(4) to the contents of register RIK.
ΔY−2ΔX) is added. After that, step (d-
1S) and subsequent steps are repeated until the contents of register RIX and register RX+ become equal.

Such a procedure is as follows: 0≦m (0,5, procedure (d
-tz) to step (d-7) via step (d-4)
When executing 0.5≦m≦1, the procedure (d-
ZS) to hand 11j (d
-19), each of the following optimal dots is
The feature is that it is generated unconditionally, regardless of the sign determination based on the amount IE multiplied by ΔX(E-0,5).

Here, a specific example of the operation of the line segment generator in the case of 0≦m(0,5 and 0.5≦mSI) will be shown.

(1) 0≦m (if 0,5, start point PO(1,2) end point P1(12,7)(2) 0
．． When 5≦m≦1, start point po (+, 2) end point PI (12, 8) Table 11 Table 2 shows IFi in the process of line segment generation in each case,
Indicates the values of XX and IY.

Table 1 (Line in case of starting point PO(:1.2), end point (12,7) Figures 4 and 5 show examples of line segment generation in each case.The numbers in Figures 4 and 5 correspond to the plot numbers in Tables 1 and 2. The dots corresponding to the numbers (■) surrounded by circles are uniquely generated regardless of the sign determination by the IE.

The operation of this generator in the case of O≦ΔY≦ΔX is 0
Although we have explained it in two ways: ≦2ΔY ≦ ΔX and ΔX ≦ 2ΔY ≦ 2ΔX, in the case of 0 ≦ ΔX ≦ IY, 0 ≦ 2 ΔX
Divide into two ways, iY and ΔY≦2ΔX (2ΔY, and replace the relationship between the X and Y coordinates (X-+Y, y→X),
Instead of the X coordinate, change the Y coordinate by 1 or 2, and set it to 0.
By performing the same operation as in the case of ≦ΔY≦ΔX,
It is possible to generate digital line segments.

Figure 1I46 shows a flowchart of the algorithm according to the method of the present invention when 0≦ΔX<IY.

ΔX≧0. The method of the present invention has been explained for the case where ΔY≧0, but (a) when ΔX≧0. ΔY(o,
(b) ΔXku0. ΔY≧0. (c) IYku0. Δy
(Also in the case of o, when ΔX→1Δxl, ΔY→1ΔY1 ΔX<0) Ix4-IX+1→IX←lX-1ΔY
When θ is IY+-IY+1->IY4-IY-1, it is possible to generate digital line segments at high speed and with high precision.

In addition, in the above explanation, the detection of the end point, that is, IX=
In order to simplify the hardware, the detection of lf or IY=Yi was executed by a microprogram based on calculations in the RALU in the register calculation unit 5, but instead of this, it can be realized by hardware. Good too.

FIG. 7 is a block diagram of the main parts in this case. In this figure, in the 5Fi end point detection section, there is a selector 51 that selects the output of the X register 21 and Y register 22 of output B2, and end point data X1 sent via the internal bus AB.
Also, a register 52 and a selector 51 that store 1iY1
Compare the signal selected with the signal from the register 52,
It is composed of a comparator 53 that detects IX=Xl or IY=Y1.

By providing the end point detection section 5 using such hardware, it is possible to generate digital line segment signals at higher speed.

(Effects of the present invention) As explained above, 1 the present invention improves Bressnham's method, and calculates the larger coordinate of the absolute values of the differences ΔX and ΔY between the X and Y coordinates of the starting point and the ending point, respectively. Dynamically change by 1 or 2 depending on the conditions, 2
When the dot is changed by 1, the optimum dot two places ahead of the already selected dot is determined using the same judgment conditions as Br@sanham's method, and at the same time, the optimum dot one place ahead is determined unambiguously regardless of the judgment conditions. Braa
While maintaining the high accuracy of enham's method, Bre
Digital line segments can be generated at a speed that even exceeds the high speed of Senham's method.

Incidentally, for each of Brosenham's method and the method of the present invention, the total dynamic step number g required to generate a line segment is calculated for the case of 1Δxl≧1Δyl.

The directions actually selected from Fig. 8 are the horizontal direction and +4
There are only two types of dots in the 50 directions, and the number of dot selections in the horizontal direction is 1ΔXllΔyl, and the number of dot selections in the 4450 direction is IΔYI, so the steps required for dot selection in the horizontal direction and dot selection in the +45' direction are When the number of blocks is d, g is general K.

It is given by g=b・(1ΔX1 ΔYI)+d・1ΔY1.

In the flowcharts of FIGS. 11 and 5, 'Pro,
When it is assumed that each step including the step and step of determining IX=X1 and IE≧0 is one step and step except for the output step of step 1, the total number of dynamic steps gh is as follows.

(a) In the case of Brasenham's method, b=A, d=
5, so g = 41ΔX1 + 1ΔY1 (bJ In the case of the method of the present invention (b-+) 21ΔY1<1ΔX1, h = 4 (IK
(0), 2(IE≧O), d=5, so g=41
ΔX1-1ΔY1 (b-z) When 21ΔY1≧1ΔX1, h= a, (
1=5(IE≧O), ! 5(IE(0), so g
=21ΔXI +31ΔY1 Therefore, according to the invention, compared to Breaenhmm's method, the total number of dynamic steps can be reduced by up to (lΔX1
= 21ΔY1) It can be reduced by about 22%. Note that 1ΔX
Similar results are obtained for I<1ΔY1.

[Brief explanation of drawings]

Fig. 1 is a diagram showing the configuration of an apparatus for implementing the method of the present invention, Fig. 2 is a flow chart showing the principle of the algorithm of the method of the present invention, and Fig. 3 is a flow chart showing an example of the algorithm according to the present invention. , FIG. 4 and FIG. 5 are diagrams showing an example of line segment generation according to the method of the present invention, FIG. 6 is a flowchart showing another example of the algorithm of the method of the present invention, and FIG. 7 is a diagram showing the main part of the end detection section. 8 is an explanatory diagram of the calculation of the number of dots required to generate a line segment, FIG. 9 is a line diagram showing an example of line segment generation using the conventional method, and FIGS. 10 and 11 are diagrams showing the algorithm of the conventional method. FIG. DESCRIPTION OF SYMBOLS 1... Input control section, 2... Output section, 3... Register calculation section, 4... Microprogram control section, sB.
...System bus, AB...Internal bus.

Claims (1)

[Claims] (1) A digital line segment signal generation method that includes the following steps (11) to (,) to generate a digital line segment signal connecting a starting point and an ending point. (&) Difference Δ between the X and Y coordinates of the start point and end point
A process of comparing the absolute values of X and ΔY. (b) In the step (a), if IΔX1≧IΔY1, a step of comparing 21ΔYI and 1ΔX1. (c) In the step (b), 21ΔYl<lΔXI
When KH11, the previous selected dot and the current dot are Y.
If the coordinate difference DX is 1, the X coordinate of the current dot is changed by 2, and if the absolute value KX of the change in the Y coordinate is greater than or equal to O,S, the X coordinate is changed to 1 as the next two consecutive dots. The only change is 9 do, g and the x coordinate is 2. Select the dot whose Y coordinate has changed by 1, then change the X coordinate by 2, and if the odor is less than 0.5, select the next two consecutive dots,
Select a dot whose X coordinate has changed by 1 and a dot whose X coordinate has changed by 2, and change the next KX coordinate by 1. On the other hand, if DX is 0, change the X coordinate of the current dot by 1. , KX is 0.5 or more, the next dot is set as the next dot, and the X coordinate is 1. Select a dot whose Y coordinate has changed by 1, then change its X coordinate by 2, and if Kx is less than 0.5,
The process of selecting a dot whose X coordinate has changed by 1 as the next dot, and changing the next KX coordinate by 1. (d) In the step (b), 21ΔY1≧1ΔX1
If DX is O, set the current dot's X coordinate to 2.
If Kx is less than 1.5, the next consecutive 2
As two dots, the X coordinate is 1. A dot whose Y coordinate changes by 1, and a dot whose X coordinate changes by 2. Select the dot whose Y coordinate has changed by 1, then change the KX coordinate by 2, and if the odor is 1.5 or more, select the next two consecutive dots whose X coordinate is 1. A dot whose Y coordinate changes by 1 and whose X coordinate changes by 2.
Select the dot whose Y coordinate has changed by 2, then change the X coordinate by 1, if the loss is 1, change the X coordinate of the current dot by 1, and if Kx is less than 0.5, select the next dot. Select a dot whose X coordinate has changed by 1, then change the X coordinate by 2, and if Kx is 0.5 or more,
The process of selecting a dot whose X coordinate has changed by 1 degree and whose Y coordinate has changed by 1 as the next dot, and then changing the X coordinate by 1. (,) In the step (a), if 1ΔX1<1ΔY1, 21Δ cutting and 1Δyl are further compared, and 21Δ
Divide into two cases: Xi<lΔY1 and 21ΔKari≧IΔY1, replace the relationship between the X coordinate and the Y coordinate, change the Y coordinate by 1 or 2 instead of the X coordinate, and then perform the step (c>
(In the case of lΔX1≧1ΔY1).