JPS5924378A - Generating circuit of rectilinear information - Google Patents

Abstract

PURPOSE:To display a smooth straight line and an optional straight line having no start point nor finish point included in an integer coordinate point, by forming a coordinate point with two coordinate points converted into integers and setting the density of both coordinate points at the value adversely proportional to the distance between coordinate points. CONSTITUTION:The Y-direction coordinate initial value IYSS, the 4-cut/5-count value IXS of the X-direction coordinate initial value XS and the first variable value (f) are stored to an up-counter 41, an up-counter 43 and a register 44, respectively. The start point of a straight line having coordinate values XS and YS of real numbers is decomposed for display into two coordinate points which are shown in the 1st and the 2nd coordinate forms converted into integers. The 1st and the 2nd coordinate informations (IXn, IYn) and (IXn, IYn+1) and the luminance informations (1-f)n and fn are transmitted every time a clock pulse CK is delivered from an AND circuit 49. Based on these information, each component point of actual straight line is virtually displayed by two points.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention provides straight line information that generates each coordinate information and associated concentration information necessary when displaying a straight line using a two-dimensional orthogonal coordinate system display means that handles integer coordinate values. Regarding generation circuits.

Conventionally, when displaying a straight line using a two-dimensional rectangular coordinate system display means such as a raster scan type graphic display device or an In other words, in the straight line generator, each interpolation point is determined by linear interpolation between two points, the starting point and the ending point, of the straight line to be displayed.However, during the linear interpolation, All integer data is used for processing.For this reason, for example, the X
If you want to display a straight line with a slope starting from the point X = 3, Y = 5 and ending at the point X = 7, Y = 7 on the Y rectangular coordinate screen, please refer to Figure 1. Starting point, #!
A point and each interpolation point are determined. Each of these interpolation points is determined using, for example, digital differential analyzer (DDA) technology. According to this technique, the slope of the straight line is continuously added to the X coordinate value of the starting point, and if a carry occurs in the addition result, the Y coordinate value of the starting point is increased by one, thereby performing each interpolation. Points are determined sequentially. When processed using this method, the set of brightness points indicated by the circles in the figure
A straight line a as shown by a solid line is interpolated and displayed.

However, since all of the conventional methods described above use integer values for processing, when viewed with the naked eye, the straight line has a step-like shape as shown by the broken line in Figure 1, and it does not look like the solid line. It has to be smooth. Moreover, since integer value data is used, the start point and end point must always be integer coordinate points.As a result, there is a drawback that conventional methods cannot display straight lines whose start and end points are not at integer coordinate points8. Ru.

By the way, as shown in Fig. 2, when a point C hypothetically exists between two real points A and B, the third
As shown in the figure, if point A is drawn larger and point B is drawn smaller, and points A and B are visually close enough, it appears as if a small point C exists between points A and B. It looks like it is.

This invention was made in consideration of the above-mentioned circumstances, and its purpose is to provide coordinate information and the accompanying density required when displaying a straight line using a two-dimensional orthogonal coordinate system display means that handles integer coordinate values. In a linear information generation circuit that generates information, one coordinate point is composed of two coordinate points that have been converted into integers, and the density of both coordinate points is set to a value inversely proportional to the distance between them and the actual coordinate point. Therefore, it is an object of the present invention to provide a straight line information generating circuit which can display a smooth straight line and can also display any straight line whose start point and end point are not at integer coordinate points.

The present invention will be described in detail below with reference to the drawings. In this embodiment circuit, an external device such as CPLI: coordinates f in the X and Y directions (one direction, the other direction) of the starting point P of the straight line from ijj to
m, (x8.Y8) and reach its end point] The change values ΔX and ΔY in the C direction and Y direction are respectively decimal points] Δ7
The straight line is given as a binary real number of feet, and the straight line is displayed on a raster scan type graphic display device.

What is generated in this circuit is a pair of integer coordinate information (IXn, IYn) to virtually display each point composing a straight line, (IXn, IYn ten and - each brightness) Information (1-f)n, fn.

However, I in IXn, IYn, etc. means an integer, and (1
-f) n is the complement of fn (iQ). For convenience of explanation, in the following explanation, it is assumed that the X and Y coordinate values are positive values, and ΔX is larger than ΔY.

FIG. 4 shows a circuit for rounding off the starting point POX value XR given by the pretext number and converting it into an integer. In the figure, this is a register that stores the integer part and decimal part of No.II-ixs. The most significant bit (MSB) signal of the decimal part stored in this register 11 and the t-bit signal in the integer part are added by an adder 12, and the result of this addition η is stored in a register 13. That is, in the circuit shown in FIG. 4, if the MSB signal of the decimal part stored in the register 11 is at the "0" level, the value of the decimal part will be less than 0.5 in lO base; If it is 1” level, it will be 0.5 or more.

Therefore, in the adder 12, the MS in the integer part and the decimal part is
If addition is performed with B@, the addition output is the real number
A rounded value IXs of s is obtained.

FIG. 5 shows a circuit diagram for obtaining the complement value XA of the decimal part of the X-direction coordinate X8 of the starting point P. In the diagram, 2 is X
This is a register that stores the integer part and decimal part of s. Each m-bit signal of the decimal part stored in this register 2 is logically determined with a 1" level signal by an exclusive OR circuit 22, and this logical result and an "1" level signal are combined. Further, they are added by an adder 23. In other words, this circuit obtains the complement value xA of the decimal part of Xs.

Figure 6 shows name coordinate information (from nominal values) used when displaying straight lines on a raster scan type graphic display device.
A circuit for obtaining the initial value IYss of the Y-direction coordinate and the variable value f among IXn, IYn) + (IXn+IY1+1) is shown. In the figure, 31 and 32 are registers that store the change values ΔX and ΔY in the X and Y directions, 33 is a register that stores the value XA obtained by the circuit in FIG. 5, and 34 is the decimal part of Ys. This is a register that stores the value YA. The values ΔX and ΔY in the registers 3 J, , 92 are supplied in parallel to the divider 35, where the quotient Q (Q=ΔVΔX) of both values is determined. However, as described above, since ΔX≧ΔY, the value of Q is smaller than l. The above quotient Q and the above register 3
The value XA within 3 is supplied to a multiplier 36, where the product M (M=CIXA) of both values is determined.

Furthermore, this i M and the value YA in the register 34 are added by an adder 37, and the sum of both values f' (f
'=Q-XA+YA) is obtained. The value f' obtained here is temporarily stored in the register 38. After storing f', if the value of f' is 1 or more, the value obtained by subtracting 1 from that value is re-stored as the variable value f, and if f' is less than 1, Then, store this f' candy in the trench. Further, in FIG. 6, 39 is a register that stores in advance the value IYI+ of the integer part of Ys, and when the value of f' is 1 or more, this register 39 adds 1 to the content IYs and updates it. This value f is used as the initial value IYss of the Y-direction marker.

That is, in this circuit of FIG. 6, the current coordinate (Xs
, Ys), as shown in FIG. First, this starting point P
The slope value tIInθ of the straight line starting from (the value of Q above)
is required. On the other hand, the multiplier 36 obtains the product of the complement value X^ of the fractional part of Xs and this gradient value -〇,
A perpendicular line t drawn on the coordinate Xil! Through the intersection point 0 of and the straight line and the Y-direction coordinates of the starting point P? ) The distance OA between the point A where the straight line t2 parallel to the x-direction coordinate axis intersects the straight line t1 is obtained. Further, in the adder 37, the multiplier 3
Since YA is added to the product of 6, the straight line starting from the starting point P is the perpendicular line t1 erected on the X coordinate X1-1-+
The distance between the point 0 that intersects with Y-direction coordinate Yj is obtained as f'. Now, when the value of f' is greater than or equal to 1, the Y-direction coordinate of point '0 is greater than or equal to Yj++, so the decimal value remaining after subtracting l from the value of f' is stored in the register 38 as f. Ru. On the other hand, when the value of fJ is less than 1, since the Y-direction coordinate of point 0 exists between Yj and Yj-H, the value of f' is stored as is in the register 38 as f. Furthermore, when the value of f' is less than 1, the point O
Since f″iYf′ exists between the coordinates Yj and Yj+1, at this time, the value of IYs is stored in the register 39 as is.
Stored as syr.

On the other hand, when the value of f' is 1 or more, the point orI'iY-direction coordinate Yj+1 is also large, so in this case, the value of IYs is corrected by adding 1 to IYs.
T! It is stored in the register 39 as .

Figure 8 shows each coordinate information (IXn, I
The circuits for obtaining each of Yn), (IXn, IYn+1) and luminance information (1-f)n and fn are shown. In the figure, 41 is Y obtained by the circuit shown in FIG.
This is an up counter that is preset by the initial value IYs of the direction coordinate. The count output of the up counter 4 is sent to a raster scan type graphic display device (not shown) as the other direction coordinate value IYn of the first coordinate information, and is added to the count output of the up counter 4 by a +1 adder 42. +1 is added, and this value is also sent to the graphic display device as the other direction coordinate value IYn+1 of the second coordinate information. Further, in FIG. 8, there is shown a synchronous up-counter which sequentially performs up-counting in synchronization with 43 clock pulses, and this counter 43 is reset to the rounded value IXq of Xs obtained by the circuit of FIG. 4. And this counter 430 count output is @1. The second coordinate information is sent to the graphic display device as a one-way coordinate value IXn. Further, in FIG. 8, 44 variable values f obtained by the circuit shown in FIG. This is a register that sequentially stores new variable values.

The output of this register 44 is connected to one input of the adder 45 and L7, and is sent to the graphic display device as luminance information fn accompanying the second coordinate ff11 information. The output of the register 44 is further processed by a complementer 46.
The binary complement of the value is taken here, and this value is sent to the graphic display device as luminance information (1-f)n accompanying the first coordinate information. The slope value Q obtained by the circuit shown in FIG. 6 is applied as the other input of the adder 45, and the carry output CARRY generated by the adder 45 is applied to the up counter 4 as a count input signal.

In FIG. 8, 47 is a down counter that is reset by an integer IΔX of the change value ΔX in the X direction of the straight line to be displayed from now on, and a clock pulse CK is given as an input for the down counter of this counter 47. . The pull output of this counter 47 is given to a flip-flop 48 as a clear input. The flip-flop 48 is set by the start signal 5TART given when starting to display a straight line, and its output FQ is output to the AND circuit 4 along with the clock signal CK.
given to 9. The output from this AND circuit 49 is given as a clock pulse to the counter 43 and register 44.

That is, in this circuit of FIG. 8, when the start signal 5TART is not yet given to the IJ block prop 48, the initial value IYss of the Y-direction coordinate is stored in the up counter 4.
However, another up counter 43 stores the rounded value IXs of ViXll, and a register 44 stores the first variable value f. At this time, the up counter 41
The output is sent as the Y-direction coordinate value IYn of the first coordinate information, and the +1 adder 42
The value obtained by adding +1 to the above value is sent as the Y-direction coordinate value IYn-1-j of the first second coordinate information. The output of the other up-counter 43 is sent out as the X-direction coordinate value IXn of the first and second coordinate information. Furthermore, the output of the register 44 is sent out as luminance information fn accompanying the first second coordinate information, and the complement value taken by the complementer 46 for the output of this register 44 is accompanied with the first first coordinate information. Brightness information (tf)
Sent as n.

Now, as shown in Fig. 7, the starting point P of the straight line exists within a square surrounded by the coordinates xi, x+, and Yj, Yj-H, and f' in Fig. 7 is less than 1. If the value of IY obtained by the circuit shown in FIG.
The value of ss is Yj. Moreover, when XA in FIG. 7 is smaller than 0.5, the lX5O value F obtained by the circuit in FIG.
It becomes iXI-H. Further, in FIG. 7, since f' is a value less than 1, the value of f is equal to the value of f'. When the above-mentioned values are given before the start signal 5TART is given in the circuit of FIG. 8, the coordinate point given by the first coordinate information (IXn, IYn) sent from this circuit, the intersection of Xi+1 and Yj, A in Figure 7
It will be 0 points. Also, the coordinate point given by the second coordinate information (IXn, IYn+1) sent out from this circuit is
The intersection of Xl-1-1 and Yj-)1 is the point BQ in FIG. And the first coordinate information (IXn, x
point A given by yn). Luminance information (l-f)n associated with
is the complement of the value of f, so the distance 0BoO in Figure 7
value. Furthermore, second coordinate information (IXn.

Brightness information fn associated with point B given by IYn+1)
is the value of f itself.

That is, in this circuit of FIG. 8, the start signal S T
When ART is not given, the starting point P of the straight line having the coordinate value Xg+Ys given by the real numbers is decomposed into two coordinate points converted into integers and represented. Moreover, the luminance information at these two decomposition points A6eBO is AO? X direction coordinate on BO X1-)1
Since the value is inversely proportional to the distance between the actual coordinate point 0, which is the intersection of the perpendicular line t1 and the straight line, and the points AO+BQ, the display is On the screen, it is displayed as if there was actually a point at point 0.

Next, the start signal 5TART of ``'0'' level is applied to the circuit in Figure 8.
and clock noyars CK'f! Give c sequentially. First, by inputting the signal 5TART, the flip-flop 48 is set, and its output FQ remains at the "1" level.Then, the AND circuit 4g opens, and the clock pulses CK pass through the AND circuit 49 in sequence.First, the first clock・When the gurus CK is input, the up counter 43 counts up by one, and the IXs and others also count up by one.
Outputs the larger value. Therefore, at this time, the X-direction coordinate value IXn of the first and second coordinate information becomes a value that is increased by one unit compared to before. On the other hand, when the first clock pulse CK is input, the register 44fi registers this pulse C
In synchronization with K, the addition output SUM from the adder 45 is stored in place of the value of f held so far. Before this, the output value f of the adder 45Fi register 44 and the sixth
The gradient value Q obtained by the circuit shown in the figure is added. Here, adding the value of f and the value of Q (ΔY/ΔX) means calculating the Y-direction coordinate at the intersection of the perpendicular line drawn on the next integerized X-direction coordinate and the actual straight line. The addition output SUM at this time is a decimal value of 1 unit or less. Then, in synchronization with the input of the clock pulse CK, this output SUM is sent to the register 44 as a new f.
is stored in Also, based on this new value of f, the following 1. Luminance information (If)n, fn accompanying the second coordinate information is sent. Furthermore, if a carry output CARRY is generated during the first addition in the adder 45, the up counter 4
outputs a value l greater than the IYs s. Therefore, at this time, the Y-direction coordinate values IYn and IYn4.1 i;t of the first and second coordinate information are each increased by one unit. On the other hand, if the carry output CARRY is not generated during the first addition in the adder 45,
At this time, the Y-direction coordinate value I of the first and second coordinate information
Yn and IYn+1 each have the same value as before. However, in this case, a pair of luminance information (1-f)n.

Since the value of fn is different from before, the virtual point displayed by the pair of coordinate information at this time is different from the previous position in the Y direction.

In the same manner as before, the clock pulse CK is output from the AND circuit 49.
The first . Second coordinate information (IXn,
IYn) + (IXn +IYn-+-4) and luminance information (l-f)n, fn are sent out, and each constituent point of the actual straight line is virtually displayed by two points based on these information. Ru. Then, when the down counter 47 finishes counting, the pollo output goes to the "0# level", which clears the shifting frontop 48 and outputs FQ.
returns to the ``0# level.Then, the AND circuit 49 that was currently open in the trench is closed, and the input of the clock pulse CK to the up counter 43 and register 44 is stopped, so that new information from the circuit in FIG. No sending takes place.

That is, since the information for displaying the end point of the straight line has already been sent at this time, the operation stops now.

Next, the operation of the above embodiment circuit using actual numerical values will be explained. 1. Information about the straight line to be displayed is that the X coordinate of the starting point P is 350° and the Y coordinate of Ys is 4.62'.
5, the change value ΔX in the X direction is given as 375, and the change value ΔY in the Y direction is given as 1.875. Then, each value can be expressed as a binary number with a fixed decimal point as shown below.

X5=(Qll.100),.

Ys=(100,101)2 ΔX=(011,110)2 ΔY=(001,l l 1)2 Now, if IXs is found using the circuit in Figure 4, (011)
2+1-(100)2, jl) IXs becomes 4 in decimal. Next, find XA using the circuit in Figure 5 (
,100)2 = 0.5.

Next, in the circuit of FIG. 6, the value of Q, which is the output of the remover 35, is found: Q=ΔY÷ΔX=1.875÷3, 75−
−=0.5=(,100)2 is obtained. Next, multiply the value of Q by the value of XA, and then add the value YA stored in the register 34 to this result (.10.0)2
X (,100)2+ (,101)2= (,111
)2==0.875 is obtained as the value of f'. Here, the value of f' is 1.1: since it is a small value, this value of 0
The value of 875 is stored in the register 38 as (i/j of f.On the other hand, the register 39 that stores the integer part of Ys is also (
100) Store the value of 2-4 as is as IYn8. That is, by the circuits shown in FIGS. 4 to 6, I
X, == (l O0)2=4 , XA= (,1
00)2=0. -5°Q = (.1.00)2 = 0
．． 5, f = (,111)2=0.875゜IY
Each value of ss = (,100)2 = 4 is obtained.

Next, in the circuit of FIG. 8, the start signal 5TART'
is not given, the contents of the up counter 4 is 4. Since the content of the up counter 43 is also 4, the first coordinate information (IXn, IYn) is Lr1 (4°4), and the second coordinate information (JXn, IYn-H) is (4
, 5). Also, since the content of the register 44 is 0.875, the second coordinate information (IXn.

The luminance information associated with IYn-H) is 0.875. The luminance information accompanying the first coordinate information (IXn, IYn) is 0.12
It becomes 5. Here, as luminance information (.l 11) 2 = 0
．． 875 has the highest brightness and is represented by the largest circle, and when (,o o, o)2 = 0, there is no brightness and this is a non-display state, and the brightness during this time is of a size corresponding to that value. If expressed as a circle, the first coordinate information (4,
4) and the associated luminance information 0.124), point A1 in FIG. 9 is displayed on the display screen. Similarly, point Bl in FIG. 9 is also displayed on the display screen based on the first second coordinate information (4, 5) and the accompanying luminance information of 0.875. .

Next, when the start signal 5TART and the clock pulse CK are input, the register 44 receives the addition η4 output S from the adder 45.
UM is given. Clock iJ now? The contents of the register 44 before the pulse CK is input are f=-(.I] 1)
2=0.875, this is KQ.

Since the value (.100)2=0.5 is added by the adder 45, the above SUMO value is (.01.1)2=0.375
Totoru. Therefore, after the first clock pulse CK is input, the contents of the register 44 are (,011).

It has changed to On the other hand, when the adder 45 performs the above addition, an output CARRY is generated, so the up counter 4 counts up and its content becomes 5. Furthermore, upon input of the first clock f pulse CK, the up counter 43 also counts up and its contents become 5.

Therefore, in this case, the second first coordinate information is (
5,'5), the brightness information accompanying this is 0625, and the second second coordinate information is (5°6), and the brightness information accompanying this is 0375.

At this time, points A2 and B2 in FIG. 9 are displayed on the display screen as points corresponding to the first and second coordinate information and the accompanying luminance information, respectively.

When the second clock pulse CK is input, register 4
4 newly stores the addition output SUM from the adder 45 in the same way as above. Here, the content of the register 44 before this second clock pulse CK is input is 0375, and adding the value of Q=O15 to this, the SUM at this time is
The O value is 0.875 and no carry occurs. That is, register 44 will now store a value of 0.875. 1, since no carry occurs during the above addition,
The content of the up counter 41 remains the previous value of 5. On the other hand, when the second clock pulse CK is input, the other up counter 43 counts up and its contents become 6. Therefore, the first
The coordinate information is (6, 5), and the associated brightness information is 0.1
25, the second coordinate information is (6°6), and the accompanying luminance information is 0875.

At this time, points A3 and B3 in FIG. 9 are respectively displayed on the display screen.

When a further third clock pulse CK is input, register 44 stores the new Kaga-output SUM from adder 46. In other words, when o, s'f: is added to 0875, 0375 + carry (J3 becomes CARRY -1, so the new contents of register 44 becomes 0375. At this time, a carry occurs in adder 45. Therefore, the up counter 4) counts up by J and its content becomes 6.

Furthermore, when the third clock pulse CK is input,
Another up counter 43 has a count of f and its contents are 7. Therefore, the first coordinate axis that is transmitted fourth is (7°6), and the associated luminance information t or 0
625, the second coordinate information is (7, 7), and the accompanying luminance information is 0375. At this time, points A4 and B4 in FIG. 9 are respectively displayed on the display screen. After this fourth information is sent, the plow output of the down counter 47 becomes the "0" level, so that the clock pulse CK is not outputted from the AND circuit 49 thereafter.

In this way, according to the above embodiment circuit, in addition to the points (A1rA41A3+A4) constituting the original line, the auxiliary points (Bl
r Bl r B31 B4 ), one point is composed of two coordinate points converted into integers, and the brightness of both coordinate points is set to a value inversely proportional to the distance between them and the actual coordinate point. Therefore, the display can be made as if a smooth straight line was being displayed, as shown by the solid line in FIG. Moreover, in the past, the starting point and ending point of a straight line had to be located at integer coordinate points, which restricted the straight lines that could be displayed. However, according to the circuit of the above embodiment, since the starting point and the ending point do not have to be on integer coordinates, there are no restrictions on the straight lines that can be displayed, and any straight line can be displayed. Therefore, when displaying a curved line such as a circle using this straight line information generating circuit, it can be displayed much more smoothly than before. In other words, a curve can be regarded as a collection of straight lines,
By displaying each straight line more smoothly, a smooth curve can be displayed as a result.

Furthermore, this straight line or curve can be displayed on a raster scan type graphic display device using a two-dimensional orthogonal coordinate system that handles only integer coordinate values.

Note that this invention is not limited to the above embodiments, and various modifications are possible. For example, in the above embodiment, ΔX
We have explained the case where ΔY is larger than ΔY;
Needless to say, it is possible to implement oJ even when Y is larger than ΔX; in this case, Xs f Ys and ΔX
may be replaced with ΔY. Furthermore, in the above embodiment, only the case where the straight line to be displayed is in the first quadrant of the X and Y coordinates is explained, but in this case, the straight line of other quadrants can be displayed by replacing the X and Y coordinates or adding polarity. It can also be displayed. Furthermore, in the above embodiment, a case has been described in which a straight line is displayed using a raster scan type graphics display device, but in this case, information from this circuit is inputted to other display means, such as an X-Yf printer, and the register 44 The information from the frame and complementer 46 may be used as density information.

Furthermore, in the above embodiment, the case where three bits below the decimal point are used as the brightness information has been explained, but the brightness may be set more precisely by increasing the number of bits, or the maximum brightness information can be set more precisely. It is also possible to set it freely and relatively change the density of the generated line segment.

Further, in the above embodiment, a case has been described in which the coordinate values of the starting point and the change values thereof are given in advance, but the coordinate values of the starting point and the ending point may also be given. However, in this case, it is necessary to find the change value from both coordinate values.

As explained above, according to this invention, integer coordinate values are taken! 7 In a straight line information generation circuit that generates coordinate information and density information that are necessary when displaying a straight line using a two-dimensional orthogonal coordinate system display means, one coordinate point is converted into two coordinate points converted into integers. Since the concentration of both coordinate points is set to a value inversely proportional to the distance between the two coordinate points, it is possible to display a smooth straight line, and the start and end points are integer coordinate points. It is possible to provide a straight line information generation circuit that can display any straight line that is not present.

[Brief explanation of the drawing]

FIG. 1 and 6 are diagrams for explaining the prior art, FIGS. 2 and 3 are diagrams for explaining the present invention in detail, and FIGS. 4, 5, 6, and 8 are diagrams for explaining the present invention, respectively. FIGS. 7 and 9 are circuit diagrams showing the configuration of an embodiment of the present invention, respectively, for explaining the circuit of the embodiment. 11.13, 21.31-34, 38, 39...
Register, J, 2.23.37.45... Adder, 2
2... Exclusive OR circuit, 35... Divider, 36...
... Multiplier, 4J', 43 ... Up counter, 42
...+1 adder, 46...complementer, 42...down counter, 48...7 rip pro, p, 49...
AND circuit. Figure 1 □X Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 39 Figure 7 Figure 9 45678

Claims (1)

[Claims] In the linear information generation circuit that generates the coordinate information and associated density information required when displaying a straight line using a two-dimensional orthogonal coordinate system display means that handles integer coordinate values, each input is input as a real number including a decimal. means for obtaining the slope value of any straight line from the starting point coordinate value and the ending point coordinate value, or from the starting point coordinate value and its change value; A means for obtaining an integer unidirectional coordinate value existing in a nearby position, and from the above starting point coordinate value and the above slope value, the actual straight line starting from the starting point given by the above real number starting point coordinate value is determined in the first direction. means for obtaining, as a variable value, a decimal value of 1 unit or less of the other direction coordinate value at a point intersecting a perpendicular line drawn on the integer coordinates; means for correcting the coordinate value in the other direction obtained by the means according to the variable value by one unit value; The corrected other direction coordinate value is used as the first coordinate information, and the same one direction coordinate (11'J and the same other direction coordinate A16) is also used as the other direction seat value, which is larger by one unit, as the second coordinate information. The means by which each occurs and the above a.
1, 282 coordinates (means for sequentially increasing the one-way coordinate value of the W signal by one unit by an integer subdivision of the change in the one-way coordinate value from the start point to the end point of the @ line, and the variable value '51 : At the same time as going to note 1, add the above gradient value to the variable E stored in synchronization with the increasing operation of the one-way ljl target value. From the addition result at this time, the digit is the residual υ after removing the value. variable value updating means for storing the value as a new variable value, and increasing the other direction coordinate value of the first and second coordinate information by 1 unit each time a carry (it+) occurs in the addition result of the above means. generating the output value of the variable value updating means as density information accompanying the 20th Zayanagi information.
1 and its complement #all as density information associated with the first coordinate information.