JP2630843B2 - Straight line drawing method and apparatus - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for drawing a straight line on a dot type plotter, printer, display and the like.

[Conventional technology]

When performing graphic processing using a plotter, word processor, personal computer, or the like, the graphic must be represented by a dot pattern. In a conventional method of forming a linear dot pattern on a dot pattern formation surface (which may be virtual) of such an apparatus, for example, a straight line having an inclination angle d with respect to the X-axis of 0 ° <d <45 ° When forming a dot, as shown in FIG.
₀ (x ₁ , y ₁ ), a point D ₁ (x ₁ +1
y ₁ ) and a point D moved by one in the X-axis direction and one in the Y-axis direction
₂ (x ₁ +1, y ₁ +1), the errors between these points D ₁ , D ₂ and the ideal straight line 1 are obtained, and the point with the smaller error is determined as the drawing point, Generate dots there. Hereinafter, a dot pattern for expressing the straight line 1 is formed in the same manner.

However, in the above-mentioned method, the calculation after the decimal point is difficult, and as an improved drawing method, "Bresenha
A method called "m line drawing algorithm" is widely known. This "Bresenham's line drawing algorithm" is described in the magazine "PIXEL" No.
11 pages 101-107.

[Problems to be solved by the invention]

The above method and "Bresenham's line drawing algorithm"
In each of the methods described above, it is necessary to calculate one point at a time to draw a line, and therefore, there is a problem that the drawing time becomes enormous.

This is because, for example, when a drawing point is calculated by a microprocessor and is written into an image memory (bitmap memory), the microprocessor uses a predetermined data bit width (for example, 8 bits in an 8-bit computer, and “word width” in the present specification). This is because, although writing and reading of data are performed every time, the calculation of the drawing point is performed for each bit, the efficiency is extremely low. In particular, in the case of a straight line having a small inclination of the dot pattern formation surface with respect to the X axis or the Y axis, it is necessary to generate a large number of dots within one word width, so that the efficiency has been extremely poor.

Accordingly, an object of the present invention is to provide a straight line drawing method and apparatus that improve the drawing speed.

[Means for solving the problem]

According to the present invention, if a scan line is set in parallel with the axis having the smaller inclination between the X-axis and the Y-axis of the dot pattern formation surface and the straight line to be formed, it should be generated on the same scan line. The number n of dots is basically N and N + 1
(N and N-1 may be considered.) This is based on the fact that only two types exist.

This fact will be described with reference to FIGS. 4th
The figure shows a dot pattern for expressing a straight line having a slope of 3/10, and the number of dots generated on the same horizontal scan line is 3 or 4 except for the vicinity of the start point a and the end point b. . FIG. 5 shows a linear dot pattern having a slope of 7/30, and the number of dots generated on the same horizontal scan line is four or five. Thus, the number of dots generated on the same scan line during straight line drawing is
Assuming that the smaller number is N, there are only two types, N and N + 1 (where N is the larger number, N and N-1) except for the start point and the end and the vicinity.

Therefore, in the straight line drawing method of the present invention, as shown in FIG. 1, scan lines parallel to one side of a matrix of dot generation points constituting a dot pattern forming surface are sequentially shifted in a direction perpendicular to the scan lines. A predetermined straight line pattern is formed on the dot pattern forming surface. At this time, an integer part of a reciprocal of an inclination of an ideal straight line to be formed with respect to the scan line is generated on one scan line. The decimal part of the reciprocal of the inclination is added and accumulated for each shift of the scan line, and the number of dots to be generated on the next scan line is obtained from the comparison result between the accumulated value and a predetermined value. n is either N or N + 1, or N
And N−1, and the number of dots corresponding to the result of the determination is held in a buffer register 104 provided corresponding to a predetermined word width. The image is drawn in the bit map memory 106 provided corresponding to the matrix of the dot generation points.

The linear drawing apparatus of the present invention used in the above method has a bitmap memory 106 having a bitmap corresponding to a matrix of dot generation points, and writing and reading are performed in a predetermined word width unit. A scan line shift means 107 for shifting a scan line parallel to one side of the matrix of the generation point in a direction perpendicular to the scan line; and an integer part of the reciprocal of the inclination of the ideal straight line to be formed with respect to the scan line, Basic dot number calculating means 101 for calculating a basic dot number N to be generated on a scan line; and a decimal part of the reciprocal of the inclination is added and accumulated for each shift of the scan line, and a comparison result between the accumulated value and a predetermined value is obtained. From the above, whether the number n of dots to be generated on the next scan line is N or N + 1, and Is the N
And N−1, a buffer register 104 provided corresponding to the word width of the bitmap memory 106, Means for holding the number of dots in the buffer register 104, and a bitmap memory 106 for storing the contents of the buffer register 104.
And a drawing unit 105 that draws the image on the screen.

[Action]

In the present invention, first, the number N of dots to be generated on the same scan line is obtained from the inclination of the ideal straight line to be formed. On the other hand, every time the scan line is shifted, the position of the already generated dot and the formation of the dot are determined. The error between the ideal line to be accumulated is accumulated, and the accumulation result indicates whether the number n of dots to be generated on the next scan line is N or N + 1, or N and N + 1. -1 is determined.

Therefore, a plurality of dots can be simultaneously generated on one scan line based on the result of the determination, and the writing to the bitmap memory 106 performed in a predetermined word width unit can be efficiently performed. It can be performed well, and the drawing speed is improved.

〔Example〕

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 2 is a block diagram showing a configuration of a straight line drawing apparatus according to one embodiment of the present invention.

This straight line drawing apparatus includes a central processing unit (CUP) 1, a ROM 2 storing a microprogram, a bit map memory 3, and a Y corresponding to a dot pattern formation surface shown in FIG. A counter 4 for determining the position in the axial direction, an accumulator (X-ACC) 5 for determining an X coordinate position for calculating the position in the X-axis direction of the dot pattern forming surface, a data bus 6,
Further, an interface (I / O) 8 with an output device 7 such as a plotter is provided. And CPU1 is an arithmetic unit (ALU)
11 and an accumulator (ACC) 12 for generating dots, which has the function of a buffer register.

In the following description, it is assumed that straight lines are drawn on a dot pattern forming surface of 32 dots in the horizontal direction (X-axis direction) and 16 dots in the vertical direction (Y-axis direction) as shown in FIGS. In this embodiment, since the bit map memory 3 is accessed every 8 bits, as shown in FIG. 4 and FIG.
The dot pattern forming surface of 32 × 16 dots is divided into four in the X-axis direction, and 64 addresses from “0000” to “003F” are stored in the bit map memory in the order of row A, row B, row C and row D. 3 (see FIG. 6). And the fourth
In the example of the figure, a straight line is drawn from the start point (0,0) to the end point (30,9). In the example of FIG. 5, the start point (0,0) is drawn to the end point (30,9).
7) A straight line is drawn.

Next, the straight line drawing method of the present embodiment will be described with reference to the flowchart of FIG.

First, the calculation unit 11 calculates the inclination Δy / Δx of the straight line to be drawn.
Is used to calculate the basic dot number N. In this embodiment, the basic dot number N is obtained from the following equation.

N = INT (Δx / Δy) (1) That is, the integer part of the reciprocal of the slope Δy / Δx of the straight line is the basic dot number N. In the example of FIG. 4, since the inclination of the straight line is 3/10, N is 3. In the example of FIG. 5, since the inclination is 7/30, N is 4.

Next, drawing of a starting point of a straight line, that is, dot generation on the first scan line is performed. In this embodiment, the scan line is set parallel to the X axis of the dot pattern forming surface. In the examples of FIGS. 4 and 5, the starting point a is (0, 0), The first scan line to be generated is the scan line at y = 0. In the start point drawing and the subsequent end point drawing, the basic rule that the number n of dots to be generated on the same scan line is one of the basic dot number N and N + 1 in the vicinity of the start point and the end point of the straight line. Does not hold, so it must be done separately.

The dots are generated on the first scan line until the y coordinate of the ideal straight line 1 to be drawn becomes closer to the next scan line, that is, y = 0 in the examples of FIGS.
You must do it until you exceed 5. The number n is
When Δx / 2Δy is not divisible, n = INT (Δx / 2Δy) +1 (2) When Δx / 2Δy is divisible, n = Δx / 2Δy (2) ′. In the example of FIG. 4, n = 2, and in the example of FIG. 5, n = 3.
It is.

Thus, for example, in the example of FIG. 4, in order to generate dots at the points (0,0) and (1,0), the data of the number of dots is reflected in the dot generation accumulator (ACC) 12 of FIG. The generated code "11000000" is generated and transferred to the address "0000" where the start point of the straight line exists in the bitmap memory 3, that is, drawn in the bitmap memory 3 (see FIG. 6). When the LSB of the code generated by the dot generation accumulator (ACC) 12 becomes "0", it means that the dot generation on the scan line has been completed, and the counter 4 shown in FIG. As y + 1, the scan line is shifted by one, and a dot is generated on the next scan line.

In order to generate dots on a scan line after y = 1, it is necessary to determine whether the number n of dots to be generated on the scan line is the basic dot number N or N + 1.

When the basic dot number N is defined as in the above equation (1), it is the decimal part of Δx / Δy that is accumulated as an error between the generated dot position and the ideal straight line l. Therefore,
The arithmetic unit 11 adds the decimal part of Δx / Δy every time the scan line is changed by 1, and sets n = N until the value exceeds 1.0, and sets n = N + 1 when the value exceeds 1.0. .

Specifically, when y = 0.5, Is used as an initial value of the judgment variable E, and an error between the ideal straight line 1 and G is defined as G = G ₁ = (Δx / Δy) −N (4). going by adding error G ₁ in the determination variable E in. Then, this determination variable E
Until E exceeds 1, the basic dot number N is output as the number n of dots to be generated on the scan line, and when E exceeds 1, n = N + 1.

After E> 1, the error G is set as follows: G = G ₂ = (Δx / Δy) −N−1 (5), and each time the scan line is changed by one, the error G Add ₂ During E> 1, N + is set as the number n of dots generated on the scan line.
1 is output, and when E becomes smaller than 1, the error G is
Back to the G _1.

That is, while the judgment variable E is smaller than ₁ , G1 is added to the judgment variable E as an error every time the scan line is changed by 1 until the judgment variable E exceeds 1, and
While the number n of dots to be generated on the scan line is continuously determined to be N, while the determination variable E is greater than 1, the determination is made every time the scan line is changed by 1 until the determination variable E falls below 1. with adding G ₂ as an error variable E, it continues to determine the number n of dots to be generated on the scan line n + 1 and.

According to this method, in the example of FIG. 4, the number of dots generated on the scan line with y = 1 is the basic dot number 3
Therefore, the accumulator for generating dots shown in FIG. 2 (AC
C) A code "00111000" is generated in 12 and transferred to an address "0004" in the bit map memory 3 (see FIG. 6). At this time, the dot generation accumulator (AC
C) In the code generated in 12, the bit position where “1” rises (the third bit from the left on the scan line with y = 1) is calculated by accumulating the number of generated dots in the X-axis direction. Is determined using an X-coordinate position accumulator (X-ACC) 5. That is, in the X-coordinate position determining accumulator (X-ACC) 5, the number of already generated dots is accumulated, and the accumulated value is divided by the word width (8 in the present embodiment) to obtain a surplus R. The next bit position is stored in the accumulator for dot generation (AC
C) As the bit position where “1” rises in 12, CPU1
Determined by

As in the case of the scan line of y = 0, as described above, even in the scan line of y = 1, when the LSB of the code generated in the accumulator (ACC) 12 for dot generation becomes "0", this scan Since the dot generation on the line has been completed, the counter 4 shown in FIG.
= Y + 1 and shift the scan line, then
A dot is generated on a scan line of y = 2.

When the scan line moves to y = 2, the decision variable E
Exceeds 1, the number of dots to be generated on this y = 2 scan line is 3 + 1 = 4. Therefore, four "1" s are set in the dot generation accumulator (ACC) 12. In this case, the rising bit position of the "1" determined by the X coordinate position determination accumulator (X-ACC) 5 is LSB. , The third bit cannot be set. Therefore, a code "00000111" consisting of three "1" s is first generated in the dot generation accumulator (ACC) 12, and this is transferred to the address "0008" of the bit map memory 3 as shown in FIG. I do. At this point, it is determined that the drawing position of the straight line has moved in the X-axis direction and has entered the area of column B, and the code “10000000” with only the remaining one bit set to “1” is assigned to the dot generation accumulator (ACC ) 12 and transfers this to the address “0009” of the bit map memory 3.

And here the accumulator for dot generation (ACC) 1
Since the LSB of the code generated in step 2 is "0", it is determined that the straight line drawing on this scan line has been completed, and the process proceeds to the straight line drawing on the next scan line. At this time, the error to be added to the determination variable E is in the G _2.

When the scan line moves to y = 3, the number n of generated dots is 3
Becomes Then, after generating dots at predetermined positions in the same manner as described above, the scan line is further moved. At this time, the error to be added to the determination variable E is in the G _1.

In the same manner, dots are generated up to the address “0026” of the bitmap memory 3 and the process enters the end point drawing step.

This end point drawing step determines whether the dot position to be generated has reached the end point coordinates, and if so, the number n of dots to be generated on the scan line
Irrespective of the above, it can be performed by clipping the dot generation position at the end point coordinate position.

By the above operation, for example, a dot pattern for drawing a straight line on the dot pattern forming surface as shown in FIG. 4 is stored in the bitmap memory 3.

As described above, in the present embodiment, dots can be generated at a time in units of the word width of the dot generation accumulator (ACC) 12 having a function as a buffer register. Therefore, the arithmetic unit (ALU) of the CPU 1 The calculation efficiency in step 11 is improved, and the drawing speed is improved.

In the above-described embodiment, X in the dot pattern forming surface
The case where a straight line having an inclination angle d with respect to the axis of 0 ° <d <45 ° is described, but other straight lines can also be drawn by using a substantially similar configuration. In such a case, a slope identifying means for identifying the slope of a straight line to be drawn is provided before the basic dot number calculating means 101 in FIG. May be provided with coordinate conversion means for performing coordinate conversion. For example, the inclination angle d of a straight line to be drawn is 45 ° <d <
In the case of 90 °, after the coordinate conversion of x = y and y = x is performed by the coordinate conversion means, dot generation and writing to the bitmap memory are performed in the same procedure as in the above-described embodiment. When reading and outputting from the coordinate system, the coordinate conversion means may perform x = y and y = x coordinate conversion again to restore the coordinate system. Alternatively, the coordinate system may be restored when writing to the bitmap memory. Similarly, when −45 ° <d <0 °, the coordinate conversion of y = −y may be performed, and when −90 ° <d <45 °, x = −y and y = What is necessary is just to perform coordinate conversion of x.

In the method of the above embodiment, the straight line of d = 0 ° and d = 90 ° cannot be drawn (because the basic dot number N cannot be calculated). Is used, the straight line can be drawn. For example, the inclination of the straight line is d = 0 by the inclination identification means.
If it is determined that ゜ or d = 90 °, the y-coordinate or x-coordinate of any point on the straight line is obtained, and based on the coordinates, the Y-axis or a specific scan line parallel to the Y-axis is determined. A dot may be generated at all dot generation points between the start point and the end point.

The method and apparatus of the present invention are applicable to all types of dot plotters, printers, displays, and the like. In that case, the dot pattern formation surface does not need to actually exist, and may be a virtual concept developed in the bitmap memory. When the present invention is applied to a display device such as a liquid crystal display, the present invention may be applied by regarding each pixel of the display device as one dot.

〔The invention's effect〕

According to the method and apparatus of the present invention, the processing speed for drawing straight lines can be made faster than that of the conventional method. In particular, the effect is more remarkable on a straight line having a smaller inclination with respect to one axis in which the processing speed is extremely slow in the past.

In addition, when a straight line is drawn by the method and the apparatus of the present invention, the division operation only needs to be performed once when the inclination of the ideal line with respect to the scan line is obtained, so that the division operation must be performed twice or more. The number of calculation steps can be reduced as compared with, and high-speed straight line drawing becomes possible. As a result, for example, image data exposed as a set of many linear elements can be drawn in an extremely short time.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a basic configuration of the present invention, FIG. 2 is a block diagram showing a configuration of a straight line drawing apparatus according to an embodiment of the present invention, FIG. 3 is a flowchart showing an operation of a CPU in FIG. 4 and 5 are conceptual diagrams showing an example of straight line drawing, FIG. 6 is an explanatory diagram showing the contents of a bitmap memory,
FIG. 7 is an explanatory view showing a conventional straight line drawing method. In the reference numerals used in the drawings, 1... CPU, 3... Bitmap memory, 4... Counter, 5... X-coordinate position determining accumulator (X-AC
C), 11 calculation unit (ALU), 12 dot accumulator (ACC, buffer register), 101 basic dot number counting means, 102 dot number determination means, 103 dot generation means ( Dot number holding means), 104 buffer register, 105 transfer means (drawing means), 106 bitmap memory, 107 scan line shift means

Claims (2)

(57) [Claims] 1. A straight line drawing method for forming a linear pattern of dots on a dot pattern forming surface in which dot generation points are arranged in a matrix, wherein a scan line parallel to one side of a matrix of the dot generation points is formed by the scan line The linear pattern is formed by sequentially shifting in a direction perpendicular to the scan line. At this time, an integer part of a reciprocal of an inclination of the ideal straight line to be formed with respect to the scan line is generated on one scan line. The number of dots to be generated on the next scan line is obtained from the result of comparison between the accumulated value and a predetermined value. Is either N or N + 1, or N
And N−1, and the number of dots corresponding to the result of the determination is held in a buffer register provided corresponding to a predetermined word width. A straight line drawing method characterized by drawing in a bit map memory provided corresponding to a matrix of occurrence points. 2. A bit map memory having a bit map corresponding to a matrix of dot generation points and performing writing and reading in units of a predetermined word width, and a scan parallel to one side of the matrix of the dot generation points. A scan line shift means for shifting a line in a direction perpendicular to the scan line; and a basic dot number N for generating an integer part of a reciprocal of an inclination of the ideal straight line to be formed with respect to the scan line on one scan line. A basic dot number calculating means, and a decimal part of the reciprocal of the inclination is added and accumulated for each shift of the scan line, and a dot to be generated on the next scan line is obtained from a comparison result between the accumulated value and a predetermined value. Is the number n of the N or N + 1, or
And N−1, a buffer register provided corresponding to the word width of the bit map memory, and a dot according to the determination result by the dot number determining unit. A straight line drawing apparatus comprising: a dot number holding unit that holds a number in the buffer register; and a drawing unit that draws the content of the buffer register in the bitmap memory.