JPH03147190A - Straight line drawing method - Google Patents

Abstract

PURPOSE:To efficiently draw a straight line at high speed by simultaneously drawing plural drawing points by utilizing a fact that the number of the drawing points arranged laterally in one line is increased for a slightly inclined straight line. CONSTITUTION:When the straight line is displayed in a pit map memory, an inverse formula 1/a=t+s((t) is an integer number, 0<=s<1) is calculated while defining the inclination of the real straight line as (a), and from the calculated inclination (a), a value (b) is calculated by a formula b=1/2-(t)X(a). Next, while defining a distance between a first point of a continuous dot sequence and the real straight line as (d), the (d) is compared with the (a) and at the time of d>=d, the number of the continuous dots is defined as t+1. Then, at the time of d<b, the number of the continuous dots is defined as the (t). The sequence of dots is drawn only by the calculated number and the value of the (d) is corrected to a formula d=(d)+(a)X(the number of drawing points)-1. Next, it is checked whether all the dot sequences are finished being drawn or not, and when it is not finished, the same drawing operation is repeated to get back to the beginning. Thus, the straight line can be efficiently drawn at high speed.

Description

[Detailed Description of the Invention] [Summary] Regarding a straight line drawing method when drawing a straight line on a bitmap memory used as a display device of a cocomputer, the purpose of this invention is to draw a straight line at high speed and efficiently. When displaying a straight line in
Let the slope of the actual straight line be a, then its reciprocal 1/a 1/a = t + s (t is an integer, 0≦s<1
), and from the obtained slope a, find the value b shown by the following formula: b-1/2=t×a. Next, calculate the distance between the first point in the series of consecutive points and the actual straight line by d. Compare d and a, and when d≧d, the number of consecutive points is (+1), and when dab, the number of consecutive points is t, draw the determined number of point sequences, and express the value of d using the following formula. Correct the value of d to be d = d + a Like (1 to cultivate.

[Industrial Application Field] The present invention relates to a straight line drawing method for drawing a straight line on a bitmap memory used as a computer display device.

In recent years, bitmap memory, which allocates memory corresponding to each pixel on the display, has come into widespread use as a computer display device, and a method for drawing pseudo straight lines on this memory has been required. There is.

[Prior art] Bitmap memory has points on a grid, so when drawing a straight line, it selects the grid points closest to the straight line and draws them to display a pseudo straight line. It looks like this. In the conventional drawing method, DDA (D
digital Differential Alg
orithm) is famous. This method uses the difference between an actual straight line and the drawing point closest to the straight line to determine the next point to be drawn.

FIG. 4 is an explanatory diagram of a conventional drawing method. It is assumed that the distance between the grid points shown in the figure is normalized to 1. In the figure, Ω is an actual straight line.

Now, assuming that Pl in the figure is a drawing point, the attachment between the actual straight line g and the drawing point 21 is d. Here, if the slope of this straight line is a (Q<a<1.), then the relationship is the fifth
The result will be as shown in the figure.

The next drawing point after Pl is P2 with the y value +1, or the y value, y
It becomes either one of P3 whose values are both +1.

In this case, d+a (d assumes a positive or negative value)
is larger than 0.5, it is determined by which point A, where the straight line Ω intersects with the grid, is closer to P2 or P3. When d+a is smaller than 0.5, P2 is close to the straight line g, and P2 becomes the next drawing point. On the other hand, d+a is 0.5
If it is larger than , P3 is closer to straight line g, and P3 becomes the next drawing point.

DDA is a method of drawing a straight line while calculating drawing points one by one in this way.

[Problems to be Solved by the Invention] The conventional straight line drawing method is a method of drawing a straight line while calculating the drawing points one by one as described above, so the access to the memory is equal to the number of drawing points. This required a long time for processing.

The present invention has been made in view of these problems, and an object of the present invention is to provide a straight line drawing method that can draw straight lines efficiently and at high speed.

[Means for Solving the Problems] FIG. 1 is a flowchart showing the principle of the method of the present invention. In the present invention, when displaying a straight line in the bitmap memory, the slope of the actual straight line is a, and its reciprocal is 1/a1, /
Calculate a = t + s (t is an integer, 0≦s×1) (Step 1), and from the obtained slope a, calculate the value b b = 1 / 2 - t x a given by the following formula (Step 2) Next, let d be the distance between the first point in the series of consecutive points and the actual straight line, and compare d and a. Step 3) When d≧d, the number of consecutive points is t+1, and when d<b, Step 4) Set the number of consecutive points to t. Step 5) Adjust the value of d to d = d + aX (number of drawing points) - 1, which is expressed by the following formula. The process is characterized in that it correctly checks step 6), then checks step 7) to see if all point sequences have been drawn, and if not, returns to step 3 and repeats the same drawing operation. Note that the values of d and b to be compared are considered in terms of their absolute values.

[Operation] We focused on the fact that a straight line with a small slope increases the number of drawing points that are lined up horizontally, so a plurality of drawing points are drawn at once. This makes it possible to provide a straight line drawing method that can draw straight lines at high speed and efficiently.

[Example] Hereinafter, an example of the present invention will be described in detail with reference to the drawings.

FIG. 2 is a diagram showing an example of a system configuration for implementing the method of the present invention. In the figure, 1 is the first register that holds the difference d between the actual straight line and the drawing point, 2 is the second register used to calculate the number of consecutive drawing points,
Prior to drawing, a constant calculated from the slope value a is set.

3 is a comparator that compares the outputs d and b of the first and second registers to determine the number of consecutive drawing points, and 4 stores points in the bitmap memory 5 according to the determined number of consecutive drawing points. This is a drawing section that draws.

Here, continuous drawing points refer to points having the same function axis value. Also, the function axis is y if the slope is 1 or more.
If the axis or inclination is 1 or more and FO or more, point to the X-axis. In the following explanation, a case where the slope is 0 or more and 1 or less will be described. For other cases, the present invention can be applied in the same manner as the conventional DDA by performing appropriate coordinate transformation.

FIG. 3 is a diagram showing an example of drawing by the method of the present invention. Second
Embodiments of the method of the present invention will be described in detail with reference to the drawings. Third
In the example shown in the figure, a straight line with an inclination of a-215 is drawn. In this case, since the reciprocal of the slope a is 5/2-2.5, the number of consecutive point sequences is considered to be 2 or 3. Here, a constant for determining the number of consecutive drawing point sequences is determined.

b-1/2-2X (215) --3/10. This value of b is stored in register 2.

On the other hand, from FIG. 3, the difference value d at point P is -115.

This difference value d is stored in register 1.

Comparator 3 compares the value of b and d stored in registers 1 and 2.
Compare the absolute values of the values of . d-115, b-3/
Since it is 10, it becomes dab. Therefore, comparator 3 is P
The number of point sequences including the points is determined to be two. The drawing section 3 is
In response to the output of the comparator 3, two images are drawn consecutively at a predetermined position in the bitmap memory 5. As a result, 2 including point P
The points with the -y coordinate value are consecutive.

Next, when calculating the difference value d at point S, the difference value d- at point P is
-115, it becomes d−1,15+(215)x2−1 −215. This value is stored in register 1. Then, the comparator 3 compares the absolute values of the value of d stored in the register 1, -215, and the value of b, 3/10, stored in the register 2. Since d is larger than b, the comparator 3 determines that the number of drawing point sequences is three. The drawing unit 3 receives the output of the comparator 3 and draws three images in succession at a predetermined position in the bitmap memory 5. As a result, three points including point S with the same -y coordinate value are consecutive.

Next, when calculating the difference value at point T, the difference value d− at point S is
-215, it becomes d−-215+ (215)X3-1 −115. This value is stored in register 1. Then, the comparator 3 compares the absolute values of the value of d stored in the register 1, -115, and the value of b, stored in the register 2, of 3/10. Since d is smaller than b, the comparator 3 determines that the number of drawing point sequences is two. The drawing section 3 receives the output of the comparator 3 and draws two consecutive images at a predetermined position in the bitmap memory 5. As a result, two points including point T with the same -y coordinate value are consecutive.

By repeating such a sequence, a straight line can be drawn. According to the present invention, since a plurality of drawing points can be obtained simultaneously, the drawing speed is improved compared to the conventional method in which drawing points are obtained one by one.

In the above explanation, fractions were used as the basis for 31 arithmetic, but
Generally, computers are not good at subtracting fractions and decimals, so processing speed is faster if they convert the numbers into integers by multiplying them by constant values, and perform calculations and comparisons using the integer values.

Also, when performing a comparison, the speed of comparison with 0 is generally faster than with a constant value, so subtract the value of the constant d from the difference value d in advance, and then use the comparison with 0 to set the condition. may be determined.

[Effects of the Invention] As described in detail above, according to the present invention, a straight line with a small slope increases the number of drawing points arranged in a horizontal line, and a plurality of drawing points are drawn at once. I decided to do so. This makes it possible to provide a straight line drawing method that can draw straight lines at high speed and efficiently.

[Brief explanation of the drawing]

Fig. 1 is a flowchart showing the principle of the method of the present invention, Fig. 2 is a diagram showing an example of a system configuration for implementing the method of the present invention, Fig. 3 is a diagram showing an example of drawing by the method of the present invention, and Fig. 4 is a diagram showing the conventional method. FIG. 5, which is an explanatory diagram of the straight line drawing method, is a diagram showing the slope of the straight line. In FIG. 2, 1.2 is a register, 3 is a comparator, 4 is a drawing section, and 5 is a bitmap memory. Fig. 2 shows an example of a system configuration for carrying out the method of the present invention. Fig. 1 is a flowchart showing the principle of the method of the invention. Fig. 3 shows an example of drawing based on the method of the invention. Diagram showing the slope of the straight line Figure 5

Claims (1)

[Claims] When displaying a straight line in a bitmap memory, the slope of the actual straight line is a, and its reciprocal 1/a1/a=t
+s (t is an integer, 0≦s<1) (step 1), and from the obtained slope a, calculate the value b shown by the following formula (step 2), then , compare d and a with d being the distance between the first point in the series of consecutive points and the actual straight line (Step 3) If d≧d, the number of consecutive points is t+1, and if d<b, the number of consecutive points is t+1. Set the number to t (step 4), draw the determined number of point sequences (step 5), and correct the value of d to the value of d shown by the following formula: d = d + a × (number of drawing points) - 1 (Step 6), and then checks whether all point sequences have been drawn (Step 7), and if not, returns to Step 3 and repeats the same drawing operation. How to draw straight lines.