JPH08297747A - Method and device for plotting - Google Patents

Abstract

PURPOSE: To smoothly connect an approximated curve and its tangent without reducing the processing speed. CONSTITUTION: In steps S301 to S303, a circular arc is divided into N parts based on inputted information of this circular arc, and a central angle α corresponding to each divided circular arc (segment) is selected. In a step S304, the central angle α is divided into two to calculate a central angle β. In steps S306 to S310, the given circular arc is approximated with segments of the length corresponding to the central angle β in accordance with a parameter (i) indicating the number of a plotted segment in the case of i=0 or i=N-1 (at the time of plotting the end points of the circular arc) and is approximated with segments of the length corresponding to the central angle α in the case of 0<i<N-1.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a drawing apparatus and a drawing method, and more particularly to a drawing apparatus and a drawing method for approximating a curved line with a minute straight line.

[0002]

2. Description of the Related Art Conventionally, the following method has been used in a drawing apparatus which draws a curve or the like by a dot matrix. That is, for example, when drawing a circular arc, a method of approximating with a set of line segments of a certain length so that the approximated circular arc has sufficient visual smoothness in order to reduce the calculation processing amount and speed up the processing. Was used. Hereinafter, this fixed length line segment is referred to as a segment. In the actual drawing process, since each line segment naturally has a constant thickness, if the center line of each segment is used as the connection point of the adjacent segment, cracks will form at the connection point. Creates a gap.

FIG. 9 is a diagram showing an example of approximation of a circular arc in a conventional example. 900 is an arc to be approximated. 921 to 923 are circular arcs 9 at the time of drawing.
00, whose center lines 911 to 913 are connected at points 941 and 942 on the arc 900. Each segment is actually a rectangle, and a crack-like gap (hereinafter, simply referred to as a gap) is generated at the connection portion, so that the gap needs to be interpolated. 9
Reference numeral 31 is an interpolating unit that interpolates a gap in the connecting portion of the segments 921 and 922. Similarly, 932 is an interpolating unit that interpolates a gap in the connecting portion of the segments 922 and 923.

The figures actually drawn with respect to the arc 900 are the segments 921 to 923, the interpolation section 931,
932 only, and the arc 900 and the like are shown only for explanation.

[0005]

However, in the above conventional example, when the tangent line 950 (the tangent line at the end point 943 of the circle including the arc 900) connected at the end point 943 of the arc 900 is individually drawn, the segment 9
Since the direction of 23 and the direction of the straight line 951 do not coincide with each other, the gap 933 naturally occurs. This means that when drawing a diagram in which the tangents of the arc are connected at the end points of the arc, the two are not connected smoothly at the contact points.

The present invention has been made in view of the above problems, and it is possible to smoothly connect an approximated curve and another line forming a tangent to the approximated curve without lowering the processing speed. To aim.

[0007]

[Means for Solving the Problems] and

In order to solve the above-mentioned problems, the drawing apparatus according to the present invention is a drawing apparatus which draws a figure by approximating a curved line with a minute straight line, and the curve is defined as another line tangential to the curved line. A dividing means for finely dividing the area in the vicinity of the contact points and roughly dividing the other areas, a linear approximation means for approximating each divided curve with a straight line, and a drawing means for drawing a figure including the approximated curve are provided. The approximated curve can be smoothly connected to other lines forming the tangential direction thereof without lowering the processing speed.

The drawing method according to the present invention is a drawing method in which a curve is approximated by a minute straight line to draw a figure, and the curve is a region in the vicinity of a contact point in contact with another line forming a tangential direction of the curve. Is fine, for other areas is roughly divided, a dividing step, a linear approximation step of approximating each divided curve by a straight line, and a drawing step of drawing a figure including the approximated curve, It is possible to smoothly connect the approximated curve and the other line forming the tangent to the approximated curve without lowering the processing speed.

[0009]

【Example】

[First Embodiment] A preferred first embodiment according to the present invention will be described below. FIG. 1 is a block diagram showing an example of the arrangement of a printing apparatus according to this embodiment. The control unit 102
A block that controls the entire printing apparatus 100, and includes a ROM that stores a control program such as a program according to a flowchart described below, a work memory, and a CPU that executes the control program. Interface 10
An interface 3 performs data communication with an external device such as the host computer 101. The print command analysis unit 104 is a block that includes a reception buffer that stores a print command input from the host computer 101 via the interface 103 and that analyzes print data. The drawing unit 105 includes a page memory, performs drawing processing according to the analyzed print command, and expands the print data into a bitmap in the page memory. Output unit 106
Is a printer such as an ink jet printer, a laser beam printer, or the like, which makes the bitmap data expanded in the page memory a permanent visible image on a recording paper.

The operation of the printing apparatus 100 will be described below with reference to the flowchart. FIG. 2 is a flowchart for explaining the overall processing flow of the printing apparatus 100. When a print command is received from the external device via the interface 103 in step S201, the next step S201 is performed.
At 202, the print command is analyzed. Step S20
In 3, it is determined whether or not the analyzed print command is a paper discharge command that prompts paper discharge. If it is not the paper discharge command,
In step S204, if the command is a paper discharge command,
In step S207, the print data is expanded into a bitmap on a page memory (not shown), and the output unit 106 forms a permanent visible image on the recording paper.

In step S204, it is determined whether or not the analyzed print command is an arc drawing command that prompts drawing of an arc. As a result, in the case of the arc drawing command, the process proceeds to step S205, a predetermined process is performed, the process returns to step S201 again, and a series of processes is repeated until the paper discharge command is received. If it is determined in step S204 that the analyzed print command is other than the circular arc drawing command, the process proceeds to step S206, the corresponding process is performed, and then the process returns to step S201 to perform a series of operations until the paper discharge command is received. Repeat the process. The above processing is controlled by the control unit 102.

Next, the flow of the arc line drawing process (S205) will be described. This processing is performed in the drawing unit 105. FIG. 3 is a flowchart showing the flow of the arc line drawing processing executed in the drawing processing unit 105. In the arc line drawing process, it is assumed that the drawing unit 105 is input with center position information, radius, start angle, end angle, and line width of the drawn arc. In this embodiment, the start and end angles are given as normalized to an angle of less than 360 degrees, and (start angle) <(end angle).

In step S301, the drawing unit 105
The center position information of the arc to be drawn, the radius, the arc start angle, the arc end angle, and the line width are input. Step S3
In 02, from the input radius, start angle, and end angle of the input arc, the number N of equal divisions for approximating the desired arc by the set of the segments described above (the desired arc is approximated using N segments). ) Is determined. When the value of N is set to a large value, the approximated arc naturally becomes smooth, but on the other hand, the processing time becomes long. Therefore, it is desirable to set the minimum value in the range in which the approximated arc is smoothly expressed. In step S303, the difference between the end angle and the start angle is divided by the number N of equal divisions to calculate the central angle α corresponding to the length of the segment.

Processing up to this point (processing for determining the value of N)
Is similar to the above-mentioned conventional example, but the following processing is performed to smooth the connection with the tangent line at the end point of the arc. In step S304, the central angle α is set to 1
Calculate β divided into / 2.

The process from step S305 is a process of actually drawing an arc (approximate by a segment). First, in step S305, a parameter i indicating the number of drawn segments is initialized. Then, step S306
In S311 and S311, the case of the drawing process is determined according to the value of the parameter i. That is, when i = 0, steps S307 and S308 are executed and step S309 is executed.
And if i = N−1, execute steps 312 and S313 and proceed to step S309. Otherwise, execute step S314 and perform step S3.
Go to 09. In step S309, the parameter i is incremented, and when the value of the parameter i becomes equal to the number N of equal divisions in step S310, that is, when the approximation of the circular arc is finished, the series of processes is ended, while the value of the parameter i is set. If is not equal to the number N of equal divisions, the process returns to step S306 to repeat the series of processes.

If i = 0, first, step S30
In 7, the arc start angle is the angle indicating the start point of the segment (hereinafter referred to as the start point angle), and the angle obtained by adding the center angle β to the start point angle is the angle indicating the end point of the segment (hereinafter referred to as the end point angle). The segment corresponding to the angle β is drawn in the page memory. Next, in step S308, the segment angle corresponding to the center angle β is rendered in a page memory (not shown) with the end point angle in the immediately preceding rendering as the start point angle, and the angle obtained by adding the central angle β to the updated start point angle as the end point angle. .

If 0 <i <N-1, step S3
In 14, the segment corresponding to the center angle α is drawn in the page memory with the end point angle in the immediately preceding drawing as the start point angle, and the angle obtained by adding the center angle α to the updated start point angle as the end point angle.

In the case of i = N-1, first, step S
At 312, the segment corresponding to the center angle β is drawn in the page memory using the end point angle in the immediately preceding drawing as the start point angle, and the angle obtained by adding the center angle β to the updated start point angle as the end point angle. In addition, step S31
Similarly in 3, the segment corresponding to the central angle β is drawn in the page memory. It should be noted that the process of interpolating the gap is performed regardless of the value of i.

As is clear from the above description, in the vicinity of the end points of the approximated arc, the arc is approximated by the segment corresponding to the central angle β (α / 2), and the other parts correspond to the central angle α. By approximating with segments, while maintaining the same processing speed as the approximation processing in the conventional example, the accuracy of approximation at the end points is improved (the direction of the segment at the end points is made closer to the tangent direction), and the connection with the tangent line is smooth. You will be able to.

FIG. 4 is a diagram for explaining the result of applying the above approximation processing. Reference numeral 400 is an arc to be approximated, 401 is a center point of a circle including the same, and 402 is an end point. 450 is a tangent to the arc 400 at the end point 402. 411 and 412 are segments (0 <i <N−1) corresponding to the central angle α, and 413 and 414 are segments (i = 0) corresponding to the central angle β. Four
Reference numeral 51 is a tangent line to be drawn.

By reducing the central angle of the segment 414, the accuracy of the approximation in the vicinity of the end points is improved, and it can be seen that the segment 414 is smoothly connected to the tangent straight line 451.

In the above approximation process, the central angle of the segment near the end point is set to 1/2 of the segment of the other part, but the present invention is not limited to this, and the center angle near the end point is not limited to this. Anything can be used as long as it accurately approximates the arc.

Further, although the above-described embodiment describes the arc approximation processing, the present invention is not limited to this, and it is needless to say that it is widely applicable to curves such as ellipses. Absent.

Further, in the above embodiment, an example is shown in which the connection between the end point of the arc and the tangent line of the arc (including the curve in the same direction as the tangent line at the contact point) is smoothed. Can also be applied when drawing a tangent line at an arbitrary point such as an arc. This can be realized, for example, by dividing the arc at the arbitrary point (using the arbitrary point as the end point of the divided arc) and applying the above-described arc drawing processing to each of the divided arcs. . [Second Embodiment] A preferred second embodiment according to the present invention will be described below. FIG. 5 is a block diagram showing the configuration of the information processing apparatus according to this embodiment. The control unit 502 is a block that controls the entire information processing apparatus 500 and controls information processing, and includes a ROM that stores a control program and the like, a work memory, a CPU that executes the control program, and the like. The VRAM 503 is a video memory that stores an image to be drawn. A display 504 displays an image, and is connected to the bus 506 via the display interface 505. The keyboard 508 is a keyboard for performing various inputs, and is connected to the bus 506 via the keyboard interface 507.

Next, the operation of displaying a desired arc on the display 504 by the control unit 502 will be described with reference to the flowchart. In the present embodiment, for convenience of description, it is assumed that the drawing of the arc specifies the center coordinates, the radius, the start angle, the end angle, and the line width numerically from the keyboard 508, but these data are not available. It may be received via the interface shown, or may be the result of calculation based on various programs stored in the ROM.

FIG. 6 is a flow chart for explaining the flow of processing for giving arc information through the keyboard 508 and displaying it on the display 604. First, step S60
1, the center coordinates, radius, start angle, end angle, and line width of an arc to be drawn are input via the keyboard 508. In step S602, the control unit 502 analyzes the input arc information and generates a bitmap image of the arc on the VRAM 503. Then, in step 603, the VRAM 503 is displayed on the display 504 by the display interface 505 scanning the VRAM 503 at regular intervals.

FIG. 7 is a flow chart showing the flow of the arc line drawing process. It is assumed that the control unit 502 is input with the center position information of the arc to be drawn, the radius, the start angle, the end angle, and the line width. In this embodiment, the start angle and the end angle are normalized to an angle less than 360 degrees, and (start angle) <(end angle). It is assumed that the color for drawing the arc is black and the background color is white. Also, the display 504
The process of drawing black or white on top is equivalent to the act of setting or resetting the bit at the corresponding position on the VRAM 503. Hereinafter, these processes will be simply referred to as “drawing in black or white”.

In step S701, the control unit 502.
The center position information of the circle including the arc to be drawn, the radius, the start angle, the end angle, and the line width are input. Step S702
Then, based on the radius, start angle, and end angle of the input arc, the number N of equal divisions when approximating the desired arc with the set of the above-mentioned segments (the desired arc is approximated using N segments) To decide. As described above, when the value of N is set to be large, the approximated arc naturally becomes smooth, but on the other hand, the processing time becomes long. Therefore, it is desirable to set the minimum value in the range in which the approximated arc is smoothly expressed. In step S703, the difference between the end angle and the start angle is divided by the number N of equal divisions to calculate the central angle α corresponding to the length of the segment, and in step S704, the central angle α is divided into ½ β. To calculate. In step S705, γ is calculated by subtracting the central angle β from the start angle.

Hereinafter, description will be made with reference to FIG. FIG.
In, 800 is an arc to be approximated, and 801 is the center of a circle including the arc. In step S706,
With the starting point angle of γ and the ending point angle of γ + α, the segments given by points 811 and 812 on the arc corresponding to each angle are drawn in black. In step S707, the starting point angle is γ and the ending point angle is γ + β (starting angle of arc),
A segment given by a point 811 corresponding to the start point angle and a point 813 corresponding to the end point angle and having a distance from the center of (radius) × cos β is drawn in white. Then, the point 813 is set as the end point of the approximated arc. As described above, the extra portion of the segment drawn in black is erased by redrawing in white.

In step S709, a parameter i indicating the number of drawn segments is initialized. Step S7
At 09, the end point angle of the previous black segment is set as the start point angle (start angle + β when i = 0), and the angle obtained by adding the central angle α to the updated start point angle is set as the end point angle. Draw the segment connecting the points in black. The parameter i is incremented in step S710, and the parameter i is incremented in step S711.
Determines whether or not the equal number of divisions N has been reached, and the equal number of divisions N
If not, the process returns to step S709 to repeat the process. It should be noted that the process of interpolating the gap is performed regardless of the value of i.

When the value of the parameter i coincides with the equal division number N, the end point angle exceeds the end angle of the arc by the central angle β. Therefore, in step S712, the last (i
= N-1), erase the part that exceeds the end angle of the arc among the segments drawn. That is, with the end point angle immediately before as the start point angle and the end angle of the arc as the end point angle, a point corresponding to the start point angle on the arc and a point corresponding to the end point angle and having a distance from the center of (radius) × cos β Draw the connecting segment in white.

As described above, by making the segments at the end points tangential to each other, the approximated arc and its tangent can be smoothly connected.

In the above approximation process, the central angle of the segment near the end point is set to 1/2 of the segment of the other part as a result. However, the present invention is not limited to this, and the end point is not limited to this. It is sufficient if the arcs in the vicinity are accurately approximated. In the above embodiment,
Although the approximation processing of a circular arc has been described, it is needless to say that the present invention is not limited to this and is widely applicable to, for example, a curve such as an ellipse.

The present invention may be applied to a system including a plurality of devices or an apparatus including a single device. Further, it goes without saying that the present invention can be applied to the case where it is achieved by supplying a program to a system or an apparatus.

[0035]

As described above, according to the present invention, it is possible to smoothly connect an approximated curve and another line forming a tangent to the approximated curve without lowering the processing speed.

[0036]

[Brief description of drawings]

FIG. 1 is a block diagram illustrating an example of a configuration of a printing apparatus according to a first embodiment.

FIG. 2 is a flowchart illustrating an overall processing flow of the printing apparatus 100.

FIG. 3 is a flowchart showing a flow of arc line drawing processing executed in a drawing processing unit 105.

FIG. 4 is a diagram illustrating a result of applying the first embodiment.

FIG. 5 is a block diagram showing a configuration of an information processing device according to a second embodiment.

FIG. 6 is a flowchart illustrating the overall processing flow of information processing apparatus 500.

FIG. 7 is a flowchart showing a flow of arc line drawing processing.

FIG. 8 is a diagram illustrating arc line drawing processing according to the second embodiment.

FIG. 9 is a diagram showing an example of approximation of arc lines according to a conventional example.

[Explanation of symbols]

 400 circular arc 401 circular arc center 402 circular arc end point 411,412,413,414 segment 451 tangent line 800 circular arc 801 circular arc center 900 circular arc 911,912,913 segment center line 921,922,923 segment 931,932 gap interpolation part

Claims (14)

[Claims] 1. A drawing device for approximating a curve with a minute straight line to draw a figure, wherein the curve is fine about a region near a contact point which is in contact with another line forming a tangential direction of the curve, and about other regions. A drawing apparatus comprising: a dividing unit that roughly divides, a linear approximation unit that approximates each divided curve by a straight line, and a drawing unit that draws a figure including the approximated curve. 2. The dividing means comprises: an equal dividing means for dividing the curve into a predetermined number of equal parts; and a re-dividing means for further dividing a curve including the contact points among the equally divided curves. The drawing apparatus according to claim 1. 3. The drawing according to claim 2, wherein the curve is a circle or an ellipse or a part thereof, and the equal dividing means is a means for equally dividing at a central angle of the circle or ellipse. apparatus. 4. The drawing according to claim 1, wherein the straight line approximating means is means for approximating a curved line including the contact point among the divided straight lines with a straight line in the same direction as the tangential direction. apparatus. 5. The drawing apparatus according to claim 1, further comprising output means for outputting the drawn figure. 6. The drawing apparatus according to claim 5, wherein the output unit is a printing unit that prints a drawn figure. 7. The drawing apparatus according to claim 5, wherein the output means is a display means for displaying a drawn figure. 8. A drawing method for drawing a figure by approximating a curved line with a minute straight line, wherein the curved line is fine for a region near a contact point which is in contact with another line forming the tangential direction, and for the other region. The drawing method is characterized by comprising a dividing step of roughly dividing, a linear approximation step of approximating each divided curve by a straight line, and a drawing step of drawing a figure including the approximated curve. 9. The dividing step comprises: an equal dividing step of equally dividing the curve into a predetermined number; and a re-dividing step of further dividing a curve including the contact point among the equally divided curves. The drawing method according to claim 8. 10. The drawing according to claim 9, wherein the curve is a circle or an ellipse or a part thereof, and the step of equally dividing is a step of equally dividing at a central angle of the circle or ellipse. Method. 11. The drawing according to claim 8, wherein the straight line approximating step is a step of approximating a curved line including the contact point among the divided straight lines with a straight line in the same direction as the tangential direction. Method. 12. The drawing method according to claim 8, further comprising an output step of outputting the drawn figure. 13. The drawing method according to claim 12, wherein the output step is a printing step of printing a drawn figure. 14. The drawing method according to claim 12, wherein the output step is a display step of displaying a drawn figure.