JP6122322B2 - Image processing apparatus, program, and integrated circuit - Google Patents

Description

  The present invention relates to an image processing technique, and more particularly to a technique for reducing aliasing that occurs during line segment drawing.

  There is a Bresenham algorithm as a line drawing algorithm. The Bresenham algorithm is an algorithm for placing an approximate straight line by placing continuous points between a given start point and end point. In the Bresenham algorithm, processing can be performed only by addition and subtraction without performing multiplication and division, so that a line segment can be drawn with a small amount of calculation.

  However, in the Bresenham algorithm, for example, since an oblique straight line is displayed by pixels arranged in a staircase pattern, jaggedness called jaggy occurs on the display screen.

  Various anti-aliasing methods have been proposed to make this jaggy inconspicuous. One of anti-aliasing methods is a power sampling method. In this power sampling method, first, a line segment is drawn at a higher resolution than the actual resolution. And when returning the line segment drawing result to the actual resolution, the pixel value of each pixel is set based on the ratio including the line segment when the line segment is drawn at a high resolution in each pixel at the actual resolution. To do. Thereby, in a power sampling method, an alias component can be suppressed and jaggy can be made not conspicuous.

  In addition, when drawing an oblique line, the area of the hatched portion of the pixel (boundary pixel) located at the boundary between the line segment and its background is calculated in order to suppress alias components and make the jaggy inconspicuous. Then, there are a method for setting the pixel value of the pixel based on the result, and a method for calculating the color density of the boundary pixel and setting the pixel value of the boundary pixel based on the calculated color density ( For example, Patent Document 1).

Japanese Patent No. 4749868

  However, in the power sampling method, it is necessary to perform line segment drawing at a higher resolution than actual, and the amount of memory required increases. Further, in the above-described prior art, it is necessary to perform complicated calculations such as calculation of the area of the boundary pixel and calculation of the density of the color of the boundary pixel.

  SUMMARY OF THE INVENTION In view of the above problems, the present invention has an object to realize an image processing apparatus and a program that effectively reduce aliasing that occurs during line segment drawing without requiring a large-capacity memory or complicated arithmetic processing. To do.

  In order to solve the above-mentioned problem, a first invention is an image processing apparatus for acquiring line segment drawing information for drawing a line segment on an image, comprising an input unit and line segment drawing information acquisition A section.

  The input unit is a functional unit for inputting information for drawing a line segment.

  The line segment drawing information acquisition unit acquires drawing information for drawing a line segment.

  The line segment drawing information acquisition unit includes an evaluation value acquisition unit, a threshold setting unit, and a drawing information determination unit.

  The evaluation value acquisition unit acquires an evaluation value D indicating the positional relationship between the pixel P (xa, ya) that is the drawing target pixel and a straight line that passes through the start point and end point of the line segment.

  The threshold setting unit calculates at least three threshold values Th1, Th2, and Th3 based on the difference amount dx in the x direction from the start point to the end point of the line segment and the difference amount dy in the y direction from the start point to the end point of the line segment. Set.

  The drawing information determination unit, based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa of the drawing target pixel in the y-axis positive direction). , Ya + 1) is determined.

The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: satisfies a positive real number,
The thresholds Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
Meet.

  The evaluation value acquisition unit updates the evaluation value D based on the difference amount dy. When the updated evaluation value D is 1.5 × dx × k or more, the evaluation value D is further updated based on the difference amount dx. In addition to updating, the next drawing target pixel is determined to be P (xa + 1, ya + 1). In addition, when the updated evaluation value D is less than 1.5 × dx × k, the evaluation value acquisition unit determines the next drawing target pixel as P (xa + 1, ya).

  In this image processing apparatus, the evaluation value D satisfies −0.5 × dx × k ≦ D ≦ 1.5 × dx × k, that is, the loop section of the evaluation value D is −0.5 × dx × k to 1. .5 × dx × k, the loop section is divided into at least four sections by at least three threshold values Th1, Th2, Th3, and the drawing target pixel P ( The density of the drawing color of xa, ya) and the density of the drawing color of the adjacent pixel P (xa, ya + 1) in the positive y-axis direction of the drawing target pixel are determined.

  That is, in this image processing apparatus, the density (pixel value) of the drawing color of the drawing target pixel P (xa, ya) and its adjacent pixel P (xa, ya + 1) is divided into halftones based on the case classification based on the evaluation value D. Therefore, aliasing that occurs during line segment drawing can be effectively reduced. Furthermore, in this image processing apparatus, since the drawing process can be executed according to the case classification based on the evaluation value D, it is not necessary to perform the process of increasing the resolution unlike the power sampling method. As a result, this image processing apparatus does not require a large-capacity memory or the like, and does not require complicated arithmetic processing such as resolution conversion and calculation of the area occupied by a line segment in one pixel.

  2nd invention is 1st invention, Comprising: The initial value of the evaluation value D is "0".

The drawing information determination unit
(1) When the evaluation value D satisfies −0.5 × dx × k ≦ D <Th1, the density of the drawing color of the pixel P (xa, ya) is the density DA,
(2) When the evaluation value D satisfies Th1 ≦ D <Th2, the density of the drawing color of the pixel P (xa, ya) is set to the density DB1, and the density of the drawing color of the pixel P (xa, ya + 1) is set to the density DB2. age,
(3) When the evaluation value D satisfies Th2 ≦ D <Th3, the density of the drawing color of the pixel P (xa, ya) is set to the density DC1, and the density of the drawing color of the pixel P (xa, ya + 1) is set to the density DC2. age,
(4) When the evaluation value D satisfies Th3 ≦ D <1.5 × dx × k, the density of the drawing color of the pixel P (xa, ya) is set to the density DD1, and the drawing of the pixel P (xa, ya + 1) is performed. The color density is set to density DD2.

When the drawing color density is set to be higher as the drawing color density value is larger, the densities DA, DB1, DB2, DC1, DC2, DD1, and DD2 are:
DA ≧ DB1 ≧ DC1 ≧ DD1
DB2 ≦ DC2 ≦ DD2
Meet.

  Thereby, in this image processing apparatus, the evaluation value D is set so that the gravity center position of the drawing pixels located in the same row (drawing pixels having the same x coordinate position) is close to the straight line passing through the start point and the end point of the line segment. Based on this, the drawing pixel and its pixel value (drawing color density) can be determined.

  That is, in this image processing apparatus, the loop section of the evaluation value D is considered in consideration of how the drawing position is shifted when the resolution is doubled in the horizontal direction (x-axis direction) and the vertical direction (y-axis direction). Threshold values Th1 to Th3 are determined, and the drawing pixel and its pixel value (drawing color density) are determined depending on which range of the divided loop section the evaluation value D is included. As with the method, alias components can be suppressed. As a result, jaggy (alias component) is not noticeable in the line segment drawn by the image processing apparatus.

  In this image processing apparatus, drawing processing can be executed depending on the case, and it is not necessary to actually perform processing for increasing the resolution. Therefore, unlike the power sampling method (oversampling method), the image processing apparatus has a large capacity. No memory is required.

  Therefore, this image processing apparatus does not require a large-capacity memory or complicated arithmetic processing, and can effectively reduce aliasing that occurs during line segment drawing.

When the density of the drawing color is set to be higher as the drawing color density value is smaller (as opposed to the above), the density DA, DB1, DB2, DC1, DC2, DD1, and DD2 are ,
DA ≦ DB1 ≦ DC1 ≦ DD1
DB2 ≧ DC2 ≧ DD2
It only has to satisfy.

3rd invention is 1st or 2nd invention, Comprising: Evaluation value acquisition part,
D = D + 2 × dy × k
Thus, the evaluation value D is updated.

If the updated evaluation value D is 1.5 × dx × k or more, the updated evaluation value D is further
D = D−2 × dx × k
And the next drawing target pixel is determined to be P (xa + 1, ya + 1).

  Thereby, similarly to the Bresenham algorithm, it is possible to appropriately specify the drawing target pixel.

  A fourth invention is any one of the first to third inventions, and further includes a coordinate conversion unit and a coordinate reverse conversion unit.

  When the slope of the straight line connecting the first point and the second point is not 0 or more and 1 or less, the coordinate conversion unit is configured so that the slope of the straight line connecting the third point and the fourth point is 0 or more and 1 or less. A coordinate conversion process is performed in which one point is converted into a third point and the second point is converted into a fourth point.

  The coordinate reverse conversion unit performs a coordinate reverse conversion process of the coordinate conversion process.

  Then, the line segment drawing information acquisition unit uses the third point as the start point of the line segment, the fourth point as the end point of the line segment, and the drawing information for drawing the line segment connecting the third point and the fourth point. get.

  The coordinate reverse conversion unit performs a coordinate reverse conversion process on the coordinate position information included in the drawing information for drawing the line segment connecting the third point and the fourth point acquired by the line segment drawing information acquisition unit. Do.

  In this image processing apparatus, coordinate conversion is performed, drawing processing similar to that of any one of the first to third inventions is performed, and then, by performing reverse coordinate conversion, any line segment (line segment having an arbitrary inclination) is performed. ) Is executed. Therefore, in this image processing apparatus, it is possible to execute the drawing process using only the same process as in any one of the first to third inventions without dividing the case for each inclination of the line segment. it can. As a result, this image processing apparatus does not require a large-capacity memory or complicated arithmetic processing, and can effectively reduce aliasing that occurs during line drawing.

The fifth invention is the invention of any one of the first to fourth, wherein the coefficient k is:
k = 2 × n (n is a natural number)
It is.

  In this image processing apparatus, since the coefficient k is a multiple of 2, rendering processing (e.g., comparison processing between the evaluation value D and the threshold value, update processing of the evaluation value D) can be realized only by integer arithmetic.

  A sixth invention is a program for causing a computer to execute an image processing method for acquiring line segment drawing information for drawing a line segment on an image.

  The image processing method includes an input step and a line segment drawing information acquisition step.

  The input step is a step for inputting information for drawing a line segment.

  The line segment drawing information acquisition step acquires drawing information for drawing a line segment.

  The line segment drawing information acquisition step includes an evaluation value acquisition step, a threshold setting step, and a drawing information determination step.

  The evaluation value acquisition step acquires an evaluation value D indicating a positional relationship between the pixel P (xa, ya) that is the drawing target pixel and a straight line passing through the start point and the end point of the line segment.

  In the threshold setting step, at least three threshold values Th1, Th2, and Th3 are set based on the difference amount dx in the x direction from the start point to the end point of the line segment and the difference amount dy in the y direction from the start point to the end point of the line segment. Set.

  In the drawing information determination step, based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa in the y-axis positive direction of the drawing target pixel) , Ya + 1) is determined.

The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: a positive real number is satisfied.

The thresholds Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
Meet.

  The evaluation value acquisition step updates the evaluation value D based on the difference amount dy. When the updated evaluation value D is 1.5 × dx × k or more, the evaluation value D is further updated based on the difference amount dx. In addition to updating, the next drawing target pixel is determined to be P (xa + 1, ya + 1). In the evaluation value acquisition step, when the updated evaluation value D is less than 1.5 × dx × k, the next drawing target pixel is determined to be P (xa + 1, ya).

  As a result, it is possible to realize a program that exhibits the same effects as those of the first invention.

  A seventh invention is an integrated circuit for image processing for acquiring line segment drawing information for drawing a line segment on an image, and includes an input unit and a line segment drawing information acquisition unit .

  The input unit is a functional unit for inputting information for drawing a line segment.

  The line segment drawing information acquisition unit acquires drawing information for drawing a line segment.

  The line segment drawing information acquisition unit includes an evaluation value acquisition unit, a threshold setting unit, and a drawing information determination unit.

  The evaluation value acquisition unit acquires an evaluation value D indicating the positional relationship between the pixel P (xa, ya) that is the drawing target pixel and a straight line that passes through the start point and end point of the line segment.

  The threshold setting unit calculates at least three threshold values Th1, Th2, and Th3 based on the difference amount dx in the x direction from the start point to the end point of the line segment and the difference amount dy in the y direction from the start point to the end point of the line segment. Set.

  The drawing information determination unit, based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa of the drawing target pixel in the y-axis positive direction). , Ya + 1) is determined.

The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: satisfies a positive real number,
The thresholds Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
Meet.

  The evaluation value acquisition unit updates the evaluation value D based on the difference amount dy. When the updated evaluation value D is 1.5 × dx × k or more, the evaluation value D is further updated based on the difference amount dx. In addition to updating, the next drawing target pixel is determined to be P (xa + 1, ya + 1). In addition, when the updated evaluation value D is less than 1.5 × dx × k, the evaluation value acquisition unit determines the next drawing target pixel as P (xa + 1, ya).

  Thus, an integrated circuit that exhibits the same effect as that of the first invention can be realized.

  The integrated circuit is a concept including a rendering module and the like.

  According to the present invention, it is possible to realize an image processing apparatus and program that can effectively reduce aliasing that occurs during line segment drawing without requiring a large-capacity memory or complicated arithmetic processing.

1 is a schematic configuration diagram of an image processing system 1000 according to a first embodiment. 5 is a process flowchart of the image processing system 1000 according to the first embodiment. The figure which shows the result (an example) of the line segment drawing process by the image processing system 1000 concerning 1st Embodiment. The figure which shows the result (an example) of the line segment drawing process by the image processing system 1000 concerning 1st Embodiment. The figure which shows the result (an example) of the line drawing process by the image processing system 1000 which concerns on 1st Embodiment, and the line drawing process result by a Bresenham algorithm. The figure for demonstrating the line segment drawing process by the conventional Bresenham algorithm. The figure which shows typically the relationship between the loop area of the evaluation value D at the time of doubling the resolution in the vertical direction (y-axis direction) and the amount of pixel shift. The figure which shows typically the relationship between the loop area of the evaluation value D at the time of doubling the resolution in the horizontal direction (x-axis direction), and the pixel shift amount. The figure which shows typically the correspondence of the evaluation value D in the case of dy <= 0.5xdx, a drawing object pixel, and a pixel value. The figure which shows typically the correspondence of the evaluation value D in the case of dy> 0.5xdx, a drawing object pixel, and a pixel value. The figure which shows typically the correspondence of the evaluation value D in the case of dy <= 0.5xdx, a drawing object pixel, and a pixel value. The figure which shows typically the correspondence of the evaluation value D in the case of dy> 0.5xdx, a drawing object pixel, and a pixel value. 6 is a flowchart when the processing of the image processing system 1000 according to the first embodiment is generalized. The schematic block diagram of 1000 A of image processing systems which concern on the 1st modification of 1st Embodiment. The figure for demonstrating coordinate transformation.

[First Embodiment]
The first embodiment will be described below with reference to the drawings.

<1.1: Configuration of Image Processing System>
FIG. 1 is a schematic configuration diagram of an image processing system 1000 according to the first embodiment.

  As shown in FIG. 1, the image processing system 1000 includes an image processing device 1, a display memory 2, and a display unit 3.

  As illustrated in FIG. 1, the image processing apparatus 1 includes an input unit 11, a threshold setting unit 12, an evaluation value acquisition unit 13, and a drawing information determination unit 14.

  The input unit 11 is a functional unit for inputting information about a line segment to be drawn (hereinafter referred to as “line segment information”). For example, when drawing a line segment from the start point (x1, y1) to the end point (x2, y2) on the image displayed on the display screen of the display unit 3, the input unit 1 includes information on the start point of the line segment, Line segment information such as end point information, line segment thickness, line segment color, and line segment color density is input. The input unit 11 outputs the line segment information to the threshold value setting unit 12, the evaluation value acquisition unit 13, and the drawing information determination unit 14.

  The threshold setting unit 12 receives the line segment information output from the input unit 11, and from the line segment information, the color density (for example, pixel value) of the drawing target pixel P (xa, ya) and the drawing target pixel P (xa , Ya) is set to at least three threshold values for determining the color density (for example, pixel value) of the adjacent pixel P (xa, ya + 1) in the y-axis positive direction. The threshold values are Th1, Th2, and Th3. Then, the threshold setting unit 12 outputs the set threshold information to the drawing information determination unit 14.

  The evaluation value acquisition unit 13 receives the line segment information output from the input unit 11, and from the line segment information, the pixel P (xa, ya) that is the drawing target pixel, the start point (x1, y1), and the end point ( An evaluation value D indicating the positional relationship with the straight line passing through x2, y2) is acquired. Then, the evaluation value acquisition unit 13 outputs information about the acquired evaluation value D to the drawing information determination unit 14.

  The drawing information determination unit 14 inputs line segment information output from the input unit 11, threshold information output from the threshold setting unit 12, and information related to the evaluation value D output from the evaluation value acquisition unit 13. The drawing information determination unit 14 determines the density of the drawing color of the drawing target pixel P (xa, ya) based on the line segment information, the threshold values Th1, Th2, Th3 set by the threshold setting unit 12, and the evaluation value D. (For example, pixel value) and the density (for example, pixel value) of the drawing color of the adjacent pixel P (xa, ya + 1) in the positive y-axis direction of the drawing target pixel are determined. The drawing information determination unit 14 then addresses corresponding to the drawing target pixel P (xa, ya) in the display memory 2 so that the drawing color density of the drawing target pixel P (xa, ya) becomes the determined value. Write data to. Further, the drawing information determination unit 14 sets an address corresponding to the drawing target pixel P (xa, ya + 1) in the display memory 2 so that the density of the drawing color of the adjacent pixel P (xa, ya + 1) becomes the determined value. Write data.

  The display memory 2 is a memory for displaying an image on the display screen of the display unit 3. By writing data to a predetermined address of the display memory 2, the pixel value of the pixel corresponding to the address (the pixel of the image displayed on the display screen of the display unit 3) is the pixel value corresponding to the written data. And displayed on the display screen of the display unit 3. For example, a video buffer, a rendering buffer, a frame memory, or a VRAM is used as the display memory 2.

  The display unit 3 has a display screen that can display an image, and displays the image on the display screen according to the data written in the display memory 2.

<1.2: Operation of the image processing system>
The operation of the image processing system 1000 configured as described above will be described with reference to the drawings.

  FIG. 2 is a process flowchart of the image processing system 1000.

  In the following, for convenience of explanation, the coordinates of the start point of the line segment are (x1, y1), the coordinates of the end point of the line segment are (x2, y2), and the line thickness is “1” (for one pixel). A case where a white line is drawn (drawn) on a black background will be described.

For convenience of explanation, an image for drawing a line segment is a luminance image (Y image), a pixel value is 8 bits, and a value from 0 to 255 (a pixel value “255” is “white” (W100%). )))).
(S1):
In the input unit 11, the coordinates of the start point of the line segment (x1, y1), the coordinates of the end point of the line segment (x2, y2), the line thickness “1” (thickness of one pixel), and the pixel value of the line segment Line segment information indicating “255” (white) is input. That is, the first drawing target pixel is set to the pixel P (x1, y1). When the x coordinate of the drawing target pixel P is x and the y coordinate is y, when the drawing target pixel is the pixel P (x1, y1),
x = x1
y = y1
It is.

In addition, the evaluation value acquisition unit 13 sets the evaluation value D to the initial value “0”.
(S2):
The threshold setting unit 12 calculates the difference amount dx in the x-axis direction and the difference amount dy in the y-axis direction between the start point and end point of the line segment from the line segment information.
dx = x2-x1
dy = y2-y1
Calculated by

Then, the threshold setting unit 12 sets thresholds Th1, Th2, and Th3 as
Th1 = dx−2 × dy
Th2 = dx
Th3 = 3 × dx−2 × dy
Set to the value calculated by.
(S3):
X is incremented by 1 from the first drawing target pixel P (x1, y1), and the processes of steps S4 to S13 are repeatedly executed until x becomes x2, which is the x coordinate of the end point of the line segment.
(S4, S7):
The drawing information determination unit 14 compares the evaluation value D with the threshold value Th1, and determines that the pixel value of the drawing target pixel P (x, y) is “255” when D <Th1.

  Then, the drawing information determination unit 14 writes the data of the pixel value “255” to the address of the display memory 2 corresponding to the pixel P (x, y).

Thereby, in the display screen of the display unit 3, the pixel value of the pixel at the coordinate position corresponding to the pixel P (x, y) is “255” (W100%).
(S4, S5, S8):
The drawing information determination unit 14 compares the evaluation value D with the threshold values Th1 and Th2, and when Th1 ≦ D <Th2, determines the pixel value of the drawing target pixel P (x, y) to “192” and draws the drawing. The pixel value of the adjacent pixel P (x, y + 1) in the positive y-axis direction of the target pixel is determined to be “64”.

  Then, the drawing information determination unit 14 writes data corresponding to the pixel value “192” at the address of the display memory 2 corresponding to the pixel P (x, y). In addition, the drawing information determination unit 14 writes data corresponding to the pixel value “64” at the address of the display memory 2 corresponding to the pixel P (x, y + 1).

Thereby, on the display screen of the display unit 3, the pixel value of the pixel at the coordinate position corresponding to the pixel P (x, y) becomes “192” (W75%), and the coordinate position corresponding to the pixel P (x, y + 1). The pixel value of this pixel is “64” (W25%).
(S4 to S6, S9):
The drawing information determination unit 14 compares the evaluation value D with the threshold values Th2 to Th3, and when Th2 ≦ D <Th3, determines the pixel value of the drawing target pixel P (x, y) to “128” and draws The pixel value of the adjacent pixel P (x, y + 1) in the positive y-axis direction of the target pixel is determined to be “128”.

  Then, the drawing information determination unit 14 writes data corresponding to the pixel value “128” to the address of the display memory 2 corresponding to the pixel P (x, y). Further, the drawing information determination unit 14 writes data corresponding to the pixel value “128” at the address of the display memory 2 corresponding to the pixel P (x, y + 1).

Thereby, on the display screen of the display unit 3, the pixel value of the pixel at the coordinate position corresponding to the pixel P (x, y) becomes “128” (W50%), and the coordinate position corresponding to the pixel P (x, y + 1). The pixel value of this pixel is “128” (W50%).
(S4 to S6, S10):
The drawing information determination unit 14 compares the evaluation value D with the threshold value Th3. When D ≧ Th3, the drawing information determination unit 14 determines the pixel value of the drawing target pixel P (x, y) to be “64” and sets the y of the drawing target pixel. The pixel value of the adjacent pixel P (x, y + 1) in the axial positive direction is determined to be “192”.

  Then, the drawing information determination unit 14 writes data corresponding to the pixel value “64” to the address of the display memory 2 corresponding to the pixel P (x, y). Further, the drawing information determination unit 14 writes data corresponding to the pixel value “192” at the address of the display memory 2 corresponding to the pixel P (x, y + 1).

Thereby, on the display screen of the display unit 3, the pixel value of the pixel at the coordinate position corresponding to the pixel P (x, y) becomes “64” (W25%), and the coordinate position corresponding to the pixel P (x, y + 1). The pixel value of this pixel is “192” (W75%).
(S11):
The evaluation value acquisition unit 13 determines the evaluation value D as
D = D + 4 × dy
Update with
(S12, S13):
The evaluation value acquisition unit 13 compares the evaluation value D updated in step S11 with 3 × dx. If D ≧ 3 × dx, the evaluation value D is D = D−4 × dx.
With further updates,
y = y + 1
The value of the y coordinate is incremented by 1. That is, the value of the y coordinate of the next drawing target pixel is set to a value larger by 1 than the value of the y coordinate of the current drawing target pixel.

  Thereafter, the process returns to step S3, and the processes of steps S3 to S13 are repeatedly executed until the value of x becomes x2, which is the x coordinate of the end point of the line segment.

  Here, an example of line segment drawing by the above processing will be described with reference to FIG.

  FIG. 3 is a diagram for explaining processing when a line segment is drawn from the start point (0, 0) to the end point (7, 3).

When drawing a line segment from the start point (0, 0) to the end point (7, 3), the threshold setting unit 12
dx = x2-x1 = 7-0 = 7
dy = y2-y1 = 3-0 = 3
To calculate dx and dy.

In addition, the threshold setting unit 12
Th1 = dx−2 × dy = 7−2 × 3 = 1
Th2 = dx = 7
Th3 = 3 * dx-2 * dy = 3 * 7-2 * 3 = 15
Thus, Th1 to Th3 are calculated.

<< First Process (Drawing Target Pixel: P (0,0)) >>
First, the pixel P (0, 0) at the start point (0, 0) is set as the drawing target pixel.

  Further, the evaluation value D is set to the initial value “0” by the evaluation value acquisition unit 13.

Since D <Th1 (= 1), the process of step S7 is executed. That means
P (0,0) = 255
Is determined. For the pixel P (x, y), the notation P (x, y) = A represents that the pixel value of the pixel P at the coordinate position (x, y) is “A”.

And in the process of step S11,
D = D + 4 × dy = 0 + 4 × 3 = 12.
Thus, the evaluation value D is updated.

  Since the updated evaluation value D (= 12) is smaller than 3 × dx (= 21) (step S12), the next drawing target pixel is determined as the pixel P (1, 0), and the next processing (2 The second process is executed.

<< Second Process (Drawing Target Pixel: P (1,0)) >>
In the second process, the drawing target pixel is the pixel P (1, 0), and the evaluation value D is “12”.

Since Th2 ≦ D <Th3 (D = 12, Th2 = 7, Th3 = 15), the process of step S9 is executed. That is, the pixel values of the pixel P (1, 0) and the pixel P (1, 1) are
P (1,0) = 128
P (1,1) = 128
Is determined.

And in the process of step S11,
D = D + 4 × dy = 12 + 4 × 3 = 24
Thus, the evaluation value D is updated.

Since the updated evaluation value D (= 24) is larger than 3 × dx (= 21) (step S12), the process of step S13 is executed. That means
D = D-4 * dx = 24-4 * 7 = -4
y = y + 1 = 0 + 1 = 1
It becomes. As a result, the next pixel to be drawn is determined as the pixel P (2, 1).

<< Third Process (Drawing Target Pixel: P (2,1)) >>
In the third process, the drawing target pixel is the pixel P (2, 1), and the evaluation value D is “−4”.

Since D <Th1 (D = −4, Th1 = 1), the process of step S7 is executed. That is, the pixel value of the pixel P (2,1) is
P (2,1) = 255
Is determined.

And in the process of step S11,
D = D + 4 × dy = −4 + 4 × 3 = 8
Thus, the evaluation value D is updated.

  Since the updated evaluation value D (= 8) is smaller than 3 × dx (= 21) (step S12), the process of step S13 is not executed, and the next drawing target pixel is the pixel P (3, 1). To be determined.

<< Fourth Process (Drawing Target Pixel: P (3,1)) >>
In the fourth process, the drawing target pixel is the pixel P (3, 1), and the evaluation value D is “8”.

Since Th2 ≦ D <Th3 (D = 8, Th2 = 7, Th3 = 15), the process of step S9 is executed. That is, the pixel values of the pixel P (3, 1) and the pixel P (3, 2) are
P (3,1) = 128
P (3,2) = 128
Is determined.

And in the process of step S11,
D = D + 4 × dy = 8 + 4 × 3 = 20
Thus, the evaluation value D is updated.

  Since the updated evaluation value D (= 20) is smaller than 3 × dx (= 21) (step S12), the process of step S13 is not executed, and the next drawing target pixel is the pixel P (4, 1). To be determined.

<< Fifth Process (Drawing Target Pixel: P (4,1)) >>
In the fifth process, the drawing target pixel is the pixel P (4, 1), and the evaluation value D is “20”.

Since Th3 <D (D = 20, Th3 = 15), the process of step S10 is executed. That is, the pixel values of the pixel P (4, 1) and the pixel P (4, 2) are
P (4,1) = 64
P (4,2) = 192
Is determined.

And in the process of step S11,
D = D + 4 × dy = 20 + 4 × 3 = 32
Thus, the evaluation value D is updated.

Since the updated evaluation value D (= 32) is larger than 3 × dx (= 21) (step S12), the process of step S13 is executed. That means
D = D-4 * dx = 32-4 * 7 = 4
y = y + 1 = 1 + 1 = 2
It becomes. As a result, the next drawing target pixel is determined to be the pixel P (5, 2).

<< Sixth Process (Drawing Target Pixel: P (5,2)) >>
In the sixth process, the drawing target pixel is the pixel P (5, 2), and the evaluation value D is “4”.

Since Th1 <D ≦ Th2 (D = 4, Th1 = 1, Th2 = 7), the process of step S8 is executed. That is, the pixel values of the pixel P (5, 2) and the pixel P (5, 3) are
P (5,2) = 192
P (4,2) = 64
Is determined.

And in the process of step S11,
D = D + 4 × dy = 4 + 4 × 3 = 16
Thus, the evaluation value D is updated.

  Since the updated evaluation value D (= 16) is smaller than 3 × dx (= 21) (step S12), the process of step S13 is not executed, and the next drawing target pixel is the pixel P (6, 2). To be determined.

<< Seventh Process (Drawing Target Pixel: P (6,2)) >>
In the seventh processing, the drawing target pixel is the pixel P (6, 2), and the evaluation value D is “16”.

Since Th3 <D (D = 16, Th3 = 15), the process of step S10 is executed. That is, the pixel values of the pixel P (6, 2) and the pixel P (6, 3) are
P (6,2) = 64
P (6,2) = 192
Is determined.

And in the process of step S11,
D = D + 4 × dy = 16 + 4 × 3 = 28
Thus, the evaluation value D is updated.

Since the updated evaluation value D (= 28) is larger than 3 × dx (= 21) (step S12), the process of step S13 is executed. That means
D = D-4 * dx = 28-4 * 7 = 0
y = y + 1 = 2 + 1 = 3
It becomes. As a result, the next drawing target pixel is determined to be the pixel P (7, 3).

<< Eighth Process (Drawing Target Pixel: P (7,3)) >>
In the eighth process, the drawing target pixel is the pixel P (7, 3), and the evaluation value D is “0”.

Since D <Th1 (D = 0, Th1 = 1), the process of step S7 is executed. That is, the pixel value P (7,3) is
P (7,3) = 255
Is determined.

  Since the value of x matches the value of x at the end point of the line segment (= 7), the line drawing process ends after the eighth process is executed.

With the above processing, a line segment is drawn from the start point (0, 0) to the end point (7, 3) as shown in FIG. 4 is a drawing pixel (a pixel whose pixel value is not “0”) having the same line segment L1 connecting the start point (0,0) and the end point (7,3) and the value of the x coordinate in FIG. It is the figure which added the position of the center of gravity with a circle. Note that the position of the center of gravity shown in FIG. 4 is (1) when there is one drawing pixel with the same x-coordinate value, and is the coordinate position of the drawing pixel, and (2) drawing with the same x-coordinate value. When there are two pixels, pixel PA (x0, y0) and pixel PB (x0, y0 + 1), the pixel value of the pixel PA is k1, and the pixel value of the pixel PB is k2, the coordinates (xc) of the barycentric position , Yc)
xc = x0
yc = y0 + k2 / (k1 + k2)
It is.

  As can be seen from FIGS. 3 and 4, the line segment from the start point (0, 0) to the end point (7, 3) is expressed by pixels having halftones by executing the above processing by the image processing system 1000. can do. Further, as can be seen from FIG. 4, the shift between the center of gravity of the drawing pixels (drawing pixels having the same x coordinate position) located in the same column and the straight line L1 passing through the start point (0, 0) and the end point (7, 3) Less is. That is, the image processing system 1000 can appropriately draw a line segment by executing the above processing.

  FIG. 5 shows a line segment LH1 and a line segment LH2 obtained by enlarging a part of the line segment LH1 drawn by the Bresenham algorithm, and a line segment LA1 and line segment LA1 drawn by the image processing system 1000. Shows a line segment LA2 in which a part of the line is enlarged.

  As can be seen from FIG. 5, jaggy (alias component) is noticeable in the line segment drawn by the Bresenham algorithm, but in the line segment drawn by the image processing system 1000, the jaggy is not noticeable and the alias component is appropriately suppressed. I understand.

  Here, the principle of the drawing process by the image processing system 1000 will be described.

  First, with reference to FIG. 6, the line drawing process by the conventional Bresenham algorithm will be described. In addition, as shown in FIG. 6, the case where a line segment is drawn from the start point P (0, 0) to the end point P (7, 3) will be described.

  In the drawing process by the Bresenham algorithm, first, the starting point P (0, 0) is set as a drawing pixel to a predetermined pixel value (in FIG. 6, it is painted black). For convenience of explanation, the pixel value of the drawing pixel will be described as “1” below.

  Next, the drawing pixel candidates are the pixel P (1, 0) and the pixel P (1, 1). Then, the positional relationship (vertical relationship) between the midpoint of these two pixels (points indicated by white circles in FIG. 6) and a straight line passing through the start point P (0, 0) and the end point P (7, 3) is determined. . As can be seen from FIG. 6, since the straight line L1 is located above the midpoint (1, 0.5) of the pixel P (1, 0) and the pixel P (1, 1), x = 1. In this case, the drawing pixel is a pixel P (1, 0) closer to the straight line L1.

  By repeating such processing until the end point (7, 3), a line segment can be drawn from the start point P (0, 0) to the end point P (7, 3) (the straight line L1 can be approximated and displayed). it can).

  The above process uses the evaluation value D, the difference amount dx in the x-axis direction between the start point P (0, 0) and the end point P (7, 3), and the difference amount dy in the y-axis direction as follows. Can be expressed.

  The evaluation value D is an initial value “0”, and 2 × dy is added every time it is incremented by 1 in the positive x-axis direction. When the addition result exceeds dx, the drawing pixel is selected so as to advance by +1 in the y direction. And when it advances +1 in the y direction, 2 × dx is subtracted from the value of the evaluation value D. By repeating this, a line segment can be drawn from the start point to the end point.

In the case of FIG.
(1) First processing D = D + 2 × dy = 0 + 2 × 3 = 6
Since D <dx (D = 6, dx = 7), the next drawing pixel is determined to be P (1, 0).
(2) Second processing D = D + 2 × dy = 6 + 2 × 3 = 12.
Since D> dx (D = 12, dx = 7), the next drawing pixel is determined to be P (2, 1).

Further, 2 × dx is subtracted from the evaluation value D. That means
D = D-2 * dx = 12-2 * 7 = -2
It becomes.
(3) Third processing D = D + 2 × dy = −2 + 2 × 3 = 4
Since D <dx (D = 4, dx = 7), the next drawing pixel is determined to be P (3, 1).
(4) Fourth processing D = D + 2 × dy = 4 + 2 × 3 = 10
Since D> dx (D = 10, dx = 7), the next drawing pixel is determined to be P (4, 2).

Further, 2 × dx is subtracted from the evaluation value D. That means
D = D−2 × dx = 10−2 × 7 = −4
It becomes.
(5) Fifth processing D = D + 2 × dy = −4 + 2 × 3 = 2
Since D <dx (D = 2, dx = 7), the next drawing pixel is determined to be P (5, 2).
(6) Sixth processing D = D + 2 × dy = 2 + 2 × 3 = 8
Since D> dx (D = 8, dx = 7), the next drawing pixel is determined to be P (6, 3).

Further, 2 × dx is subtracted from the evaluation value D. That means
D = D−2 × dx = 8−2 × 7 = −6
It becomes.
(7) Seventh processing D = D + 2 × dy = −6 + 2 × 3 = 0
Since D <dx (D = 0, dx = 7), the next drawing pixel is determined to be P (7, 3).

  Through the above processing, as shown in FIG. 6, a line segment is drawn from the start point P (0, 0) to the end point P (7, 3) by the Bresenham algorithm.

  As can be seen from the above processing, in the Bresenham algorithm, the evaluation value D increases from 0 by 2 × dy and loops between −dx and dx.

  In the image processing system 1000, in the Bresenham algorithm, the loop section of the evaluation value D that was -dx to dx is changed from -0.5 * dx to 1.5 * dx, and the section is further divided into three sections. Drawing processing is executed by dividing the threshold values by Th1, Th2, and Th3. Thereby, in the image processing system 1000, aliasing that occurs during line segment drawing can be effectively reduced only by case classification. This will be described below.

  Consider a case where the resolution is doubled in the vertical direction (y-axis direction) and a case where the resolution is doubled in the horizontal direction (x-axis direction).

  First, consider a case where the resolution is doubled in the vertical direction (y-axis direction).

  FIG. 7 is a diagram schematically showing the relationship between the loop section of the evaluation value D and the pixel shift amount when the resolution is doubled in the vertical direction (y-axis direction).

  As shown in FIG. 7, when the line is drawn by the Bresenham algorithm with the resolution doubled in the vertical direction (y-axis direction), the line is drawn by the Bresenham algorithm without increasing the resolution (1) When the evaluation value D is a value in a section of −dx to −0.5 × dx, there is a possibility that the evaluation value D is shifted by one pixel, and (2) a value of a section in which the evaluation value D is 0.5 × dx to dx In such a case, there is a possibility of shifting down by one pixel.

  Note that when the evaluation value D is a value in the interval of −0.5 × dx to 0.5 × dx, no pixel shift occurs.

  Next, consider a case where the resolution is doubled in the horizontal direction (x-axis direction).

  FIG. 8 is a diagram schematically showing the relationship between the loop section of the evaluation value D and the pixel shift amount when the resolution is doubled in the horizontal direction (x-axis direction).

  As shown in FIG. 8, when the line is drawn by the Bresenham algorithm with the resolution doubled in the horizontal direction (x-axis direction), the evaluation value D is higher than when the line is drawn by the Bresenham algorithm without increasing the resolution. Is a value in the interval from dx-dy to dx, there is a possibility that the pixel is shifted in an oblique direction.

  Note that when the evaluation value D is a value in the interval from -dx to dx-dy, no pixel shift occurs.

  Therefore, in consideration of the above, -0.5 × dx, 0.5 × dx, and values obtained by subtracting dy from them—0.5 × dx-dy and 0.5 × dx-dy are used as threshold values, and evaluation is performed. By dividing the loop section of the value D and making the pixel value a halftone depending on which section the evaluation value D is, line drawing can be performed while suppressing the alias component. If dy> 0.5 × dx, −0.5 × dx-dy does not fall within the range of −dx to dx, and instead, 1.5 × dx-dy is used as the threshold value.

  Specifically, as shown in FIG. 9 and FIG.

  FIG. 9 is a diagram schematically illustrating a correspondence relationship between the evaluation value D, the drawing target pixel, and the pixel value when dy ≦ 0.5 × dx.

As shown in FIG. 9, when dy ≦ 0.5 × dx, assuming that the drawing target pixel is P (x, y) and the pixel value is 0 to 1, the following (1) to (5) Depending on the case, the pixel value may be determined.
(1) When −dx ≦ D <−0.5 × dx−dy,
P (x, y-1) = 0.5
P (x, y) = 0.5
(2) When −0.5 × dx−dy ≦ D <−0.5 × dx,
P (x, y-1) = 0.25
P (x, y) = 0.75
(3) In the case of −0.5 × dx ≦ D <0.5 × dx−dy,
P (x, y) = 1
(4) In the case of 0.5 × dx−dy ≦ D <0.5 × dx,
P (x, y) = 0.75
P (x, y + 1) = 0.25
(5) When 0.5 × dx ≦ D <dx,
P (x, y) = 0.50
P (x, y + 1) = 0.50
FIG. 10 is a diagram schematically illustrating a correspondence relationship between the evaluation value D, the drawing target pixel, and the pixel value when dy> 0.5 × dx.

As shown in FIG. 10, when dy> 0.5 × dx, assuming that the drawing target pixel is P (x, y) and the pixel value is 0 to 1, the following (1) to (5) Depending on the case, the pixel value may be determined.
(1) When −dx ≦ D <−0.5 × dx,
P (x, y-1) = 0.25
P (x, y) = 0.75
(2) In the case of −0.5 × dx ≦ D <0.5 × dx−dy,
P (x, y) = 1
(3) In the case of 0.5 × dx−dy ≦ D <0.5 × dx,
P (x, y) = 0.75
P (x, y + 1) = 0.25
(4) In the case of 0.5 × dx ≦ D <1.5 × dx−dy,
P (x, y) = 0.5
P (x, y + 1) = 0.5
(5) When 1.5 × dx−dy ≦ D <dx,
P (x, y) = 0.25
P (x, y + 1) = 0.75
The above case classification is complicated because the loop section of the evaluation value D is set to −dx to dx. Therefore, the number of cases can be reduced by setting the loop section of the evaluation value D to −0.5 × dx to 1.5 × dx. This will be described with reference to FIGS.

  FIG. 11 is a diagram schematically illustrating a correspondence relationship between the evaluation value D, the drawing target pixel, and the pixel value when dy ≦ 0.5 × dx, as in FIG. 9.

  FIG. 12 is a diagram schematically illustrating a correspondence relationship between the evaluation value D, the drawing target pixel, and the pixel value when dy> 0.5 × dx, as in FIG. 10.

  As shown in FIG. 11, a section Ta1 (−dx ≦ D <−0.5 × dx−dy) when the loop section of the evaluation value D is −dx to dx (section T1 in FIG. 11) is evaluated. The same processing as the section Tb1 (dx ≦ D <0.5 × dx−dy) is executed when the loop section of the value D is −0.5 × dx to 1.5 × dx (section T2 in FIG. 11). Means that That is, in the Bresenham algorithm, when the evaluation value D exceeds dx, the pixel advanced by +1 in the y direction is used as the drawing pixel. Therefore, the pixel adjacent to the drawing pixel in the section Ta1 (pixel Pa1 in FIG. 11) is in the section Tb1. It can be considered the same as the drawing pixel (pixel Pb1 in FIG. 11).

  Similarly, the interval Ta2 (−0.5 × dx ≦ D <−0.5 × dx) when the loop interval of the evaluation value D is set to −dx to dx is −0. It means that the same processing as that in the section Tb2 (−0.5 × dx−dy ≦ D <1.5) in the case of .5 × dx to 1.5 × dx is executed. In other words, in the Bresenham algorithm, when the evaluation value D exceeds dx, the pixel advanced by +1 in the y direction is used as the drawing pixel. Therefore, the pixel adjacent to the drawing pixel in the section Ta2 (pixel Pa2 in FIG. 11) is in the section Tb2. It can be considered the same as the drawing pixel (pixel Pb2 in FIG. 11).

  Also, as shown in FIG. 12, the section Tc1 (−dx ≦ D <−0.5 × dx) when the loop section of the evaluation value D is −dx to dx (section T1 in FIG. 12) is evaluated. The same processing as that of the section Td1 (dx ≦ D <1.5 × dx) when the loop section of the value D is −0.5 × dx to 1.5 × dx (section T2 in FIG. 12) is executed. Means that. That is, in the Bresenham algorithm, when the evaluation value D exceeds dx, the pixel advanced by +1 in the y direction is used as the drawing pixel. Therefore, the pixel adjacent to the drawing pixel in the section Tc1 (pixel Pc1 in FIG. 12) It can be considered the same as the drawing pixel (pixel Pd1 in FIG. 12).

In the case of FIG. 11 (when dy ≦ 0.5 × dx), when the loop section of the evaluation value D is −0.5 × dx to 1.5 × dx,
(1) In the case of −0.5 × dx ≦ D <0.5 × dx−dy,
P (x, y) = 1
(2) In the case of 0.5 × dx−dy ≦ D <0.5 × dx,
P (x, y) = 0.75
P (x, y + 1) = 0.25
(3) In the case of 0.5 × dx ≦ D <1.5 × dx−dy,
P (x, y) = 0.5
P (x, y + 1) = 0.5
(4) When 1.5 × dx−dy ≦ D <1.5 × dx,
P (x, y) = 0.25
P (x, y + 1) = 0.75
It becomes.

In the case of FIG. 12 (when dy> 0.5 × dx), when the loop section of the evaluation value D is −0.5 × dx to 1.5 × dx,
(1) In the case of −0.5 × dx ≦ D <0.5 × dx−dy,
P (x, y) = 1
(2) In the case of 0.5 × dx−dy ≦ D <0.5 × dx,
P (x, y) = 0.75
P (x, y + 1) = 0.25
(3) In the case of 0.5 × dx ≦ D <1.5 × dx−dy,
P (x, y) = 0.5
P (x, y + 1) = 0.5
(4) When 1.5 × dx−dy ≦ D <1.5 × dx,
P (x, y) = 0.25
P (x, y + 1) = 0.75
It becomes.

  As can be seen from the above, the same processing by the same case is performed in both the case of FIG. 11 (when dy ≦ 0.5 × dx) and the case of FIG. 12 (when dy> 0.5 × dx).

That is, the loop section of the evaluation value D is −0.5 × dx to 1.5 × dx, and the three threshold values Th1, Th2, and Th3 are set as follows:
Th1 = 0.5 × dx−dy
Th2 = 0.5 × dx
Th3 = 1.5 × dx−dy
The drawing process may be performed by dividing the loop section of the evaluation value D into four sections.

Further, the drawing processing in the image processing system 1000 is similar to the drawing processing by the Bresenham algorithm. If the pixel to be drawn in the N-th processing is the pixel P (xn, yn), the drawing target pixel in the N + 1-th processing is , Pixel P (xn + 1, yn) or pixel P (xn + 1, yn + 1),
dy / dx ≦ 1
dy ≦ dx
Holds.

Therefore,
−0.5 × dx ≦ 0.5 × dx−dy ≦ 0.5 × dx ≦ 1.5 × dx−dy ≦ 1.5 × dx
Holds.

That means
−0.5 × dx ≦ Th1 ≦ Th2 ≦ Th3 ≦ 1.5 × dx
Therefore, in the case of FIG. 11 (when dy ≦ 0.5 × dx) and the case of FIG. 12 (when dy> 0.5 × dx), −0.5 dx, Th1 to Th3, 1.5 The size relationship of xdx is the same.

  Accordingly, in the case of FIG. 11 (in the case of dy ≦ 0.5 × dx) and in the case of FIG. 12 (in the case of dy> 0.5 × dx), it is only necessary to execute the same processing by the same case classification. .

  In this way, by setting the loop section of the evaluation value D to be −0.5 × dx to 1.5 × dx, the number of cases is different from the case of setting the loop section of the evaluation value D to be −dx to dx. Can be reduced.

  In the image processing system 1000, the loop section of the evaluation value D is set to −0.5 × dx to 1.5 × dx, and the loop section is set to 4 by the three threshold values Th1, Th2, and Th3 set as described above. A drawing pixel and its pixel value (drawing color density) are determined according to which section the evaluation value D is divided into two sections. In the image processing system 1000, based on the evaluation value D, the gravity center position of the drawing pixels (drawing pixels having the same x coordinate position) located in the same column is close to the straight line passing through the start point and the end point of the line segment. Thus, the drawing pixel and its pixel value (drawing color density) are determined.

  In other words, the image processing system 1000 considers how the drawing position shifts when the resolution is doubled in the horizontal direction (x-axis direction) and the vertical direction (y-axis direction), and evaluates as described above. The threshold values Th1 to Th3 for dividing the loop section of the value D are determined, and the drawing pixel and its pixel value (the density of the drawing color) are determined depending on which range of the divided loop section the evaluation value D is included. Similar to the sampling method (oversampling method), alias components can be suppressed. As a result, the jaggy (alias component) is not noticeable in the line segment drawn by the image processing system 1000.

  In the image processing system 1000, drawing processing can be executed depending on the case, and it is not necessary to actually perform processing for increasing the resolution. Therefore, unlike the power sampling method (oversampling method), the image processing system 1000 has a large capacity. No memory is required.

  As described above, the image processing system 1000 does not require a large-capacity memory and complicated arithmetic processing, and can effectively reduce aliasing that occurs during line segment drawing at low cost.

  In the process of the image processing system 1000 described with reference to the flowchart of FIG. 2, the threshold value Th1 to Th3, the update process of the evaluation value D, and the like are changed so that the process can be executed only by integer arithmetic. In the processing of the image processing system 1000, if the magnitude relationship between the evaluation value D, the loop section of the evaluation value D, -0.5 × dx, 1.5 × dx, and the threshold values Th1 to Th3 is known, the processing is performed. Since it can be executed, the threshold value Th1 to Th3, the update process of the evaluation value D, and the like can be adjusted so that the process can be executed only by integer arithmetic.

  FIG. 13 shows a flowchart when the processing of the image processing system 1000 is generalized.

  The flowchart of FIG. 13 replaces step S2 with step S2 ′, replaces step S11 with step S11 ′, replaces step S12 with step S12 ′, and replaces step S13 with step S13 ′ in the flowchart of FIG. It is a thing. Otherwise, the flowchart of FIG. 13 is the same as the flowchart of FIG.

  In the flowchart of FIG. 13, k is a positive real number.

The case where k = 1 is the case described above. That is, if k = 1,
Loop section of evaluation value D: −0.5 × dx to 1.5 × dx
Th1 = 0.5 × dx−dy
Th2 = 0.5 × dx
Th3 = 1.5 × dx−dy
It becomes.

The flowchart in FIG. 2 is for k = 2. That is, if k = 2,
Loop section of evaluation value D: −dx to 3 × dx
Th1 = dx−2 × dy
Th2 = dx
Th3 = 3 × dx-2 × dy
It becomes.

  In this case, the drawing process can be executed only by integer arithmetic.

  In the above description, the drawing process on the premise of dy / dx ≦ 1, that is, the drawing process of a line segment having an inclination of 0 or more and 1 or less is described, but the present invention is not limited to this. With respect to the drawing process of a line segment having a line segment inclination of 1 or more or less than 0, the drawing process may be executed by dividing into cases according to the same concept as described above.

≪First modification≫
Next, a first modification of the first embodiment will be described.

  FIG. 14 is a schematic configuration diagram of an image processing system 1000A according to the present modification.

  An image processing system 1000A according to this modification has a configuration in which the image processing apparatus 1 is replaced with the image processing apparatus 1A in the image processing system 1000 according to the first embodiment.

  The image processing apparatus 1 </ b> A has a configuration in which a coordinate conversion unit 15 and a coordinate reverse conversion unit 16 are added to the image processing apparatus 1.

  Other than that, the image processing system 1000A of the present modification is the same as the image processing system 1000 of the first embodiment.

  Below, the part peculiar to this modification is demonstrated. Moreover, in this modification, about the part similar to the said embodiment, the same code | symbol is attached | subjected and detailed description is abbreviate | omitted.

  The coordinate conversion unit 15 receives the line segment information output from the input unit 11, and performs coordinate conversion of the start point coordinates (x1, y1) and the end point coordinates (x2, y2). This coordinate conversion will be described with reference to FIG.

  FIG. 15 is a diagram for explaining the coordinate conversion.

  As shown in FIG. 15, the coordinate conversion unit 15 sets the x-axis and the y-axis, and the eight regions divided by the x-axis, the y-axis, the y = x straight line, and the y = −x straight line. , Region 1 to region 8 are set.

The coordinate conversion unit 15 performs coordinate conversion so that the starting point (x1, y1) of the line segment becomes the origin (0, 0) of the coordinates shown in FIG. Thereby, the coordinates of the end point of the line segment are converted to (x2-x1, y2-y1).
(1) When the converted point (x2-x1, y2-y1) exists in the region 1 in FIG.
xa = x2-x1
ya = y2-y1
As described above, the drawing process is executed by the same process as in the first embodiment.
(2) When the converted point (x2-x1, y2-y1) exists in the area 2 of FIG. 15, the value of the x coordinate and the value of the y coordinate are switched. That means
ya = x2-x1
xa = y2-y1
And

Thereby, the line segment drawing process from the point (0, 0) to the point (xa, ya) can be performed in the same manner as in the first embodiment. That is, the line segment from the origin to the point included in the area 2 is converted into the line segment from the origin to the point included in the area 1 and the same as in the first embodiment is applied.
(3) Even when the converted point (x2-x1, y2-y1) is present in the regions 3 to 8 in FIG. 15, as described above, from the origin to a point included in any of the regions 3 to 8 Is converted into a line segment from the origin to a point included in the region 1, and the same as in the first embodiment is applied.

  Then, the coordinate conversion unit 15 converts the coordinates as described above, and includes the start point (0, 0) of the line segment and the end point (xa, ya) of the line segment in the line segment information. In addition, the coordinate conversion unit 15 performs information for coordinate conversion, that is, information about the start point (x1, y1) of the line segment before the coordinate conversion, and conversion performed so that the end point of the line segment is included in the region 1 Information about the method (for example, when converting from region 8 to region 1, information indicating that the x coordinate value remains unchanged and the sign of the y coordinate value is inverted (multiplied by −1)) is included in the line segment information. .

  Then, the coordinate conversion unit 15 outputs the line segment information updated as described above to the threshold setting unit 12, the evaluation value acquisition unit 13, the drawing information determination unit 14, and the coordinate reverse conversion unit 16.

  In the threshold setting unit 12, the evaluation value acquisition unit 13, and the drawing information determination unit 14, processing similar to that in the first embodiment is executed.

  The coordinate inverse conversion unit 16 inputs the drawing pixel output from the drawing information determination unit 14 and information regarding the pixel value (drawing color density) and the line segment information output from the coordinate conversion unit 15.

  Then, the coordinate inverse conversion unit 16 performs a conversion opposite to the conversion performed by the coordinate conversion unit 15 and determines the position of the drawing pixel.

  For example, when the conversion executed by the coordinate conversion unit 15 is a process of converting from the region 8 to the region 1, the coordinate reverse conversion unit converts the drawing pixel P (xb, yb) output from the drawing information determination unit 14 to Coordinate conversion is performed to the pixel P (xb, -yb), and further, coordinate conversion is performed to restore the movement from the start point (x1, y1) of the line segment to the origin of the coordinates in FIG. That is, the coordinate reverse conversion unit converts the drawing pixel P (xb, yb) output from the drawing information determination unit 14 into the pixel P (xb + x1, −yb + y1).

  Then, the coordinate inverse transform unit outputs the pixel corresponding to the pixel P (xb + x1, −yb + y1) as the pixel value output from the drawing information determination unit 14 (the pixel value of the drawing pixel P (xb, yb)). Value), data (data corresponding to the pixel value) is written at the address of the display memory 2.

  As described above, in the image processing system 1000A according to the present modification, the coordinate conversion is performed, the drawing process similar to that of the first embodiment is performed, and then the coordinate reverse conversion is performed, so that an arbitrary line segment (the arbitrary line (Slope line segment) is drawn. Therefore, in the image processing system 1000A according to the present modification, the drawing process can be executed using only the process shown in the first embodiment without dividing the case for each inclination of the line segment. . As a result, the image processing system 1000A according to the present modification does not require a large-capacity memory or complicated arithmetic processing, and can effectively reduce aliasing that occurs during line segment drawing.

[Other Embodiments]
In the above embodiment and the modification, the case where the line thickness is one pixel has been described as an example, but the present invention is not limited to this, and the thickness of the line segment may be another thickness. There may be. When the thickness of the line segment is equal to or greater than 2 pixels, the rendering process of the above embodiment is performed in an area (the upper end or lower end area of the line segment) located in the boundary area between the line segment and the background on the image. The same processing as that described above may be applied. Thereby, it is possible to execute a drawing process in which alias components are appropriately suppressed in the boundary region between the line segment and the background.

  In the embodiment and the modification, the pixel values set in steps S7 to S10 in FIGS. 2 and 13 are “255”, “192”, “128”, and “64”. There is no limitation, and other values are set so that the barycentric positions of the drawing pixels located in the same row (drawing pixels having the same x coordinate position) are close to a straight line passing through the start point and end point of the line segment. You may do it.

  You may make it comprise an image processing system and an image processing apparatus combining a part or all of the said embodiment and modification.

  In addition, part or all of the image processing system and the image processing apparatus according to the above-described embodiment may be realized as an integrated circuit (for example, an LSI, a system LSI, or the like).

  Part or all of the processing of each functional block in the above embodiment may be realized by a program. A part or all of the processing of each functional block in the above embodiment is performed by a central processing unit (CPU) in the computer. In addition, a program for performing each processing is stored in a storage device such as a hard disk or a ROM, and is read out and executed in the ROM or the RAM.

  Each processing of the above embodiment may be realized by hardware, or may be realized by software (including a case where the processing is realized together with an OS (Operating System), middleware, or a predetermined library). Further, it may be realized by mixed processing of software and hardware. Needless to say, when the image processing system and the image processing apparatus according to the above-described embodiment are realized by hardware, it is necessary to adjust the timing for performing each process. In the above embodiment, for convenience of explanation, details of timing adjustment of various signals generated in actual hardware design are omitted.

  Moreover, the execution order of the processing method in the said embodiment is not necessarily restricted to description of the said embodiment, The execution order can be changed in the range which does not deviate from the summary of invention.

  A computer program that causes a computer to execute the above-described method and a computer-readable recording medium that records the program are included in the scope of the present invention. Here, examples of the computer-readable recording medium include a flexible disk, a hard disk, a CD-ROM, an MO, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray Disc), and a semiconductor memory. .

  The computer program is not limited to the one recorded on the recording medium, and may be transmitted via a telecommunication line, a wireless or wired communication line, a network represented by the Internet, or the like.

  The specific configuration of the present invention is not limited to the above-described embodiment, and various changes and modifications can be made without departing from the scope of the invention.

1000, 1000A image processing system 1, 1A image processing device 11 input unit 12 threshold setting unit 13 evaluation value acquisition unit 14 drawing information determination unit 15 coordinate conversion unit 16 coordinate reverse conversion unit

Claims (7)

An image processing apparatus for acquiring line segment drawing information for drawing a line segment on an image,
An input unit for inputting information for drawing the line segment;
A line segment drawing information acquisition unit for acquiring drawing information for drawing the line segment;
With
The line segment drawing information acquisition unit
An evaluation value acquisition unit that acquires an evaluation value D indicating a positional relationship between a pixel P (xa, ya) that is a drawing target pixel and a straight line that passes through the start point and end point of the line segment;
A threshold value setting unit that sets at least three threshold values Th1, Th2, and Th3 based on a difference amount dx in the x direction from the start point to the end point and a difference amount dy in the y direction from the start point to the end point;
Based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa, ya + 1) in the y-axis positive direction of the drawing target pixel A drawing information determination unit that determines the density of the drawing color of
With
The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: satisfies a positive real number,
The threshold values Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
The filling,
The evaluation value acquisition unit
Updating the evaluation value D based on the difference amount dy;
When the updated evaluation value D is 1.5 × dx × k or more, the updated evaluation value D is further updated based on the difference amount dx, and the next drawing target pixel is set to P (xa + 1, ya + 1). Decide
When the updated evaluation value D is less than 1.5 × dx × k, the next drawing target pixel is determined to be P (xa + 1, ya).
Image processing device. The initial value of the evaluation value D is “0”,
The drawing information determination unit
(1) When the evaluation value D satisfies −0.5 × dx × k ≦ D <Th1, the density of the drawing color of the pixel P (xa, ya) is the density DA,
(2) When the evaluation value D satisfies Th1 ≦ D <Th2, the density of the drawing color of the pixel P (xa, ya) is set to the density DB1, and the density of the drawing color of the pixel P (xa, ya + 1) is set to the density. DB2
(3) When the evaluation value D satisfies Th2 ≦ D <Th3, the density of the drawing color of the pixel P (xa, ya) is set to the density DC1, and the density of the drawing color of the pixel P (xa, ya + 1) is set to the density. DC2
(4) When the evaluation value D satisfies Th3 ≦ D <1.5 × dx × k, the density of the drawing color of the pixel P (xa, ya) is set to the density DD1, and the pixel P (xa, ya + 1) The density of the drawing color is density DD2,
When the drawing color density is set to be larger as the drawing color density value is larger, the densities DA, DB1, DB2, DC1, DC2, DD1, and DD2 are:
DA ≧ DB1 ≧ DC1 ≧ DD1
DB2 ≦ DC2 ≦ DD2
Meet,
The image processing apparatus according to claim 1. The evaluation value acquisition unit
D = D + 2 × dy × k
To update the evaluation value D,
When the updated evaluation value D is 1.5 × dx × k or more, the updated evaluation value D is further
D = D−2 × dx × k
And the next drawing target pixel is determined to be P (xa + 1, ya + 1).
The image processing apparatus according to claim 1. When the slope of the straight line connecting the first point that is the start point of the line segment and the second point that is the end point of the line segment is not greater than 0 and less than 1, the slope of the straight line connecting the third point and the fourth point is 0. A coordinate conversion process in which the third point and the fourth point are set to be 1 or less, the first point is coordinate-converted to the third point, and the second point is coordinate-converted to the fourth point. A coordinate conversion unit for performing
A coordinate inverse transform unit for performing the coordinate inverse transform process of the coordinate transform process;
Further comprising
The line segment drawing information acquisition unit selects a line segment connecting the third point and the fourth point with the third point as the start point of the line segment and the fourth point as the end point of the line segment. Get drawing information for drawing,
The coordinate reverse conversion unit is configured to perform the processing for the coordinate position information included in the drawing information for drawing the line segment connecting the third point and the fourth point acquired by the line segment drawing information acquisition unit. Perform coordinate reverse transformation processing,
The image processing apparatus according to claim 1.

The coefficient k is
k = 2 × n (n is a natural number)
Is,
The image processing apparatus according to claim 1. A program for causing a computer to execute an image processing method for acquiring line segment drawing information for drawing a line segment on an image,
An input step for inputting information for drawing the line segment;
A line segment drawing information acquisition step for acquiring drawing information for drawing the line segment;
With
The line segment drawing information acquisition step includes:
An evaluation value acquisition step of acquiring an evaluation value D indicating a positional relationship between a pixel P (xa, ya) that is a drawing target pixel and a straight line passing through the start point of the line segment and the end point of the line segment;
A threshold setting step for setting at least three threshold values Th1, Th2 and Th3 based on a difference amount dx in the x direction from the start point to the end point and a difference amount dy in the y direction from the start point to the end point;
Based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa, ya + 1) in the y-axis positive direction of the drawing target pixel A drawing information determination step for determining the density of the drawing color of
With
The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: satisfies a positive real number,
The threshold values Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
The filling,
The evaluation value acquisition step
Updating the evaluation value D based on the difference amount dy;
When the updated evaluation value D is 1.5 × dx × k or more, the updated evaluation value D is further updated based on the difference amount dx, and the next drawing target pixel is set to P (xa + 1, ya + 1). Decide
When the updated evaluation value D is less than 1.5 × dx × k, the next drawing target pixel is determined to be P (xa + 1, ya).
A program for causing a computer to execute an image processing method. An integrated circuit for image processing for acquiring line segment drawing information for drawing a line segment on an image,
An input unit for inputting information for drawing the line segment;
A line segment drawing information acquisition unit for acquiring drawing information for drawing the line segment;
With
The line segment drawing information acquisition unit
An evaluation value acquisition unit that acquires an evaluation value D indicating a positional relationship between a pixel P (xa, ya) that is a drawing target pixel and a straight line that passes through the start point and end point of the line segment;
A threshold value setting unit that sets at least three threshold values Th1, Th2, and Th3 based on a difference amount dx in the x direction from the start point to the end point and a difference amount dy in the y direction from the start point to the end point;
Based on the evaluation value D and the threshold values Th1, Th2, and Th3, the density of the drawing color of the drawing target pixel P (xa, ya) and the adjacent pixel P (xa, ya + 1) in the y-axis positive direction of the drawing target pixel A drawing information determination unit that determines the density of the drawing color of
With
The evaluation value D is
−0.5 × dx × k ≦ D ≦ 1.5 × dx × k
Coefficient k: satisfies a positive real number,
The threshold values Th1, Th2 and Th3 are:
−0.5 × dx × k <Th1 <Th2 <Th3 <1.5 × dx × k
The filling,
The evaluation value acquisition unit
Updating the evaluation value D based on the difference amount dy;
When the updated evaluation value D is 1.5 × dx × k or more, the updated evaluation value D is further updated based on the difference amount dx, and the next drawing target pixel is set to P (xa + 1, ya + 1). Decide
When the updated evaluation value D is less than 1.5 × dx × k, the next drawing target pixel is determined to be P (xa + 1, ya).
Integrated circuit.