JP4899957B2 - Anti-aliasing processing method and anti-aliasing processing apparatus - Google Patents

Description

  The present invention relates to an anti-aliasing processing method and an anti-aliasing processing device, and more particularly to an anti-aliasing processing method and an anti-aliasing processing device that suppress a jagged phenomenon based on an area surrounded by an image boundary line and a pixel crossing a pixel.

When displaying a figure such as a line or a triangle on a display device such as a CRT (Cathode Ray Tube) display of a computer, the diagonal line may become a stepped jagged shape.
FIG. 9 is a schematic diagram illustrating a jagged phenomenon in the display device.

  As shown in FIG. 9, the display area 200 is composed of a plurality of pixels (pixels) 221, and the drawing target boundary line 210 is drawn across the pixel 221 (however, the inclination of the boundary line 210 k is -1 <k <0 or 0 <k <1.) Below this boundary line 210 (the area below the boundary line 210 in FIG. 9 and colored) is a drawing area 220, and the outline of the drawing area 220 and the boundary line 210 is stepped. The jagged portion of jas. When this jagged phenomenon occurs, the contours of the output image and characters are jagged and are displayed indistinctly, so that the jagged phenomenon is devised to suppress the jagged phenomenon. Note that the size of one pixel is 1 × 1.

Therefore, a technique called anti-aliasing is used to suppress such a jagged phenomenon.
Anti-aliasing is based on the area of the figure surrounded by the border line and pixels, and uses the area ratio as the blending rate to match (blend) the existing color of the figure with the drawing color. This is a method of placing a blended color around the.

Below, a blend rate is demonstrated.
FIG. 10 is a schematic diagram for explaining the blend ratio.
FIG. 10 shows a boundary line to be drawn across the pixels in the drawing area. In FIG. 10A, the boundary line crosses one pixel, and in FIG. 10B, the boundary line crosses two pixels. In FIG. 10, unless otherwise specified, the same reference numerals as those in FIG. 9 and the size and inclination of one pixel are used.

In FIG. 10A, both end points of the boundary line 210 crossing one pixel 221a are set to (X _α , Y _α ), (X _{α + 1} , Y _{α + 1} ) (Y _α > Y _{α + 1} ). In this case, each length can be expressed as follows: Note that frac (Y _α ) is a fractional part of Y _α , k is the slope of the boundary line 210, and | k | is the absolute value of the slope k.

Length ac = frac (Y _α ), length cd = 1, length a′b = | k |
Therefore, the area S _{α of the} shaded portion can be expressed as follows.
S _α = frac (Y _α ) × 1-1 × | k | × (1/2) = frac (Y _α ) − | k | / 2
The ratio of the area S _α calculated in this way to one pixel is S _α . Accordingly, this percentage as a blend ratio, and the existing color and foreground color, 1-S _alpha: to draw 1 pixel by using the color obtained by blending a proportion of the S _alpha.

On the other hand, in the same way even FIG. 10 (B), the both end points of the boundary line 210 crossing the pixel _{221b (X β, Y β)} , (X β + 1, Y β + 1) (Y β> Y β + 1 ), Each length can be expressed as follows: Here, frac (Y _β ) is a decimal part of Y _β , k is the slope of the boundary line 210, and | k | is the absolute value of the slope k.

Length ei = frac (Y _β), the length _{ij = frac (Y β) /} | k |, the length _{jk = 1- (frac (Y β} ) / | k |), the length kf = | k | - frac (Y _β )
Accordingly, the area S _β1 (the area of the upper triangle ej) and the area S _β2 (the area of the lower pentagon ijfgh) of the shaded portion can be expressed as follows.

_{S β1 = 1/2 × (} frac (Y β) / | k |) × frac (Y β) = (frac (Y β)) 2/2 | k |
S _β2 = 1−1 / 2 × (1- (frac (Y _β ) / | k |)) × (| k | -frac (Y _β )) = 1− (| k | −frac (Y _β )) ^2/2 | k |
Also in this case, one pixel is drawn using a color obtained by blending the existing color and the drawing color at the blend rate using the area calculated in the same manner.

Therefore, according to such an algorithm (Bresenham algorithm), the area of the drawing region can be calculated.
However, in such Bresenham algorithm, the calculation is complicated, the calculation amount is enormous, and processing time is required. Therefore, there is a method of calculating the area surrounded by the boundary line and the pixel using approximation. Used (see, for example, Patent Document 1).

FIG. 11 is a schematic diagram for explaining an area calculation method used for a conventional blend ratio.
In FIG. 11, approximation is used to calculate the area used for the blend ratio. Unless otherwise specified, the same reference numerals as those in FIGS. 9 and 10 and the size and inclination of one pixel are used. Further, in FIG. 11, the end points crossing the pixel 222a of the boundary line 210 are ( _Xα1 , _Yα1 ), ( _{Xα1 + 1} , _{Yα1 + 1} ), and a point d = (0, 0).

In FIG. 11A, since the boundary line 210 intersects with only two lines parallel to each other at the boundary of the pixel 222a in the y-axis direction, the area S _{α of the} quadrangle efcd can be expressed as follows.
S _α = (Y _α1 + Y _{α1 + 1} ) / 2
That is, since this indicates the shortest distance from the center point of the boundary line 210 to the x-axis of the pixel 222a, the length ji (= La) can be used as the area used for the blend rate. Accordingly, the shortest distance from the center point of the boundary line 210 to the x-axis of the pixel is regarded as an area, and the description of FIGS. 11B and 11C is continued below.

  Next, in FIG. 11B, the boundary line 210 intersects with two lines parallel to the y-axis direction of the pixel 222b boundary and also intersects with a line parallel to the x-axis direction of the pixel 222b boundary to obtain a length al. Is taken as an example when the length is smaller than the length ad / 2. The shortest distance ji from the center point of the boundary line 210 to the x-axis of the pixel is Lb. At this time, the area efcd surrounded by the boundary line 210 and the pixel 222b was obtained by setting the area of the triangle ela to 0 and the area of the pentagon alfcd to Lb.

  Similarly, FIG. 11C also intersects with two lines parallel to the y-axis direction of the boundary of the pixel 222c and also intersects with a line parallel to the x-axis direction of the boundary of the pixel 222c. Is taken as an example when the length is larger than the length ad / 2. The shortest distance ji from the center point of the boundary line 210 to the x-axis of the pixel is Lc. At this time, the area efcd surrounded by the boundary line 210 and the pixel 222c was obtained by setting the area of the triangle ela to Lc and the area of the pentagonal alfcd to 1.

As described above, by approximating the area surrounded by the boundary line and the pixels, it is possible to simplify the complex calculation and perform the anti-aliasing processing.
JP-A-9-245181

  However, as in the above-mentioned patent document, if approximation is used to calculate the area surrounded by the boundary line and the pixel, the accurate area cannot be calculated, so that a high-accuracy blend rate cannot be obtained. was there.

  The present invention has been made in view of such a point, and an object thereof is to provide an anti-aliasing processing method and a processing apparatus capable of calculating an area surrounded by a boundary line and a pixel accurately and at high speed. To do.

  In the present invention, in order to solve the above problem, in the anti-aliasing processing method for suppressing the jagged phenomenon based on the area surrounded by the boundary line of the drawing area crossing the pixel and the pixel, as shown in FIG. A step (S11) of inputting two points at both ends of a boundary line that is provided with x and y axis directions and has intersections with the sides of pixels arranged according to the direction, and a step of calculating a slope value of the boundary line from the two points (S12) If the boundary line is parallel to the x-axis or y-axis, a step (S14) of calculating a square area surrounded by the boundary line and the pixel, and the boundary line parallel to the x-axis or y-axis Furthermore, if there is no other intersection with the side between adjacent intersections among equally spaced intersections, if there is a square area (S18) surrounded by the boundary line and one pixel and another intersection, A triangle surrounded by a border and one pixel An area (S19), a square area (S20) surrounded by the boundary line and the two pixels, and a polygonal area (S21) obtained by removing the triangle from the quadrangle surrounded by the boundary line and the two pixels. And an output step. An antialiasing processing method is provided.

  According to such an anti-aliasing processing method, two points at both ends of the boundary line having intersections with the sides of the pixels arranged in the x and y axis directions provided in the display area are input, and the boundary line becomes the x axis. Alternatively, if it is parallel to the y axis, a square area surrounded by the boundary line and the pixel is output, the boundary line is not parallel to the x axis or the y axis, and further, between adjacent intersections at equal intervals. If there is no other intersection with the side, the area of the rectangle surrounded by the boundary line and one pixel, and if there is another intersection, the area of the triangle surrounded by the boundary line and one pixel, and the boundary line A square area surrounded by the two pixels and a polygonal area obtained by removing the triangle from the square surrounded by the boundary line and the two pixels are output.

  In order to solve the above-described problem, an x- and y-axis directions are provided in a display area in an anti-aliasing processing apparatus that suppresses a jagged phenomenon based on an area surrounded by a boundary line of a drawing area that crosses a pixel and the pixel. Means for inputting two points at both ends of the boundary line having intersections with sides of the pixels arranged according to the direction, means for calculating an inclination value of the boundary line by the two points, and the boundary line Is parallel to the x-axis or the y-axis, means for calculating the area of the rectangle surrounded by the boundary line and the pixel, and the boundary line is not parallel to the x-axis or the y-axis, Furthermore, if there is no other intersection with the side between the adjacent intersections among the equally spaced intersections, the square area surrounded by the boundary line and the one pixel and the other intersection are present. For example, the boundary line The triangle is excluded from the area of the triangle surrounded by the one pixel, the area of the rectangle surrounded by the boundary line and the two pixels, and the rectangle surrounded by the boundary line and the two pixels. There is provided an anti-aliasing processing device comprising means for outputting the area of the polygon.

  According to such an anti-aliasing processing device, two points on both ends of a boundary line having intersections with sides of pixels arranged in the x and y axis directions provided in the display area are input, and the boundary line is converted to the x axis. Or if it is parallel to the y-axis, the square area surrounded by the boundary line and the pixel is output, the boundary line is not parallel to the x-axis or y-axis, and is separated from the adjacent intersections at equal intervals. If there is no intersection, the area of a rectangle surrounded by the boundary line and one pixel, and if there is another intersection, the area of a triangle surrounded by the boundary line and one pixel, and the boundary line and two pixels And the area of a polygon obtained by removing the triangle from the quadrangle surrounded by the boundary line and the two pixels are output.

  In the present invention, two points on both ends of a boundary line having intersections with the sides of pixels arranged in the x and y axis directions provided in the display area are input, and the boundary line is parallel to the x axis or the y axis. For example, the square area surrounded by the boundary line and the pixel is output, and the boundary line is not parallel to the x-axis or the y-axis. If there is not, the area of the rectangle surrounded by the boundary line and one pixel, and if there is another intersection, the area of the triangle surrounded by the boundary line and one pixel, and the boundary line and the two pixels The area of the quadrangle and the area of the polygon excluding the triangle from the quadrangle surrounded by the boundary line and the two pixels are output. Thereby, the area surrounded by the boundary line and the pixels can be calculated accurately, complicated calculations can be simplified, and the time required for the calculation can be shortened.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. However, the technical scope of the present invention is not limited to these embodiments.
First, an outline of the present invention will be described, and then an embodiment will be described. In the present embodiment, as described above, the size of one pixel is assumed to be 1 × 1.

FIG. 1 is a schematic diagram of a processing flow of the present invention, and FIG. 2 is a schematic diagram of a display area in which a boundary line is displayed.
FIG. 10 is a flowchart for explaining the outline of the processing according to the present invention. The x and y axis directions are set in the display area, and one pixel is laid out in each direction. A line is drawn, and the area surrounded by the boundary line and the pixel can be calculated with high accuracy and high speed according to the inclination of the boundary line.

Hereinafter, the outline of the present invention will be described with reference to FIG.
[Step S11] Two points that are both ends of the boundary line are input.
In FIG. 2, as the both ends of the boundary line, (x1, y1) and (x1, y1 ′) if the boundary line 31a, (x2, y2) and (x2 ′, y2) if the boundary line 31b, For the boundary line 31c, (x3, y3) and (x4, y4) are two points at both ends.

[Step S12] The slope of the boundary line is calculated from the two input points.
In the case of the boundary line 31c in FIG. 2, the slope k can be calculated by k = (y3-y4) / (x3-x4).

[Step S13] It is determined whether the boundary line is parallel to either the x-axis or the y-axis.
As a result of calculating the inclination in step S12, as shown in FIG. 2, if the inclination of the boundary line is infinite or 0, that is, the boundary line is parallel to either the y-axis or the x-axis (boundary lines 31a and 31b). The process proceeds to step S14, and if the gradient of the boundary line is other than that, that is, if it is not parallel to the x axis or the y axis (boundary line 31c), the process proceeds to step S15.

[Step S14] From two points at both ends of the input boundary line, a square area surrounded by the boundary line and the pixel is calculated and output.
As shown in FIG. 2, when the boundary line 31a and the y-axis are parallel, the two points at both ends of the boundary line 31a are (x1, y1) and (x1, y1 ′), so the length of the boundary line 31a | Y1−y1 ′ | and the width between the boundary line and the y-axis can be | x1 |. When the boundary line 31b and the x-axis are parallel, the two points at both ends of the boundary line 31b are (x2, y2) and (x2 ′, y2), so the length of the boundary line 31b is set to | x2−. x2 ′ |, and the width between the boundary line and the x-axis can be | y2 |. From the above, it is possible to easily calculate a region surrounded by the boundary lines 31a and 31b and the pixels.

It should be noted that the area needs to be calculated by appropriately setting the width as 1- | x1 | or 1- | y2 | depending on whether the drawing area exists on the left or right or upper and lower sides of the boundary lines 31a and 31b.
[Step S15] If the boundary line is not parallel to the x-axis or the y-axis, the intersection between the boundary line and the pixel is checked and an initial setting is made.

  In the initial setting, as shown in FIG. 2, the intersection of the boundary line 31c and the pixel is checked, and the initial quadrangular area that is the area of the quadrangle abdc, the initial triangular area that is the area of the triangle aic, and the like are calculated in advance. .

[Step S16] An intersection between the checked boundary line and the pixel is selected. It should be noted that processing is performed, and adjacent points that have moved by 1 in the x-axis direction of the previously selected point are sequentially selected.
In FIG. 2, for example, the point a (x3, y3) is first selected. When the process proceeds to the next step S16, next, the point b moved by 1 in the x-axis direction is selected, and in the same manner, the point e, the point j, etc. are selected next. Select an adjacent point.

  [Step S17] It is determined whether there is an intersection with the pixel between the point selected in step S16 and its adjacent point. If there is no intersection, the process proceeds to step S18, and if there is an intersection, the process proceeds to step S19. Note that such an intersection existence region is hereinafter referred to as a “conversion region” or a “conversion point”.

In FIG. 2, for example, since there is no intersection with the pixel between the point a selected in step S17 and the adjacent point b, the process proceeds to step S18 in this case.
On the other hand, if the point e is selected in step S17, there is a point i as an intersection with the pixel between the adjacent point j and it is a conversion point. In this case, the process proceeds to step S19.

[Step S18] The area surrounding the pixel by the point selected in Step S16 and its adjacent points is calculated and output.
By the way, the area surrounded by the boundary line and the pixel will be described below.

In FIG. 2, the area of the quadrangle abdc can be expressed as S _abdc = (| ac | + | bd |) / 2 as already described. However, | ac | and | bd | are the lengths of ac and bd.

On the other hand, the area of the square befd can be similarly _expressed as S _befd = (| bd | + | ef |) / 2. However, | bd | and | ef | are the lengths of bd and ef.

In this case, the difference between these _{area, S abdc -S befd = (|} ac | - | ef |) / 2 and can be represented, which is the slope of the boundary line 31 | with a value equivalent to | k is there.
Using this property, first, the area S _{abdc of the} quadrangle abdc surrounded by the point a to be selected and the point b of the adjacent point is the initial square area calculated in step S15 and is adjacent to the point b to be selected next. area S _befd square befd surrounded by the point e point, S _abdc - | k | and can be expressed.

[Step S19] If there is a conversion point that is the intersection of the boundary line and the pixel in step S17, the area of the triangle at the conversion point by the selected point and the intersection is calculated and output.
In FIG. 2, for example, since there is a point i at the intersection of the selected point e and the adjacent point j, the triangle eif of the conversion point is calculated and output. Further, as this calculation method, the area of the triangle eif of the conversion point is obtained by subtracting the area of the quadrangle aefc obtained by adding the quadrangle calculated in step S18 from the initial triangular area of the triangle aic obtained in step S15. Calculated.

  [Step S20] If there is a conversion point that is the intersection of the boundary line and the pixel in step S17, the area of the rectangle at the conversion point of the pixel surrounded by the selected point and its adjacent points is calculated and output.

In FIG. 2, the area of the square ejkg at the transformation point surrounded by the point j adjacent to the selected point e is calculated and output.
[Step S21] When there is a conversion point that is the intersection of the boundary line and the pixel in step S17, the area of the triangle at the conversion point calculated in step S19 is subtracted from the area of the quadrangle at the conversion point calculated in step S20. To calculate and output the pentagonal area at the transformation point.

In FIG. 2, the area of the pentagonal fijkg is calculated and output by subtracting the area of the triangle eif from the square ejkg.
[Step S22] It is determined whether there is an adjacent point in the adjacent point of the selected point. If there are other adjacent points, the process proceeds to step S16. If there are no other adjacent points, the process ends.

In FIG. 2, for example, since there is no further adjacent point to the point n that is the adjacent point of the selected point l, in this case, the process ends.
As described above, the area surrounded by the boundary line and the pixel can be accurately calculated, and complicated calculation can be simplified by repeatedly subtracting the slope from the area to calculate the area. Time can be shortened. Therefore, it is possible to perform highly accurate anti-aliasing processing by using the area calculated at high speed and accurately as the blend ratio.

Embodiments using the present invention will be described below with reference to the drawings.
In the present embodiment, the area used as the blending ratio of the anti-aliasing process can be calculated by inputting two points at both ends of the boundary line of the drawing area from the user to the anti-aliasing processing apparatus.

FIG. 3 is a block diagram illustrating functions of the anti-aliasing processing apparatus.
The anti-aliasing processing device 40 includes an initial value data unit 41, an area value data unit 42, an inclination value calculation unit 43, an initial setting unit 44, and an area calculation unit 45.

  The initial value data unit 41 stores data such as area values of a quadrangle and a triangle that are initially set in advance and are surrounded by a boundary line and pixels. In addition, about the area of the quadrangle | tetragon and triangle calculated by initial setting, the detail is demonstrated in the specific example given later.

The area value data unit 42 stores area value data surrounded by the boundary line and the pixel calculated by the anti-aliasing processing device.
The inclination value calculation unit 43 calculates the inclination of the boundary line based on two points at both ends of the input boundary line.

  When the boundary line is not parallel to the x-axis and the y-axis, the initial setting unit 44 calculates and calculates the area of the rectangle and the triangle surrounded by the boundary line and the pixel according to the inclination calculated by the inclination value calculation unit 43. The area value is stored in the initial value data unit 41.

The area calculation unit 45 further includes a square calculation unit 45a, a quadrangle calculation unit 45b, a triangle calculation unit 45c, and a pentagon calculation unit 45d.
When the boundary line having the inclination calculated by the inclination value calculation unit 43 is parallel to the x-axis or the y-axis, the square calculation unit 45a uses the two points at both ends of the boundary line to generate a boundary line and a pixel. Calculate the area of the enclosed square.

  When the boundary line is not parallel to the x-axis and the y-axis, the quadrangle calculation unit 45b calculates the area of the quadrangle surrounded by the boundary line and the pixel or the square at the conversion point. As an area calculation method, the area of the region surrounded by the boundary line and one pixel adjacent to the initial rectangle obtained by the initial setting unit 44 is obtained by subtracting the inclination value of the boundary line from the area of the initial rectangle. Similarly, the area of the adjacent quadrangle can be calculated by subtracting the slope from the area of the obtained quadrangle. The area of the quadrangle at the conversion point can be calculated by adding 1 to the area of the quadrangle adjacent to the triangle at the conversion point and subtracting the slope value.

  When the boundary line is not parallel to the x axis and the y axis, the triangle calculation unit 45c calculates the area of the triangle at the conversion point surrounded by the boundary line and the pixel. For the calculation, the area of the triangle at the conversion point can be calculated by subtracting the area added by the quadrangle calculated by the quadrangle calculation unit 45b from the area of the initial triangle obtained by the initial setting unit 44.

  When the boundary line is not parallel to the x axis or the y axis, the pentagon calculation unit 45d calculates the area of the pentagon at the conversion point surrounded by the boundary line and the pixel. For calculation, the area of the pentagon can be calculated by subtracting the area of the triangle at the conversion point calculated by the triangle calculation unit 45c from the square at the conversion point obtained by the rectangle calculation unit 45b.

In this way, the calculated area is stored in the area value data unit 42.
Next, processing for calculating the area surrounded by the boundary line and the pixels by the anti-aliasing processing device 40 will be described.

  FIG. 4 is a flowchart showing the area calculation process of the anti-aliasing process in the embodiment of the present invention, and FIG. 6 is a schematic diagram of the display area in which the boundary line of the drawing area having an inclination in the present embodiment is displayed. .

  FIG. 4 shows the flow of the area calculation process surrounded by the boundary line and the pixel in the anti-aliasing processing device 40, and FIG. 6 is drawn so that the boundary line 71 having an inclination in the display area 70 crosses the pixel. It shows the place. The lower side of the boundary line 71 is a drawing area.

Hereinafter, the area calculation processing by the anti-aliasing processing device 40 will be described with reference to FIG.
[Step S <b> 51] Two points that are both ends of the boundary line are input to the slope value calculation unit 43 by the user.

Examples of the two input points include point A (X1, Y1) and point B (Xn, Yn) as shown in FIG.
[Step S52] The slope value calculation unit 43 calculates the slope of the boundary line from the two input points.

As already described, the calculated slopes are obtained for three cases: zero, infinity, and other cases.
[Step S <b> 53] The inclination value calculation unit 43 determines whether the obtained inclination is zero, that is, whether it is parallel to the x-axis. If it is parallel to the x axis, the process proceeds to step S54. If it is not parallel to the x axis, the process proceeds to step S56.

  [Step S54] If it is parallel to the x axis, the square calculation unit 45a of the area calculation unit 45 calculates the horizontal length of the boundary line and the vertical length from the x axis to the boundary line from the two input points. By calculating and multiplying them, the area of the drawing region surrounded by the boundary line and the pixel is calculated. Depending on whether the drawing area exists above or below the boundary line parallel to the x axis, the vertical height is appropriately adjusted by, for example, using a value obtained by subtracting the input y value from 1. There is a need to.

[Step S55] The square area calculated in step S54 is stored in the area value data section 42 by the square calculation unit 45a.
[Step S56] The slope value calculation unit 43 determines whether or not the obtained slope is infinite, that is, parallel to the y-axis. If it is parallel to the y axis, the process proceeds to step S57, and if not parallel to the y axis, the process proceeds to step S59.

  [Step S57] If parallel to the y-axis, the square calculation unit 45a of the area calculation unit 45 calculates the vertical length of the boundary line and the horizontal length from the y-axis to the boundary line from the two input points. By calculating and multiplying them, the area of the drawing region surrounded by the boundary line and the pixel is calculated. Depending on whether the drawing area exists on the left or right side of the boundary line parallel to the y-axis, the horizontal length is appropriately adjusted by using a value obtained by subtracting the input x value from 1. There is a need to.

[Step S58] The square area calculated in step S57 is stored in the area value data section 42 by the square calculation unit 45a.
[Step S59] When the boundary line is not parallel to both the x-axis and the y-axis, the initial setting unit 44 calculates in advance the area of a portion necessary for the subsequent area calculation, and sets the calculated area value and other data as initial value data. Stored in the unit 41.

  In the case where the boundary line has an inclination, as shown in FIG. 6, the areas of the quadrangle ABB1A1, the triangle ADA1, and the triangle FKF1 are calculated in advance and stored in the initial value data unit 41 as shown in FIG.

Note that the slope k of the boundary line 71 in the present embodiment is -1 <k <0 or 0 <k <1.
[Step S60] The area of the drawing region surrounded by the boundary line and the pixels is calculated by the quadrangle calculation unit 45b, the triangle calculation unit 45c, and the pentagon calculation unit 45d of the area calculation unit 45.

Details of the process in step S60 will be described later.
[Step S61] The area calculation unit 45 stores the areas of all the drawing regions in the area value data unit 42, and the process ends.

And the process performed by step S60 is demonstrated below.
FIG. 5 is a flowchart showing details of the area calculation process of the anti-aliasing process in the embodiment of the present invention. Hereinafter, description will be made in the same manner with reference to FIGS.

  In step S59, the initial setting unit 44 checks the intersection between the boundary line 71 and the pixel in FIG. 6 and calculates the area as described above. Note that one by one is added to X1 of A (X1, Y1), and adjacent points of intersections between the boundary line 71 and the pixels are defined as B (X2, Y2), C (X3, Y3),..., N (Xn, Yn). ).

After the above initial setting is completed, the following processing is performed.
[Step S60a] The processing from Step S60b to Step S60m is repeated for i = 1, 2,..., N−1 of Xi.

  [Step S60b] The area calculation unit 45 selects a point Xi and determines whether i = 1 of the selected Xi. If i = 1, the process proceeds to step S60c, and if i = 1, the process proceeds to step S60d.

  [Step S60c] When i = 1, that is, when A (X1, Y1) is selected, the area of a quadrangle ABB1A1 surrounded by A (X1, Y1), B (X2, Y2) that is an adjacent point, and one pixel. Are extracted from the initial value data portion 41 and the initial rectangular area already stored is output.

  [Step S60d] When i = 1 is not satisfied, for example, when B (X2, Y2) is selected, it is determined whether or not there is an intersection with a pixel between point B and point C. If there is no intersection, the process proceeds to step S60e, and if there is an intersection, the process proceeds to step S60h.

  When B (X2, Y2) is selected, there is no intersection with one pixel between C (X3, Y3) of the adjacent point, and the process proceeds to step S60e. On the other hand, when the point D is selected, since there is a point E that is an intersection with one pixel between the point D and the adjacent point F, the process proceeds to step S60h.

  [Step S60e] When there is no intersection, the quadrangle calculation unit 45b selects an area of a region surrounded by the previously selected point and its adjacent points and one pixel (hereinafter referred to as a preceding area or a leading rectangle). .

In FIG. 6, for example, in the case of i = 2, the area of the quadrangle ABB1A1, which is an area surrounded by the point A selected before the point B and its adjacent point B and one pixel, is selected.
[Step S60f] The quadrangle calculation unit 45b calculates the area of the region surrounded by the selected point, its neighboring points, and one pixel by subtracting the slope of the boundary line 71 from the preceding area selected in Step S60e.

  When i = 2 is selected, the area of the rectangle BCC1B1 surrounded by B (X2, Y2), C (X3, Y3) and one pixel is obtained by subtracting the slope value of the boundary 71 from the area of the rectangle ABB1A1. Can be calculated.

[Step S60g] The quadrangle calculation unit 45b stores the area value data calculated in Step S60f in the area value data unit 42.
[Step S60h] When there is an intersection, the triangle calculation unit 45c extracts the initial triangle area already stored from the initial value data unit 41, and subtracts the sum of the previous preceding areas from the initial triangle area. Thus, the area of the triangle at the conversion point is calculated.

  Assuming that there is an intersection, when the point D is selected, the area of the quadrilateral ADD1A1 obtained by adding up the previous preceding areas is calculated. Then, by extracting the area of the triangle AEA1 already stored in the initial value data section 41 and subtracting the quadrilateral ADD1A1 from the triangle AEA1, the area of the triangle DED1 at the conversion point can be calculated.

[Step S60i] The triangle calculation unit 45c outputs the area of the triangle DED1 calculated in step S60h to the area value data unit 42.
[Step S60j] The quadrangle calculation unit 45b adds 1 to the area of the preceding quadrilateral of the triangle at the conversion point calculated in step S60h, and subtracts the slope value of the boundary 71 to thereby calculate the triangle at the conversion point calculated in step S60h. The rectangle at the transformation point including is calculated.

  In FIG. 6, the quadrangle calculation unit 45b adds 1 to the quadrangle CDD1C1 that is the preceding quadrangle at the conversion point including the triangle DED1 at the conversion point calculated in step S60h (that is, the area of the quadrangle CDD2C2). The area of the square DFF1D2 at the conversion point can be calculated by subtracting the slope value.

[Step S60k] The quadrangle calculation unit 45b stores the area of the quadrangle DFF1D2 at the conversion point calculated in step S60j in the area value data unit 42.
[Step S601] The pentagon calculation unit 45d subtracts the triangle at the conversion point calculated at Step S60h from the quadrangle at the conversion point calculated at Step S60j, thereby obtaining the area of the pentagon at the conversion point surrounded by the boundary line 71 and the pixel. Can be calculated.

  In FIG. 6, the area of the pentagon D1EFF1D2 at the conversion point can be calculated by subtracting the triangle DED1 at the conversion point from the quadrangle DFF1D2 at the conversion point.

[Step S60m] The pentagon calculation unit 45d stores the area of the pentagon at the conversion point calculated in step S601 in the area value data unit 42.
These processes are performed for all i = 1, 2,..., N−1.

With the above processing, the area of the drawing region surrounded by the boundary line and the pixel is calculated, and the calculated area is used as the blend rate.
Next, a hardware device that actually calculates the area of a region surrounded by a boundary line and pixels will be described with reference to FIG.

FIG. 7 is a configuration diagram of a hardware device that performs area calculation processing of the anti-aliasing processing device.
7 includes an inclination determination unit 81, an area calculation unit 82, an initial setting unit 83, a drawing control unit 84, an adder / subtracter (rectangle) 85a, an adder / subtractor (triangle) 85b, an adder / subtracter (pentagon) 85c, The multiplexer includes mux 86a, 86b, 86c, 86d, 86e, 86f, and 86g, and the register includes regs 87a, 87b, 87c, and 87d.

The inclination determination unit 81 calculates the inclination of the boundary line from two points at both ends of the input boundary line, and determines whether the boundary line is parallel to the x axis or the y axis.
When the boundary line is parallel to the x axis or the y axis, the area calculation unit 82 calculates the area surrounded by the boundary line and the pixel.

  If the boundary line is not parallel to the x-axis or y-axis, the initial setting unit 83 checks all the intersections between the boundary line and the pixel and calculates the area of a quadrangular or triangular area surrounded by the boundary line and the pixel in advance. To do.

  The drawing control unit 84 inputs the initial value calculated by the initial setting unit 83 to a block having each function, and inputs the data output from the block to another block. I do.

  The adder / subtracter (rectangle) 85a adds a plurality of input data according to the control of the drawing control unit 84 for the calculation process of the area enclosed by the boundary line and the pixel and the area of the rectangle at the conversion point, Output the subtracted data.

  The adder / subtractor (triangle) 85b adds or subtracts a plurality of input data in accordance with the control of the drawing control unit 84 in order to calculate the area of the triangle at the conversion point surrounded by the boundary line and the pixel. Output the data.

  An adder / subtracter (pentagon) 85c adds or subtracts a plurality of input data in accordance with the control of the drawing control unit 84 in order to calculate the area of the pentagon at the conversion point surrounded by the boundary line and the pixel. Output the data.

  The muxes 86a, 86b, 86c, 86d, 86e, 86f, and 86g receive a plurality of signal data from the drawing control unit 84 and the adder / subtracter, select one signal according to the control of the drawing control unit 84, and the adder / subtracter. Output to. In particular, each area value data is input to the mux 86g.

The regs 87a, 87b, 87c, and 87d hold the signal data input from the adder / subtracter.
The actual calculation of the area of FIG. 6 will be described below with reference to FIGS. 4 and 5 using the hardware device 80 constituted by the above elements.

First, the inclination determination unit 81 calculates the inclination of the boundary line from two points of the input boundary line. From the calculation result, it is determined whether the boundary line is parallel to the x-axis or the y-axis.
When the boundary line is parallel to the x-axis or the y-axis, the area calculation unit 82 calculates the area of a square region surrounded by the boundary line and the pixels (this corresponds to the processing from step S51 to step S58). .

  If the boundary line is not parallel to the x-axis or the y-axis, the initial setting unit 83 checks all the intersections between the boundary line and the pixel, and in advance, the rectangle ABB1A1, the triangle AEA1, and the triangle FKF1 surrounded by the boundary line and the pixel The area of each region is calculated as an initial square area, a first initial triangle area, and a second initial triangle area (step S59).

  The drawing control unit 84 refers to the intersection of the boundary line and the pixel, selects the point A, and the initial square area that is the area of the square ABB1A1 surrounded by the point A, the point B adjacent to the point A, and one pixel. Is input to mux 86g (step S60c).

  In addition, the drawing control unit 84 inputs the slope value of the boundary line into the mux 86a and the initial square area into the mux 86b. Then, the adder / subtracter (rectangle) 85a subtracts the inclination value from the initial square area and inputs the area of the square BCC1B1 to the reg 87a under the control of the drawing control unit 84.

  The drawing control unit 84 again inputs the area of the quadrangle BCC1B1 of the reg 87a to the mux 86b, and next calculates the area of the quadrangle CDD1C1 by subtracting the slope value from the area of the quadrangle BCC1B1.

  As described above, the adder / subtracter (rectangle) 85a calculates the area of the rectangle surrounded by the boundary line and the pixels by repeatedly subtracting the inclination value from the preceding area in accordance with the control of the drawing control unit 84 ( Step S60e to Step S60g).

  In addition, the drawing control unit 84 adds 1 to the preceding area square CDD1C1 to the adder / subtractor (square) 85a to subtract the slope value and calculate the area of the square DFF1D2 in order to calculate the area of the square DFF1D2. Is input to the mux 86f via the reg 87a (steps S60j to S60k).

  On the other hand, the drawing control unit 84 inputs the initial square area to the mux 86c and the first initial triangular area to the mux 86d. The adder / subtractor (triangle) 85b subtracts the area of the quadrilateral ADD1A1 that is the sum of the preceding areas from the area of the triangle AEA1 of the first initial triangle according to the control of the drawing control unit 84, thereby obtaining the area of the triangle DED1. Is input to reg87b.

Then, the drawing control unit 84 inputs the area of the triangle DED1 from reg 87b to reg 87c and mux 86g (steps S60h to S60i).
Finally, the adder / subtracter (pentagon) 85c subtracts the triangle DED1 of the mux 86e from the quadrilateral DFF1D2 of the mux 86f and inputs the area of the pentagon D1EFF1D2 to the reg 87d in order to output the area of the pentagon D1EFF1D2 according to the control of the drawing control unit 84. .

Then, the drawing control unit 84 inputs the area of the pentagon D1EF1D2 from the reg 87d to the mux 86g (steps S601 to S60m).
By repeating the same processing, the remaining area can be calculated.

  By using the hardware device 80 as described above, it is possible not only to accurately calculate the area surrounded by the boundary line and the pixels, but also by using the adder / subtractor, so that the conversion is performed while calculating the square area. For example, the area of a triangle at a point can be calculated, which can contribute to speeding up the processing.

Next, an outline of source code for performing such processing will be described.
FIG. 8 is an example of source code for calculating the area of the anti-aliasing process.
Note that the source code 90 displays only relevant parts, and for example, the return value of the function is omitted. The source code 90 will be briefly described below.

In the code 91, the area of the region surrounded by the boundary line and the pixel is calculated when the inclination is parallel to the x-axis.
In the code 92, the area of the region surrounded by the boundary line and the pixel is calculated when the inclination is parallel to the y-axis.

In the code 93, when the x-axis and the y-axis are not parallel, initial settings are made and the inclination, start point, and end point are determined.
In the code 94, the area of the first initial triangle AEA1, the second initial triangle FKF1, and the initial quadrangle ABB1A1 is calculated when the start point is located above the end point in the y-axis.

  In the code 95, the quadrangle BCC1B1 is calculated by subtracting the inclination value from the initial quadrangle ABB1A1, and the quadrangle CDD1C1 is calculated by subtracting the inclination value again from the calculated quadrangle BCC1B1. The triangle DED1 is calculated by subtracting the sum of the squares ADD1A1 so far from the first initial triangle AEA1.

  In the code 96, the quadrangle DFF1D2 is calculated by subtracting the inclination value from the quadrangle CDD2C2. The area of the pentagon D1EFF1D2 is calculated by subtracting the slope value from the calculated quadrangle DFF1D2.

By repeating such processing, the area of the region surrounded by the boundary line and the pixel can be calculated.
As described above, the area surrounded by the boundary line and the pixel can be accurately calculated, and complicated calculation can be simplified by repeatedly subtracting the slope from the area to calculate the area. Time can be shortened. Therefore, it is possible to perform highly accurate anti-aliasing processing by using the area calculated at high speed and accurately as the blend ratio.

(Additional remark 1) In the anti-aliasing processing method which suppresses a jagged phenomenon based on the area enclosed by the boundary line of the drawing area which crosses a pixel, and the said pixel,
Inputting two points at both ends of the boundary line having an x and y axis direction in the display area and having an intersection with a side of the pixel arranged according to the direction;
Calculating an inclination value of the boundary line from the two points;
If the boundary line is parallel to the x-axis or the y-axis, calculating the area of the square surrounded by the boundary line and the pixel;
If the boundary line is not parallel to the x-axis or the y-axis, and there is no other intersection point with the side between the adjacent intersection points of the equally spaced intersection points, the boundary line and one pixel If there is the area of the quadrangle surrounded by and the another intersection, the area of the triangle surrounded by the boundary line and the one pixel, and the square of the quadrangle surrounded by the boundary line and the two pixels Outputting the area and the area of the polygon excluding the triangle from a quadrangle surrounded by the boundary line and the two pixels; and
An anti-aliasing processing method comprising:

  (Supplementary note 2) When the boundary line is not parallel to the x-axis or the y-axis, a large triangle including the triangle and the triangle enclosed by the boundary line and one pixel, which is calculated in advance at the beginning of processing The anti-aliasing processing method according to claim 1, further comprising a step of calculating the area.

  (Supplementary note 3) Supplementary note 1 or 2, wherein when the boundary line is not parallel to the x-axis or the y-axis, the inclination value is larger than -1 and smaller than zero, or larger than zero and smaller than 1. An anti-aliasing processing method according to 1.

  (Supplementary note 4) The area of a quadrangle between the boundary line and one pixel is calculated by subtracting the slope value from the area of a preceding quadrilateral that is another quadrangle adjacent to the quadrangle. The anti-aliasing processing method according to any one of supplementary notes 1 to 3.

  (Supplementary Note 5) The area of the quadrangle between the boundary line and the two pixels is calculated by adding the area of one pixel to the area of the preceding quadrilateral of the triangle and subtracting the slope value. The anti-aliasing processing method according to any one of supplementary notes 1 to 4, which is characterized by the following.

(Additional remark 6) In the anti-aliasing processing apparatus which suppresses a jagged phenomenon based on the area enclosed by the boundary line of the drawing area which crosses a pixel, and the said pixel,
Means for inputting two points at both ends of the boundary line having x and y axis directions in the display area and having intersections with sides of the pixels arranged according to the direction;
Means for calculating an inclination value of the boundary line by the two points;
If the boundary line is parallel to the x-axis or the y-axis, means for calculating the area of the rectangle surrounded by the boundary line and the pixel;
If the boundary line is not parallel to the x-axis or the y-axis, and there is no other intersection point with the side between the adjacent intersection points of the equally spaced intersection points, the boundary line and one pixel If there is the area of the quadrangle surrounded by and the another intersection, the area of the triangle surrounded by the boundary line and the one pixel, and the square of the quadrangle surrounded by the boundary line and the two pixels Means for outputting the area and the area of the polygon excluding the triangle from the quadrangle surrounded by the boundary line and the two pixels;
An anti-aliasing processing apparatus comprising:

  (Supplementary note 7) When the boundary line is not parallel to the x-axis or the y-axis, a large triangle including the rectangle and the triangle enclosed by the boundary line and one pixel, which is calculated in advance at the beginning of processing The anti-aliasing processing apparatus according to appendix 6, further comprising means for calculating the area.

  (Supplementary note 8) The supplementary note 6 or 7, wherein when the boundary line is not parallel to the x-axis or the y-axis, the slope value is larger than -1 and smaller than zero, or larger than zero and smaller than one. The anti-aliasing processing apparatus according to 1.

  (Supplementary Note 9) The area of a quadrangle between the boundary line and one pixel is calculated by subtracting the slope value from the area of a preceding quadrilateral that is another quadrangle adjacent to the quadrangle. The anti-aliasing processing device according to any one of appendices 6 to 8.

  (Supplementary Note 10) The area of the quadrangle between the boundary line and the two pixels is calculated by adding the area of one pixel to the area of the preceding quadrilateral of the triangle and subtracting the slope value. The anti-aliasing processing apparatus according to any one of appendices 6 to 9, which is characterized by the following.

It is a schematic diagram of the processing flow of this invention. It is a schematic diagram of the display area where the boundary line is displayed. It is a block diagram which shows the function of an anti-aliasing processing apparatus. It is a flowchart which shows the area calculation process of the anti-aliasing process in embodiment of this invention. It is a flowchart which shows the detail of the area calculation process of the anti-aliasing process in embodiment of this invention. It is a schematic diagram of the display area in which the boundary line of the drawing area having an inclination in the present embodiment is displayed. It is a block diagram of the hardware apparatus which performs the area calculation process of an anti-aliasing processing apparatus. It is an example of the source code for calculating the area of anti-aliasing processing. It is a schematic diagram which shows the jagged phenomenon in a display apparatus. It is a schematic diagram for demonstrating a blend rate. It is a schematic diagram explaining the area calculation method used for the conventional blend rate.

Explanation of symbols

DESCRIPTION OF SYMBOLS 40 Anti-aliasing processing apparatus 41 Initial value data part 42 Area value data part 43 Inclination value calculation part 44 Initial setting part 45 Area calculation part 45a Rectangular calculation part 45b Rectangle calculation part 45c Triangle calculation part 45d Pentagon calculation part

Claims (5)

In the anti-aliasing processing method for suppressing the jagged phenomenon based on the area surrounded by the boundary line of the drawing region crossing the pixel and the pixel,
Information processing device
X, y-axis directions are provided in the display area, and input of coordinates of two points at both ends of the boundary line having an intersection with a side of the pixel arranged according to the direction is received ;
Based on the coordinates of the two points, it calculates a gradient value of the boundary line,
If the boundary line is parallel to the x-axis or the y-axis, the area of the rectangle surrounded by the boundary line and the pixel is calculated and stored in the storage means ,
If the boundary line is not parallel to the x-axis or the y-axis, and there is no other intersection point with the side between the adjacent intersection points of the equally spaced intersection points, the boundary line and one pixel If there is the area of the quadrangle surrounded by and the another intersection, the area of the triangle surrounded by the boundary line and the one pixel, and the two pixels in contact with the boundary and the other intersection And the area of the polygon excluding the triangle from the quadrangle surrounded by the two bordering pixels and the two pixels in contact with the other intersection , and outputs to the storage means Store ,
Anti-aliasing process wherein a call. The information processing apparatus includes a quadrangle and a triangle enclosed by the boundary line and one pixel, which are calculated in advance at the beginning of processing when the boundary line is not parallel to the x-axis or the y-axis. anti-aliasing processing method according to claim 1, wherein the benzalkonium to calculate the area of the large triangle. The area of a quadrangle between the boundary line and one pixel is calculated by subtracting the absolute value of the slope value from the area of a preceding quadrilateral that is another quadrangle adjacent to the quadrangle. The anti-aliasing processing method according to claim 1 or 2. The area of the quadrangle between the boundary line and the two pixels is calculated by adding an area of one pixel to the area of the preceding square of the triangle and subtracting the absolute value of the slope value. The anti-aliasing processing method according to claim 1. In the anti-aliasing processing apparatus that suppresses the jagged phenomenon based on the area surrounded by the boundary line of the drawing region that crosses the pixel and the pixel,
Means for inputting two points at both ends of the boundary line having x and y axis directions in the display area and having intersections with sides of the pixels arranged according to the direction;
Means for calculating an inclination value of the boundary line by the two points;
If the boundary line is parallel to the x-axis or the y-axis, means for calculating the area of the rectangle surrounded by the boundary line and the pixel;
If the boundary line is not parallel to the x-axis or the y-axis, and there is no other intersection point with the side between the adjacent intersection points of the equally spaced intersection points, the boundary line and one pixel If there is the area of the quadrangle surrounded by and the another intersection, the area of the triangle surrounded by the boundary line and the one pixel, and the two pixels in contact with the boundary and the other intersection Means for outputting the area of the quadrangle surrounded by and the area of the polygon excluding the triangle from the quadrangle surrounded by the boundary line and the two pixels in contact with the other intersection ;
An anti-aliasing processing apparatus comprising:

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