WO2006129943A1

WO2006129943A1 - Fast anti-aliasing method

Info

Publication number: WO2006129943A1
Application number: PCT/KR2006/002053
Authority: WO
Inventors: Jae Min Kang
Original assignee: Polidigm Co., Ltd.
Priority date: 2005-06-03
Filing date: 2006-05-29
Publication date: 2006-12-07

Abstract

The present invention relates to a fast anti-aliasing method. In the fast anti-aliasing method, when pixels overlapping each segment of a graphic forming a vector graphic are extracted, a pixel is divided into multiple sub-pixels, simple calculation is performed to find whether specific sub-pixels overlap the graphic or not, and the intensity of the pixel is determined by calculating how many sub-pixels among sub-pixels composing one pixel overlap the graphic, without calculating areas of the overlapped pixel portions. Therefore, multiplication and division operations for the area calculation of the graphic are removed, thereby more rapidly displaying mathematically described graphics. According to the invention, a more rapid operation can be made due to a display process of the graphic. Therefore, there is an advantage in that the system efficiency can be maximized and the quality of service can also be enhanced.

Description

FAST ANTI-ALIASING METHOD

Technical Field

[1] The present invention relates to a fast anti-aliasing method. In the fast anti-aliasing method, when pixels overlapping each segment of a graphic forming a vector graphic are extracted, a pixel is divided into multiple sub-pixels, simple calculation is performed to find whether specific sub-pixels overlap the graphic or not, and the intensity of the pixel is determined by calculating how many sub-pixels among sub- pixels composing one pixel overlap the graphic, without calculating areas of the overlapped pixel portions. Therefore, multiplication and division operations for the area calculation of the graphic are removed, thereby more rapidly displaying mathematically described graphics.

[2]

Background Art

[3] As is generally known, the utility value of display devices has incessantly been increased in a modern society with the rapid development of computers, information telecommunications, electronic telecommunication industries and the relevant technologies. In particular, there are frequent occasions when mathematically described graphics should be displayed on display devices, and thus, studies on the technologies related thereto have been actively conducted.

[4] At this time, when mathematically described graphics are displayed on a display device, a distorted image is generally caused due to the characteristics of the display device. For example, a mathematically described triangle should be drawn as shown in Fig. 1, but it will be displayed as shown in Fig. 2 because each coordinate thereof should be assigned only to relevant pixel on an actual display device. The phenomenon shown in Fig. 2 is called a jagging effect. To remove it, anti-aliasing is generally performed in computer graphics. At this time, the anti-aliasing means an operation of reducing a jagging effect by adjusting the intensity of brightness of pixels located in the vicinity of borders where the jagging effect occurs. Therefore, if the anti-aliasing is performed on a graphic of Fig. 2, the graphic is displayed as an image as shown in Fig. 3.

[5] At this time, the intensity of the border pixel is calculated according to what percent of one pixel a triangle described with an actual mathematical expression covers. In such a case, an algorithm for this calculation is called area-sampling. As shown in Fig. 4, when there is a pixel located in a side of a triangle, the intensity of brightness of the pixel is calculated and displayed on the basis of an area where the triangle covers the pixel.

[6] Meanwhile, in order to apply such an area-sampling algorithm, contact points where the segments of a triangle come into contact with each pixel with respect to x and y axes should be found and the multiplication operations or the like are necessary for the area calculation. Therefore, there is a problem in that a large amount of computing power is required. For example, when rendering a triangle having three coordinates such as "(3, 1), (1, 6), (7, 8)", the mathematical triangle can be first shown in Fig. 5. At this time, if the intensity of pixels located in the vicinity of borders of the triangle is calculated, each segment of the triangle is traced to find cells overlapping the segments and then to calculate areas of the cells (which indicates how many pixels the triangle covers). In other words, the areas shown in Fig. 6 are calculated with respect to a segment connecting the coordinates (3, 1) and (1, 6), and the area calculation for a pixel is made as shown in Fig. 7. In this case, the area is calculated by the following expression.

[7] [Expression 1]

[8] ((Ll + L2) * pixel height) / 2

[9] At this time, assuming that each of the length and width of a pixel be " 1 " , each of

Ll and S2 is expressed as a decimal point which is smaller than "1". Since this requires a floating point operation, the length and width of a pixel are up-scaled as "256" in most algorithms. Accordingly, the foregoing coordinates of the triangle "(3, 1), (1, 6), (7, 8)" are used in a state where the coordinates are up-scaled as "(3 * 256, 1 * 256), (1 * 256, 6 * 256), (7 * 256, 8 * 256)" while the algorithm is executed by a certain program. Further, the up-scaled coordinates are down-scaled by again dividing them by "256" in a final step. At this time, a process of multiplying or dividing the coordinates by "256" can be performed very fast through an 8-bit shift operation.

[10] In a conventional area-sampling algorithm in which an area is calculated as described above, however, the intersection points where segments intersect X and Y axes of each pixel should be calculated and the multiplication and division operations are inevitably included in the course of the area calculation, even though the floating point operation is eliminated in this manner. Therefore, there is still a problem in that a great deal of time should be consequently required.

[H]

Disclosure of Invention Technical Problem

[12] The present invention provides a fast anti-aliasing method that enables graphics to be more rapidly displayed when displaying the mathematically described graphics on a display device. Technical Solution

[14] According to an aspect of the invention, a fast anti-aliasing method, applied to a display device which is provided with a graphic information storage unit, a sub-pixel information storage unit, and a display buffer, includes extracting sub-pixels overlapping along segments of a graphic and then storing the sub-pixels into the sub- pixel information storage unit, using graphic information stored in the graphic information storage unit; sorting the sub-pixels stored in the sub-pixel information storage unit with respect to X and Y coordinates; and calculating intensity of each pixel through the sorted sub-pixels in the sub-pixel information storage unit and then storing result values into the display buffer such that the intensity of each pixel is reflected into a physical display unit.

[15] According to another aspect of the invention, the extracting of the sub-pixels includes extracting X and Y coordinates of the sub-pixels through scanning along each segment of a graphic to extract the sub-pixels overlapping along the segments of the graphic using the graphic information stored in the graphic information storage unit and then storing the extracted coordinates into the sub-pixel information storage unit; and determining whether remaining segments of the graphic stored in the graphic information storage unit are present, so that the step returns to the extracting of X and Y coordinates if there exists any segments or the step proceeds to the sorting of the sub- pixels if there exists no segment.

[16] In the extracting of the X and Y coordinates, when the X and Y coordinates of the sub-pixels are stored in the sub-pixel information storage unit, the values of coverage and intensity thereof are recorded simultaneously.

Advantageous Effects

[17] According to the fast anti-aliasing method, when pixels overlapping each segment of a graphic are extracted, it is determined only whether or not sub-pixels overlap the segments of the graphic without calculating areas of the overlapped pixels. Therefore, a process of multiplication and division operations due to the area calculation of the graphic is removed, thereby more rapidly displaying mathematically described graphics. As a result, system efficiency can be maximized and a service quality can also be enhanced.

[18]

Brief Description of the Drawings

[19] Figs. 1 to 4 are reference views illustrating a general anti-aliasing method.

[20] Figs. 5 to 7 are reference views illustrating the problem of a conventional antialiasing method. [21] Fig. 8 is a functional block diagram showing the configuration of a display device to which a fast anti-aliasing method is applied according to an embodiment of the present invention.

[22] Fig. 9 is an operational flow chart illustrating the fast anti-aliasing method according to an embodiment of the present invention.

[23] Figs. 10 to 12 are reference views illustrating the tenth step SlO in the fast antialiasing method of Fig. 9.

[24] Figs. 13 to 15 are reference views illustrating a process of displaying a triangle using 16 pixels.

[25] Figs. 16 to 35 are reference views illustrating a process of recording coordinates, intensity and coverage of each pixel through the tenth step SlO in the fast anti-aliasing method of Fig. 9.

[26] Fig. 36 is a view showing result values of the twentieth step S20 in the fast antialiasing method of Fig. 9.

[27] Fig. 37 is a view showing result values of the thirtieth step S30 in the fast antialiasing method of Fig. 9.

[28] Reference Numerals

[29] 10 Operator

[30] 11 Sub-pixel information extraction module

[31] 12 Sub-pixel information sorting module

[32] 13 Pixel color value calculation module

[33] 20 Memory

[34] 21 Graphic information storage unit

[35] 22 Sub-pixel information storage unit

[36] 23 Display buffer

[37] 30 Display unit

[38]

Best Mode for Carrying Out the Invention

[39] Hereinafter, a fast anti-aliasing method according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

[40] Fig. 8 is a diagram illustrating the configuration of a display device to which the fast anti-aliasing method according to an embodiment of the invention is applied. The display device includes an operator 10 having a sub-pixel information extraction module 11, a sub-pixel information sorting module 12, and a pixel color value calculation module 13; a memory 20 having a graphic information storage unit 21, a sub-pixel information storage unit 22 and a display buffer 23; and a display unit 30.

[41] First, the configuration of the operator 10 will be described. The sub-pixel in- formation extraction module 11 of the operator 10 extracts sub-pixels overlapping along segments of a graphic and then stores the result values thereof into the sub-pixel information storage unit 21, using coordinate information of the graphic stored in the graphic information storage unit 21 of the memory 20. The sub-pixel information sorting module 12 sorts the sub-pixels stored in the sub-pixel information storage unit 22 with respect to X and Y coordinates. For example, the sub-pixel information sorting module 12 performs sorting primarily in an ascending order of Y coordinates and secondarily in an ascending order of X coordinates. The pixel color value calculation module 13 calculates the intensity of each pixel based on the sub-pixels sorted by the sub-pixel information storage unit 22 and then stores the result values thereof into the display buffer 21 such that contents of the display buffer 21 are reflected to the physical display 30.

[42] Next, the configuration of the memory 20 will be described. The graphic information storage unit 21 is a memory for holding information on a graphic, i.e. information on the segments forming the graphic or information on Bezier curves. At this time, the Bezier curves can be easily approximated into segments. The sub-pixel information storage unit 22 is a memory for holding sub-pixel coordinates extracted along segments forming a graphic and is also a memory for additionally holding various information tables used in a progress step of an algorithm on anti-aliasing processing according to the invention. The display buffer 23 is a memory for holding the intensity of each pixel of a graphic that will be finally displayed on the display unit 30.

[43] Now, the fast anti-aliasing method according to an embodiment of the present invention, which has been applied to a display device having the above-described configuration, will be described with reference to Fig. 9. Conceptually, in an algorithm according to the present invention, when cells overlapping each segment of a graphic are extracted, area calculation is made not for the overlapped cell but for each of 4, 16, 64 or 256 sub-pixel into which a single pixel is divided.

[44] The sub-pixel information extraction module 11 extracts sub-pixels overlapping along the segments of a graphic and then stores the sub-pixels in the sub-pixel information storage unit 22, using coordinate information of the graphic stored in the graphic information storage unit 21 (SlO).

[45] The aforementioned tenth step SlO includes an eleventh step Sl 1 in which the sub- pixel information extraction module 11 extracts x and y coordinates of the sub-pixels while scanning along each segment of a graphic to extract the sub-pixels overlapping along the segments of the graphic using the coordinate information of the graphic stored in the graphic information storage unit 21 of the memory 20 and then stores the extracted coordinates into the sub-pixel information storage unit 22; and a twelfth step S 12 in which the sub-pixel information extraction module 11 determines whether or not the remaining segments of the graphic stored in the graphic information storage unit 21 are present and the step returns to the eleventh step Sl 1 if there exists any segments or proceeds to a twentieth step S20 if there exists no segments.

[46] In relation to the twentieth step S20, the method in which the sub pixel sorting module 12 sorts the sub-pixels stored in the sub-pixel information storage unit 22 with respect to X and Y coordinates can be variously set as described above. Fig. 9 shows a case where the sub-pixel information sorting module 12 performs sorting primarily in an ascending order of Y coordinates and secondarily in an ascending order of X coordinates.

[47] Hereinafter, a process of executing the aforementioned tenth step SlO will be described in detail with reference to Figs. 10 to 35.

[48] In Fig. 10, one pixel is divided into 16 sub-pixels. In such a case, it is calculated only which sub-pixels overlap the segment forming a triangle. That is, the area of sub- pixels overlapping the segment needs not be calculated. At this time, in a case where one pixel is divided into 16 sub-pixels, the respective coordinates of the triangle are up-scaled as "(3 * 16, 1 * 16), (1 * 16, 6 * 16), (7 * 16, 8 * 16)". Here, a process of multiplying the original coordinates by 16 can be performed very fast by performing a 4-bit shift operation.

[49] If cells overlapping the segment are found ass shown in Fig. 10, the results shown in Fig. 11 can be obtained. A "Bresenham Line Drawing" algorithm or DDA (Digital Differential Analyzer) algorithm can be used to trace the cells overlapping the segment.

[50] To determine the intensity of the pixels of Fig. 10, the number of sub-pixels covered by a graphic should be counted. The sub-pixels covered by a graphic are as shown in Fig. 12. However, this can be found by merely checking the 4 low-order bits of each sub-pixel obtained in Fig. 11 . Consequently, the intensity of the pixels is calculated as 12/16 (75%). At this time, higher quality can also be obtained according to how many sub-pixels one pixel is divided into. In a case where one pixel is divided into 256 sub-pixels, values having 256 gradations can be obtained, which enables the anti-aliasing with a high quality.

[51] Meanwhile, a process of displaying a triangle shown in Fig. 13 using 16 sub-pixels will be described hereinafter as an example.

[52] First, the coordinates of the triangle are up-scaled by multiplying the coordinates by 16, as shown in Fig. 14. The coordinates of the triangle are changed from (1, 0) to (16, 0), from (0, 1) to (0, 16), and from (2, 2) to (32, 32), respectively. At this time, the intensity and coverage of each pixel are recorded simultaneously when sub-pixels overlapping segments of the triangle are traced. To this end, a modified line drawing algorithm, i.e. a "Bresenham Line Drawing" algorithm, a DDA (Digital Differential Analyzer) algorithm or the like can be used. In other words, the intensity and coverage of actual pixels are recorded while the relevant sub-pixels are found out.

[53] At this time, a sign of the intensity is recorded differently for each segment proceeding to an upward or downward direction. In addition, the coverage is recorded according to how high the height of one pixel is covered by a segment, and a sign of the coverage is also recorded differently for each segment proceeding to the upward or downward direction. Therefore, the intensity and coverage of the pixel are consequently recorded while the sub-pixels are traced and consequently found, as shown in Fig. 15.

[54] A process of performing the aforementioned calculation will be shown in Figs. 16 to 35. Fig. 16 shows that a first table entry is added. The intensity and coverage values are initialized as "0" when each table entry is added. At this time, the intensity and coverage have a negative value when the direction of a segment is downward, whereas the intensity and coverage have a positive value when the direction of a segment is upward. (In this case, intensity and coverage of the pixel are reversely recorded depending on a processing method of the pixel color value calculation module. In the present specification, it is assumed that the intensity and coverage have a negative value when the direction of a segment is downward and have a positive value when the direction of a segment is upward. However, the scope of the invention is not limited thereto.)

[55] In Fig. 16, the segment of the triangle currently proceeds from (16, 0) to (0, 16), and thus, the intensity and coverage have a negative value. Since sub-pixels on the same sub Y-scan line within a pixel respectively have the intensity of "0", "1", "2", and "3" from left to right, the sub-pixel of Fig. 16 is located in the leftmost position within one pixel and thus has the intensity of "0". Further, since the coverage is always increased or decreased by " 1 " in accordance with the direction of the segment, the coverage of the sub-pixel is decreased by " 1 ". The intensity of "0" and the coverage of "-1" of the sub pixel shown in Fig. 16 are reflected as in a table of Fig. 16.

[56] Next, a new table entry is added, because a sub-pixel shown in Fig. 17 is located at

(0, 0) which is different from the coordinates (0, 1) of the last entry of the table. In this case, the initial values of intensity and coverage for the current sub-pixel are initialized as "0", as shown in the table of Fig. 17. The sub-pixel shown in Fig. 17 has an intensity of "-3" and a coverage of "-1". These are reflected as in the table of Fig. 17.

[57] In Fig. 18, the pixel coordinate for the current sub-pixel is the same as that for the pixel coordinate of the last entry. Therefore, a new table entry is not added. In such a case, the intensity and the coverage of the sub-pixel are added to the just previous table entry, as shown in the table of Fig. 18. [58] Fig. 19 and Fig. 20 shows the last sub-pixel corresponding to the segment proceeding from (16, 0) to (0, 16). In such a case, the values of intensity and coverage are shown in the table of Fig. 20.

[59] Fig. 21 shows that edge tracking for the segment proceeding from (0, 16) to (32,

32) starts. At this time, a sub-pixel located at a point where two segments intersect each other is always detected twice. That is, the sub-pixel (0, 16) is first detected (has been recorded in the just previous step) while a segment proceeds from (16, 0) to (0, 16), and detected once again while a segment proceeds from (0, 16) to (32, 32). As such, a sub-pixel located at a point where two segments intersect each other is recorded when the directions of the segments are changed, whereas it is not recorded when the directions of the segments are not changed. In Fig. 21, since the directions of the segment proceeding from (16, 0) to (0, 16) and the segment proceeding from (0, 16) to (32, 32) are all downward, the sub-pixel is not recorded.

[60] Figs. 22 to 24 show that new table entries are added while a new segment proceeds from (0, 16) to (32, 32). Fig. 25 shows the last sub-pixel corresponding to the segment proceeding from (0, 16) to (32, 32). In such a case, the values of intensity and coverage are shown in the table of Fig. 25.

[61] Fig. 26 shows that edge tracking for the segment proceeding from (32, 32) to (16,

0) starts. At this time, since the directions of the previous segment proceeding from (0, 16) to (32, 32) and the current segment proceeding from (32, 32) to (16, 0) are opposite to each other, a first sub-pixel (32, 32) is recorded as shown in the table of Fig. 26.

[62] Furthermore, Figs. 27 to 33 show that new table entries are added while a new segment proceeds from (32, 32) to (16, 0). Fig. 34 shows the last sub-pixel corresponding to the segment proceeding from (32, 32) to (16, 0). In such a case, the values of intensity and coverage are shown in the table of Fig. 34. At this time, whether the first sub-pixel is recorded should be determined according to whether the proceeding directions of the first and last segments are the same as or different from each other. In the above process, such a determination is omitted herein for the sake of convenience.

[63] Through the aforementioned processes, the table shown in Fig 35 is finally obtained. In such a case, the values in the table are stored in the sub-pixel information storage unit 22 of the memory 20.

[64] Thereafter, the sub-pixel information sorting module 12 sorts the sub-pixels stored in the sub-pixel information storage unit 22 with respect to X and Y coordinates, as shown in Fig. 36 (S20). Generally, an order of the sorting is performed primarily in an ascending order of Y coordinate and secondly in an ascending order of X coordinate. However, it can be selected differently depending on a direction of drawing a picture (from the top to the bottom or from the bottom to the top of a screen) or a direction of drawing each line (from the left to the right or from the right to the left of a screen). Further, "Quick Sort" or "Shell Sort" sorting algorithm can be used as a sorting method.

[65] The pixel color value calculation module 13 adds up the values of intensity and coverage of the same pixel coordinates. For example, there exist two table entries having a coordinate value of (1, 0) in the table of Fig. 36. In Fig. 37, however, there exists one table entry having a coordinate value of (1, 0), because the values of intensity and coverage of two table entries are added up. When such a process is completed by the pixel color value calculation module, the result of Fig. 37 is obtained from the table of Fig. 36. Continuously, from the finally-obtained table of Fig. 37, the pixel color value calculation module reflects color values of the pixels into the display buffer 23 such that the contents of the display buffer 23 are reflected to the physical display unit 30 (S30). Thus, respective Y-pixel lines are drawn from top to bottom with appropriate intensity using the information shown in Fig. 37.

[66] The pixel color value calculation module 13 can calculate the intensity of each pixel using pseudo codes described below.

[67] In the codes, a table indicates the table of Fig. 37. Through a 'While' iteration structure, information of each table entry is accessed so as to draw a span (an image of each row which should be drawn in order to output a picture in a span-raster device). Further, X and Y coordinates of a pixel, which is being drawn, are maintained by $CurrX and $CurrY, and color intensity of a pixel is represted by $C. In addition, $Coverage maintains a coverage value of a table entry which is currently accessed. In the below processing, it is assumed that a picture is drawn from the top to the bottom of a screen and from the left to the right of the screen. However, this can be implemented reversely in accordance with an implementing method. Further, it is assumed in the following codes that one pixel is divided into 16 sub-pixels.

[68]

Function Raster ize

Select the first element in the table While Cui rent element is not exceed table $CurrY = Current element's Y

O; Do

If SCoverage <> 0 $C ~ -$Covcrage * 4 'There arc 4 subpixels in row in one pixel SCurrX = $CurrX + 1 Miile SCurrX < Current element's X

Draw pixel at ($CurrX, $CurrY) with $C intensity. $CurrX = SCurrX + 1 End While End If

$CurrX = Current element's X

$C = -(Current element's intcnsit>) + -$Coverage * 4 Draw pixel at ($CuπX, SCurrY) with $C intensity Select the next element. While $CurrY = Current element's Y; End While End Function

[69] While the present invention has been described with reference to exemplary embodiments thereof, it will be understood that various changes and modifications in form and detail may be made therein without departing from the scope of the present invention as defined by the following claims.

Claims

[1] A fast anti-aliasing method applied to a display device which is provided with a graphic information storage unit, a sub-pixel information storage unit, and a display buffer, the method comprising: extracting sub-pixels overlapping along segments of a graphic and then storing the sub-pixels into the sub-pixel information storage unit, using graphic information stored in the graphic information storage unit; sorting the sub-pixels stored in the sub-pixel information storage unit with respect to X and Y coordinates; and calculating intensity of each pixel through the sorted sub-pixels in the sub-pixel information storage unit and then storing result values into the display buffer such that the intensity of each pixel is reflected into a physical display unit.

[2] The fast anti-aliasing method according to claim 1, wherein the extracting of the sub-pixels includes extracting X and Y coordinates of the sub-pixels through scanning along each segment of a graphic to extract the sub-pixels overlapping along the segments of the graphic using the graphic information stored in the graphic information storage unit and then storing the extracted coordinates into the sub-pixel information storage unit; and determining whether remaining segments of the graphic stored in the graphic information storage unit are present, so that the step returns to the extracting of X and Y coordinates if there exists any segments or the step proceeds to the sorting of the sub-pixels if there exists no segment.

[3] The fast anti-aliasing method according to claim 2, wherein, in the extracting of the X and Y coordinates, when the X and Y coordinates of the sub-pixels are stored in the sub-pixel information storage unit, the values of coverage and intensity thereof are recorded simultaneously.