Four commonly used techniques for anti aliasing

This paper is compiled from the school of software, Xi'an Jiaotong University Mr. Zhu Jihua Computer graphics courseware , Do not reprint

When displaying graphics on raster display , Line segments or graphic boundaries are more or less jagged

The graphic signal is continuous , In raster display system , The graphics are represented by discrete pixels

• Anamorphosis ： The distortion caused by continuous quantity is represented by discrete quantity .

  • Stepped boundary ;

    

  • Distortion of graphic details ;

    

  • The narrow figure is missing （ Left ）： In the animation sequence , Produce flicker （ Right ）.

Anti aliasing

In the process of graphic display , A method or technique for reducing or eliminating aliasing

Several methods of anti aliasing ：

• Methods to improve resolution ;
• Unweighted area sampling ;
• Weighted area sampling ;
• Halftone technology .

Improve resolution

Set the display resolution （ level 、 vertical ） Double

The frame buffer capacity is increased to the original 4 times , Scanning and converting graphics of the same size takes 4 Times as long

evaluation ： Simple method , But the price is very high , It's not economical

Area sampling

• The contribution of a straight line segment to the brightness of a pixel ：
  • It is proportional to the area of the area where the two intersect ;
  • It is inversely proportional to the distance between the pixel center point and the straight line segment .
• When a line segment does not intersect a pixel , It has no effect on the brightness of the pixel ;
• The intersection area of the same area contributes the same to the brightness of the pixel , It has nothing to do with the position of the intersection area in the pixel .

Unweighted area sampling

Suppose the slope of a straight line segment is m(0≤m≤1), And the drawn line is a pixel unit , Then there are five situations when the straight line segment intersects with the pixel .

Area calculation ：

• situation （1）（5） The shadow area is ：$D^2/2m$;
• situation （2）（4） The shadow area is ：$D-m/2$;
• situation （3） The shadow area is ：$1-[(1-D{)}^2+E^2]/2m,E=D+m-sqrt(1+m^2)$.

The actual gray value displayed by the pixel = Area obtained (0-1 between )* The maximum gray value of this pixel

In order to simplify the calculation, we can use discrete Methods

• First, divide the screen pixels into n Sub pixels ;
• Then calculate the number of sub pixels whose center point falls in the straight line segment k;
• Setting the brightness of the pixel on the screen as the approximate value of the area of the intersecting area can k/n.

Weighted area sampling

thought ： The second step of improving the unweighted region sampling method 3 Article nature , The contribution of object pixel brightness in the intersection region depends on the distance between the region and the pixel center

Discrete calculation method can be adopted

• Divide pixels into n Sub pixels of equal area , Calculate the contribution of each sub-pixel to the original pixel , And save it in a two-dimensional weighting table ;
• Find all sub pixels whose centers fall in the straight line segment ;
• Calculate the sum of the contributions of all these sub pixels to the brightness of the original pixel ;
• This value is multiplied by the maximum gray value of the pixel as the display gray value of the pixel .

Yes n=9 The situation of ：

Yes n=25 The situation of ：

Example

Halftone technology

For a given resolution , The multi-level gray level is obtained by combining several pixels into a unit ;

example ： In a display, four pixels form a unit , Can produce 5 Light intensity .

evaluation

• For a two-level gray-scale display, the number of gray levels that may be formed is equal to the number of pixels in the unit plus 1;
• If you have any m Grey level ,$n\times n$ Pixels form a unit , Then the number of gray levels is $n\times n\times (m-1)+1$;
• The larger the unit , The higher the gray level ;
• It is at the expense of spatial resolution .

• example ： Gray level =4, Each unit =2*2