Antialiasing. Overview. Antialiasing Techniques. Antialiasing Techniques. Aliasing, jagged edges or staircasing can be reduced by:

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1 Overview Anialiasing Techniques Super sampling Area sampling unweighed weighed Clipping Cohen-Suherland line clipping algorihm line clipping algorihm Suherland-Hogeman polygon clipping Anialiasing Aliasing, jagged edges or saircasing can be reduced by: Higher screen resoluion Need a huge frame buffer Anialiasing echniques Vary pixel inensiies along boundaries o smooh he edge. Anialiasing Techniques Super Sampling Compue inensiies a sub-pixel grid posiions and combine he resuls o obain he pixel inensiy. Unweighed Area Sampling Find pixel inensiy by calculaing he areas of overlap of each pixel wihin he objecs o be displayed. Pixel inensiy is proporional o he amoun of area covered. Anialiasing Techniques Weighed Area Sampling Define a weighing funcion ha deermines he influence on he inensiy of he pixel. Pixel Phasing Lines are smoohed by moving he elecron beam o a closer approximae of he mahemaical line.

2 Supersampling (zero line widh) Example: a sraigh line on a gray scale display Divide each pixel ino sub-pixels. The number of inensiies are he max number of sub-pixels seleced on he line segmen wihin a pixel. Supersamling (finie line widh) The inensiy level for each pixel is proporional o he number of sub-pixels inside he polygon represening he line area. Line inensiy is disribued over more pixels. Supersamling (finie line widh) Disadvanages More calculaions involved o idenify inerior pixels. Posiioning of he line depends on he slope of he line line cenered in polygon Horizonal or verical line line pah on polygon boundary m < 1 line pah closer o lower boundary m > 1 line pah closer o upper boundary Unweiged Area Sampling 1. The inensiy of a pixel decreases as he disance beween he pixel cener and he edge increases. 2. The primiive mus inersec he pixel o have some effec. 3. Equal areas conribue equally o he pixel inensiy. Inensiy of a pixel is proporional o is area covered by he line

3 Weighed Area Sampling Equal areas can conribue o unequal inensiy. (We change propery 3). Circular pixel geomery. Weighing (Filer) Funcion Deermines he influence on he inensiy of a pixel of a given small area da of a primiive. This funcion is consan for unweighed and decreases wih increasing disance for weighed. Toal inensiy is he inegral of he weighing (filer) funcion over he area of overlap. W s is he volume (always beween 0 and 1) I = I max W s Box Filer: Unweighed Area Sampling W s is a wedge of he box. Heigh of he box normalizes o 1 (box volume = 1) A hick line covering he enire pixel has inensiy: I = I max 1 = I max Cone Filer: Weighed Area Sampling A circular cone, where he base is he radius of he uni disance of he ineger grid. Roaional symmery. Linear decrease of he funcion wih radial disance. Normalized o 1 (volume under enire cone is 1)

4 Filer Funcions Opimal filers are compuaionally more expensive. Cone filers are a very reasonable compromise beween cos and qualiy. Pixel Phasing: Ani-Aliasing Pixel posiions can be shifed by a fracion of a pixel diameer (1/4, 1/2, or 3/4) o plo poins closer o he mahemaical line. Line Inensiy Differences: The diagonal line appears less brigh han he horizonal. (The diagonal line is longer han he horizonal line by a facor of sqr(2)). Toal inensiy is proporional o heir lengh. Line Clipping: Clipping Algorihms Cohen-Suerland (encoding) Oldes and mos commonly used Nicholl-Lee-Nicholl (encoding) (more efficien) Cyrus-Beck and (parameric) More efficien han Cohen-Suherland Polygon Clipping: Suherland-Hodgeman (divide and conquer sraegy) Weiler-Aheron (modified for concave polygons) 1. Encode end poins Bi 0 = poin is lef of window Bi 1 = poin is righ of window Bi 2 = poin is below window Bi 3 = poin is above window < 2. If C 1 C 2 0 hen P 1 P 2 is rivially rejeced < Cohen-Suherland If C 1 C 2 = 0 hen P 1 P 2 is rivially acceped C 1 = Bi code of P1 C 2 = Bi code of P2 4. Oherwise subdivide and go o sep 1 wih new segmen.

5 Cohen-Suherland Clip order: Lef, Righ, Boom, Top C1 E2 1) A1C1 1) A2E B D2 2) B1C1 2) B2E2 3) rejec 3) B2D2 C2 4) B2C2 A1 5) accep 0001 B A3 1) A3D3 B3 2) A3C3 A C3 3) A3B3 4) accep D3 Cohen-Suherland Will do unnecessary clipping. No he mos efficien. Clipping and esing are done in fixed order. Efficien when mos of he lines o be clipped are eiher rejeced or acceped (no so many subdivisions). Easy o program. Parameric clipping are he mos efficien. (Liang- Barsky and Cyrus-Beck) More efficien han Cohen-Suherland Clipping condiions: A line is inside he clipping region for values of such ha: x y min min x 1 y 1 + x x + y y max max x = x 2 y = y 2 x 1 y 1 The infiniely line inersecs he clip region edges when: qk k = p k where p 1 = x q 1 = x 1 x min p 2 = x q 2 = x max x 1 p 3 = y q 3 = y 1 y min p 4 = y q 4 = y max y 1 Lef boundary Righ boundary Boom boundary Top boundary

6 When p k < 0, as increases line goes from ouside o inside - enering When p k > 0, line goes from inside o ouside - exiing When p k = 0, line is parallel o an edge Ener Exi Ener Exi Exi Exi Clip region If here is a segmen of he line inside he clip region, a sequence of infinie line inersecions mus go: enering, enering, exiing, exiing Ener Ener Se min = 0 and max = 1. Calculae he values: If < min or > max ignore i. Oherwise classify he values as enering or exiing. If min < max hen draw a line from: (x 1 + x min,y 1 + y min ) o (x 1 + x max,y 1 + y max ) lef righ boom op P(-5,3) 0,10 10,10 Q(15,9) 0,0 10,0 q1 x1 xmin = = = = p1 x (15 ( 5)) 4 Enering min = 1/4 q2 xmax x1 10 ( 5) 3 p2 x 15 ( 5) 4 Exiing max = 3/4 q3 y1 ymin p3 y (9 3) 2 < 0 hen ignore q4 ymax y p y > 1 hen ignore 4 Example

7 We have min = 1/4 and max = 3/4 Q-P = (15+5,9-3) = (20,6) x y If min < max, here is a line segmen compue endpoins by subsiuing values Draw a line from (-5+(20) (1/4), 3+(6) (1/4)) o (-5+(20) (3/4), 3+(6) (3/4)) lef righ boom op P(-8,2) 0,0 q1 x1 xmin p1 x (2 ( 8)) 5 q2 xmax x1 10 ( 8) 9 p2 x 2 ( 8) 5 q3 y1 ymin p3 y (14 2) 6 q4 ymax y p y Example Q(2,14) 0,10 10,10 10,0 Enering min = 4/5 > 1 hen ignore < 0 hen ignore Exiing max = 2/3 We have min = 4/5 and max = 2/3 Q-P = (2+8,14-2) = (10,12) Nicholl-Lee-Nicholl Line Clipping Avoids muliple clipping of an individual line by creaing more regions. Only hree regions need o be considered. P 1 min > max, here is no line segmen do draw P 1 P 1 inside edge region corner region Find posiion of P2 relaive o P 1.

8 If P 1 inside and P 2 ouside: Nicholl-Lee-Nicholl Line Clipping Lef Top Boom Righ If P 1 is o he lef: If P 1 is o he lef and above: P1 Nicholl-Lee-Nicholl Line Clipping To find which region P 2 is in, compare he slope of he line o he slopes of he clip recangle. If P 1 is lef of clip recangle, hen P 2 is in region Lef Top if: slopep 1 P TR < slopep 1 P 2 < slope P 1 P TL Lef Top P1 P1 Lef Lef Lef Righ Lef Lef Boom Top Top Righ Lef Top Lef Boom Top Boom Number of cases explodes in 3D, making i unsuiable. Suerland-Hodgeman Polygon Clipping Four es cases: 1. Firs verex inside and he second ouside (in-ou pair) 2. Boh verices inside clip window 3. Firs verex ouside and he second inside (ou-in pair) 4. Boh verices ouside he clip window Concave polygons may be displayed wih exra lines. Weiler-Aheron Polygon Clipping Clips concave polygons correcly. Insead of always going around he polygon edges, we also, wan o follow window boundaries. 1. For an ouside-o-inside pair of verices, follow he polygon boundary. 2. For an inside-o-ouside pair of verices, follow he window boundary in a clockwise direcion.